Type H Personalities

The Canary is Dead: It's Time to Exit Public Schools

2012-02-15T10:59:00.000-08:00

Author's Note: I hate the literary device of a "fictional argument" in philosophical or persuasive writing. It is far too convenient for an author to set up his side of the contest to be the winner, and the other side to be the loser. In fact, I think that very few of these types of writings are anything more than a glorified straw-man argument. With that said, this blog post is written in this very form I despise and is probably guilty of a straw-man here and there. My reason for using this device is that it is derived from 10 years of real conversations about home-schooling along with things I wished I would have said at the time, but now plan to say in similar future conversations. Feedback is welcome to help me improve the dialogue.

CHARACTERS:

Seth Nielson - A hot-headed, argumentative home-schooling dad
Amy Nielson - Seth's beautiful, fiery wife who converted her husband to home-schooling in the first place
Abby Normal - An excellent public school teacher
Mary Olivia Moore - Just your average MOM of three.

SETTING: A party at the Nielson's house for friends and family. All the other guests have left except for Mary (who left the kids with her husband) and her ride, Abby.

PART I.

During some small talk in the living room, Mary, who hasn't known the Nielsons very long opens up a new topic. "So, I hear that you guys homeschool."

"Yes we do," Amy replies.

"That sounds like lots of work. Why do you do it?"

"Well," Seth says, "like everything in life there are pros and cons."

"Yeah, I guess that's true." Mary nods seeming satisfied with the answer

But before a new conversation topic can open up, Seth shakes his head, looks up at the ceiling and shaking his fists exclaims, "I CANT TAKE IT ANYMORE!"

Both Abby and Mary stare in surprise. "Umm, is there something wrong?" Abby ventures.

"What's wrong with him?" Mary asks with a tone of worry.

Amy, realizing what is happening, sighs. "I'm afraid he's grown tired of being polite," she states.

"YES!" Seth says looking at the two women in frustration. "I am SO tired of trying to not offend everyone instead of just saying what I think! Do you know what Carbon Monoxide is?"

This seemingly disconnected question further convinces Mary and Abby that Seth is having a "special" moment and they think that maybe the party is "over," but the frustrated man proceeds. "Carbon Monoxide is a 'silent' killer. It is a colorless, odorless, and tasteless gas and before you realize you're being affected by it, it will kill you. Death comes because the carbon monoxide molecules have blocked the blood's ability to carry oxygen.

"The risks of carbon monoxide poisoning increase in enclosed spaces for obvious reasons. Miners were especially prone to this destroying angel but were generally capable of rapid detection of the gas through the use of a canary. The small (bright yellow) bird, with a more sensitive metabolism, would visibly sway (and then drop) when the concentration of CO was still low enough that a human being could continue to function and effect an escape."

"What in the world does this have to do with anything?" Abby asks in annoyance.

"Well," Seth states, "when people ask me why I homeschool my children, I haven't been very honest. In the interest of being polite and kind and 'tolerant' I usually avoid saying what I really think."

"And that is," Mary presses.

"What I really think is that I've seen too many children swaying and dropping from their exposure to a colorless, odorless, and tasteless educational system. We value being 'nice' in our society over telling the truth to such an extent that I don't usually have the guts to tell you," he says looking at Mary, "that it's the impact of public schools on your obviously bright children that sends me running in the other direction as quickly as possible."

Mary and Abby both gasp while Amy shakes her head and mouths an "I told you so."

"I beg your pardon!" Mary fumes when she's recovered.

"Have you ever read about the symptoms of CO poisoning? At a 15% exposure, you get a mild headache, at 25% the headache increases accompanied by nausea but you'll get better if you can get out quickly. But by 30% you start having long-term irreversible effects. At 45% your unconscious and at 50% or more you'll just die."

"Are you comparing education to carbon monoxide poisoning?" Abby asks incredulously.

"No, I'm comparing public education to carbon monoxide poisoning and I think the symptoms are astonishingly similar. I wish that more parents would recognize that the canary is dead and get the heck out. I wouldn't put my child in most of the public schools for just about any reason. And those few schools that might be passable would be a temporary education solution until I could find something better."

"But, but, but," Mary protests, "my child's school is wonderful!"

"Based on what metric?"

"What?"

"How are you judging your child's school to be wonderful?"

"Their school has some of the highest test scores in the state!" Mary responds proudly. To the ladies' surprise, both Amy and Seth start laughing almost uncontrollably. "What's so funny!" Mary demands.

"So," Seth says finally catching his breath, "you're going to judge an institution by tests created by that institution?"

"Well," Abby jumps in, "whatever you want to say about them, I think that the testing is reasonably fair and accurate."

"And I don't," he replies evenly. "But even if I did, those tests are NOT a good judge of the school's effectiveness with the children. More importantly, they aren't a good judge of the school's effectiveness on a specific child. Shoot, we haven't even started talking about how those tests have negatively impacted curriculum and teaching methods."

"Whatever," Mary answers. "My children are doing very well and are near the top of their classes."

"Wait, what?" Amy speaks up. "You're saying your children are doing well because they're doing better than other children in the same school? Hey, why don't you move into inner-city Baltimore so they can move right up to the top of their class."

"I'm sorry to offend you ladies," Seth says, "but with some exceptions, I have rarely found public schools to help children reach their potential."

"Seriously?" Abby says disgusted, "You think that little of all the people you know? All the people you've gone to college with? All the people in the world are suffering in ignorance while those few homeschoolers are the only ones reaching their potential?"

"Actually, to some degree, yes, I think that a good segment of our society coming out of public schools can't think critically. I think a good chunk of them are also coming out with damaged creativity and an inability to continue learning out of a school environment. From where I stand, those public school children that manage to emerge more-or-less educated and functional, is more often than not thanks to caring parents, a reasonably stable and well adjusted peer-group, and the natural resiliency of their minds."

"How can you presume to judge my child's school?" Mary retorts. "You don't send your children there so what do you know about it?"

"Well, let me try to reduce it to one sentence. The public school system is a centralized, bureaucratic, authoritarian institution dominated by politics, a bankrupt education philosophy protected by a government monopoly, and far too many academically substandard teachers all supported and upheld by a disturbing number of uninformed, detached, and oblivious parents."

Abby shakes her head in exasperation. "You're so elitist. You can use all the big words you want, but I teach in these schools and I see all the good that's being done every day."

"Ok... if I understand you correctly, you're saying that my belief that the public schools are failures is wrong for two reasons. First, you think I'm wrong because I'm viewing it from an 'elitist' viewpoint as evidenced by the words I chose to describe its problems and, second, I'm wrong because you have personally witnessed the system doing good."

"You're still making it too complicated, but yes, I know the schools are not failures because I teach in the schools and know that, despite occasional problems, we do a lot of good in the lives of our students."

"And that, really, is where we disagree. I don't think the public school system has occasional problems. I think it is built on a dangerous and inherently broken foundation. When I gave you my one-sentence description before, it was not to use 'big words,' but to describe using as few words as possible the core problems of it. I said, for example, that it was 'centralized' and 'bureaucratic' and those are serious problem."

"How so?" Mary asks with a hint of curiosity.

"Well, the problem for the student sitting in his or her desk for about 180 days a year for 13 years is that the congressman/senator/president sitting in DC has never met them, except for the occasional political dog and pony show. I think trusting Congress, made up of a few hundred people of questionable motivations and interests, to dictate the education of millions of children is inherently unsafe and unwise."

"Most of the controls on education happen at the state level," Abby retorts.

"Even the state controls on education are far too centralized. As an anecdotal example, when we lived in Houston, we read a report in the city paper that the Houston Independent School District had its own lobbyists for the state government. Does that make any sense to you?"

"Yes, actually," Abby says, "the school districts need to make sure that the state government understands our problems."

"You don't see what strange situation it is that the state government controls what your district teaches? The other day, I browsed some of Maryland's mandated education curriculum and examined the math section. The fourth grade curriculum, for example, states that the child should be able to recognize right triangles. Can you believe that a detail that specific was decided by a state bureaucracy?"

"You don't think a fourth grader should be able to recognize right triangles?"

"I don't think that bunch of state bureaucrats can decide what each and every child can and should know at each grade level. My fourth grader doesn't know what a right triangle is because we've been working on learning abstract thinking through computer programming. So because I think that abstract thinking is more important, my second child is 'behind' according to these guys. At the same time, my 5th grader is way beyond their math curriculum. These guys don't know my kids and they don't know my kids needs."

"But there have to be basic guidelines for the schools to work from," Abby replies. "There's nothing wrong with that."

"I think there is something wrong with having people I have little or no control over decide what 'normal' education means. The day-to-day impact of education is largely determined by bureaucrats that can't even be voted out of office! These bureaucrats have incredible influence over how the policies are implemented, and there are very few mechanisms within the system for preventing them from overstepping their authority. Homeschoolers deal with this constantly in the school districts they live within. School administrators and other public officials at all levels often attempt to impose requirements on the home-schooled students and only with the help of legal groups such as the HSLDA are they thwarted."

Abby snorts. "Thwarted? You're making a mountain out of a mole-hill."

"You really think so? I repeat: the public school system is fundamentally broken because an ever-increasing number of decisions about what is taught is determined by state and federal legislatures and bureaucracies. And that, in turn, reinforces the public school system as an arm of an authoritative government."

Abby laughs. "Oh seriously, Seth? Now you're starting to sound like a conspiracy theorist."

"Conspiracy? Homeschoolers are probably the most informed group in the country on what happens if you don't show up for school. Do you ladies know?"

Abby shrugs, but Mary shakes her head.

"The parents can be sent to jail."

"Oh no that's not true," Abby says hotly, "you're exaggerating again. The Truant officer will come by and make sure you know the kids have been absent."

"I am not exaggerating anything. In Nebraska there was a case where a home-schooling family, because of some scheduling problems was accused of truancy and given criminal convictions. And sometimes instead of jail time, you can have your kids taken away by CPS for a paperwork miscommunication."

"You're kidding!" Mary exclaims.

"Mary," Abby jumps in, "these sorts of things happen so rarely."

"Oh? And how do you know that?"

"Fine! Do you know how often they happen?"

"No, and I didn't claim to. The real problem here isn't how often they happen, the real problem is that the Government has the authority to do so. The fact that it can happen should be disturbing to anyone. Has it ever crossed your mind what mandatory education really means?"

"Yes, it means that everyone must be educated."

"Oh no it doesn't! You can't force someone to be educated, and you can't mandate wisdom. But you can mandate attendance, and with the full weight and power of the government behind it including police, jails, and forced dissolution of non-compliant families. Mandatory education means that the government orders you, at gun point, to put your children in their care, at the ages they dictate, in the places they dictate, at the times of day they dictate, to be presented the curriculum they dictate, with the other children they dictate, by the people they dictate, and under the rules they dictate. During the times of your child's incarceration, they will have little or no personal property protections, little or no protections of free speech, and (ever increasingly) little protection of religion."

At this point, Amy speaks up. "A good example of this was a young child I knew that was a member of our faith (LDS). When doing some kind of get-to-know-you paper, the child included a sibling that had passed away in accordance with our beliefs in eternal families. The teacher refused to accept this child's explanation and made him erase the name!"

"That's it!" Abby states jumping to her feet. "You guys are unbelievable. You pick out every example of bad teachers, or bad schools, or bad policies and try and say that those very rare events are how things are every day in every school."

"I most certainly did not say that. What I am saying is that no matter how rare or occasional these negative experiences are, the biggest problem is they were put upon the child by force! In the case my wife just described, the parents were required by law to keep that child with that teacher for the remainder of the year. By law, the child was forced to continue "learning" from that teacher lest his parents be sent to jail. The parents had little or no ability to have the teacher fired or even reprimanded.

"It doesn't matter that it was one nutty teacher in one school district. What matters is that the government has the power to force that child to be where they say, when they say and when the government has that kind of power, parents have little recourse if they find themselves on the business end of a nut-job. And it doesn't take too much living in too many places to find out that the nut jobs, whether teachers, curriculum, or policies, are not just occasional outliers, but increasingly common norms."

"But I actually like the teachers at my kids' school," Mary says sincerely. "And I generally do like the curriculum."

"But what if you didn't? What options would you have? Mr. Hayes who was here earlier at the party tonight lives across the county line and is in a different school district. He was describing to me the math education his children are getting. I was surprised because it was the first time in five states that I've been even remotely impressed with a public school math curriculum. But Mr. Hayes better hope and pray that the Powers that Be continue to use that curriculum. They did not consult with the parents when they hired those teachers, and they did not consider their feelings when they purchased the curriculum. As with the arbitrary and capricious sovereigns of old, the State giveth, and the State taketh away."

"Why would they take away a good curriculum?"

"Because good is subjective! Mr. Hayes tells me that during parent-teacher conferences he congratulated the math teacher for using such an amazing math program and the teacher said he was the only parent that approved! Because it is different, most other parents don't trust it. At some point in the future, the school may change its mind and go right back to teaching the crappy math that's characterized our schools for fifty years."

"Doesn't that kind of contradict your point that parents should control their children's educations?" Abby asks. "If it was up to these parents you're referring to, the children would be getting what you've described as 'crappy math.'"

"A very good point, Abby, but I'll begin to answer with a question. How well do your students learn what you teach if their parents are actively working against you at home?" The teacher refuses to answer but Seth continues anyway. "Not too well, do they? How well do you think this good math is going for these young children when their parents are openly hostile to it? And what if it was a crappy math program they were pushing down their throats instead? The fundamental problem is that the State can decide what your children learn and force you to accept their decision."

"But, if we didn't force children to go to school, some children wouldn't get educated." Mary proposes

"Your argument is that a child can be forced to be educated against his or her will? You think that forcibly putting a child in a desk for a certain number of hours in a day will somehow make them learn something? How many inner-city kids have you worked with? They've been stuck in desks from k-12 and can hardly read, so I have a hard time buying your argument."

"Fine," Abby responds, "but if they hadn't been in those desks, they would have been out getting into more trouble and we'd have an increase in gangs, vandalism, and drugs."

"At last!" Seth enthuses, "you're admitting that much of our school system isn't about education. Why don't we build some day prisons, call them that, and stop pussy-footing around. In the mean time, excuse me if I refuse to submit my child to those institutions. The public school system is fundamentally broken because it is built on a theory of dictating education and indoctrination to the parents and children."

Stay tuned for PART II...

Education Without Critical Thinking is Indoctrination

2012-02-10T07:30:00.000-08:00

One of the biggest reasons we chose to homeschool our children was because of the phenomenally poor mathematics education provided in United States public schools. A close second was the equally dismal education of history, especially United States history. We refused to trust these two subjects to the whims of bureaucrats, teachers' unions, and (occasionally) less concerned parents. As a well-known action hero exclaims, "We have no time to discuss this in committee!"

Now with several years of experience under our belts, and with exposure to a wide array of teaching materials, I have altered my priorities. As important as mathematics and history are as subjects, they do not represent the core foundation of education. In fact, no subject does.

The foundation of education is critical thinking. Without this foundation, education becomes nothing more than skills training in the best case. And in the worst case, it is indoctrination.

Consider the ongoing debates about teaching evolution or creation in schools. The parties engaged in this contest do not believe in critical thinking as evidenced by their fear of the other side. If each side had full confidence in the strength of their beliefs, they wouldn't fear the exposure of students to alternate points of view or interpretation of evidence. If one theory is so much stronger than the other, no one should fear seeing them side-by-side because the students will be able to see it for themselves. As a mentor taught me, "truth withstands scrutiny."

What truly terrifies me in the evolution versus creationism debate is that the government can decide which one to throw its weight behind and enforce that view upon students.

Of course, homeschoolers are not immune to indoctrination of students. It's impossible to teach without bias even when aware of, and attempting to compensate for, one's personal slant. But in our homeschooling program, we are trying to give the students opportunities to learn the skills that will allow them to be effectively and appropriately critical of any principle, training, theory, or message including those of their parents.

One of these skills to watch out for "straw man" arguments. Consider our children's history book when discussing McCarthyism. The following quote is the only reason the author gives for why Americans were fearful of communism: "Some Americans disliked and feared communists because communists do not believe in God."

The book conveniently doesn't mention that the stated method of "change" in the communist manifesto is violence as I quote below (emphasis mine).

The Communists disdain to conceal their views and aims. They openly declare that their ends can be attained only by the forcible overthrow of all existing social conditions. Let the ruling classes tremble at a Communistic revolution. The proletarians have nothing to lose but their chains. They have a world to win.

Working Men of All Countries, Unite!

Even the religion angle is more frightening when you consider that religion was one of the social conditions communists looked to "forcibly overthrow."

None of this is to say that McCarthy wasn't a liar, a con-artist, and a power-hungry opportunist. Recognition of legitimate concerns about communism does not justify the infringement on civil liberties during the 50's.

But you don't get to the truth by artificially weakening the lies. The lesson I gave my children in response to this excerpt is that when you want to attack something, you build it up as strong as you can before you go after it. The older children are taking fencing lessons and I asked if they would become good at fencing by fighting a straw man? They immediately saw the connection.

Another skill we're working on with the kids is recognizing emotional cover-ups for poor logical reasoning. Our 10 year old child, Alex, is currently studying Geometry and has been learning foundation concepts of logical reasoning. We applied some of that thinking to another quote in this textbook (emphasis original):

Good times?

The Eisenhower years were prosperous. Jobs were plentiful, People had money to spend... Now you could buy... almost anything you wanted...

These were good times.

But not for everybody.

Let's look at the argument so far.

If jobs are plentiful, there is money to spend, and you can buy things,
Then these are good times

So, what do you think is coming next? What should follow is an assertion that some people couldn't get jobs, money, or make purchases. Instead, what we get is:

Some citizens were kept out of the good times. In the South, blacks couldn't eat in the same restaurants as whites, shop in the same stores, use the same bathrooms, drink from the same water fountains, or go to the same schools. It was humiliating - and unfair...

The logic here is extremely poor. She doesn't say that blacks couldn't get jobs, spend money, or buy things. Instead, she covers her bad logical reasoning with an emotional connection to "good times." She contrasts the positive feelings humans feel when spending money against the negative feelings they have being physically restrained from movement.

What's especially frustrating about this is that blacks couldn't get as many jobs, they didn't get paid the same, and I wouldn't be surprised if their were things they couldn't buy. She should have used these facts as her contrast or, alternatively, she could have have started with concepts of mobility. The 50's were also a time of travel, and other forms of movement previously unknown to the American public. If she had started with these examples of 50's lifestyle for whites, her comparison to the 50's lifestyle for blacks would have made more sense.

Sigh.

On the positive side, this poorly constructed argument served as a excellent lesson in reasoning and persuasive writing. The two older children are becoming aware that the things they are told and taught need to be evaluated, weighed, and considered. In these discussions, they were active participants and made thoughtful insights and observations. The seeds of real education are growing and their minds are expanding.

I used to think that Math and History were two subjects I couldn't trust to other people. But now I know that even more crucially, you should never trust the instruction of critical thinking to a committee.

Reading: Reason to Celebrate

2012-02-05T17:54:00.000-08:00

Every now and then, I see articles on new sources that headline: "How to get your children to read." I've never read these articles because the only problem we seem to have at our house is getting our children NOT to read (i.e., when they're supposed to be going to bed or doing something else). Alex (age 10), in particular, has been blasting through books faster than he can check them out from the library, and Drystan (age 8), although reading fewer books, has been digesting literary works far beyond his age and experience level.

We've done a lot of things wrong in our home-schooling, but (thankfully) a love of books was one thing we managed to do right. I thought it would be fun to list here the books that the boys have are reading or have completed in the last few months (* indicates currently reading, Amazon links included where possible).

Drystan's Recent Books:

The Odyssey, Fagles translation (http://www.amazon.com/Odyssey-Robert-Fagles/dp/0140268863)
On Wings of Faith (http://www.amazon.com/Wings-Faith-Frederick-Babbel/dp/1555173543)
The Lost Hero (http://www.amazon.com/Lost-Hero-Heroes-Olympus-Book/dp/142311339X)
The Son of Neptune (http://www.amazon.com/Son-Neptune-Heroes-Olympus-Book/dp/1423140591)
High Tide in Hawaii (http://www.amazon.com/High-Tide-Hawaii-Magic-House/dp/0375806164)
Some random Scooby-Doo chapter books checked out from the library
*To Kill a Mockingbird (http://www.amazon.com/Kill-Mockingbird-Harper-Lee/dp/0446310786)
*Halo: Ghosts of Onyx (http://www.amazon.com/Ghosts-Onyx-Halo-Eric-Nylund/dp/0765315688)
*Animorphs: The Invasion (http://www.amazon.com/Invasion-Animorphs-1-K-Applegate/dp/0590629778)
*Naya Nuki: Shoshoni Girl Who Ran (http://www.amazon.com/Naya-Nuki-Shoshoni-Girl-Who/dp/0801088682)

Alex's Recent Books:

The Book of Three (http://www.amazon.com/Book-Three-Prydain-Chronicles/dp/0440407028)
The Black Cauldron (http://www.amazon.com/Black-Cauldron-Prydain-Chronicles/dp/0440406498)
The Castle of Llyr (http://www.amazon.com/Castle-Llyr-Pyrdain-Chronicles/dp/0440411254)
Animorphs: The Invasion ( http://www.amazon.com/Invasion-Animorphs-1-K-Applegate/dp/0590629778)
Animorphs: The Visitor (http://www.amazon.com/Animorphs-02-Visitor-K-Applegate/dp/0590629786)
Animorphs: The Encounter (http://www.amazon.com/Encounter-Animorphs-3-K-Applegate/dp/0590629794)
[RE-READ] Ranger's Apprentice Book 1 (http://www.amazon.com/Ruins-Gorlan-Rangers-Apprentice-Book/dp/0142406635)
[RE-READ] Percy Jackson: The Lightning Thief (http://www.amazon.com/Lightning-Thief-Percy-Jackson-Olympians/dp/0786856297)
Last Apprentice: Revenge of the Witch (http://www.amazon.com/Revenge-Witch-Apprentice-Joseph-Delaney/dp/0060766182)
Last Apprentice: Curse of the Bane (http://www.amazon.com/Curse-Bane-Apprentice-Joseph-Delaney/dp/0060766212)
Last Apprentice: A Coven of Witches (http://www.amazon.com/Last-Apprentice-Coven-Witches/dp/0061960381)
Halo: Ghosts of Onyx (http://www.amazon.com/Ghosts-Onyx-Halo-Eric-Nylund/dp/0765315688)
Leviathan (http://www.amazon.com/Leviathan-Scott-Westerfeld/dp/B005OHSDXA)
Naya Nuki: Shoshoni Girl Who Ran (http://www.amazon.com/Naya-Nuki-Shoshoni-Girl-Who/dp/0801088682)
The Odyssey, Fagles translation (http://www.amazon.com/Odyssey-Robert-Fagles/dp/0140268863)
On Wings of Faith (http://www.amazon.com/Wings-Faith-Frederick-Babbel/dp/1555173543)
To Kill a Mockingbird (http://www.amazon.com/Kill-Mockingbird-Harper-Lee/dp/0446310786)
Fahrenheit 451 (http://www.amazon.com/Fahrenheit-451-Ray-Bradbury/dp/0345342968)
Day of Infamy (http://www.amazon.com/Day-Infamy-60th-Anniversary-Classic/dp/0805068031)
*Soviet Babyboomers (http://www.amazon.com/Soviet-Baby-Boomers-History-Generation/dp/0199744343)
* [RE-READ] The Sea of Monsters (http://www.amazon.com/Monsters-Percy-Jackson-Olympians-Book/dp/1423103343)

Miracles in Government-managed Education

2012-01-25T09:37:00.000-08:00

I am constantly reminded by Real Life (tm) that it requires a lot of work to understand my children's goals, needs, desires, strengths, and weaknesses. It isn't easy, especially because of the language barrier. For example, we gave Alex (age 10) the opportunity to add some "elective studies" into his history class this semester. We're studying American History from 1945-1990 but we told him that he could choose books from the library on subjects from that time period and write his assigned papers from those. He indicated he was interested in "economics" under the different forms of government (e.g., Communist, Free-market, etc.).

No problem, right?

Except that every time we found an economics book, he was completely uninterested and became increasingly frustrated. Only after a lot of listening and discussing were we able to figure out that what he was actually interested in was personal stories about individuals living under those different types of governments. We found a book about individual stories from the Soviet Union (http://www.amazon.com/Soviet-Baby-Boomers-History-Generation/dp/0199744343) at the library, and he is hungrily devouring it.

Now, I don't know why or how Alex came to associate these kinds of personal stories with the word "economics," but he did. And that little misunderstanding was no small source of consternation.

With that story as a backdrop, consider the amazing and miraculous experience my friends (blogs here and here) are having in Europe. They just moved from Pittsburgh in the USA to Zurich, Switzerland. They also home-school their children and have decided to continue to do so while they live abroad. The Swiss canton they live in allows homeschooling with Government approval.

The mother has been preparing her curriculum for the Government's review with another woman helping her to translate it into German, and also giving her advice on content. I quote from the mother's email:

It's kind of funny, I sent [the woman helping us] our schedule and she
said I'd need to amend it because otherwise they will consider it to
be too much work [for my 8 year old]... I guess they don't really consider
history or geography necessary, and science is pretty weak, until they
get to HS. So when I had strong curriculums for those they feel it's
too hard/too much, and if they think your school curriculum is too
rigorous, they won't approve you... but she should be
doing crafts every day, and they want to make sure she knows all her
colors and shapes...

When I read this email, I was overwhelmed in amazement and wonder! Just think, it took me weeks to understand the type of History book my 10 year old was interested in. And yet, in Switzerland, one or more appointed officials, through some extraordinary power, know what is too much work for a specific 8-year old girl. Keep in mind that they have never met this girl, know nothing about her previous studies, nothing about her parents' educations, nothing about her interests, and nothing about her personality.

How incredible! To know exactly what someone needs without knowing anything about them! To know it so well, that they can enforce it with all the weight and power of the Government over the objections or concerns of the mere-mortal parents! My friends' children should be grateful they moved to a country where telepathy, crystal balls, and tea leaves are requirements for civil service.

But I'm not being fair to the good ol' USA, I guess. Our own education departments here in the States sometimes exhibit these super-human powers as well. For example, some committee in the Maryland state Government knows that my child needs both an art class and a music class every semester. Let me emphasize that they know this. It is not a suggestion, a guideline, or a starting point. If I do not give my children both an art class and a music class every semester, the state will prohibit me from educating them at home. And they will make that prohibition regardless of the school district I live in. They know that both an art and music class are so vital to my children they've never met, that they would rather send them to a Baltimore city school (for fun, look that up on the Internet sometime) than they experience the tragedy of a semester with just one class or the other. Thank goodness they have those superpowers to help them make such a decision!

There is even more good news! These powers seem to be expanding to other groups! In a recent NEA document, this teacher's union asserts that home schooling cannot give children a comprehensive education, but that public schooling can. Note, they do not assert this for "many," "some," or "most," children. They assert this for every child in the entire United States. They know, without any reservations or conditions, that an elementary teacher that they've never met and whose motives, academic achievements, scholastic interests, and talents are unknown to them, can give my children a "comprehensive" education. They similarly know that my wife and I cannot educate our children with an equal lack of personal exposure.

Maybe if I joined the NEA I could understand what my 10-year old meant by "economics!"

Truly, we live in wondrous times. How blind I have been to the miracles happening all around me! My heart swells with gratitude for being able to have knowledgeable people running our country. Can you imagine what other visions these bureaucrats in the Government are having right now? I'm sure that with such oracular knowledge, it won't be long before they expand their benevolence out into other areas of our lives.

I don't know about you, but I can hardly wait!

Pop Quiz: What is the Value of Testing?

2012-01-04T08:55:00.000-08:00

Remember what your mother said about the two topics not to discuss in company? Religion and politics, right? If you're a tech geek, you might also be aware of other "ideological" wars like emacs versus vi, C++ versus Java, and so on.

In my experience, many teachers have similarly explosive reactions to testing. And that goes double for homeschooling parents.

I, myself, am very neutral on the topic. Perhaps a better description is to say that I have very mixed feelings. I am not blind to the extreme insanity that drives "standardized" testing. Nor am I ignorant of "teaching to the test" problems since NCLB.

On the other hand, I believe that I benefited from some of the testing I experienced in college. While I had some teachers that created very poor tests, I felt that many classes had effective tests that required consistent attention to classroom instruction, reduction of broad swaths of information to core principles, and disciplined preparation for the test itself. I have no idea how valuable those tests were to the other students, but they were valuable to me.

One of the common complaints about testing is that you cram your head full of information you will forget the next day. Such a charge could be easily leveled at me. Despite my proclamation that tests were valuable for me, I doubt I remember even 20% of the material that I was tested on.

The problem with that criticism, of course, is that it assumes that the test was purely memorization based. In other words, the test was simple gauge of one's ability to remember facts and was devoid of any critical thinking. Such a description is simply not true for most of the testing I experienced in college. Memorization was often required, but the facts brought into the testing room were simply tools used to build more intricate mental productions.

A second reason I do not find the "test-it-and-forget-it" criticism to be valid is that it assumes that there is no practical value in "learning-and-forgetting." In my current work I often assist lawyers on the technical issues in their (generally copyright or patent) cases. Gearing up for writing a report, or someone's deposition, I am cramming information into my brain as quickly as I can that I will forget most of the moment my task is over. Given that I often have multiple cases overlapping, I have to be able to quickly absorb significant quantities of information on different and unrelated topics in rapid succession. Information is going in and out of my mind at very high speeds.

Of course, not everyone is the same. Some individuals might not be well-served by test taking. Moreover, testing is most often used to evaluate, and when a test does not accurately evaluate someone, they resent the unfair categorization of their ability and/or hard work. I honestly do not know how to solve this problem generally. I am not convinced that testing can be eliminated completely.

But within the walls of our own home schooling program, I do know how to make testing useful and positive. The reason is, I already know how the children are doing and that means I can eliminate testing for evaluation. Instead, I can use testing as both a pedagogical tool and for diagnostics on the classroom instruction.

During the last semester, our older two children were given a spelling test every Friday and for these tests, we required 100%. Our children have good memories, and we knew they were capable of getting every single word correct. In this case, the testing was a tool for teaching precision, discipline, and early preparation. The two boys learned those principles and, by the end of the semester, they were both getting 100% regularly.

On the other hand, Alex (age 10) got an 85% on his History mid-term, and Drystan (age 8) got a 55%. We weren't concerned at all about the actual scores because we knew that both boys know and understand history really well and had studied very hard. Because of this, the tests revealed things we might not otherwise have seen about our teaching and their learning.

For example, both boys missed almost every question about religious conflict on the test, despite repeated discussion of the topic in class. This was really interesting to us and we spent some time trying to figure out what happened. Our current guess is that the boys struggle to relate to religious persecution (something they haven't experienced) and can't connect it to conflicts in history. On the other hand, they do understand food, and got questions right about conflicts related to hunger (e.g., the Irish Potato Famine). Of course there might be other reasons they struggled with these questions, but the point is we now know that they struggle with them. Now we are prepared to pay more attention to those issues in class.

Drystan expressed concerns to me about his "low" score on the test.

"Do you know what you learn when you don't prepare for a test and you do poorly on it?" I asked him.

"What?"

"That you didn't prepare for the test. And because you already knew that, you haven't learned anything new. When you have worked hard to prepare for a test and you still don't do well, you can learn something from it." Then, I pointed out to him all the things that his mother and I were learning from the test. I explained that the test was diagnostic for us precisely because he had worked very hard to be prepare for it.

He came away from the experience with the lesson that hard-earned "failures" can be just another valuable opportunity to learn.

So what is the value of testing? For me, it is simply another tool in my "teaching toolbox" and one that I believe was used to good effect in instructing my children over the last semester.

And if that answer isn't worth full credit, I'll probably still do well when graded on the curve.

Drystan Demands a Math Test! Or, Pedagogical Engineering: Separation of Concerns

2011-12-13T08:10:00.000-08:00

In Computer Science and Software Engineering, there is a concept of "separation of concerns." Computer programs these days are often enormous. The only way a software engineering team (or even a single software engineer) can handle the overwhelming amount of information is to break the program into pieces. The concept of "separation of concerns" is that a module should only do its job, and not the job of any other modules. It seems obvious, but in practice is is very difficult. Still, once a software engineer is aware that the principle even exists, it generally improves his or her software development even if (s)he is imperfect at applying the same.

It has occurred to me that "separation of concerns" has a lot of applications to "Real Life," and today I was thinking about a particular application to education. It seems to me that in education many people make the inappropriate connection between how talented one is with a subject with how much one enjoys that subject. While I am certain that some of this connection is natural to mankind, I do believe that some of it is created and reinforced by society.

I was elated today to hear Drystan demand a final exam in math. Demand! I told both of my older children that I was pleased with their mid-term tests and the work over the semester, so there would be no math final. Drystan, who is just 8, pleaded and begged me to change my mind. I finally agreed to come up with a math exam for him and he cheered! Why was I elated? Because Drystan is the child that has struggled the most with math since he was just three years old. I am elated that he has not associated enjoying a subject to his corresponding talents.

Consider that in my college career, I had to take a number of math classes. Some of them were more "pure" math classes from the math department, while others were more "computational science." The point is, they all relied on the "mathy" part of my brain.

I literally had to take each one of these mathematics classes twice because I either failed or nearly-failed the first time.

This fact often surprises people. They are shocked that I, with a Ph.D. in Computer Science, performed poorly in my mathematics classes. I understand that. What I don't understand is when I see their surprise increase as they hear how much I loved and love these classes that I failed.

To repeat, I am certain that some connection between talent and enjoyment is natural. I am sure that people generally are happy to perform well at a task independent of everyone else.

But I also assume that human beings crave validation and positive reinforcement. Given that assumption, it worries me to hear parents (and sometimes teachers!) tell me they are helping their child "find what they are good at." I'm sure this is fine to a reasonable extent, but my worry matures into full-blown horror when I see this attitude coupled with assertions that the children shouldn't spend much time or energy on subjects that aren't talents. Why is there so little emphasis on loving to learn about everything?

Of all the subjects where the false-coupling of talent and enjoyment occurs, I think that mathematics is one of the worst. In my conversations with parents across the country I hear over and over that elementary math teachers "bucket" children into the "good-at-math" and "bad-at-math" groups. Not only are the so-called "bad-at-math" children probably just in need of decent instruction, but in many cases they are encouraged to focus on other school subjects. Sometimes the encouragement is just in the form of hints, but other times they are told so explicitly!

It seems to me that in most schools, Drystan would have been bucketed into the "bad-at-math" category. From a very, very young age, he viewed the world around him very literally. He has plenty of imagination, but he cannot move from literal to abstract easily. So, for him, "11" should be "2". See? there are two 1's, and he knew that 1 and 1 is 2.

This first showed up when he was three years old, and I assumed he would just grow out of it. I didn't think too much about it.

Then he was four...

and five...

and six...

and seven...!

And just this past summer we had a situation where he still struggled to understand the difference between a number in the ten's column, and a number in the one's column. He was able to figure it out eventually and he could do it because he has had a lot of practice with dad, but it isn't natural. He still has to be very careful when adding and subtracting multiple-digit numbers because it is so non-intuitive.

To make matters worse, his older brother was practically born thinking abstractly. Numbers are easy for Alex and he's pretty quick on the mathematics uptake. I have always worried that Drystan would develop some kind of complex about Alex being the "good-at-math" kid, and he being the "bad-at-math" kid.

Yet, somewhere, somehow, I managed to do something right because Drystan still enjoys math. He enjoys math enough to beg me for a final exam! I am certain that part of it is that he wants to make his dad proud of him. But even if that is true, at least he knows that I am proud of him in math for enjoying it and working hard rather than being naturally talented at it!

None of this is to say that Drystan doesn't work hard to increase his mathematical abilities. To the contrary, we require him to continually improve. But that is the point of separating the concerns; they can be evaluated and improved individually. One can approach learning to love a subject differently from improving one's performance thereof. These two components are individually strengthened, but subsequently reinforce each other. At the same time, mistakes made in one of the two areas has a more limited impact on the other. The system is more stable and resilient for appropriately separating concerns!

In conclusion, loving learning should be an independent component of an educational system. It should be distinct from identifying talents and increasing capabilities. As with software engineering, though, the hard part is figuring out how to put such separation into practice. In the tradition of those who can neither do, nor teach, I have criticized without providing a lot of constructive counter-examples. But in the tradition of those who do teach, I will leave such banal matters as an exercise to the reader.

In the mean time, I have an unexpected math final to write...

Lush Vegetation of the Mind: Math Edition

2011-12-09T07:03:00.001-08:00

It will come as no shock to anyone that I am extremely opinionated. Good heavens, my twitter handle is "SethHasOpinions." And one of the topics that I am most extremely opinionated about is that of mathematics education.

In yesterday's blog post, I mentioned some of the struggles we have had over the last year. Today, I want to talk about one of our successes.

Alex and Drystan enjoy a mathematical world full of ideas.

I realized long ago that the way mathematics is often taught is devoid of any ideas. Think about it this way. When a child comes home from school and you ask them what they did in class today, you very rarely get a response about mathematics. They can tell you about the Greeks and Romans from their history class, the different types of rocks they learned about in science, and the new book they're reading in English.

But what are they going to say about math?

"Math? Oh... um... not much. We did long division. Again."

I am not saying that one doesn't benefit from learning to divide numbers, but I am pointing out that it was only the first day or two that division was taught that there was probably any discussion in the class room about the ideas. And truthfully, in a lot of schools, the ideas are never taught. The emphasis is on a skill devoid of imaginative thinking and wonder.

This was brought home to me earlier this week when I was teaching a ten-year old boy about the inner-workings of a computer for a scouting requirement. He is a bright kid who attends a Magnet School and is, I believe, in the gifted and talented program. I decided to give him a quick introduction to binary numbers. He picked up very quickly the concepts, but what absolutely shocked me was how little this very intelligent child had ever thought about any mathematical ideas. Oh, he knew all the formulas of addition, subtraction, and so forth. But he didn't know anything about how or why any of it worked. He told me he had never even thought about it.

For example, I asked him to think about the number "11" and why the two 1's were of different values. He stared at the board like I was speaking parseltongue. Even when I asked him about the differences between the ten's column and the one's column he seemed completely lost. I think he finally connected it to carrying in addition and subtraction and understood. But the idea that the 1 in the 10's column was worth more than the 1 in the 1's column seemed novel to him. And he was actually excited about it!

Can you imagine? Ten years old before someone tells him about the ideas that underlie our base-10 number system?

For the last four months, Alex has been working through a "Introduction to Algebra" book I found on our shelf. To be completely honest, it is one of the most boring and dry algebra books I have ever seen. But because Alex is only 9 (turning 10 this month) it seemed really interesting to him. I tried out a few lessons with him and he was doing alright, but I was worried maybe he needed something easier. When I asked him if he wanted to stop doing Algebra and go back to other arithmetic work, he vehemently stated his opinion that he did NOT want to go back to that "boring" stuff. So, while it looks like he is "ahead" in math, all we are really working for is keeping his brain buzzing.

On the flip side, Drystan is "behind" in computation according to most curriculum standards. We consider him in fourth grade, but he has never done multiple-digit multiplication. He's done very little with division, and certainly nothing with long division.

Instead, I have been giving him lessons I made up for a course I called, "An Introduction to Sets, Geometry, and Algebra." To my surprise, sets have really excited him. In particular, he was thrilled when he began to grasp the ideas of union and intersection. He just loved being able to take sets in his head and arrange and re-arrange them. Sets have also given us a way to discuss mathematical properties outside of their application to numbers. For example, in most elementary math books, children are taught:

Commutative property: 3 + 4 = 4 + 3
Associative property: (3 + 4) + 1 = 3 + (4 + 1)
Distributive property of multiplication over addition: (3 + 4) X 2 = (3 X 2) + (4 X 2)

In our work we have also shown that union and intersection of sets have the commutative and associative properties and that union distributes over intersection and vice versa. Seeing these properties apply to other ideas makes them more conceptual rather than computational.

What is funny is that Drystan has a really good grasp, now, on the distributive property. He understands how to distribute intersection over union, union over intersection, and multiplication over addition. Why is this funny? Because distributing multiplication over addition is how one often does multiple-digit multiplication. In fact, that was the lesson that Drystan and I had yesterday.

I showed Drystan a rectangle. In previous classes, we have been computing area of small rectangles like 3x4 and so forth, but now I had him look at one that was 16 x 5. I asked him if he knew what the area was, and I expected him to say no. He surprised me by correctly stating the area was "80."

"How did you know that?"

"Well, I knew that 5 times 10 was 50, and 6 times 5 was 30."

He had used the distributive property in his head! I had him work out on paper a couple of problems showing him that for a single digit times a double digit it was really easy to make into solvable problems:

42 x 7 = (40+2) x 7 = (40 x 7) + (2 x 7)
29 x 4 = (20+9) x 4 = (20 x 4) + (9 x 4)
63 x 5 = (60+3) x 5 = (60 x 5) + (3 x 5)

And he thought this was all really neat and exciting. And then I showed him how we can make this a shorter process for convenience:

42
x 7

In this format, you multiply the 7 x 2 (just like in the longer version a few lines ago), but you only write the one's value and carry the tens:

1
42
x 7
4

Then, you multiply the 7 x 4, but that's really a lie, right? What you're really doing is multiplying the 7 x 40, just like before in the longer version. 7 x 40 = 280. We add the "4" already in the ones column, and carry the "1" in the tens column and get:

1
42
x 7
294

My point to him was that we're still doing the (2 x 7) + (40 x 7) based on the distributive property. "It's the same thing," I said.

Drystan looked at this all for a moment and replied, "Ah... but less fun." That's right, he would rather do 42 x 7 = (40 + 2) x 7 = (40 x 7) + (2 x 7) even though it is longer and takes more time because he understands the ideas of distributing the multiplication and thinks it is more fun to show it!

Math for Drystan isn't just about getting the right answer. It's about getting the right answer and having fun. Ideas do that for people. You plant them, and they grow up into into trees you can play in, shade you can sit under, provide space for animals, and produce fruit you can eat. Trees spread the seeds and more trees grow until, after time, a lush forest and a complete ecosystem fills the formerly empty space.

As I was laying in bed this morning, ignoring the alarm clock, I meditated on these ideas. It occurred to me that teaching math as just a bunch of formulas to crunch was like giving kids plastic plants and trees instead of seeds. Plastic plants are much easier to grade because the kids can line them up or move them around in whatever format demanded. Parents, journalists, and politicians can be shown how "effective" the teachers are in having the children line up the plants into a faux forest.

Seeds are so much harder to evaluate. They grow under ground for a long time so it isn't always obvious what is happening. Once the seed starts to grow out of the ground, it cannot be easily moved and it doesn't always take the expected or desired shape (I am well aware of the over-simplifications I have made on some of these points, but I think the core analogy is sound). But it becomes a magical world that is full of unexpected experiences, fantastic exploration, and wondrous discoveries.

In the spirit of that analogy, here are the last few words from the last Calvin and Hobbes comic strip: "It's a magical world," Calvin says to Hobbes before darting off on a sled. "Let's go exploring!"

The Process of Becoming

2011-12-08T16:08:00.001-08:00

That's right, it's been a year (+2 days) since I last posted to Type-H personalities.

It's been a busy time since that last post. My wife and I spent the first part of the year finding a house, the middle part of the year moving into the house, and this last part of the year dealing with the crazy schedules after my job changed slightly.

On top of that, we've certainly had more than our share of struggles with Home Schooling. One of those struggles has been our efforts to help our oldest child learn how to work and take advantage of his plethora of talents.

Alex, who turns ten in less than two weeks, was having so much trouble getting any work done that it significantly reduced my desire to post to Type-H personalities. Oh, I believe in posting struggles as well as successes, but it was reaching such a point that we almost considered putting Alex in public school. It was getting that bad.

In an earlier post, I mentioned some successes we had with Alex by allowing him to fail. (http://typehpersonalities.blogspot.com/2010/10/my-b-is-worth-more-than-our.html). While that was somewhat successful for a short period of time, after a while, Alex began working less and less. Eventually it got to the point that he was turning in no assignments. None. For weeks.

I was so frustrated with these developments that I felt I had little to talk about on my blog about home schooling. If I couldn't think of anything I wanted to share about our family's successes without feeling overwhelmed at what I perceived as my own failures. It was a silly way of looking at things, but that is how I felt.

Besides, it seemed like if I had a spare minute to think about home schooling, I needed to spend it thinking about how to help my child.

Thus, the blog has languished for the last 12 months while we struggled to help Alex.

And struggle we did. I couldn't being to count the hours that Amy and I discussed and implemented different things to try and inspire him or find more enjoyable subjects. Nor could I count all the discussions I have had with Alex trying to find out what is going on in his mind. There has been no end to the negative consequences we have tried, nor the rewards and positive reinforcement we have offered for even small successes. Note that on top of trying to figure out how to help Alex learn to work, I have had to worry and fret about doing so in a way that will not damage our relationship with each other. I have done everything I could to express love even when giving punishments.

There were many times it seemed like nothing was improving or changing. But slowly, ever so slowly, we would make some progress. It was often a two-steps-forward-one-step-back kind of process, but that is still progress. We would have a few successes and then a series of failures that seemed to place us back at square-one. But then we would bounce back and get farther faster on our next try.

Then, all of the sudden, all of the work and effort seemed to just "click." Almost as if by magic, Alex seemed to get traction. To our surprise and relief, he began to do his school assignments. There was a turning point and instead of failure punctuated with successes we began to have successes with occasional failures.

Of course, it wasn't all of the sudden, and it wasn't magical. We, Alex, Amy, and I, had planted and nurtured seeds of future success for these last twelve months. There had been worry, frustration, tears, and hurt feelings. Every one of us had faced self-doubt, pessimism, and maybe even depression. But through all the difficulties, we continued to nurture the little plot of ground, not quite realizing the sprouting that was going on beneath us.

But oh! what joy and thanksgiving when the little seedling first broke the soil!

Certainly we are happy to see Alex doing better with his work ethic as well as his school studies. But the thing I am most grateful for in this last year's experience is the chance to struggle together with my wife and my child. We have come out of it stronger and with a greater ability to work together. Going through the fire together refines everyone and binds them in ways not easily broken.

The other night, I was driving Alex home from cub scouts. I asked him how he sees school differently now. I expected him to say it was more fun, or more interesting, or so on. Instead, he simply said,

"I appreciate it more now."

Wow.

You know what, Alex? So do I.

Making Math Fun, One Egg Breakfast at a Time

2010-12-06T08:45:00.000-08:00

Today was "Math and Eggs" in the Nielson Academy. By way of quick reminder, in our house we separate "Computation" and "Mathematics". Computation is crunching numbers according to formulas, while mathematics is exploring unknown mathematical puzzles, questions, and problems. (Interesting side note, the question of "how much is 3+3?" is computation for my 7 and 9 year olds, and mathematics for my 4 year old.)

This semester, we've been focusing on asking questions as a way of getting started with Mathematics. Alex has been exploring some questions of his own making related to the volume of 3-D shapes, while Drystan has been mostly focusing on questions relating to number patterns.

Another reason the kids look forward to mathematics is the yummy egg breakfasts that accompany them. Eggs and puzzles... what's not to like?

Well today, whilst cooking said eggs, I had Drystan looking at the pattern 1/3, 1/9, 1/27... and the related 1/3 + 1/9 + 1/27 + .... These patterns are taken from Don Cohen's book "Calculus by and for Young People". Last week, Drystan figured out that 1/3 + 1/9 = 4/9. He doesn't know the "rules" of fractions yet, but he could visually see the answer from drawing out a 9x9 grid and coloring in the appropriate fractions. Today, I asked him what 1/3 + 1/9 is in thirds. He's used to these kinds of questions now and immediately responded "One and a third thirds!"

So, I asked him to draw 1/27th. He didn't want to try and divide his 9x9 grid in to 27ths, but I asked him to look for the pattern. Ten seconds later, he realized it was "one third of one ninth". He had the pattern figured out now. He filled in three squares on the 9x9 grid.

But now I asked him to figure out what the next term in the series was. Now that he had the pattern down, he knew he needed to multiply "3x27". But he has only done single digit multiplication, and hasn't been taught the "rules" of this type of multiplication. I wasn't sure how he would do.

But to my surprise, he broke up "3x27" into "three twenty's" and "three seven's". I was so thrilled to see him figure that out on his own. I wrote on the board "3x27" in the vertical form and showed him that one of the common ways of multiplying is to do exactly what he did. You multiply the 3x7 first, carry the 2 (well, the 20 really), then multiply the 3x2 (well, 3x20 really), and get 81. The eggs were done at this point, and we could talk about it while munching.

We had a good morning. Final score, "Math and Eggs: 1, Mathphobias: 0"

Alex's Essay About the Steam Engine

2010-11-17T07:52:00.000-08:00

This year, we have been working with Alex on the writing process. We have him apply the principles he is learning in his writing class to papers in other classes. In history class, for example, Alex is expected to write three papers this semester. He's already written one about the Lewis and Clark expedition, and yesterday he finished a paper about the Steam Engine.

For all of these papers, the expected length is a page of cursive writing. He first writes out an outline, followed by two or three drafts. When he has a final draft finished in cursive, he types it on the computer.

I thought his steam engine paper was pretty good, so I'll reproduce it here (complete with a few errors that he missed):

Alex Nielson

November 16 2010

The Steam Engine

Steam power is where steam causes movement. A coal fire boils water and creates steam. The steam causes pressure to push pistons.

There are many parts of a steam engine. A coal fire heats a boiler and creates steam. The steam goes through pipes and its direction is controlled by two valves into the cylinder. The steam in the cylinder pushes pistons which turns the crankshaft. The steam goes thorough the valves on the end of the cylinder. The steam enters the condenser and cools into water and goes into the boiler.

A steam engine can be used for creating propulsion. When the crankshaft turns it can turn a wheel or propel something that would cause propulsion. In the forward stroke the steam pushes the pistons forward to a certain point and then the steam goes down one of two valves. In the backward stroke the steam pushes the pistons backward to a certain and the steam goes down a different one of the two valves. In both the forward and the backward stroke the steam enters the condesener and cools into water and goes back into the boiler and the process starts over again.

My "B" is worth more than our "A"

2010-10-27T07:12:00.000-07:00

In a previous post, I mentioned the importance of failure in learning as exemplified in mathematical thinking. There are a lot of different ways that we can experience "constructive failure." These kinds of "mistakes" are an essential part of exploration and true education.

But what about non-constructive mistakes? What about poor choices for short-term benefits at long-term expense? What about known but missed opportunities because of idleness, or self-harm because of rebellion against known principles?

These mistakes are much harder for a parent to watch.

But they are just as important and necessary for proper childhood development.

Parents need to allow children to make even non-constructive mistakes safely within the walls of a loving home so that they learn by their own experience to recognize the difference between good and bad principles. They need to learn the consequences of their actions, especially long term consequences, when there are parents there to help them up and get them going again. The alternative is learning about failures years later when parental safety nets have long since been obsoleted.

This is a tough principle for me. I didn't recognize this problem in myself at first, because I believe in giving children negative as well as positive consequences for their behavior. As I saw it, I was allowing the children to fail and experience the results.

But the problem was the long-term component. I would give my children severe short-term pressure to prevent any long-term failures. There was little time for them to think about their behavior and adjust it under their own powers.

The concrete example I want to use is getting their schoolwork done. Alex, the nearly 9 year old, has trouble staying focused even on assignments he really enjoys. He was capable of doing it, and some days he would. But other days, he'd get so lost in his imagination that he wouldn't get anything done at all. My solution for a long time has been to penalize his actions immediately. Normal punishments were to not allow him to go play until his work was done, and if he didn't get it done, he would have to write sentences on top of normal homework the next day.

This kind of disciplining was very draining on us as parents, and it wasn't doing good things for our relationship with Alex.

Then, one day, after a lot of thought, prayers, and discussions with trusted (more experienced) friends, I realized that we were double-penalizing him. First, we would penalize him for not getting his work done that day, and second we would penalize him at the end of a semester for not getting good grades. Well, I thought to myself, that isn't fair, and it certainly hasn't been effective. So, after discussing things over with Amy, we decided to get rid of all "immediate" penalties. Completely contrary to our previous way of thinking, we would not reprimand or punish Alex if he did not get his assignments done.

Well, not right away, at least.

Instead, he would have to deal with longer-term penalties. He could choose to not get assignments done, but unless his grades were at acceptable levels, he would not get video game or movie privileges. Grades would be evaluated each weekend. Furthermore, while we would not punish him for not getting homework done, the new policy was that 1-day late homework was worth 50%, and after 2 days it was worth nothing.

The changes had some immediate impacts. First and foremost, it relieved Amy and me of a very difficult "babysitting" job. More importantly, the atmosphere in the home improved dramatically. Instead of me coming home from work worrying about whether or not Alex had his assignments done, I could come home and focus on spending time with the kids and enjoying their company. At dinner, I would ask them how their school work went, including Alex. And if he said he didn't get much done, I would sympathize with him, ask him if he needed help, and encourage him to work harder the next day. That kind of communication felt good.

But the changes in Alex were much slower. The first week was very difficult because without the babysitting he didn't get much done. Home work assignments were late, or missed completely, piano practice was slipshod, and, as expected, his grades at the end of the week were not good.

It was hard to watch, and I wanted to jump back in and "save" him.

But we stuck to our guns and continued our new approach. We would ask him if he wanted help, offer encouragement, express sincere sympathy that he had no media privileges, and then leave him to himself.

Then a strange thing started happening. For the first time since we've started giving Alex grades, he started caring that he was getting a bad grade. Oh, don't get me wrong, he's always wanted to get "100%" on his spelling tests, but he's never cared much about how he was doing overall. Some of that, of course, is his age. But the sudden switch had nothing to do with getting older.

I think it was because now the grades were his, and (mostly) his alone.

After giving him a 3/10 on a piano lesson (he hadn't practiced at all that week), he was very sad. I pointed out to him that Drystan had worked hard every day that week and had made significant progress. I asked him if he thought it would be fair for Drystan and him to get the same grade when Drystan had spent so much more time and effort. He agreed that doing so would not be fair. He acknowledged that he had not worked much at all.

Another week went by. Things started to improve. Alex was still wasting a lot of time, but he started getting things done. His piano practice wasn't stellar, but he did more than before. When it came time for his new piano lesson, it was better, but still not up to expectations. I gave him an 8/10. At first he was sad, but I pointed out to him that the improvement was all his. And if he continued to improve, he would earn a 10/10.

Alex was also making progress in his other subjects. Without reminders, threats, or (short-term) incentives, he began to get to his work all by himself. He completed papers, finished computation assignments, and read his literature. At the end of a week, I would open the assignment-turn-in box and find all of his work ready to be graded.

This Sunday past, he scored a 10/10 on his piano lesson.

Of course, he still has room for improvement, and he knows it. The key is, he knows it, because it is his work. In a few short weeks, he has gone from a "renter" of learning to an "owner". And the change has been remarkable.

At last, we come to the event that is the title for this post. Alex recently finished the "Secret Garden" and took a comprehension test. His final score was an 85. That's a good score, but he missed some questions that were taken straight from review sheets I had created for him. I pointed out to him that in the future, it would be good for him to come talk to me and ask for help with his work. With even a little bit of review, he could have easily answered all the questions correctly.

But later that night, I realized that I had missed an opportunity to reinforce the "ownership" principle.

The next morning, I pulled him aside and pointed out to him that he had earned that "B" in the secret garden all by himself. It had been his readings, his study, his preparation that had earned him that score. Nobody else could take credit for it.

I said to him, "Alex, you're going to find in life that sometimes things you earn by yourself are worth more to you than 'better' things that somebody gives to you."

I was gratified to see a light go on behind his eyes, a smile touch his lips, and his characteristic "hmmmmm" he makes whenever he learns something new.

Alex realizes, at an 8-year-old level anyway, that he is the owner of his own education. And that is something that he is proud of.

Tell me again why we do this? Oh yeah, because it rocks!

2010-10-25T08:06:00.001-07:00

I have to admit that as I was finally getting ready for bed last night near midnight, I was tired, worn out, and just plain spent. Sundays are busy days because of Church meetings and other religious assignments. But since we started our school semester 5 weeks ago, it has been even busier because Sundays have been some of the only days I have to plan upcoming lessons and assignments.

Yesterday, between giving two piano lessons, planning three new testament lectures, grading 10 different computation assignments and a book report on the Secret Garden, finding a short biography for Sir Arthur Conan Doyle, and writing a computation test and a Secret Garden comprehension test, I spent somewhere between 6-7 hours on my children's education. My wife spent a comparable amount of time working up history lesson materials, grading her own papers, and so forth.

As we were getting ready to stumble into bed, I jokingly asked her, "Tell me again why we do this?"

Actually, a funny quote popped into my head from Jane Eyre. "We have to teach fat little boys lessons they don't want to learn!"

But even as I joked about how much pain our home schooling was costing us, I was smiling. And even as my body complained about exhaustion, my heart was light. Just a few hours early, whilst talking with my father, I listed how much our children have accomplished in just five weeks of school getting done with everything including homework by 3pm.

Alex, for example, has flown through more than half of his 5th grade math book in those 5 short weeks, and just sucked the geometry chapter into his brain as fast as he could gobble it up. He's also been learning the writing process from writing a rough draft through various revisions to a final draft. He's used what he's learning in his writing class to help him complete 1 page papers for both history and the Secret Garden. But beyond just "getting things done", he has been improving his "academic toolkit" by learning to take notes in his New Testament class, learning to practice piano with precision, and learning to manage his time so that he gets his assignments done in a timely manner. And trust me, this is the "short list".

Drystan has also made great strides in his various assignments. He now completes his tripple digit addition and subtraction with 90% proficiency. More interestingly, he has enjoyed participating in the math classes where we work on "thinking outside the box" more. For example, we worked one day on coming up with a notation for repeated multiplication (similar to exponents). He came up with his own name for it: "Bervate" and the ideas stuck in his mind in a way that no lecture could have. He's also accelerated his cursive practice until he could write a full paragraph in cursive. The reason he was so focused? We don't let the children learn to type until they can write in cursive and he really wanted to learn typing. Alex is up to 20 words-per-minute, and I think Drystan wants to catch up to him.

And little four-year-old Kael doesn't want to be left behind. We teach beginning reading using whole-word memorization, and he currently knows a good number of words that he likes to find anywhere and everywhere he can. He thinks "in" is a pretty cool word. He also decided he likes mathematics and started working out in his head basic single digit addition.

So, I'm sure next Sunday night, I'll be joking with Amy again at midnight, "Why do we keep doing this?" But I know why. Because every good thing in life costs us something. And as I watch my children's explosive academic experiences, I smile and think about how much of a bargain I'm getting.

Math: Failure IS an Option

2010-10-13T08:08:00.000-07:00

One of the truly depressing things about computation (i.e., crunching numbers) is that the experience is somewhat binary. Either you succeed or you fail; end of story. The student has already been provided the algorithm for computing the result, so there was no exploration, really. After being taught the steps of multiplying multiple-digit numbers, for example, the student either remembers the steps and can execute them correctly and efficiently, or s/he cannot.

If you have at least half of your neurons turned on, you should already be criticizing my last paragraph for over-simplification. A student might have really made a lot of mathematical connections by performing an algorithm, such as multiplication, many times. Another student might find their discipline improved and their concentration sharpened. Because we have pattern-matching brains, a curious mind can find a lot of interesting things in "simple" number crunching.

Sadly, the goal in mainstream American mathematical instruction is almost always the final result. A child is considered "bad at math" if they fail to crunch a number no matter what other insights or mathematical experiences happend along the way. Even worse, the child's failure is almost never used as a learning tool.

Consider this: how many times in your own life have you learned or grasped a powerful principle because you failed? Can you think of times where your failure exposed underlying truths to you that you hadn't noticed before?

Did you know there is a field called cognitive neuroscience that uses failure as one of its chief experimentation methods? Cog-sci is interested in figuring out how the brain organizes itself. One of the things people in this field do is study people who have been brain damaged, usually through physical accident. By observing what is missing from somebody's cognition, they can theorize about that cognitive subsystem. Because we cannot dissect cognition directly, other people's physical defects provide an opportunity to "see inside".

Mathematics is often very, very similar. Because mathematics is inherently imaginative (e.g., you cannot touch "two", you can only imagine it), it is sometimes very difficult to dissect. Students with proper training can often learn a great deal by trying to compute using some algorithm, and failing. The failure can expose underlying principles previously unseen.

Early great mathematicians made mistakes with things called infinite series. One of the really cool ways you can misuse these, for example, is to prove that infinity is equal to negative one! These early mathematicians looked at these "failures" and found new truths inside their broken answers.

Today, in our family's "Math and Eggs", we had our own opportunity to learn from failures.

I put on our whiteboard a bunch of different ways to write "1/16" including "1/2 x 1/8" and "1/2 of 1/8" (these are not my ideas; they are taken from Don Cohen's Calculus By and For Young People). I put the numbers on the board and did not tell the children that they were the same thing. As I was making the egg burritos, the children were instructed to "play around" with the numbers and see if they had any interesting questions.

When I came back, Drystan hadn't written a single question, and the first thought in my head was, "why isn't he getting this assignment?". Whoops! Fortunately, I caught myself before I opened my mouth. Instead, I asked him what he had been doing.

"I was drawing," he said, looking a little confused at his paper.

"Drawing what?" as I looked at the weird boxes drawn with "+" signs between them.

"I was drawing halves added together."

"Oh," I said, again. Unable to catch myself this time, I blurted out, "But 1/2 x 1/2 isn't the same as 1/2 + 1/2."

I assumed he was trying to do multiplication of fractions like you do multiplication of whole numbers: with repeated addition. When talking about 2x3 the other day, we had written down on the board that 2+2+2 was equivalent. I was positive that he was trying to do the same thing with multiplying fractions. In fact, I started to expand on this for a few sentences before I realized how frustrated Drystan was. He managed to stop my blathering (a difficult thing to do) and convince me that he knew that 1/2x1/2 was not the same as 1/2+1/2. Finally, I asked him again what it was he had been doing, and opened my ears to listen.

He had trouble expressing it, but after a few attempts, I finally saw what he was trying to say. I asked permission to restate it. After he agreed, I suggested, "You know what you're doing isn't what is written on the board, but you were playing with the 1/2's using different operations." Drystan smiled. Now he and I were on the same page.

"So what did you learn?" I asked. Again, he had trouble putting ideas into words. I decided that I did want him to try and think about the problems on the board, hoping that what he had been doing on his paper had put him in the right mindset.

"OK, Drystan, do me a favor. While I go clean up something in the kitchen, can you think about what 1/2 x 1/2 is? I'm just curious to see what you think."

I came back two minutes later and asked him what "1/2 x 1/2 is", and he hesitantly responded, "I think it is 1/4".

After a congratulations, I asked him how he had figured it out. He said, "Well, as I looked at the board, it came into my head that 1/2 x 1/2 was probably 1/2 of 1/2."

Looking over again what he had been doing, I could see that he had been adding a variety of 1/2's and visualizing it in different ways. His mind had grasped before I even arrived at the table that 1/2 + 1/2 was not the same as 1/2 x 1/2. He didn't think this because he had been taught it, but because he was observing it.

Of course his 7 year old language skills aren't always running parallel with his mathematical experiences. He was struggling to put into words what he was seeing. But he had grasped for himself through his failures to understand that multiplying fractions was not the same as addition of fractions. He could see it, he could visualize it, and he was ready now to think about what multiplication of fractions might be.

Obviously, my job as a teacher is to help him not get too lost in failures. Hopefully there will come a day where he will know how to handle failures all by himself. Right now, I help him not get too lost, recognize that he is lost, and find his way back when he is ready.

But deep at the core, I am coming to understand this truth. In mathematics, failure is not only an option, but sometimes it is an excellent one.

Math and Computation in Practice

2010-10-12T07:52:00.000-07:00

After posting details of the Math Instruction Method, I thought I would give a quick overview of an its actual usage in our home.

We do Math and Eggs 3 times a week, and Computation 5 times a week. Yesterday, a Monday, was one of the Math and Eggs days. Class started at 8:00AM, and I invited Alex, nearly 9, and Drystan, age 7, to sit down and think about the following numbers:

3/4
(1 1/2)/2
0.75
1/2+1/4

This example is a small part of a larger problem in the book "Calculus, By and For Young People" by The Mathman, Don Cohen.

But for yesterday's Math class, I just want them to look at those four numbers, play with them in their heads, and see what interesting questions they can come up with.

By now, my kids are used to these kinds of exercises and immediately noticed that each number is another name for the quantity three-fourths. Alex, before I get out of the room, started asking himself if they make some kind of pattern. Drystan wanted to come up with other ways of writing the number.

Upon hearing Drystan's comment, I said to him, "Drystan! You just asked a question and didn't even realize it!"

"I did?"

"Sure, think about what question had to go through your mind before you'd try and write this a different way!"

"Uh....," he thought slowly, "is ... there another... way of writing it?"

"YES! Give me five!" I exclaimed, and I headedoff to the kitchen to start on the hashbrowns and eggs while the children sit ant think about the concepts on the board.

I spent the next 20 minutes putting together scrambled eggs and hash browns with cheese, and some hot cider. When I rejoined the children, I had them put their notebooks away and we started talking about their questions as we eat our morning feast.

Drystan didn't come up with any more questions, but he spent his time drawing pictures of an 8x8 grid trying to see different ways of visualizing 3/4ths. He got pretty stuck, but in Mathematics, that's a good place to be. Because he had fought with it himself and really tried hard to understand the concept, my subsequent illustration of 3/4ths and 6/8ths really resonated in his mind. His struggles prepared him to grasp and digest the pictures I showed him.

Alex, for his part, had asked a number of questions about patterns in the numbers, and had also tried to figure out some computations adding 1/1 and 2/2. Again, he too had "failed" from a computational perspective by thinking that 1/1 + 1/1 = 2/2. But from the mathematics perspective, he had been very successful trying to figure out how these different pieces fit together. Again, with his mind self-prepared and in tune with these little concepts in mind, our discussion of 1-out-of-1 and 2-out-of-2 being the same thing made perfect sense to him.

For my part, I asked the kids my questions about these four representations. I asked if they thought one was "better" than another. I also asked them if they thought they understood or learned something about the quantity better from one version or another. Finally, I asked them to think about how the different notations brought different visualizations to their minds.

And with the final bites of breakfast, Math class ended. I switched gears into computation and gave Drystan his addition and subtraction worksheet, as well as a worksheet on multiplying by 6. Drystan up until a month ago, struggled with computation like nothing I ever expected. Computation seemed always out of his grasp. And then, to our surprise, everything just clicked and he woke up one morning with some computational intuition. Having struggled forever with simple 7+5 and 12-2 type problems, he was suddenly able to do tripple digit addition and subtraction with a 90% success rate. So, we're now helping him memorize times tables while doing 10 or so such addition/subtraction problems each day for practice.

For Alex, I have been teaching him computation out of an old 5th grade math book from about 30 years ago. I like that as part of the arithmetic, it also teaches sets and set operations. Yesterday was review for chapters 1-4 covering addition, subtraction, multiplication, and division (including long division). Alex took a test today covering those four subjects and scored a 92% in 1 hour. For reference, I've included the test below.

Perhaps the thing that has me the happiest about our instruction is that the children are finding that they enjoy both math and computation, especially as they become more and more successful. They are finding that math is interesting, and that computation is interesting because it provides ideas and skills for doing math. And they are getting a sense of both "wonder" and "accomplishment".

In all fairness, I find a lot of weaknesses in how the math instruction is going, so it continues to be a work in progress as I go on correcting and adjusting the ideas and the implementation. But I 'd say we're off to a great start. For those of you who have expressed interest in the math instruction, please make comments, suggest feedback, or ask questions. Thanks!

PS The Computation Test

CONCEPTS:

(1 points) TRUE OR FALSE: The empty set a subset of the empty set.
(1 points) TRUE OR FALSE: The union of any set with itself is itself.
(1 points) TRUE OR FALSE: Two sets {a,b,c} and {a,e,f} are disjoint.
(2 points) Write two different subsets of {alex, drystan, kael, saige}
(1 points) Write the set of people in our house who are male. Label this set MALE
(1 points) Write the set of people in our house who are female. Label this set FEMALE
(1 points) Write the set of people in our house who are five years old or older. Label this set SCHOOL_AGE
(2 points) Create a set whose elements are in BOTH the set MALE and SCHOOL_AGE. Label this set SCHOOL_AGE_MALES
(1 points) TRUE OR FALSE: SCHOOL_AGE_MALES is a subset of MALE
(1 points) TRUE OR FALSE: MALE is a subset of SCHOOL_AGE_MALES
(4 points) Convert ((a+b) + c) * x into x * (a + (b+c)). You must write which properties are used for which operations (e.g., "commutative property of addition", not just "commutative")
(4 points) Convert ((a+b) + (c+d)) * x into (x * a) + (x * (b+c)) + (x * d)

COMPUTATION:

(10 points) 7 x 96
(10 points) 36 x 2,591
(10 points) 789 x 543
(10 points) 4096 divided by 2
(10 points)455 divided by 20
(10 points) 15,729 divided by 49
(10 points) Average this set of numbers {2,4,8,16,32,64}
(10 points) Average this set of numbers {12,23,34,45,56}

Math Development Update

2010-10-10T20:02:00.001-07:00

Long time followers of this blog are aware that I have been talking about Mathematics for a long time. Some of you have pestered me for updates, and I have been slow to post because I'm still in beta.

But, it occurs to me tonight that perhaps I need to have some beta testers. And so, I'll unleash upon you the Mathematics that I have been using this semester with my children.

Before I do, let me note a few things.

First, as a reminder, one fundamental concept underlying this whole work is that there is a difference between mathematics and computation. A good rule of thumb is that if you're looking for a problem a computer can solve (e.g., what is 3+4?) it is computation. On the other hand, if you're looking for a problem that a computer cannot solve (e.g., what is the difference between the two threes in 33?) it is mathematics.

So, the ideas I'm posting here are about mathematics. If you are looking for computation, just about any book will do. I found a 25 year old 5th grade arithmetic book that works just fine for my 8 year old's computation needs. The mathematics I do with him is related, but separate.

Second, the ideas herein about mathematics are implementable at any level of computational knowledge. For parent-educators, it is key that they, themselves, undo any ideas of them being "bad at math". Chances are, they haven't ever tried math or been taught it. For children, these ideas and exercises can be worked in at any age, and any level of computation. I have been trying these ideas out on my two oldest (age 7 and 8), and an inner-city kid that I am tutoring.

Third, this is very experimental. In the links below is an overview of my plans for the math curriculum, but I only have 9 lessons so far, on a very small part of it. I generally develop a weeks worth of exercises on Sunday night, so watch for weekly updates. Furthermore, your feedback, positive or negative, will be invaluable.

So, without further delay:

"Unnamed" Mathematics Instruction (Beta!)

PS, any suggestions for a name would also be appreciated!

Why I Choose to Homeschool

2010-08-19T19:10:00.000-07:00

The video is not as crisp as I would like. Hopefully I can get a new one done in the next week or so.

The Infusion of Wonder into Modern Education

2010-08-01T17:44:00.000-07:00

I finally have an answer to something that has bothered me for a long time! Well, I can't say it is "the" answer, but I finally understand something about the nature of the following conundrum. "What is the balance between getting an 'education' for education's sake, and getting an education for being a productive member of society (i.e., getting a job)?"

I once listened to two parents argue about this question. The mother of the family came from an rich-almost-aristocratic family tradition from another country. In their family, getting an education was about a very nebulous form of personal progress (truthfully, it was almost a status symbol and a way for distinguishing themselves from the 'working' class). The father came from a long line of blue-collar providers. Their tradition was hard work, and earning money to feed little hungry mouths. As I listened to their debate, I was perplexed. I felt the need to agree and disagree with both of them at the same time! But I couldn't do it, and I remained silent (one of the few times in my life I was not spouting an opinion...).

But today, I hit upon a deeper question that, in my mind at least, answers this one as well. I was trying to explain to my oldest child why he should spend a little bit more time reading his scriptures. In his view, he had completed the checklist item. That is, he had read his chapter, so what more was there to do?

As readers of this blog will remember, I have been toying around with a somewhat non-traditional approach to mathematics. Some of you have even asked me why I haven't posted more about this promised topic. Well, between nearly 6 weeks in Chicago on business, a move, and various family drama I haven't had a lot of time. Even more significantly, I am still exploring the methods that I want to employ and the goals I think we can achieve.

But I can, at least, clearly and succinctly define my underlying theory. My basic premise is that what in taught in schools today is not mathematics, but computation. Computation is something a computer can do; a computer can be given a formula and crunch numbers accurately and efficiently. Mathematics is the process of discovering relationships and patterns with abstract numerical concepts. In a word, the difference between computation and mathematics is "wonder".

"I wonder..."

This short simple two-word phrase is the difference between monotony and excitement, between soul-draining and personal satisfaction, and between training and education. The computer (human or machine) can add two and two without the least bit of wonder. Truthfully, a computer can compute even some of the most complicated, but understood, problems without a single "I wonder" neuron firing in his or her head.

But a five year old might look at 2 + 2 and wonder. "I wonder," the five year old thinks to himself, "why is two plus two equal to four?" "Is it always equal to four?" "What does plus mean anyway?" "What does equal mean too?"

"I wonder" is mathematics.

Coming back to the story with my eight year old child, I asked him if he remembered the difference between computation and mathematics. He said that it was the difference between just adding numbers versus exploring. I acknowledged that this is, indeed, true, but I reminded him about the "I wonder" principle.

I went on to talk about other "I wonder" differences in other subjects. History is another subject poorly taught in schools for the same reason that mathematics is taught poorly. They kill the wonder. The "Math" teacher gives out a formula, expects memorization, and endless drills that sharpen the computational efficiency of the little computers, but continue to starve their souls. The "History" teacher hands out a history textbook that tells the students what the people in centuries past think and why they did what they did. Never are the curious and exploratory children given the real words of the actual historical figures along with an injunction to "wonder" about them.

At the end of this, I explained to him that scripture reading was just a checklist item. But scripture study infuses the life of "I wonder" into an otherwise dead process. I asked him to read for just a bit longer and, instead of just reading what the words say, to go a bit farther and wonder about why they say it.

The truth is, "wonder" brings life to our intellects. It moves us beyond what we know and into what we don't. It provides a never-ending antidote to the poisonous monotony of a comfortable life. Sadly, my observation is that most subjects are taught, from preschool to college, with the wonder surgically removed.

But some might scoff that "wonder" sounds all warm and fuzzy, but is too vague for any meaningful discussion. It sounds suspiciously like the "new math" craze that has done so much damage to so many students. In fact, it might sound like an argument for an abandonment of the teaching of computation, an invitation for subjective grading, and other ills that have failed repeatedly.

This leads back to my original story about the husband and wife arguing about an education for an education's sake, versus an education for vocational proficiency. If the husband were to read this article, he would argue with me passionately that children need computational skills in order to compete in today's job market. He would tell me that I am naive for suggesting we abandon teaching computation. The wife, if she were to read this post, would thank me for agreeing with her.

But they would both be wrong.

I recognize that computation is necessary and it is taught within the walls of my home. But I can tell you that now that my children understand that computation is simply a prerequisite to the more satisfying "I wonder" subject of Mathematics, they have a lot less animosity to the subject. It is a tool to a higher purpose, rather then an end unto itself. Computation has purpose, and the purpose makes the admitted tedium more palatable. To the husband I would say that "I wonder" makes a child a better computer, not a weaker one, because mathematics gives computation life.

At this point, the wife of this couple is still confused. Surely I can see that this is what she has in mind?

Unfortunately, the answer is no. I do not think that her notion of "education for an education's sake" is the same as I my desire to encourage and enable the "I wonder" in my children. Because the truth in the type of education I see her holding up as a standard neuters the "I wonder" replacing it with a cheap substitute. I don't have a short and pithy name for this charlatan, but it is exactly the thing that the husband was worrying about. It is the subjective, uncritical approach to education. It is the academic relativism that says that no answer is right or wrong, just different (unless it is politically incorrect, but that's a different story). It is wondering without critical thinking and without responsibility.

A perfect example of this was a friend of mine that was pursuing a degree in philosophy. While discussing my own children's education, I emphasized mathematics. He loftily informed me that mathematics wasn't that important, but instead, I should focus on the critical thinking skills that are learned in philosophical reasoning. In the same breath, he went on to say that he was doing well with all of his philosophical classes except for one that dealt with a form of propositional logic. It turns out that propositional logic is all based in mathematical reasoning. He couldn't understand why I thought his position was illogical. But then again, maybe that was the problem.

What is truly astounding to me about most of the "liberal arts" education in this country today is how far it has come from its mathematical (not computational) roots. The liberal arts are supposed to be the domain of critical thinking; the bastion of education for education's sake; the pinnacle of "wondering". And yet, like my philosophy friend, they have generally excised the mathematics that formed such a critical part of their educational tradition. When universities really began to gain prestige and import in Europe during the renaissance, the primary subjects were what we would now call "liberal arts" plus mathematics. Those scholars of yesteryear recognized the value that mathematics added to their philosophical and linguistic studies.

What does this all have to do with "wondering"? My point is that even "wondering" needs form and structure. It requires training and critical analysis. The desire for "wondering" might be natural, but the skills to wonder successfully are not.

One example of wondering skills is prioritizing "I wonder" time. I went on to teach my eight year old today that wondering how many words are on a page of the scriptures might not be as important as wondering how the principles taught apply to his own life. In other words, not all wondering is of equal importance.

In mathematics, I have thought of a number of other important skills for the "I wonder"-er. One is the ability to critically examine two different ideas (produced during "I wonder" time) and compare and contrast them. Being forced to recognize the deficiencies in the results of our wonderment is an important aspect of education. It is a skill to be able to not take offense when somebody critiques an idea that we feel emotionally bonded to.

There are many, many more "I wonder" skills. It takes training and practice to manage intellectual resources that can be used to solve "I wonder" problems. It takes a lot of time to develop a good intuition for the best approaches to answering different "I wonder" questions. The mind must be trained and conditioned to effectively identify, evaluate, and solve the "I wonder"s. This is the essence of true education.

My quest, at the present time, is to develop a mathematics education that trains my children how to wonder about numbers, shapes, and patterns. I'm still identifying the principles of this subject, which is hard enough, as well as the methods for teaching said principles, which is harder still. In the mean time, I continue to teach computation, inviting the children to take time out for unstructured "wondering" about the computation they engage in.

As I identify principles or methods I will be certain to blog about it. In the mean time, please feel free to send me principles or methods that you have observed or used in your own teaching. I am searching everywhere, absorbing and stealing every good idea I can find. I look forward to hearing yours!

A Day in the Life of....

2010-05-13T15:42:00.000-07:00

I often have people ask me how our school schedule works during the day. There are many ways to run a good home school but I tend to favor a somewhat traditional approach. We typically do classroom work 4 days a week, with Friday being reserved for field trips and special events (more on those later!). Our days look something like this:

Morning (while Mom is showering and feeding the baby): clean rooms, do other chores

10:00: Start school. Scriptures, music (singing), prayer

Math: every day, about 30-45 minutes

Language Arts: Spelling, Literature, and Composition daily, Reading and Grammar on alternate days, about 60 minutes

12:00: Lunch: 30 minutes

History or Science: Alternate Days, about 30-60 minutes, depending on activities or science experiments

Art, French, Geography, or Cooking: One each day, usually about 30-60 minutes, depending on the activity

We're usually done around 2:00. Catherine typically doesn't have much homework although we did start to give her some small independent assignments at the end of the year. She's usually working on a book as well, but I don't have to do any assigning for those!

***cross-posted at Three C's and a Grace Note***

Whole Grain Education

2010-03-02T19:46:00.001-08:00

Well hi!

It's been about six months since I last posted. I was first distacted by finishing my phd. But I did in fact finish. At long last I am finally Dr Seth Nielson. More importantly, my evenings are no longer crazy busy.

Then the baby came. Our beautiful daughter (child number four but daughter number one) was born on December 2nd. She is absolutely fantastic and we love her to death. But blogging took a back seat for a while.

And now, actually, education has gotten in the way of blogging about education! Of all the nerve! You see, we have been pushing our oldest child Alex, now 8, to work more Independently. The next two kids need mom's attention so child number one has to step up. To free up mom's attention, I have been working with Alex on math in the mornings as well as prepping his assignments in literature, history, science, and so forth. He works on these on his own during the day and then he and I review and discuss his work in the evenings. The key is that he works (largely) without mom during the day. It took him a few weeks to get the hang of it and during those weeks my evenings were every bit as busy as when I was doing my phd. I would come home and spend hours helping him through the work he ignored all day long.

But now, Alex seems to be figured it out. He still gets distracted a lot but manages to get most of his assignments done every day.

There is one subject, however, that requires a dedicated hour of my time every night. This semester, we are studying the Constitution of the United States. We're learning both about the history and the content.

Month one, we read biographies of the founders including Madison (the primary author). But this month we have been reading primary source documents that illustrate the development of colonial law and government from the mayflower compact up to the first state constitutions. The goal is that Alex can understand the where the ideas in the constitution came from and what the people at the convention thought about government.

I want to emphasize that we are not reading about these documents, we are reading the documents themselves (or large excerpts at least). Here is the list:

The experience has been in incredibly powerful for both of us. I am thrilled to listen to my 8 year old child read the words of history unedited and unfiltered. I have enjoyed asking him his thoughts about what he is reading.

Have you ever heard about the Massachusetts Body of Liberties? I hadn't. It's dated about 1650 and it contains many rights that we would consider "modern".

Joseph Galloway wrote an article about the importance of an independent judiciary. His reasoning? Because people are untrustworthy and judges would be tempted by greed or promotion to do injustice.

It's hard to describe the feelings I have as my son and I study together. In previous posts I described how I felt when I first started reading primary sources. But to actually be teaching from the pages is even more enjoyable. I call this "whole grain education". And it tastes wonderful.

I feel this post is already too long. But it is amazing to me that that so much of our education today is preprocessed. The real food tastes so good. I love it. And I look forward to feasting with my children on the pages of history for many years to come.

Explaining the Delay

2009-09-21T07:55:00.001-07:00

Followers of this blog are probably frustrated that I promised details of a math method, and then there was just static.

Patience! It turns out I will be defending my PhD Thesis within the next month and I'm a wee bit busy until then. And (unsurprisingly) actually teaching math means I have a lot less time to write about it.

But I'll give a sneak preview! The other night, at bed time, I asked Alex about a thinking assignment I had given him. I had asked him to figure out how multiplying things inside parentheses works. Specifically, I asked him to figure out 6(x+3). He's been trying all kinds of things and has been doing all sorts of number experiments in his head. One of the other concepts we've been working on is exponents like 3 to the 4 power, etc.

So, I asked him to tell me what he had experimented with on this multiplication problem and he said, "Well, I was thinking about what multiplication is and I realized that with exponents you multiply the number over and over and over, and with multiplication you just add the number over and over and over!"

Mathematicians will be quick to point out that multiplication is not just repeated addition (what is a negative times a negative?) and exponents is not just repeated multiplication. But it is just amazing that after 6 weeks of this Lockhart-Cohen style math that I've been doing (I need a name for this math method) Alex is already exploring numbers, patterns, and having lots of fun!

PS... after this amazing observation on multiplication and exponents, the very next day Alex went back to saying that 3 to the 2 power was 6... so, we have room to keep working!

PPS... I hope to update the math method on the Google Sites even before my Thesis Defense, but if I don't, you'll know what's holding me up.

-- Seth

Developing a Math Method - Part 2: The Prototype

2009-08-31T14:20:00.000-07:00

I love all the initials used around the Internet. One of my favorites is IANAL (I Am Not a Lawyer). I think I'll add a new one: IANAMBT (I Am Not a Mathematician By Trade). But I do love it.

Despite a lack of "credentials" in education, which some Californian courts suggested somehow made a teacher "good", I am a full-time educator for my children. Education is on my mind constantly. I sometimes dream about teaching the kids various subjects. Truthfully, I think I'm pretty good at it.

It is largely because of my skills as an educator, and not as a mathematician that I am developing my own math method. I would almost call it novel, except that it is based extensively on Don Cohen's work and on the principles discussed in "A Mathematician's Lament" by Lockhart. In fact, as I have been developing this method, I rely on the two aforementioned mathematicians as well as others for mathematics principles. But I think my pedagogical ideas are sound and solid.

Still, this method is in early development and is not even close to a finished product. It is currently undergoing testing for a single pupil. But I believe that the core of the method is effective and practical. I am convinced that any parent, with any level of mathematics background can get started with it immediately.

As a point of emphasis, I have been using the work method as opposed to curriculum. The principles presented are intended to help home-schooling parents develop their own curriculum. Interested parties should feel free to contact me for suggestions on implementation, although I hope that most of the ideas are self-explanatory.

Below is the link to my Google Sites page where I am slowly getting down on e-paper all of the ideas, principles, and experiments that have been developing in the last six months. Criticisms of all kinds (mathematical, pedagogical, grammatical, etc.) are welcome. I believe that comments are enabled for the pages.

LINK: Liberare Cogitatus Mathematics

Enjoy!!

Developing a Math Method - Part 1: The History

2009-08-19T20:54:00.000-07:00

The last two weeks have been some of the most amazing weeks of my life as a home educator. I used to say to my wife that some day our children would thank us for giving them the gift of home education. Now I believe that we will be thanking them. The experience of instructing your own children is absolutely unparalleled and priceless.

In previous posts, I discussed some of the ideas that have been influencing our math education in terms of philosophy, curriculum, and expectations. In particular, the influence of Don Cohen and Paul Lockhart drive much of our approach. These ideas have been coalescing in the last few months, so it is only in the last few weeks that we have begun actual instruction.

It has been so overwhelmingly positive for all parties, that I wrote an email to Don Cohen thanking him for getting me started on this journey. The Mathman was nice enough to respond to my email and to post my message and a link to this blog on his own website. Thanks Don! And welcome to the many new-comers who have been posting as of late.

But I'm getting ahead of myself. The purpose of this post is to explain a bit of what has happened in our Math Program for Alex in the last few weeks. Actuall, the story begins with Alex's instruction in mathematics last semester when Alex was starting to get frustrated with math. He had already learned addition and subtraction for any number of digits, and he had already learned his times-tables (through 10x10) reasonably well. But as we attempted to teach multiplication for many digits, things seemed to bog down, and he began to get frustrated.

And math frustration was one of the very things we were trying to prevent by home-schooling. Something had to change.

We had already looked at Don Cohen's book, "Calculus By and For Young People" several times. We had intended to start teaching from that book as soon as Alex could do basic addition, subtraction, multiplication, and division. Don's book doesn't require that (his first chapter assumes only that the student can count), but because of our own weakness with the teaching materials, we decided to do arithmetic first.

But as Alex became frustrated with how we were teaching him, we decided to try out some of Cohen's book just for fun the last few weeks of last semester. While we didn't feel that the experience was totally successful, it seemed to really lessen Alex's frustration, and we figured it was a good "test run" for us before we would start using the book as his primary math textbook the next semester.

During the summer months as Amy and I began to put together the curriculum for the upcoming fall semester we received the Lockhart paper that I've mentioned previously. We were both impressed with the principles Lockhart laid out, and found that they worked hand-in-hand with, and helped us understand better, the Cohen book. The two major points we took away from the article are:

Mathematics is the art of exploring for simple solutions to unknown problems
"Drilling", while important, is NOT mathematics.

In fact, we began to use the words computation and mathematics.

Computation is being able to solve problems with known algorithms, and learning which algorithms solve which types of problems.
Mathematics is the process of exploring ways of solving problems for which the student does NOT yet know the algorithm.

With these principles in mind, we began preparing to teach a new semester of Mathematics to Alex. Unfortunately, our first week didn't go so well. Amy realized that the History and English curricula that she was developing meant that she didn't have the time to rethink mathematics as well. Additionally, she admitted to me that, while she liked the Lockhart and Cohen principles, she didn't really grasp how to move from principles to implementation.

Thankfully, the principles really clicked in my own head, and I almost immediately came up with ideas for how to get started with Alex. We decided that I would take over Alex's mathematics class, and Amy would continue to teach Drystan arithmetic using traditional methods. That isn't to say that Drystan wouldn't benefit from the Lockhart/Cohen approach. Rather, it reflects that the teacher (that would be me) needs time to completely retrain himself in mathematics education. This teacher has a lot of bad habits that need to be broken and new habits that have to be formed. For now, the teacher will work with one student but with the expectation of taking on a new student either next semester or next year.

So, two weeks ago, Alex and I began a new adventure. I am happy to report that it has been an almost miraculous success. In two short weeks, Alex has found that he enjoys math class again (well, maybe not as much as he enjoys History, but his attitude is a billion times better). Alex is finding that exploring numbers is fun and exciting. It's experimentation, pattern matching, trying and failing, trying and succeeding, forming hypotheses, shooting them down, and then trying some more.

And computation is still part of the game. In two weeks, Alex has learned to add some simple fractions, compute double-digit by double-digit multiplication problems, some basic decimal manipulation, some graphing , and even some very basics of an infinite series! But these drills are no longer "doing math". He knows (or at least, I remind him daily) that these drills are simply tools in a toolkit for exploring the wonderful world of Mathematics.

I would be amiss if I didn't describe the experience as it relates to me as the teacher. In two weeks, I have learned to stop trying to explain everything, but let my child explore the mathematical waters for himself. I have learned that you can tell a child something a million times, but until they find out the truth for themselves, it does not stick with them. I have discovered many ways to leave "breadcrumbs" on the mathematical trail, so that the child is not left floundering, but still gets to find his way through the forest of discovery. And I have also experienced the joy of watching my child smile when he uncovers something new.

The journey is just beginning, but already it has changed my life and my child's life forever. I just can't wait to see what the next two weeks will bring!

And on that note, I think I will conclude this historical backdrop. In the next post, I will describe some of the details of our day-to-day mathematics instruction in greater detail.

So, stay tuned!!!

History for Preschoolers

2009-08-17T08:17:00.000-07:00

We started our new school semester on August 3rd because the baby is due at the beginning of December and we wanted to have the semester done by then. Things are going great! Alex and Drystan have jumped into Colonial American History, Alex is learning to write paragraphs, and Drystan just started on cursive. We're doing all sorts of fun stuff along with the math that Seth has written about before.

My only regret is that I haven't been doing as much preschool with Kael (age 3) as I did with the other boys. Fortunately, we have a lot of alphabet and number puzzles, and every once in a while, Kael gives us a glimpse of things that he's been absorbing from class with the big boys.

In history we read that John Smith (an early leader of the Jamestown colony) nearly died from getting stung by a sting ray while exploring the Chesapeake Bay. Then on Sunday, I was reading "The Joseph Smith Story" to Kael. He kept asking when the story was going to talk about the sting ray. I was totally confused until I realized that Kael was associating Joseph Smith with what we had been studying about John Smith.

I thought it was funny.

The History is a Lie!

2009-08-06T07:08:00.000-07:00

It has been a number of years now that I have felt that the current instruction of History in most American schools is a lie.

I first wrote a politically slanted post about this some months ago, but retracted it after a close friend suggested that the tone was too negative and that what I was describing was not, in fact, "lying". Since that time I've turned the issue over and over in my head to re-evaluate my own assessment. In the end, I've returned to my original conclusion: history education is, in fact, a lie.

My new political post references this assessment.

But I understand why my friend's response was incredulous. It is my job to explain my assessment to others. Their lack of understanding reflects poorly on me and not on them. It is difficult, of course, to transfer my own context in a small Blog post to a reader, especially since my context is somewhat outside the mainstream. I will do my best.

I am hopeful, however, that a new reading of mine about mathematics will help me to explain myself. As referenced in previous posts, Paul Lockhart's article, "A Mathematician's Lament" is an excellent discussion of what is wrong with mathematics education in the American system. Lockhart's primary assertion is that crunching numbers repeatedly on worksheets is not mathematics. He compares it to teaching music: learning key signatures, music notation, and so forth is NOT music. He also compares it to teaching painting: learning color mixtures, brush types, and so forth is NOT painting. Oh, of course math drills are important to a mathematician as learning key signatures is important to a pianist and learning color mixtures is important to a painer. But the drills are not the mathematics itself.

For more on the mathematics, read Lockhart's article, as I must return to History.

My primary assertion is that History education in America is (largely) reading textbooks and other "compilation" sources. I strongly reject this textbook reading as "History" just as Lockhart rejects drills and formulas as "Mathematics". As with Lockhart, I'm not saying that textbook reading isn't important, useful, or even necessary, but I am clearly stating that I do not believe that it is "studying History". I do not believe that History is what somebody says somebody else said.

So then, what is History? I suggest that History involves cutting out the commentary and the middlemen and going straight to the primary, original sources.

But that's impossible or insufficient for a "good" history education, you might say, for any or all of the following reasons:

I don't have access to even a small fraction of the primary sources I would need for a complete history education
Even if I did have such access, I have no capacity for determining which primary sources are better than others. (You might argue, for example, that reading about the Civil War from Jefferson Davis is probably not very "accurate")
There is no way I would have enough time to read all the primary sources from a single period of time, let alone from all of recorded history

My response is, what constitutes a "good" history education? What are your goals?

Looking at these three concerns, they seem to stem from a single concept that a good history education involves dates, names, and places. The more dates, names, and places you know, the better your historical prowess. This is, in my opinion, a lie.

To this assertion, I already hear two additional arguments against it.

But you need to know dates, names, and places!
Alright, I agree history isn't names, dates, and places; History is learning about the past and applying it to the present. But you need names, dates, and places for context.

To argument number one, I would respond, How many names, dates, and places do you remember from history? Make a list. Can you come up with 50 distinct names, dates, and places? 100?

Now cut out all the ones you learned before you left High School. What do you have left? Are you certain that names, dates, and places are the best way to measure the effectiveness of History education?

Counter-argument #2 is better. The core here is that if you don't remember all the dates, names, and places from k-12, that's alright. It provided you essential context for learning about "real" history during those formative years.

But if this is true, then this "counter-argument" simply proves my point. If you require dates, names, and places for context, don't you think that you might also require the "original" words of the speakers involved for context? Don't believe me? Here's an experiment. Go read Federalist #78 and then read Anti-Federalist #78 (the response) and tell me if your application of the past to the present hasn't changed (assuming that you've never read them before). Mine changed when I read these, and it was these kinds of readings that first convinced me that my history instruction was, in fact, a lie.

Again, the counter-argument: could you have understood Federalist #78 and Anti-Federalist #78 if you hadn't been taught the names, places, and dates? Weren't your teachers just preparing you to advance "to the next step"?

Obviously, the response to the first question is "no". But I couldn't have played piano as well as I do if I hadn't been taught to read music. But reading music is not playing music, even though the one is essential to the other. My teachers did me a great service by teaching me names, dates, and places, but they did not teach me history. They never taught me to look to the primary sources, to search for myself, to compare and analyze, and to investigate historical questions.

As for preparing me to advance to the next step, I have already stated that there was no suggestion that there was a next step. But even still, as I have read about the education of individuals in previous centuries, I have been overwhelmed by the amount of primary sources they were expected to digest. Anna Ella Carroll, a woman in the 19th century, was educated deeply in politics and history by the time she was 16. Her historical background was to read Blackstone, not read about him. That was her normal history education. There was no concept that reading primary sources was the "next step". Reading primary sources was history. Everything else was simply for support and context.

I have left some questions and counter-arguments unanswered in this post, unfortunately. The post is too long, and I have spent too much time on it as it is. But I hope that it has provided some insight into my conviction of that contemporary history education is a lie. And whether you agree with me or not, I hope that the reader might take a moment to add some primary sources to their "future reading list".

(I recommend reading about Anna Ella Carroll, by the way. And although the book I've linked to is largely a secondary source, it contains a significant amount of Carroll's publications, unaltered and unedited.)

Meta-Teaching

2009-07-17T10:01:00.000-07:00

I love to teach. It is exhilarating to see a student having a "lightbulb" moment. And it is fantastic to have your own "lightbulb" moments in the preparation of a lesson. One of the cool things about my job is getting to do presentations, which are like mini-lessons.

I work for a computer security consulting company. We help clients discover and correct security issues in their systems. We're a small group and we have a really enjoyable corporate culture. Once a week, we have a lunch where one of us takes a turn presenting on a given topic. Most of our presentations are about things we're doing at work. But the CEO recently opened up these presentations to any subject, including non-technical hobbies.

A week ago, It was my turn and I presented on teaching children mathematics. I am happy to report that the presentation was well received.

So, attached, are the powerpoint (MS Office 2003 for Mac) slides that I used. Feel free to read and use, but please do not redistribute without permission.

Teaching Kids Math Presentation, 2009.

The Joy of Mathematics (Part 4)

2009-06-27T05:28:00.001-07:00

"Dad? If you had a bird house with five holes down and ten holes across, how big would the diagonal be?"

That is the question my seven year old, Alex, asked me just hours after reading Paul Lockhart's article about mathematics education. At the end of parts one, two, and three of this series, I have implied that I would finish the story in the next installment.

And now, in the concluding post, I am finally ready to finish the story.

I was doing dishes the morning after I read Lockhart. Alex rushed into the kitchen and posed to me the aforementioned mathematics problem. The question was completely unexpected, but it made me so excited! A chance to do Lockhart-style mathematics!!!

So, I asked him a clarifying question: I asked if he meant that it had five rows of ten holes each, and he said yes. I also asked why he wanted to know, and he said, "For a story I'm writing."

I very excitedly told him I would love to help him answer that, and we sat down with some graph paper and blocked off a rectangle that was 5x10. As we were getting started, I asked him how many bird-holes total there were. He thought about it for just a minue and said, "50". Good job!

We drew the 5x10 rectangle
Then I asked Alex to make a guess at how he wanted to do his diagonal. He thought about it and did this:That's good, I said, now let's see if we can come up with something that goes across from one corner to another. I said why don't we draw a perfect line for corner to corner and see if we can use that to help us.

So we grabbed a ruler and drew a line from corner to corner. I asked Alex how we could decide which squares should be used in the diagonal of bird holes. Should the bird hole be "on" the diagonal if the line touches it at all? If the line cuts it in half?

Alex decided that if 3/4ths of the line was above the line, it would be on his diagonal. We came up with this
We noted that this policy did not include the bird hole in the top left corner. But Alex liked this diagonal and counted up that his diagonal had 9 holes. This gave me another idea and I had him measure the width, length, and diagonal with the ruler. Alex found that the perfect diagonal line was longer than the width, whereas the diagonal of bird holes was shorter than the width. I asked him why he thought that was.

He thought for a bit, then said, "Because we were only counting 3/4 holes."

Very insightful.

I did a few other experiments while I had his attention. I pulled the Lockhart's example of a triangle in a box from the article and posed the question to Alex. How much of the box does the triangle take up, I asked? But I showed him a right triangle first and asked him how much of that box the right-triangle would take up? Just by looking he could see that it was half. So then, showing him the triangle from the article again:
I asked him if he could see any problems he could solve. He said he couldn't. I decided to give him the next step. I asked him if this helped:
Now Alex could see it. He said yes, I can see two right triangles. But funny enough, it wasn't the two I expected, it was the one in the top left corner, and the right half of the original triangle. And from looking at that Alex immediately figured out it was half of the box.

We did a few other puzzles together, and he made some additional connections all by himself, and the lesson was over.

I was so happy at the end of it, and so was Alex. He had his answer for his story, and I had learned a little bit more about teaching math. It was great!

Of course, I'm still learning, and I hope to get much better before this fall semester. As I review this Math Moment I reflect on the things that went right and the things that could have been done better.

The Good:

It was an exploratory problem that Alex was interested in
We looked at the problem from multiple directions
I asked a lot of questions

The Bad:

I didn't do enough math critiquing. When Alex drew his first diagonal, I should have asked him to come up with another diagonal and then compare the two. In paritcular, would his first diagonal change if the width increased? Does that matter and why? When using the perfect diagonal, Alex came up with his "3/4ths" policy. I should have had him try to come up with other policies and compare them.
I suggested the perfect diagonal approach but didn't give Alex a chance to explore his own options.
I didn't guide him towards generalizing his problem

Still, I felt the overall experience was a success. It was another building block in my own development as a teacher and a math teacher. And it was a good chance for Alex to find out that math is interesting, fun, and relevant. In short, we both got to experience the joy of mathematics together.

(P.S. Feedback is welcome! How could I have taught the lesson better? What did I do well? What did I miss?)

The Joy of Mathematics (Part 3)

2009-06-25T05:13:00.000-07:00

I apologize to the reader for implying at the end of part 1 and part 2 of this series that I would begin the next installment talking about a discussion with my oldest son about the length of a diagonal. I fully admit that it was a bit of a bait and switch. This is the last one, I promise. Here, in part 3, I want to talk a bit about the book we'll be using for Alex's math this fall: "Calculus by and for Young People".

I first purchased this book a few years ago. I had been having notions in my own mind about how many human-invented and unnatural barriers our society has placed on mathematics. For example, I think it is insane that we collectively believe that children cannot learn anything about algebra until junior high, and nothing about calculus until high school. So I started searching on Google for something about calculus for kids. I happened across a guy who's picked up the nickname "The Mathman".

The Mathman has been teaching children mathematics for over thirty years. I don't know for sure, but I expect that he and Paul Lockhart would get along very well. The Mathman approaches mathematics as a process of discovery and pattern matching and is also frustrated with how math is taught in schools. The Mathman likes to focus on inifnite series (things that go on forever) and so has focused his teaching around Calculus.

A word of caution to the reader: the Mathman is a horrible writer. His website is a disorganized jumble of ideas, links, and diagrams. Truthfully, his book "Calculus by and for Young People" is also poorly organized. You have to read it a few times; not because of the math, but because of the organization.

That said, I remember the first time I really read the book. I was coming home from Rice University on a metro bus. The book impacted me in a way I had never felt about mathematics before. I got home and jokingly told Amy that I was "converted". I told her that it had felt like I was reading Scriptures instead of a Math book. I felt like I was getting a glimpse of "pure truth".

There were two things about this book that were so powerful. First, the manner in which infinite series were explained was incredibly natural and easy. But more importantly, the manner in which it suggested the concepts be taught was revolutionary (to my mind anyway). Some of the main concepts were:

Let the student look for patterns themselves
There are many ways of doing something. Let the student come up with their own. Then see if they can come up with another. Let them see how other students came up with it. Guide them to other solutions they may have missed.
Ask questions: what are we trying to do? what have we done so far? why did it work? why didn't it work? could we have done it a simpler way?

To illustrate, I'll briefly describe chapter 1. The first chapter is about adding the fractions 1/2, 1/4, 1/8, 1/16,... forever! The overarching question is, "If we could add this up forever, what would it add up to?"

Why would a child care about such a question?

Well, first let me suggest we sometimes underestimate children's interests. My oldest child realized that numbers went on forever (infinity) at four years old and he is not a math genius. Trust me. I know.

Second, the question in the book is phrased in a way that children (and adults!) might be more interested in. Suppose you had a cake and served half (1/2) of it to someone. Then someone else shows up and takes half of what's left (1/4). How much of the cake is gone? Now somebody shows up and wants half of what's left (1/8). You get the idea. The question is, if this went on forever, how much of the cake would be left?

Alex, my oldest, is always interested in money. So I asked him about this series assuming we could get arbitrarily small coins. In other words, if you could get a fraction of a penny as payment, how much would you get paid if you were paid 50 cents the first day, 25 cents the second day, 12.5 cents the third day, and so on, forever? He thought that was interesting.

What is interesting is that the book does not assume that the children know fractions. In fact, it begins teaching fraction adding, multiplication, and exponents as a component of trying to learn about infinite series. The truth is, it is easy and natural to learn mathematics operations like fraction aritmetic when you need it to answer other interesting questions.

Even though Amy and I decided not to start this book until this fall, we tested it on Alex the last few weeks of our Winter Sememester that ended in May. What we learned very quickly is that the book was great for Alex and tough for us. Why is it tough for us? Because we are used to the "traditional" method of teaching and learning math. Standard lesson plans do not work with this style of learning. There were days that Alex figured out the pattern that we wanted him to find in thirty seconds and we had nothing else prepared. Other days, things we thought he would pick up easily took the entire mathematics period and completely threw off the schedule. And to be completely honest, Amy and I are still learning how to let Alex experiment and search for answers instead of us jumping to the end and giving away the punchline.

Truthfully, we did a pretty horrid job teaching it and Alex still did well. He made really good progress with adding fractions and in identifying the patterns in the series. We probably only had ten or so class periods before we were done, and we dobut that Alex will remember much when we start over this fall, but it was essential for us to get a handle on the book before we start it for "real".

We've continued to review the book, especially the first chapter, as we're preparing to start fall semester in August (we have to start early because we have a baby due in December). We feel like we have a much better handle on it now.

As a trivial example of something that was hard before that seems easy now is what the book says about kids learning to add the fractions (1/2 + 1/4). The book shows that kids naturally understand (1/2) without much training. When the kids see the cake cut in half, and then cut in half again, they will often treat the (1/4) as half of a half. Thus, when adding, they will get (1 1/2)/2.

The answer is correct, it just isn't in the format that adults considered standard. Rather than telling them that they are wrong, recognize that the answer is correct and try to figure out what they learned from the experience of coming up with that answer on their own. Then, lead them on to the (1/2+1/4 = 3/4) representation.

It is at this part that Paul Lockhart's article jumps back into the discussion. One of the things he said was woefully missing from our society's mathematics education is mathematical critique. What makes on solution or representation better than another?

When we teach this chapter again this fall, we expect that Alex will put that (1/2 + 1/4 = (1 1/2)/2). Then, we expect that he will again discover (1/2 + 1/4 = 3/4). And the cool part will be when we ask him to compare and contrast those two forms. At first, he might not se anything different. But then when we add in the next term (1/8), we'll ask which one will be easier to add: ((1 1/2)/2 + 1/8) or (3/4 + 1/8). Neat!

The chapter continues forward looking at the answer with graphing, pictorially, and numerically as the student begins to recognize that the series tends to 1. Then it tries other related series such as (1/3 + 1/9 + 1/27 + ....) and (1/4 + 1/16 + 1/64 + ...). Eventually it guides the students to a generalization for all series of this form.

This book really altered my view of calculus and mathematics teaching in general. Then, when I was lucky enough to get the aforementioned Paul Lockhart article, the two combined together in an incredibly synthesis. I am so excited about the upcoming semester and the math experiments it holds.

Although truthfully, I got a chance to test out some of Lockhart's principles a few days ago, when my son said,

"Dad? If you had a bird house with five holes down and ten holes across, how big would the diagonal be?"

.... To be continued (just one more, I promise)!!!!!

The Joy of Mathematics (Part 2)

2009-06-24T09:26:00.000-07:00

The first part of this series ended with my 7 year old son asking how to compute the diagonal in a rectangle. But before I get to that story, I am going to back up and review the article from Paul Lockhart that I mentioned. It is necessary because it provides some essential context to the story.

The primary contention of Paul Lockhart's article is that what we teach in schools right now is not mathematics. He make an interesting comparison between mathematics and fine arts. Music, he says, is not key signatures, meters, or learning to draw the clefs. Painting, he continues, is not brush strokes, or other aspects of technique. That is not to say that a musician does not use key signatures, meters, and notation; nor is it to say that the painter does not practice and exercise techniques and brush strokes. But the tools are to help create. They are not the thing itself.

Lockhart then says that our mathematics education is just like a world where music is taught without actually playing and painting is taught without actually painting. In fact, he says, and I quote:

"Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. "

He feels that the fundamental problem is that people in society do not know what mathematics is. He defines math this way:

"So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of ideas? Ideas about the rhinoceros? No, those we leave to the biologists. Ideas about language and culture? No, not usually. These things are all far too complicated for most mathematicians’ taste. If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things..."

He then goes on to show the following:

He wonders (because he's curious, no other reason) how much space the triangle takes up. He describes the process of coming up with an answer. At last he sees something "simple and pretty."

It becomes obvious, immediately, that on each side of the dotted line, the two new triangles are taking up exactly half of their respective boxes. It follows, then, that the combined trinagle is half of the box.

Lockhart says, "This is what a piece of mathematics looks and feels like. That little narrative is an example he mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations."

But how did he know to put down that dotted line? He answers by returning to the metaphor of painting. "How does a painter know where to put his brush? Inspiration, experience, trial and error, dumb luck."

He goes on:

"This is why it is so heartbreaking to see what is being done to mathematics in school. This rich and fascinating adventure of the imagination has been reduced to a sterile set of “facts” to be memorized and procedures to be followed. In place of a simple and natural question about shapes, and a creative and rewarding process of invention and discovery, students are treated to this: "
"'The area of a triangle is equal to one-half its base times its height.' Students are asked to memorize this formula and then 'apply' it over and over in the 'exercises.' Gone is the thrill, the joy, even the pain and frustration of the creative act. There is not even a problem anymore. The question has been asked and answered at the same time— there is nothing left for the student to do. "

I'm sure there are a few parents who would find this article disturbing because they think it is the equivalent of "New Math" that is taught in various schools around the country. Trust me. It isn't. Mr Lockhart goes on to say, "... formulas [and] memorizing interesting facts... in context ... has its place [in mathematics education] just as learning a vocabulary does." He makes it clear in the article that there's nothing wrong with drills and exercises. And he admits that sometimes the student just won't figure out the answer for themselves and will need to be helped. If you have more arguments with his article, read the entire article first before coming to any conclusions or judgements.

That said, I'll interject my only complaint with his reasoning. Lockhart compared mathematics to painting and music and there is a big flaw with this, from a pedigogical perspective. Music and painting are not essential components of a large number of careers and professions. You cannot be succesful in science and engineering fields without a good mathematics toolset. The engineer or scientist may not be interested in mathematical questions, but in questions that require mathematical skills.

Nevertheless, as I read this article, I had a very strong "A ha!" moment. All of the suddent, mathematical teaching principles that I had been playing with became so much more clear.

You see, I have been teaching my children math from the time they were two years old. And in teaching them math, I have always been focused on teaching them why math works the way it does.

For example, everyone knows that when you add two numbers that you add by column. And if the numbers you add together in the column add up to more than nine, you carry a one to the next column. Everyone knows that, right?

But why do we do that?

Well, it was important to me that when I teach my children arithmetic that they understand why, and so I worked really hard to explain it. I showed the children a multi-digit number like "24". Then I would ask them if the "two" in 24 was just "two". After a lot of discussion they would realize that it wasn't just two, but actually 20. With some more discussion I would point out to them that we can't come up with a unique symbol for each number. I asked them would want to have to memorize 20 symbols to represent the first 20 numbers. They admitted that they didn't want to.

Then I explained that the way numbers are written are to help us. To make things easier for us.

"24" is written that way so that we only have to have ten symbols. The first column just counted ones, like pennies, while the second column counted tens, like dimes (my kids like money). Pretty soon we talked about how when adding numbers, if you got more than ten in the ones column, you could add another ten (carry) into the tens column.

My second child, Drystan, didn't like a lot of these explanations until we used an Abacus. I asked him how high he could count on the Abacus and he demonstrated that he could count to 99. I told him that I could use the abacus to add even higher. "Really?!" he asked. Then I showed him how I could count much higher if I treated the first row of beads as ones and the second row as tens and so on. He got really excited as he saw how high he could count with it.

I then showed him how much easier this "place value" system made adding. He knows a bit about roman numerals, so I wrote two big numbers in roman numerals on the board and asked him to add them together. He obviously couldn't do it (and truthfully, neither could I). But then, I rewrote the numbers in decimal. The light when on above his head and he saw how easy it was to add them.

What does all this have to do with Lockhart?

In all the math I've done with my children, I believed that showing them how things worked would help them know how to perform the computations, and it did. I also believed that having them figure out why things worked would also help them remember how to do the computations.

But all of the sudden, I realized that thinking about the why was not a tool! Thinking about the why was the thing I actually want them to learn!

In that moment everything expanded! My wife and I are planning on teaching Alex's math this fall from a book called, "Calculus by and for Young People". It is designed around thinking about why and trying things in different ways and from different angles. I had thought that teaching in that way would help them learn Calculus... and it will. But now, I understand that even more importantly, if I do it right, it will help them learn the Joy of Mathematics!

Which brings me back to Alex:

"Dad? If you had a bird house with five holes down and ten holes across, how big would the diagonal be?"

.... To be continued (again)!!!!!

The Joy of Mathematics

2009-06-23T09:53:00.000-07:00

There are many reasons that we chose to home-school. I will not bore the reader with a list of these reasons in order of importance, but I will say that "mathematics instruction" is in the top ten. Both my wife and I value our own math backgrounds not just because they enabled us to pursue the technical majors we wanted, but also because mathematics has enlarged our view of the world around us, improved our logical thinking, and sharpened our perceptions.

One of the first times my wife considered home-schooling was years before we were married. During her university studies, she had acquaintances who informed her that they chose to be Elementary Education majors in college because they were not good at Math and Science. This absolutely freaked my wife out. She asked them what they would do if a child asked them something about those subjects they didn't know. Their answer was that the children wouldn't be ready for those answers anyway! Yikes!

Fast forward to when our oldest child, Alex, was about five. We have never been "militant" home-schoolers, and we always check out the schools in our area to see if we think they can do a better job than we can. In Houston, there are many schools called "magnet" schools. These schools have extra emphasis programs for their students. Some are music magnets and have amazing orchestras and personal music instruction, others are language magnets and produce children that can speak Japanese by fourth grade. Truthfully, we were interested in good all-around education or perhaps a math-magnet. It turned out there weren't any true math-magnets. There were "math and science" magnets, but those always turned out to be "science" magnets.

At length, we toured a literature magnet school that was universally acclaimed to be incredible all-around education. I had a brilliant professor at Rice University who was paying for her daughter to go to private school. She told me she would rather get her daughter into this particular magnet school if she could. With that kind of endorsement from somebody I admire and respect, we went somewhat hopeful that the school would impress us as well.

And the school really was wonderful in a lot of ways. The atmosphere was pleasant and the school children seemed happy and engaged. Unfortunately, there were a number of issues with the school that would have made it difficult for us to send our own child there. I won't catalog them all but I will mention the Moment that Amy and I looked at each other, and just walked off the tour early. It was a "deal breaker" Moment.

During the tour, we were constantly told about this program they followed that integrates all the curriculum. They were so proud of this feature of their program. I had to admit that it sounded good, although at the same time, I was thinking that home-schoolers do that by default all the time. I mentioned to Amy later that some of the public schools are beginning to catch up with what Type-H'ers have known forever.

In any event, we got to a fourth-grade gifted and talented Math class. The teacher came out and spoke to us for a few minutes. Immediately Amy and I were underwhelmed with the curriculum. Gifted and Talented fourth grade math involved some very mind-numbing physical manipulations that were supposed to be related to fractions. They weren't all that different from what our five year old was already doing with measuring cups when helping Mom cook.

But that wasn't what made us walk away. No, what did it was when another woman in our group asked the G&T 4th grade math teacher about curriculum integration. She mentioned how we had been inundated with how wonderful their curriculum was because it was integrated. She asked how the Math curriculum was integrated into other subjects. And the G&T 4th grade math teacher said:

"Oh, you can't integrate math. It's its own thing."

Amy and I looked at each other and we knew the tour was over.

Because math is so important to us, we absolutely demand that our children's math education be exceptional. Acceptable isn't enough. Nor is "supplementing", as is constantly suggested to us by our friends and family.

To be clear, our biggest worry about math education is not actually the rigor nor speed of the instruction. Our biggest worry is that a math-ignorant, math-apathetic, and math-phobic system will install ignorance, apathy, and phobias into our children. Then they'll have the gall to tell us everything is okay because they scored in the 99th percentile against other ignorant, apathetic, and phobic children.

I know that sounds harsh. You, the reader, might be a math teacher, or the parent of one of these children. I mean you no ill will, nor do I mean to denegrate your individual contribution.

But I do believe that the system is ignorant, apathetic, and phobic, even if individual teachers are not. And I do believe that our current generation of students reflect that, even if individual students do not.

I'm not willing to risk my child in that system. I can't, and I won't.

Why? Because math is exciting, and interesting, and mind expanding! To paraphrase from LDS scriptures, math can enlarge us, and be delicious to us! That is what my wife and I want for our children, regardless of what career they choose. In fact, it is like music. We want our children to appreciate music even if they are not musicians. And we want them to apprciate math even if they are not mathematicians.

Which brings me to Paul Lockhart's "A Mathematician's Lament". This incredible article was sent to me Sunday night and it resonates deeply with me. I'll admit that I disagree with the author strongly at times, but the core of his message is, I believe, "Truth". After reading this article, ideas that I had already been working on became clearer, and successes and failures in our children's education made more sense.

Oddly enough, we got the article by email at the same time that we were planning our Math curriculum for Fall Semester. It turns out that what and how we were preparing to teach already employed a number of Lockhart's principles. But after reading the article, those principles stood out more clearly, and we could explain them to each other in ways we couldn't before. Then we found that Lockhart had inspired us and we worked out some of the problems he mentions in his paper. Not only was it fun, but Amy and I saw how we might provide similar experiences to Alex. We didn't know when, though...

But imagine our surprise when he came down the stairs the next morning and asked me,

"Dad? If you had a bird house with five holes down and ten holes across, how big would the diagonal be?"

.... To be continued!!!!!

Homeschool Conference

2009-06-15T08:46:00.000-07:00

On May 28-29 I went to the LDS Eastern Home Educators conference held at Southern Virginia University in Buena Vista, Virginia. I am so glad that I got to go to this conference. I feel like it was a huge help for me as a home educator and a good boost for our homeschool program.

Here at the end of our school year, I confess to being more than a little burned out. Some of that has to do with the fourth pregnancy I'm experiencing, and some of it is just that homeschooling is hard work. I was running out of ideas for some of our subjects.

Don't get me wrong, we'd made a lot of progress by the time we finished our semester in May. Alex and Drystan had completed a lot of their goals. Alex was doing double digit multiplication with enough confidence that he was bored. We were trying some more math concepts with him from the book, "Calculus By and For Young People." He was learning how to add fractions and experimenting with an infinite series, but it's a very different approach to math teaching and I was struggling to get on top of it. Drystan was getting double digit subtraction with carrying (or regrouping, as it's called now). We finished up our science textbook, we finished our history. We had done some great stuff with Shakespeare and the defeat of the Spanish Armada at the end and it was a good place to stop at the end of May. Still, I was feeling a little drained.

Going to the LDSEHE conference felt like going back to college for me. We got to stay in dorms and the schedule was brimming full with really useful classes from professionals and experienced homeschool parents. Just after the first day, I felt like my brain was full and I had so many ideas. Then I went back for even more on the second day. I've learned so much that I can use for our homeschool program going forward. Obviously, I don't need to implement them all at once, but I love thinking ahead and planning to use various ideas for the different stages that the kids will experience as they progress and get older. I felt really rejuvinated.

Here are the classes I attended:

World History: What If? - Making history exciting and exploring comparative history.
A Homeschool Built Upon the Rock: Building Upon the Foundation - Better homeschooling starts with family scripture reading.
Homeschooling Through Trials - Families have lots of different kinds of trials and distractions, for me, they gave some good ideas of how to keep teaching through difficult pregnancy and a newborn.
If You Build It, They Will Come: Successful Homeschool Groups - They had some good ideas, but it's not something I'll be able to implement within the next year.
Teach Your Kids to Work Their Britches Off - Finding ways to teach and motivate kids in their housework assignments.
Get Organized: Learn How To Plan - Priorities, Calendars, and Lists, Oh My!
The S-Word: Socialization and its Implications for Homeschoolers - presentation by a homeschool Dad who just happens to be a sociologist.
Dual Enrollment: The Best-Kept Secret - in some states the public school can pay for a high school student's tuition at community college. Something to think about for the future.
Southern Virginia University Panel Discussion - Great information about this small eastern university with LDS standards. Also something to think about for the future.
A Young Man Prepared - Focus on teaching and raising boys.

(There are more descriptions of these talks, and some of the handouts are available in .pdf, on www.ldsehe.org)

After all of that inspiration, it's no wonder I'm excited. Seth and I have already started laying out our lesson plans and goals for starting the next semester in August. We hope to be posting some of those ideas soon.

Our Homeschooling Overview

2009-04-02T11:27:00.000-07:00

A friend recently asked us about what we did for homeschool. I ended up emailing her this big, detailed description, and I thought it gave a great story of our experience:

The Philosophy:

I don't think we've picked a specific homeschool philosophy. I have not studied the Waldorf method, but I know people who like it. There are certain aspects of the "unschooling" that I like - lots of field trips, learning from the world around us, etc. I don't like "100% child led" aspect of unschooling, though. Our kids have really thrived as we introduce things and see where they go with it. There are a lot of things they really enjoy that I don't think they would have known to pursue if we only did child led education. We also found "The Well Trained Mind", by Jessie Wise and Susan Wise Bauer, to be very helpful, even though we didn't follow their outline to the letter.

Getting Started:

For preschool, I found a number of fun, easy-to-use tools at places like Walmart and dollar stores. I got, for example,

flashcards and card games for the alphabet, matching, and opposites.
laminated "placemats" of the US Presidents and the United States map with states and capitals.
a hard wipe-off board for tracing the alphabet.
Crayola "Color Wonder" markers (I could write a word in pencil and they would color over the top of it... useful for learning to read words too!)

For reading, we took some ideas from "Teach your baby to read", which uses whole-word learning from early ages. Seth's mom used this to teach him to read, and he really liked it, but there are plenty of people who think that whole-word learning is ineffective. We used whole-word learning to get the kids started before introducing phonics concepts later.

We actually used the book "Hop on Pop" by Dr. Seuss as a starting point in the kids reading. We typed the text into the computer and printed it without the pictures so that they could learn the words without getting cues from the pictures. We made it a big goal. When Alex, and then Drystan, "passed off" Hop on Pop by reading the whole thing aloud without help, they each got a party and we counted that as reading their first book.

Early Lessons:

For preschool and kindergarten (I was nursing Kael when we started Alex's kindergarten), we started each day's class reading a book to the kids. I let them pick, and it got them sitting down and into the schedule.

Since we've moved more into "grade levels," the way we do it most of the time is that Seth and I sit down during the summer and figure out what goals we want to accomplish for the coming year. As we go through out the year, we evaluate the goals and if we're on track, we keep going, if we're accomplishing more than what we thought, we add to our goals, and if we're behind, we figure out what we need to adjust. More often than not, the kids blow us away and surpass our goals. Occasionally, we find that a concept or skill is harder than we expected and the goal needs to be dropped

During participation in a Houston LDS co-op, we followed a lot of curriculum ideas from this LDS group:

http://www.kindredlearning.com/

Their curriculum plans are specifically aimed at teaching children of different ages within the family. That way you can have the whole family studying the same era of history or the same subject in science at the same time, but then give harder assignments to the older kids than the younger kids. We didn't follow it to the letter, but they had some great ideas for helping parents be organized and stay on top of things without going crazy.

Kindred Learning recommends, for example, "The Story of the World", by the same people who did "The Well Trained Mind," (see more at www.peacehillpress.com). We did an Ancient History unit with the Houston Co-op. Even though Alex was only 5, he really got into it. The co-op did a ton of things together. They dyed pasta purple like the Phoenicians did. They practiced hieroglyphs. They made a stamp of a personal seal out of clay.

All the kids got into history in one form or another. All three of them went with Seth to a Pompeii Exhibit at the Houston Museum of Fine Art. Kael wasn't even 2 yet and he would say "Pom-pay es-ibit" every time he saw the book that we bought that had pictures from it.

The other thing that we did with the co-op was a "Literature Group." Some other moms and I sat down at the beginning of the year and picked a list of books we wanted the kids to read or have read to them, depending on the age. We picked favorites like "Little House on the Prairie" and "Wizard of Oz" as well as classics like "The Prince and the Pauper" and "Journey to the Center of the Earth." It was a smaller group that met twice a month. The first time each month we'd introduce the book for that month (a mom was assigned certain books for the year to be "in charge of"). The second time we met we'd play a game around the book or do a hands on project. For Little House on the Prairie we made butter by shaking up cream in a closed container with cold marbles. For "Heidi" we tasted goats milk and cheese. You get the idea.

All other subjects: math, spelling, writing, etc. we did on our own. We had our own schedule and our own goals. I use a ton of websites that have great worksheets for free:

www.learningpage.com (you have to sign up, but it's free. Great resources for pre-school through about 3rd grade level.)
www.kidzone.ws
www.superteacherworksheets.com (I have been getting my entire spelling curriculum from this website this year. They also have some good grammar exercises.)
http://www.mathsisfun.com/numbers/math-trainer-multiply.html (The default is multiplication, but you can set it for addition and subtraction, too. My kids respond well to timed drills, but I know not every kid does.)

After a semester of history, the Co-op also did a semester of chemistry. The Kindred Learning plan suggested a particular Physical Science textbook. It was a 5th or 6th grade level, but when we read it at home, we could customize it to what we needed. Then when we got together as a class, we did all the labs, mostly using suggestions from the lesson manual.

To organize the class, we had 4 home-schooled teenagers serving as TA's, each TA worked with 3 other younger students (4 groups of 4 each). The teenagers also did harder science assignments at a different time. We also sang a bunch of songs that covered chemistry concepts.

Once again, Alex ate it up. The first time I showed him a periodic table and told him how it worked, he grabbed the book out of my hand and started pouring over it. It really converted me to the idea that kids have a lot more potential than schools and parents give them credit for a lot of times. Don't get me wrong, there have been sometimes when I put concepts in front of the kids that they don't get at all, and I back off and decide to go over it later, but you never know until you try.

And obviously, kids have certain things that they're more interested in others. My kids like dinosaurs so much that we have used dinosaurs to teach the alphabet, math, and a couple of branches of science. :) For example: if you have 3 dinosaur nests and there are 2 eggs in each nest, how many eggs are there all together? Welcome to my world.

Starting last fall, the Kindred Learning plan had us doing the second phase of "The Story of the World" (Fall of Rome to the year 1600) and a biology class. We're using a Life Science textbook from the same publisher as the Physical Science book from last year. I really like these text books. They're very detailed and cover a lot of stuff, but in manageable chunks. And once again, we can tailor it to the age of the kids we're dealing with. Kindred Learning recommended these textbooks even though they're out of print, from 1986, and we really had to search for them. In a lot of ways, more recent science textbooks tend to be more politicized, and in some cases, more "dumbed down." We also picked a whole list of books for "Literature Group" that go along with the topics we're studying in history.

What we're doing now:

Then we moved from Houston to Baltimore. I actually think that it helped the kids adjust to our new surroundings that we were able to go back to our school schedule almost as soon as we got here. Even though I don't meet with the group, we're following a lot of our same schedules. Our current school program looks a lot like this:

History: We average a chapter of history a week. Every time we read history, the boys write a "narration" and draw a picture of what we read about. Alex makes up 3 sentences of his own and uses the history book to help with his spelling. Drystan copies 2 sentences that I write for him.

Spelling: Each boy gets a new spelling list each week. For a normal week, on Monday they write each word twice, on Tuesday they put the list in alphabetical order, on Wednesday I write up sentences using the spelling words for them to copy, and on Thursday they have a spelling test. Mostly we do the spelling and the spelling test as good practice for writing and studying so they can get used to learning material over a period of time and being responsible for studying for a test. They're doing a great job of learning studying techniques, quizzing each other, and trying a variety of memory techniques to get ready for that test.

Math: we do everything and anything to introduce and reinforce concepts. We first started doing math when the kids were little counting, adding, and subtracting with Cheerios and raisins and M&Ms. We use real pennies and coins and play money. We even use an Abacus. We use worksheets, flashcards, and online-drill programs. Mostly, we use whatever is holding the kid's attention at the moment. Currently, for example, both Alex and Drystan really enjoy online timed drills. When the phase passes, we'll move on to something else.

Science: The kids see science in everything. A couple of weeks ago we were studying the parts of a seed. We soaked some beans over night and then opened them up and looked inside. We could see the plant embryo just like the diagram in the textbook.

Having fun: We find that there are fun things to do in just about every subject. We still manage occasional hands on craft-ish things that go with history and literature even though we're not able to work with the group. We're reading a book about Johann Gutenberg inventing the book press. We used rubber letter stamps to simulate printing. Not only is school fun and interesting for the kids, but it is fun and interesting for us. We wonder why more people don't do it!

Origin of the Title

2009-03-27T07:13:00.000-07:00

I love education. It fascinates me. I love figuring out how to explain or teach something. It doesn't matter what it is: math, English, science, and even things like tying shoes, or religion, or morality.

Homeschooling was not something I advocated until I met and married my amazing wife Amy. But after converting me, I am surprised it wasn't more obvious to me from the start, given my love of teaching. As anyone who knows me personally knows, I am just about the biggest proponent of homeschooling that you can find.

So, the title of the blog. It came, actually, from an "unbeliever". I still have the chat transcript, of which I reproduce in part here (edited to protect the guilty):

<friend>: can i vent for a seconde
**edited conversation about poor behavior of other family's 17 year old kid **
<friend>: i just get so mad at the total lack of respect that their kids show when they come to my house
<friend>: well, this is the constant struggle with their kids, frankly
<friend>: less trained at home, more of a jungle atmosphere there
<friend> and then in public it's embarrassing and the kids aren't being raised to understand the social world around them
<friend>: but today at lunch i was talking to my son about it and he described their kids as being "type h"
<friend>: i asked him what type h was
<me>: what is it?
<friend>: homeschooled

Obviously, this little conversation caused us some discussion. I thought it was funny that my friend said that the problem was what the 17 year old was not being taught at home. Moreover, this kid was a public schooled kid, but was somehow an indication of what home schoolers are like.

Well, anyway, we're good friends, so we keep our debates clean of course. And we kept coming back to "type h" repeatedly. One of the best ones was when I mentioned a friend who was partially home schooled.

<me>: his wife was partially home-schooled.
<friend>: type pH
<me>: home-schooled + Christian high school.
<friend>: :)
<me>: He'd decided on home-schooling before he met her.
<me>: It was one of the things that drew them together, actually
<friend>: did you think "type pH" was clever?
<me>: no.
<friend>: lol
<friend>: c'mon!!!
<me>: ph-balanced
<me>: that would have been clever

Obviously, I disliked their analysis of type-h, but I did have to admit that the name itself is pretty clever. Our last conversation went like this:

<friend>: but i cracked up when they said he was home schooled... thought of you :)
<friend>: and type H personalities ;)
<me>: We're such nutjobs
<friend>: lol
<friend>: this is a thread that we will take to our graves, I'm afraid :)
<me>: Oh, probably
<me>: The "right or wrongness" of the type-h description is overshadowed by the cleverness of it

So, there you have it. The long story of the clever name of the Blog. Hope you enjoy reading herein.