Alex and Athens: Another Bountiful Harvest

Yesterday's post about Drystan's multiplication was a lot of fun. Of course 99% of homeschooling is planting for both the teacher (e.g., lesson-planning, worrying, evaluating, struggling, crying, praying, and not sleeping) and the learner (e.g., studying, focusing, practicing, testing, crying, and wondering why his/her parents are making them learn something). Only 1% of the time is really the harvesting. But the harvest, when you get to see some beautiful fruit come out of the ground you have tilled and cultivated, makes the other 99% worth while.

One of my other homeschooling friends read my post about Drystan and succinctly tweeted, "That is freakin' awesome." She told me about her own "harvest" today when her six-year old read a magic tree-house book all by herself, all on her own, just for fun. It's been a hard road to help this child read but my friend tweeted a beautiful observation: "Parenting...turns out it works."

With the twenty minutes I have before dinner, I felt inspired to post one more "harvest" moment we reaped this week with Alex. For school, this Semester, we've really pushed Alex into a much more rigorous and difficult academic mode. We are expecting a lot more out of him, but none of it is busy work. We are pushing him to really expand his world-view and his critical thinking.

One area that I helped plan was his History classes. Teaching history to a 10, 9, and 6 year old is complicated to say the least. For our "basic" history, we are using the Story of the World textbook on Ancient History. The older two boys have to read this on their own while Amy reads it out loud with the 6 year old. Amy and the three boys meet together in a history "class" once a week to discuss and to do hands-on projects (like creating cuneiform tablets!). The older two boys also have to take tests on the material.

But to be honest, I'm not particularly fond of the the book. The chapters are more like pamphlets and devoid of much in the way of meaningful content. The events related in the book are often put in a misleading light even with regard to the chronology. On the flip side, until my children start getting 100% on the tests, I grudgingly have to admit that it's a worthwhile exercise. And it does provide us a basic timeline to work with.

But for Alex, it isn't enough and we developed an extra history class for him this semester focused on Greek history. This class is largely devoid of chronology and timelines because we expect him to learn that from the other class. Instead, his Greek history class if focused on Greek philosophy, politics, law, art, and architecture. The goal is to better understand the Greek impact on the world.

The fist several weeks have been mini-lessons (mostly from encyclopedias and so forth) on the famous three Greek philosophers: Socrates, Plato, and Aristotle.

This last week, was the first one about politics. I found a series of articles for him about Athenian politics.

1. Athenian Democracy, A Brief Overview
2. The Development of Athenian Democracy
3. Athens to Empire
4. Athenian Politics and Government

His assignment was to read these and write a two-page paper about the topic.

As I was taking him to cub scouts on Wednesday night, I asked him if he had read these articles and what he thought. I wish I could play the recording of his response because it was the tone of his voice that made this a "harvesting" moment for me.

"That was the coolest thing I have ever read."

I was so excited to hear my nearly 11-year old express such joy and excitement from reading about this early political experiment in democracy. As I think about him learning about Greek political thought this semester, Roman political thought next semester, and the development of law in England up to the Revolutionary war, I feel happy and confident that when we teach the Constitution of the United States, he will understand it better than almost any of his peers. When we talk about politics and law in the contemporary United States, he will perceive and understand in ways I cannot yet fathom.

More than anything else, I have great faith that this anchoring knowledge will keep him safe from political, social, and media manipulation.

If that isn't a bountiful harvest to look forward to, I don't know what is.

Drystan sees the light(s)

During our cross-country trip, we visited Amy's grandmother in southern California. "GG" (Great Grandma, as our children call her) lives a comfortable life in an assisted living facility. She has her own apartment with her own kitchen and is very independent. There is a dining hall, though, and she enjoyed treating our family to dinner a number of times during our stay with her.

While eating dinner one night, Drystan points up to the chandeliers throughout the hall. "Dad," he said, "there are two-hundred and forty-three light bulbs in the lights." [It has been several months since this conversation took place, so I am paraphrasing slightly]

Astounded at this unexpected and unprompted announcement, I asked him how he knew that.

"Because," he went on, "there are nine chandeliers, and each one has twenty-seven lightbulbs. Nine times twenty-seven is two-hundred and forty-three."

I was practically speechless at Drystan's correct computation. To understand my amazement, you have to backup a few years.

FLASH BACK FIVE YEARS

When we were teaching the four-year old Drystan basic addition, he was absolutely convinced that "1+1" should be "11." He could see one "1" plus added to another "1" and he believed that two "1"s should be "11." We explained it many times, but he never really got it. We assumed it was because he was just four years old and didn't think to much about it.

FAST FORWARD THREE YEARS

But by age seven and eight, we finally understood that Drystan's approach to mathematical computation was very literal and nonsymbolic. It didn't matter how many times you explained the rules to Drystan, he couldn't accept the instruction unless he was emotionally connected to the solution.

Did you know there are multiple "pathways" through the brain that allow us to recognize something or someone? I took a cognitive neuroscience class in college (as part of my Master's degree in Computer Science, if you can believe it) and we learned about a man with brain damage that affected an emotional recognition pathway. When he looked at his mother, the visual pattern-matching pathway still worked. He would, in great frustration say, "you look like my mom, but you're not my mom!"

Drystan, I believe, has some kind of similar experience with even basic adding and subtracting. No amount of intellectual explanation will ever be sufficient until he can emotionally connect with the solution. I would watch him try to add two-digit numbers and struggle against his internal intuition that kept telling him that the right way to do something was wrong. You could see his little mind spinning (I would have him explain out loud each step) as he would struggle through it. Even as he would force himself to say the correct steps for doing the carrying, you could see that he didn't believe it!

Needless to say, teaching him mathematical computation has been a challenge. He struggles even with a lot of practice to do some relatively basic arithmetic, and if he goes cold (e.g., he doesn't do some arithmetic problems for a few days) he can completely unlearn everything.

Summer breaks were especially problematic...

BACK TO THE PRESENT

And here was my Drystan, who has struggled from the beginning with anything relating to numbers, throwing out 9x27 without pencil and paper, fairly quickly, and accurately.

"Drystan!" I enthused, "How did you work that out?"

At this point, I will backtrack in history just one more time. I have never believed in just teaching my children "rules" and have always tried to explain fundamental principles happening below the rules. With multiplication, I have always emphasized learning the distributive rule. You can break a problem like 9x27 in to (9x20) + (9x7). We have discussed at great length why the distributive rule even works and looked at visualization of this property in the computing of the area of a rectangle. But despite it all, it never seemed as if Drystan was internalizing any of it.

"Well," the present Drystan explained, "I know that I can figure out 9x27 by splitting it into 9x20 plus 9x7. 9x20 is just 180 and 9x7 is 63. 180 plus 63 is 243."

He said it so confidently. He understood it so well. I just stared at him in disbelief! He really had been listening after all? He understood them well enough to apply them in a real life circumstance? Wasn't this the kid that had struggled with multiplication all through the last semester?

That was one of the best days in my life. It really gave me hope that the work I'm doing with the kids is actually meaningful. Even when it isn't always apparent, the lessons I'm teaching are actually being stored somewhere inside their brains waiting for an opportunity to germinate.

We've already moved into the new semester and we're working on division now. Drystan is successfully multiplying three-digit numbers by three-digit numbers. He still struggles, and it still takes a lot of very slow and careful work. But it isn't like it used to be. He's turned a corner and his progress is accelerating.

I don't know what his future holds. Drystan still wants to become a special forces soldier in the army because despite my explanations about war, death, dismemberment, emotional trauma, and immoral governments, he's still emotionally connected to the idea of being a warrior. But he is also expressing some interest in science and engineering. I wonder if he'll choose one of those fields.

I hope if he does pick something that requires strong math skills that I'm still alive and able to tell him about when he first saw the light! And how he told me that there were 243 of them.

The Untouchables

[UPDATE: This post has nothing to do with parents. Apparently, somebody mistook my post to imply something about parents teaching their own children. That was the farthest thing from my mind and the opposite of my intent. This is what I get for attempting to be clever. See a follow up comment at the end of the post for further discussion.]

While observing my two oldest children at a soccer practice, I overheard another mother discussing something about building a house. I don't know a lot about this woman, but it seemed from my observations that she probably isn't that great at building houses. Whenever I talk to people in her profession, I have to be careful not to let them know how unqualified I find them in general. And, of course, I have to make sure I don't lay any of the blame for the ever-growing numbers of collapsing and shoddy houses at their feet.

I suppose it kind of makes sense. I mean, someone doesn't become a house builder to make money. While there are a few bad apples, most home builders choose their profession to make a difference. They want to see people with roofs over their heads, and they really love working with houses.

Given how little they make, and how much they love houses, it makes sense that they are not actually required to have high qualifications. It's a labor of love, after all.

It's like the bumper sticker I saw. "If you live in a house, thank a home builder." As I listened to this woman talk about the shoddy materials, the schedules that are nothing short of ridiculous, and the unnecessary rooms being added at the expense of the foundation, I was tempted to cringe. But then I reminded myself of how much love and sacrifice she was putting into these houses. I'm sure the people living in them are grateful.

Even though I know that these home builders have some of the worst construction scores; even though I know that most of what these home builders build needs to be corrected by the buyer; and even though I know that they don't understand the role that foundations, support beams, and effective space management, I have to balance that against how hard they work for me. "Do you know how little I work for?" one asked me once. "I get paid a small salary, deal with incompetent foremen, and federal regulation like No House Left Behind so that people can have a roof over their heads. And some of these people I'm trying so hard to help think that they should have input into how I build their house. Don't they know I'm building thirty houses this year?"

I nodded. She was absolutely right. People needed to be grateful for the houses getting built for them and learn to appreciate what they were being given.

... wait, I see someone in the audience of my blog objecting. What is that you're saying? Hold on, now... is that right?

This isn't how home builders are treated?

You're telling me that people have higher expectations for their home builders than that? Are you sure? It seems like you're trying to say that in our society we expect that someone that's going to build a home be capable of doing a good job of it. Correct me if I'm wrong, but it sounds like you're saying you might interview the people that want to build your home? You're saying that you might want to see previous samples of their work? You're saying that you might get multiple bids and compare them?

No, I've never heard of Angie's list. Oh seriously? You mean that home builders are rated and reported on so that someone can pick one that will do a good job?

Well, maybe I'm remember my story wrong. Maybe you're right. Maybe home builders are expected to actually be good at what they do. I must be confusing two professions here. I'm trying to think of a profession in our country where those receiving their services have no input into who does the work or how it is done, a profession where their poor results are not their fault and not to be criticized, and where the general population generally accepts the work no matter how bad it is.

Can anyone help me out here?

------------------------------------

AUTHOR's FOLLOW-UP NOTES: After the comment about this post referring to parents, I went and re-read it and saw how someone misunderstand what I am trying to say.

Obviously you cannot "fire" parents, and a parent will remain a parent no matter how good or bad they are at the job (except for extreme circumstances like abuse). But this post has nothing to do with that nor would the analogy apply. You cannot compare parent-provided education with any other kind of education.

Why?

There are many, many reasons, but from the point-of-view of this analogy, it is purely economic. There are more important reasons than economics, but just for the purposes of the analogy here, it is entirely economic. Parents are not providing goods and services in exchange for goods and services. Parenting is not a profession provided to others in exchange for payment.

My point in this analogy is that, in our (largely) free-market economic system, we assume that providers of services are not entitled to provide us those services. We assume that the provider of a service must recognize that we will have expectations of their service and go elsewhere when those expectations are not met. We assume that (in general) customers will not choose a provider of services based on if they are a "nice person."

What struck me, and led to this post, is that teachers, in general, do take it personally if you say that they are unqualified or under-qualified. What's more, non-teachers jump to their defense and point out how hard they work and how little they get paid. Teachers are seen as sweet and loving and kind; therefore, they cannot be criticized for poor performance. I know of no other equivalent in our society.

To this point, I would argue that we hold waiters and waitresses to a higher standard than we hold our teachers. We expect good service from the food staff or we go elsewhere. No matter how "nice" the waiter is, nor how hard he works for the college money, most people will not put up with poor restaurant service.

Why do we not hold our teachers to the highest standards? Can parents ask about the morals and character of those that will be the primary mentor for their elementary children for 6+ hours five days a week? Can parents ask to see the teacher's grades and other academic indicators? Can parents evaluate the teacher's curriculum and portfolio?

They cannot. Until parents demand the same level of service from their teachers as they do their home builders (or waiters), our education system will remain hopelessly broken.

Education: What Matters Most?

There is very little our country agrees on these days. Now that I'm in a line of work that involves testifying in court as an expert on technological matters, I no longer write about political matters online. But if I could, I would use this as an opportunity to opine on the value of federalism. Why should a country of our size, with our population, generally agree on things anyway? I think that such a believe is either naive or arrogant.

Alas, this is not a political blog, but with that backdrop let me point out how amazing it is that our country is in general agreement that our schools are performing poorly. You will rarely find someone that says, "You know? I think American schools are really good!"

Obviously, nobody agrees as to how to solve this problem.

More amusing to me is that almost everybody I talk to says that their school is fine. Much like Congress has an 11% approval rate yet most congress-persons will get re-elected, everybody says that the schools are bad, but not my school!

I think that part of the problem is that measuring education performance is very hard. Even if one thinks, as I do, that testing is a generally effective tool in an educator's toolkit, does testing itself provide good metrics about a student's progress? Or does one think that a class grade is an accurate indicator of how well someone will make use of that knowledge in the future? Or does the number of books a student has read about civics serve as a useful indicator as to whether said student will participate meaningfully in the community and nation?

But the biggest problem I see is that we don't even know what the real objective of education should be!

Did you notice that I described three different metrics for measuring education but I also described three different objectives? What matters most in education? What is its purpose? We put our children in school for 6-8 hours a day, for 180 days a year, for 13 years to "learn." But to learn what? In education, the what we believe that students should learn drives the how. In theory, it should also drive the measurements of effectiveness.

I have a very low opinion of public schools in general, but this is an issue where they really showcase their bureaucratic incompetence. Because they are forced to have (and force) everyone in their system, it is very difficult to come up with an education goal that suits everyone. Without a clear end-goal, they have no clear insight into how they should teach, let alone how progress should be measured. But they can give out tests to every child born in the same twelve month period! And testing a kid from an inner-city, broken, drug infested home along with a kid from a stable, tax-paying, voting family makes the voting parents feel good about their kid's education. "We don't really know what Johnny's learning," voting Mom tells me, "but we know his school has some of the highest test scores in the state!"

(I so wish I was exaggerating that)

But not everyone is so willingly blind, or intentionally ignorant. With such individuals, I have had a number of conversations (or sometimes arguments) about what the purpose of education is and how it should be taught. Even with all the differences from one person's priorities in education to another, most of the people I have talked to believe in a knowledge based education. More specifically, they believe in a knowledge distribution education system.

The idea behind such a system is that you simply dispense knowledge to an individual. The receiver of such knowledge proves to the giver that he or she has internalized the information in some way. The more knowledge one can prove to be in possession of, the more educated that person is.

As best as I can tell from what I've studied of history, this system was invented by people that became educated, recognized the benefits that came from their education, and desired that others might have the same experience. Initially, this system was through 8th grade, and then through 12th.

Knowledge based education was perpetuated by a new crop of Americans that, during the early half of the twentieth century, sacrificed time and money to go to Universities and gain more education. The experiences they had cemented the people they became and they were deeply grateful for the value their education had in their lives. They were so convinced that University education was essential to becoming educated (based on their own experiences) that they continued to sacrifice time and money so that their children could have the same experience.

The knowledge distribution education system is so entrenched in American values that the Government makes it possible for virtually everyone to go to college through grants and subsidized student loans. Because almost everyone is convinced that all that is required for an education (for whatever end goal you choose) is to pay for someone to have knowledge dispensed to them. Our people believe in college so much that the thought of a college educated person being unemployed is seen as a sign of calamity. How could an educated person not be able to find a job?

In my opinion, all of these well meaning people trying to dispense education to others have fundamentally misunderstood their own experiences.

Knowledge, in my opinion, is a by-product of a good education. It is the consequence of becoming an educated person. Figuratively, it is simply the fruit of the tree, but not the tree itself.

Sadly, many from the previous generation that sacrificed so much to obtain a college education didn't understand somehow that the sacrifice was necessary in giving life to the education they were obtaining. Those that went hungry to stretch their meager college funds didn't understand how important that hunger was in appreciating mathematics. Those that sacrificed time with friends to earn money part-time to pay for books didn't understand how important that part-time job was in coming to value books like gold. And those that married in their undergraduate (unheard of today at most schools) didn't understand how their families helped them balance the knowledge they were gaining with the drive to put such knowledge to use in service to others.

They didn't realize that the mathematics, and books, and knowledge were all just natural consequences of the people they were becoming. They didn't understand that without the experiences that they struggled through to reach their educational goal, their education would have been empty and hollow.

Which leads us to today's college students. Many of them are fully bank-rolled by their parents or living on money borrowed from the Government that they'll pay back some day. Truthfully, it costs someone very little to get into college today, and make it through with a four year degree. Most emerge unchanged by their experience and expect that, having done their "time," the world will continue to provide them with their adult needs (job, house, etc.).

And things are worse in the K-12 education. We don't expect anything from our children today in terms of responsibility and sacrifice. As long as they can demonstrate obtained knowledge at a level commensurate with their peers, we are satisfied. The assembly line begins and five years old, and we expect our schools to pop out a kid stuffed with enough knowledge by age eighteen. The only important experiences in this whole process are the social ones (such as Junior Prom, for example.)

I want something more for my children. Of course I want them to have knowledge, but I want that because they themselves value learning and understanding. I want them to seek out their education and be willing to sacrifice to obtain it. I want it to hurt them a little. I want children that know that education is so valuable, it is worth paying a price for. I want them to understand that we only value something to the extent that it cost us something.

That's a wonderful goal, but how does one go about teaching those kinds of lessons? Truthfully, I don't know. Long time readers of this blog will recognize this objective in many of the previous posts. It's something I try to figure out every day.

But as hard as the how is, the measurement of progress for such a goal is all but impossible. How do you judge if someone is actually becoming something?

I don't know that either.

But a few months ago, I saw a spark of it in the words of my oldest child Alex, then about ten and a half. Alex had attended a three week summer class put on by the Johns Hopkins Center for Talented Youth. He chose "Flight Science" for his class and learned a great deal. After the class was over, I asked him what he felt he got out of it.

"Well," he said, "I came to the conclusion that I really like home schooling."

Somewhat surprised by this unexpected answer, I asked him why.

"At my flight science class," he explained, "what we do each day is completely dictated to us. They tell us when we're going to do something and what we're going to do. It is always really fun, but I have no input whatsoever. At home, I have some influence over what I'm learning and how."

I don't know of any words that could have made me happier. Alex recognized the value of being in charge of his own education and how that is superior to being a passive passenger. He's already feeling like education should involve ownership and when ownership is taken away, even if what's left is a really fun class, it just isn't education. Alex's words gave me far more hope that his education is doing well than any 100% on a spelling test, or a five page paper on our state bird. His words give me hope that he is awakening to the potential within himself and an understanding that he has the power to shape his own destiny.

And in the end, isn't that what matters most?

Around the USA in 30 Days...

I hope you will excuse the lack of posting here on Type-H Personalities. I'm afraid we have been away on a "Grand Adventure." (Notice, the lack of the word "vacation." This omission is intentional...) In a letter to a friend, I described our travels and selections of that letter follow.

I hope you will forgive me for not writing to you in such a long time. I thought for sure I would have time once I was on “vacation.” The problem was, travelling with four children across the United States to see family might be a vacation for the kids, but it isn’t for the grown-ups!

You might like to hear a brief retelling of all that happened to us as we went along our way. We left Baltimore at about 5am Monday July 16th and arrived in Redlands California (near LA) by Wednesday evening! We drove the 3,000 miles across the country in just three days! We broke up our drive so that we were on the road 14 hours day 1, 16 hours day 2, and 12 hours day 3. Our little van, that we call “The Vandersnapper” or just “Snappy,” gave us no problems travelling there or back.

I had worked out things with my Boss so that I would be away from Baltimore for an entire month. Of course, I don’t actually have a month of vacation, nor would our clients be very happy to lose me for that length of time. So, the first week of the trip, including a good part of the drive, I was working. And I had worked extra the week before we left to get certain critical projects done. In order to be able to work while driving, my Boss got me a “MiFi.” It’s a little device that provides a wireless network while connecting like a cell phone to the Internet. So often, Amy would drive while I sat in the passenger seat working on my projects. I did a fair bit of driving too, though.

And while the two of us were cruising across the country, the four kids sat in the back seats glued to DVD players. We limit how much they can watch the TV or movies when we’re at home, so being able to watch movies all day while driving is actually a treat for them. For our van, we bought two DVD players, and each player has a second screen. So we had one movie playing on two screens in the back row, and a different DVD player showing a second movie on two screens in the middle row.

If you have a map handy, I can describe the route we took from Maryland to California. We started by taking I-70 up through Pennsylvania, through a small chunk of West Virginia, through Ohio, through Indiana, and finally through Illinois until we reached St. Louis. That’s where we stopped on the first night of travelling. On day 2, we left St. Louis very early and drove South-West on I-44 through Missouri toward Oklahoma City. At that point, we switched over to the West-bound I-40 to exit Oklahoma, passed through the top tip of Texas and made our way through New Mexico until we reached Albuquerque, where we stayed on the second night. On the third day we kept to I-40 through New Mexico and Nevada. “40” dead-ends into smaller highways in California that we followed slightly south-west until we reached I-15.  We reached Redlands (I think we had to go on I-10 for a short bit there at the end?) by about dinner time.

Amy’s grandmother lives in Redlands in a retirement community. This community has cottages that the residents can rent for guests, so we were able to stay less than 100 yards from her. We had a good time visiting her and she was so happy to see her great-grandchildren that live on the other side of the country. Alex played his Saxophone for her, Drystan played the Piano, and Kael recited a poem. And, of course, Saige being only 2 years old just “cuted” everyone out.

While in Redlands, we also made trips to the Beach. The kids has been to the Atlantic ocean back in April, so in a three-month period, they visited both beaches of the United States! We also made a trip down to San Diego to see my Mission President.

We were in Redlands for less than a week. On Monday, July 23rd, we loaded up in Snappy and drove the 11 hours up I-15 through Nevada into Utah. Because we were going to be in Utah for three weeks, we rented a townhouse that would hold all of our family plus Amy’s parents. Steve and Jeanette (her parents) stayed with us for most of the time. It was great because they got to see their only grandchildren quite a bit, and we got free babysitting. Amy and I don’t usually get out much, but during the trip we were able to have some “alone” time every now and then.

Our first week in Utah we went to a Family Reunion for Amy’s mother, Jeanette. It started on Friday the 27th and went through Sunday the 29th. Amy’s family is pretty big, so there were lots of people there, and a lot of children too. Our kids, used to the East Coast where nobody has many children, were excited to have lots of other children to play with. One of the days of the Reunion was held at the “This is the Place” monument in Salt Lake. It’s a park that commemorates when Brigham Young came into Utah, looked over the Desert, and said, “This is the Right Place.” The park recreates homes and shops from the pioneer era and has a lot of fun activities for families.

Our second week in Utah we had promised to my father. So, we went and did a lot of activities with him. We went to a water park called 7-Peaks, a dinosaur museum, Temple Square, and a bunch of places like that. My kids are still really into dinosaurs, and we ended up going to several while we there. While hanging out with my Dad, I also saw my oldest brother, Blake, and my sister Lecia. I also found some time to go visit my mother’s grave and pay my respects.

During the last week we were there, things got more complicated. I had to start working again and, in fact, I had an emergency business trip in San Francisco. Amy ended up driving to Idaho with her parents to visit their home while I worked for a good part of the week. We both got home Thursday night so we planned to visit a few friends over Friday and Saturday. These were all very good friends of ours that we haven’t seen in years, so it was nice to be able to visit.

Saturday night, my second-oldest brother Chris and his wife Roxie hosted a big family BBQ. They’re much older than I and their kids are actually about my age. And that, of course, meant that their kids were my kids’ ages, so everyone had a really good time. Sunday night I went to another cousin’s house for dinner and visited with one last batch of family before it was time to come home.

Monday, August 13th, we started home for Maryland once again. Because we were coming from Utah, and not California, we took I-80 most of the way. We passed through Wyoming and Nebraska on the first day, stopping to sleep in Lincoln. The next day we followed I-80 again, travelling through Iowa, Illinois, Indiana, and finally stopping in Ohio near Cleveland. We had to travel really far each day because I had to be back in Baltimore for a Lunch meeting on Wednesday! The third day of travel was pretty easy because once we got to Pittsburgh (and back on I-76) it was a route we were really familiar with.

I did, in fact, make it back for my Lunch meeting and I have been working ever since... 

For the benefit of the blog readers, I have attached this image of our travels:

It was a beautiful drive through the country. I really enjoyed seeing the geography change as we traveled from one region to another. And our children, though largely watching their movies, also got a chance to see the country they live in.

Now that we're back, I'll be adding a few blog posts about some of the other events of the summer and our plans for the new school year. Until then, enjoy this video about the states and the capitals (we made the kids be able to identify them all before we left on the trip...)

Animaniacs: The States and their Capitals

An Open Letter to Parents that Think they are "Bad At Math"

Dear Parent,

I may or may not know you, but if you are reading this it probably means you and I have one thing in common: we love our children desperately and ache to see them happy and successful. So, without further delay, I will jump to the point. Loving mathematics is a critical component in your child's development.

Now, assuming you really are a parent to whom this article is addressed, you believe that you are "bad at math."

PLEASE STOP BELIEVING THAT.

You honestly do not know if your bad at math because this country struggles to teach people what mathematics is. I have written about this at length here, here, and here, and a real mathematician wrote about it here. But the shortened summary is that learning "steps" to compute an answer is NOT mathematics. Pretty much everything they taught you before college (and much of what they taught you in college) is not mathematics.

Did you struggle in grade school with getting the multiplication quizzes done on time? It doesn't matter. THAT IS NOT MATHEMATICS.

Did you struggle in middle school with remembering how to solve the "two trains leaving a station" problems? It doesn't matter. THAT IS NOT MATHEMATICS.

Did you struggle in high school to remember which formula and/or "trick" to use to solve some problem? It doesn't matter. THAT IS NOT MATHEMATICS.

Different people call these examples different things; in our house we call them computation. Computation is important especially to subjects like science and engineering (and it is great for balancing a checkbook, etc), but truthfully it has very little to do with mathematics.

So, please, take a big deep breath and let go all of your "I'm bad at math" tension. I want to start over with you on a new clean slate.

Yes, with you. While we started this conversation about your child's education, please believe me when I say that it starts with you. If you can't believe that mathematics (real mathematics) can be fun and interesting, your child will struggle to believe it unless they have a natural affinity for it. And even if they have an affinity for it, wouldn't you want to understand and appreciate your child's gifts?

Again, please forget everything you think you know about the math you think you're bad at.

Let's start with a game. This game has a game board with exactly three squares and exactly three pieces. For convenience, let's use game pieces from a popular game like Monopoly. We'll use the car, the hat, and the iron. Here's a visualization.

There is only one other additional piece. The "room" piece. The room piece fits over either square 1 and 2 or square 2 and 3. Let's start with it around square 1 and 2 (the car and the hat):

The objective of this game is simple. You want the board to look like this:

Here are the rules:

1. Any two adjacent pieces can switch places.
1. NOTE: For this rule, the room and its contents are treated as a single piece (so the room and its two pieces could switch places with a piece adjacent to the room).
2. NOTE: Pieces may not change places across room boundaries (a piece within the room cannot switch with a piece outside the room).
2. The room can switched at any time from its current two squares to the other two squares (e.g., it can move from being around 1,2 to being around 2,3 or back).

If it isn't immediately obvious how to reach objective, it is probably because I described the rules poorly. Nevertheless, try the different rules on the pieces of the board and see what you can do with it.

Did you try it? If you didn't, please go back and do it at least in your head. Did you reach the objective?

Here is how I did it.

START:

STEP 1 (using rule 2, moving the room):

STEP 2 (using rule 1, swapping adjacent pieces):

FINAL STEP (using rule 2, moving the room):

As you were doing this game, you were experimenting with math. Did you know that? Did you know that you were messing around with some of the core math ideas that make the steps we use in our multi-digit multiplication work?

In mathematics, multiplication is said to have certain properties. These properties say how you can change a certain multiplication problem and still get the same answer.

1. The commutative property of multiplication says that 3 x 4 is the same as 4 x 3. In our game, it is like swapping the two adjacent pieces. Note that the "room" piece is just parentheses. So, you can also say that (3 x 4) x 3 is the same as 3 x (3 x 4). Did you see the whole room move like a single piece?
2. The associative property of multiplication says that (3 x 4) x 3 is the same as 3 x (4 x 3). In our game, it is moving the room from squares 1 and 2 to squares 2 and 3.

We use these two properties extensively and all the time without thinking. Here is an example.

What is 2000 x 3? You probably think that is pretty easy if you remember your grade school computation. I was taught you multiply the 2 and the 3, then add as many zeros as there were in both numbers. The answer is just 6000.

But why? Why does that work?

Please note that asking why is not to be able to remember the steps better. Asking "why" is not to make us better computers. Asking "why" IS MATHEMATICS.

It turns out that we can show why the way my teacher told me to solve 2000 x 3 is correct using the game we played earlier. It can be done with just the commutative and associative properties. Watch.

1. 2000 x 3 = (2 x 1000) x 3
2. 2 x (1000 x 3)      associative rule
3. 2 x (3 x 1000)      commutative rule
4. (2 x 3) x 1000      associative rule
5. 6 x 1000
6. 6000

Did you have any fun with the numbers? Any fun whatsoever? Or did you have any fun with the puzzle game?

Alternatively, did you think it was the least bit interesting?

If so, you have just had a spark of enjoying real mathematics. For fun, why don't you see how you need to extend the game to solve a problem like 2000 x 300 = (2x1000) x (3x100). This introduces a small additional wrench into the game and rules, but you still solve it using just the associative and commutative properties. If you still don't like numbers, can you just extend the puzzle game above and play with it? Notice that you will have "two rooms" now instead of one. How do the rules need to be augmented? What makes the most sense?

I have yet to work with a child that didn't think this was fun. My second child really struggles with computation, but he absolutely loved this exercise the other day. I didn't even have him "solve" the multiplication problem; I just wanted him to get some experience to using mathematical properties (i.e., game rules) to be able to move around the numbers (i.e., the game pieces). He was so excited about it he didn't want to stop.

And please don't ask me how this is "practical." Of course we want education to be useful and practical to students in modern society. But we also want our children to be come educated. And by educated, I mean capable of meaningful, critical thinking. The convenient side effect of learning mathematics is that eventually it can be really helpful in computation.

But far more importantly, mathematics, real mathematics, stretches the mind and opens up new avenues of exploration and adventure. 

So, in closing, please stop thinking you were bad at math. Give it another try. Look for some fun and adventure in the mathematical world. If you don't know where to start, ask someone who does. Find that little spark of joy at solving a puzzle or crafting something new.

I promise that your little spark can turn into something wonderful for you, and for your child. It can become a treasure you will carry with you all the days of your life.

Sincerely,

-- A guy who failed all his math classes in college and had to re-take them but still loves math and thinks it's really, really interesting.

The Canary is Dead: It's Time to Exit the Public Schools (Part IV)

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.


Author's Second Note: I apologize for the long delay between episodes. My work schedule has kept me barely able to catch my breath.

CHARACTERS:

1. Seth Nielson - A hot-headed, argumentative home-schooling dad
2. Amy Nielson - Seth's beautiful, fiery wife who converted her husband to home-schooling in the first place
3. Abby Normal - An excellent public school teacher
4. 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.

THIS IS PART III of the story. You might wish to read PART I, PART II, and PART III if you have not done so.


"So," Abby says rolling her eyes, "you are trying to tell me that the majority of home-schoolers are teaching this type of mathematics?"

"No, absolutely not," Seth replies. "I know of very few home-schooling families that teach math the way I think it should be taught."

"Then how is there mathematics any better than the mathematics taught by the schools?"

"In a lot of cases, it probably isn't. But there are some big picture ideas that I think you are missing.

"First, how other families teach their children math is none of my business. We've already talked about this at length tonight, so let's not pursue that any further for now. I think a far more important point is that while I want my kids to know a lot, I am far more concerned about their ability to think.

"One of the things that impressed me about home-schoolers as I began to get to know a lot of them is their capacity for independent thought and self-management. These kids may know more or less than their public-school peers on individual subjects, but on average they were better critical thinkers, self managers, and had a better capacity for learning new subjects."

"Can you back that up?" Abby asks.

"Statistically? No. Some things are difficult to measure especially when trying to isolate a single factor when hundreds of factors are in play. But it is my belief based off my experiences. If you want to find out for yourself, you would have to do your own investigation. What I am stressing is that, in our house, this is the way we try to teach that kind of thinking even with mathematics. It is also a huge part of our history education. In my opinion, next to mathematics, history is the worst taught subject in school."

"Why?"

"For the same reason as the mathematics. There is not enough critical thinking. Kids are taught to 'know' history based on the textbook and the teacher's viewpoint. Have you read your children's history textbook?"

"I haven't," Mary admits.

"Chances are, it has bias. And the kids aren't being taught how to recognize and analyze bias."

"Every textbook will be biased one direction or another." Abby asserts.

"I agree. But our schools teach the kids to be braindead about it. Just answer multiple-choice questions for a test, and somehow that means you 'know' history.

"Not only is critical thinking not taught, but neither are primary sources. For example, are either of you familiar with the English jurist Blackstone?" Both of the listeners shake their heads. "He was a fantastic legal thinker and a lot of his ideas underlie our entire Republic. Your rights under the law are directly influenced by this man that lived in the 1700's."

"So?" Abby asks.

"Don't you think it might be a good idea to understand a little bit about where your legal system came from?"

"I don't know," Mary says. "Maybe? Are you saying our history books don't discuss him?"

"Some of them might. But I have yet to find a public school that has the students read any of his writings."

Seth waits for his comment to sink in. Abby speaks first. "Wait, you want the school children to actually read Blackstone's writings?"

"Yes. That is what I mean by primary sources."

"At what grade level?"

"I don't know. As soon as the child is capable. It will depend on each child."

"That sounds more like college level reading. Through high-school, I think we focus on helping them get the 'big picture.'"

"I understand that point of view. The problem is, the kids spend the first 18 years of their lives and the first 13 years of the education believing that history is reading what somebody else says about someone rather than reading for one's self what that person said.

"As another example, most school kids in the United States have to study about the Constitution, but very few have to actually read the Constitution, and even fewer are required to read the Federalist papers or similar primary sources."

"What are the Federalist papers?" Mary asks.

"Newspaper articles written by those that supported the ratification of the Constitution when it was being debated by the states. Those opposed were known as the 'Anti-Federalists' and published response articles as well."

"Why should we read them?"

"I can't even being to list all the reasons!" Seth exclaims. "How about this one. We're in the middle of a very 'spirited' political campaign season. Have you ever asked yourself if the campaign promises that are being made on either side are legal?"

"I think that's a little unreasonable for the average citizen. That's the job of the Supreme Court," Abby suggests.

"I thought you might say that," Seth says rising and heading to a bookshelf. "But what you are suggesting is that the common-man cannot be trusted to do any critical thinking for himself. Or, at the very least, he does not have the education to do so. Only specialists could possibly decide if they think the government is acting appropriately.

"Well," Seth continues returning to his seat with a book, "While it is true that our population generally acts like sheep waiting patiently and obediently for the government to tell them how to think about government, it was not always so. This book here is Democracy in America by Alexis De Tocqueville. He toured the united states in the first half of the 1800's to examine the American nation. He made an interesting observation about the ability of the American people to know the limits of the Federal government."

Nothing has made me admire the good sense and practical intelligence of the Americans more than the way they avoid the innumerable difficulties deriving from their federal Constitution. I have hardly ever met one of the common people in America who did not surprisingly and easily perceive which obligations derived from a law of Congress and which were based on the laws of his state and who, having distinguished the matters falling within the general prerogatives of the Union from those suitable to the local legislature, could not indicate the point where the competence of the federal courts commences and that of the state court ends.

"He explains in other parts of the book how involved the citizens were with their government, especially at the local level, and how well these relatively uneducated persons were capable of what he called advanced political thought. Do you think our 'common' citizen is like that today? While we're on that topic, you really should read the Federalist papers, which were op-ed pieces, and see how they compare to our op-ed pieces today."

"And you really think this problem is related to how we teach history?" Mary asks.

"Absolutely. I didn't read any of the federalist papers until I was graduated with my first four-year college degree. And as I read it, I remember thinking that when my teachers said they were teaching history, they were lying. Why did they keep this from me?"

"It's just about time to leave," Mary says looking at her watch. "Any other school subjects you want to discuss before we go?"

"Maybe just one more. Literature."

"Literature?"

"Yes, literature. When I see the crap they have kids reading today, even in supposed Gifted and Talented programs, I want to puke."

"You think it is that bad?"

"I do. Not only is the difficulty level insanely too easy, but the content is often banal and intellectually sterile. The teacher's almost never push the kids to really stretch their abilities."

"How do you do things?"

"Again, this is our personal home-schooling choice, but we decided that for our kids schooling they needed at least some of their reading to be such that they could only grasp 50-75% of the content."

"50%?!"

"Well, in the sense that they would grasp most of the story but maybe not get all the deeper meanings. And, yes, in some cases, they don't even get all of the story."

"That seems really frustrating."

"Maybe it's just our kids, but they have really thrived on it. We had our oldest two kids read The Odyssey last semester. They were 8 and 9 at the time. They loved it but I'm sure they didn't get more than 75% out of it. But what they did grasp, they thought was really cool. More to the point, it stretched the heck out of their brains, and the book won't seem daunting in the future.

And maybe our approach wouldn't work for every child, but it has worked for our children. With my kids reading books like The Odyssey, To Kill a Mockingbird, and so on in their elementary grades, there really isn't a public school reading program I can find that would be close to their levels."

Mary and Abby are quiet for a minute before Mary speaks again. "Look, Seth and Amy, it sounds like what you guys do is really great. And maybe parents like you can be amazing, fantastic teachers. But I don't think there is any way I could do what you do."

"Mary, I won't even ask you why you feel that way, because it won't be something I haven't heard before. You may feel inadequate and clueless, you may feel that you don't have the attention span to sit with your children for a couple of hours each day, you may feel like your children wouldn't listen to you, you may feel like you don't have the time, and/or you may just feel it would be too overwhelming to keep three kids at home for the entire day."

"Yeah, something like that."

"Let me wrap up this whole conversation and bring us back to the very beginning.

"First, I want you to just think about my point-of-view that it is dangerous to allow the government to force you to educate your kids according to their dictates.

"Second, I want you to think about my point-of-view that the people you have entrusted to teach your children are, on average, substandard.

"Third, I want you to think about my point-of-view that the curriculum is weak and there is an absence of critical thinking."

After waiting for Seth to continue, Mary finally probes him. "And then...?"

"Then," he goes on, "if you don't agree, you can go on as before.

"But, if you come to believe that the public schools are broken, you will be able to make a choice with your eyes wide open. You will be acting with knowledge instead of just being acted upon in ignorance.

"You may choose that home-schooling is something you should consider more strongly. It's not anywhere near as scary as it sounds and you need not do everything or anything the way we do it. We've found what works for us and our children, and the beauty of homeschooling is that you would get to explore and discover what works best for you and yours. There are so many resources on the Internet now, there is no shortage of materials. There are a lot of home-schoolers all around the country now, and we love to help each other out. Home-schooling parents form co-op's together, or in other ways pool resources and talents.

"Alternatively, you may decide that you just cannot home-school. Maybe that will be true. But you may decide that even though your children are in school, you are still the one primarily responsible for their education, and that from now on you will be more aggressive in dealing with the teachers. You will demand that they be accountable to you for how they are educating your child. You will visit their school every day if necessary arguing with teachers, administrators, and other petty bureaucrats about what they are or are not doing. And wherever they are failing, you will acknowledge it to your child and work at home to undo the damage. If the reading list is weak, you'll get your kids to the library and give them something more advanced. If the mathematics is brain dead, you'll pull out some books on math puzzles and go through them together. If the history is non-existent, then you'll make it a family project to go do some personal study.

"Finally, if you decide that the schools are broken, but you aren't going to do anything about it, you will be doing so by choice. You will have to take responsibility for your actions rather than just sticking your head in the sand and pretending everything is fine. That's what being a grown-up means, and that's what being a parent is all about. That probably sounds pretty harsh, but the truth is, a lot of parents think that they can just send their kids to school, leave everything in the hands of the teachers, and everything will be alright. That's not true, and I want to start making a point of saying so."

Again, the room is silent. Mary finally rises. "Well, you have given me a lot to think about. I hope we can talk about this more some time."

Abby rises too. "For my part, I think public schools are doing a great job and that you guys are pretty self-righteous."

"It's good that we can be frank with each other," Seth responds smiling. "I don't mean that sarcastically. I think this debate should move out into the open instead of being hidden behind politeness, sincere or insincere."

At the door, Mary turns back to Seth and Amy and asks, "Would you mind if I borrow that book by De Tocqueville?"

"Democracy in America? Sure. It's a great book. Kind of dense though."

Mary smiles as Seth hands her the book. "It's ok. Even if I only get 50-75% out of it, I'm sure it will give my brain a good stretch."