Freedom to Learn

This problem is enormous. Teachers don't understand the material they are teaching, and so they can't answer questions from intellectually curious students. Instead, they shut down that kind of thought.

Case in point:

Some years ago, my (now ex-) wife was involved in a "trivia night" fundraiser at her elementary school, and they wanted me on their "teacher team" to round out their knowledge. They had almost everything covered except some technology-related topics and I was an IT guy. In round four, my moment to shine arrived, as the category was "Math & Science" and one of the questions was, "give the first five digits of pi." I quickly said, "3.1415." The 9 teachers at the table ignored me and wrote down "22/7" on scrap paper and began to divide it out. I observed this quietly at first, assuming that 22/7ths gave the right answer for the first 5 digits, but it doesn't. It gives something like 3.1427. I said, "Whoops, that won't work." They ignored me and consulted among themselves, concluding that they had all done the division properly on 22/7ths out to five digits. I said, "That's not right, it's 3.1415."

They shot me insolent looks and one said, "We're math teachers. This is what the book says and this is what we're teaching the students." I said, "The TEXTBOOK in school says that?" "Yes, it does." I thought, "No wonder we graduate generations of ignorant boobs, the book is wrong." But the more I thought about it, the more I found it unlikely that the book contained this error. They wrote down "3.1427" or whatever on our answer sheet and I doggedly insisted that their answer was wrong. I explained that pi was equal to the ratio of a circle's circumference to its diameter, and after an uncertain pause, one of the teachers summoned this fact from her vague recollection of her lesson plan: "Pi is an irrational number, so it can't be a ratio." The other teachers at the table exchanged knowing glances and murmured with approval with that "A-ha! Gotcha!" look on their faces, as they recalled that same fact and found their colleague's logic unimpeachable.

I pointed out that an irrational number was a number that could not be expressed as a ratio of integers, and that 22/7 was a ratio of integers, and so it was THEM who were clearly wrong, because the circumference and diameter of a circle are real numbers, not integers. There was apparently some confusion since they weren't entirely sure what an integer was, but when one of them remembered she triumphantly told me that she just had her class full of 5th graders calculate the area of a circle whose diameter was 10, and 10 is an integer, so HA! At this point I realized I was in the company of idiots. My ex-wife, who was extremely argumentative with me most of the time, wisely kept quiet. She knew I was smarter than her cohorts and probably right.

The debate continued, and one of the teachers finally cut me off and said, "I'm sorry, what's your background?" I said, "I'm a software engineer." The teacher said, "Degree?" I said, "English." She smiled and said, "I can settle this." She called over a friend who was collecting answer sheets, and said to the friend, "Sally, this gentleman thinks pi is not equal to 22/7, what do you think?" Sally looked at me with sympathy and said, "Of course it is. I just read that in Joseph's book the other day." (Joseph is her son at the school). I insisted they were wrong and explained why, and while she looked confused and insecure upon hearing my explanation, she finally cut me off and said, "I'm sorry, but I'm a civil engineer, and math is my job. Pi is 22/7ths."

At this point I began to lose my patience. I said, "There is no way that textbook says it's 22/7ths. Somebody go get a copy." My wife volunteered to run to her classroom and retrieve the textbook.

Despite Sally's authority, I basically bullied the teachers into begrudgingly writing down my answer, and we turned it in. When the round finished, the MC announced the answer, and the answer was that pi is equal to 22/7ths, or 3.1427 or whatever. They all turned to me with furious indignation and practically screamed, "WE TOLD YOU!!!!!"

I gritted my teeth and said, "They. Are. WRONG. Who wrote the questions?" They said, "Sally!"

God save us.

A great murmur arose at a few other tables as well, and my wife returned with the text book. The teacher with whom I had been butting heads the most grabbed it, thumbed through to the area of a circle chapter, jabbed her finger at a sentence, and shoved the book across the table at me. The sentence said, "Pi is an irrational number approximately equal to 22/7ths." The teacher sat back, crossed her arms triumphantly, and said, "I hope they taught you to read with your English degree." I read it, and slid the book back across and said, "They also taught us to read the footnotes." As she read looked back at the page, the blood drained from her face. At the end of the sentence was a little "1" in superscript, and dutifully noted in the footnote were the first 20 digits of the actual value of pi.

Of which the first five are 3.1415.

As if on cue, the MC then said, "We've got a correction on the 'pi' question, apparently there's been confusion, but we will now be accepting 3.1415 as a correct answer as well." I argued that 3.1427 was NOT CORRECT and shouldn't be accepted, but I was advised by my wife to accept the victory, such as it was, and let it go. Our table sat in sullen silence for a few moments, with the open math book still open before us.

I couldn't help myself. I said, "So, you teach math to future civil engineers, huh?"

It was a funny story I used to enjoyed telling, until several years later when a bridge spontaneously collapsed in Minneapolis, killing a half dozen people.

My five children, all young adults now, all learned early and practical math from authentic, child-driven experiences. As pre-shcool children, they learned to count by setting the table (seven plates, seven forks, etc.); they sang counting somgs, counted their toys in "cleanup games." One son, at age two, was fascinated with the numbers on the mileage gauge in the car, watching from his car seat, as the numbers rolled in order. He soon learned to count to hundred. All five kids learned to read recipes, measurements, how to divide and how to double or triple a recipe's ingredients. They read maps and figured out the mileage (long before GPS). They all played various card games and board games that utilized numbers and/or reasoning skills -- Uno, Skip-bo, Pinochle. etc. As they became involved in local sports, they learned how to keep the scorebook and figure out out averages, etc. One son learned how to make a spreadsheet to keep track of his team's batting averages. They all kept their own ledgers in their bank savings accounts.
Math, when applied to resl-life situations, can be fun and interesting. The "book math" in public school often became boring and difficult at times.
I agree with the author's observations. When a child is motivated, then add in the "readiness" component for a particular math skill, he/ she will learn the math they need at that time.
How many of us. college-graduates, use all those 12- 16 years of math? "Math" time in the early grades can be better spent on ,any other practical situatios that involved common sense, logic, reasoning, and math skills.

my personal opinion on maths in school is that they keep changing the way they teach it. for example my daughter who is 10 is being taught long division sums a totally different way from my wife and myself this means when she is stuck on a long division question it is hard for us to help her without confusing her, i just wish they would teach maths and arithmetic the old way because it works upvc windows

The correct url for the Scott Kim talk is:

http://www.ted.com/talks/lang/eng/scott_kim_takes_apart_the_art_of_puzzl...

I disagree with Sue here
"...but I think you're too dismissive of schools. Many families need them, and I think they could be transformed if we respected teachers and kids more."
I don't think we can transform schools. Teachers, especially in the younger years are respected where i live, and they still don't do a good job of 'Éducating' the children. They do a great job, however of 'schooling' them. School was never set up to truly educate, just to give enough information to people so they could do what their employer asks them to. It never has and never will consistently grow young minds who can think for themselves, sure there are some every year, who despite being 'schooled' can still think for themselves, but this is by far the abnormal. More often than not this is an outcome of their home life, not their schooling.
I do agree however that some families need school, and 'schooling' is all they require of it. That's fine, just don't get the two ideals mixed up with each other. That's why we are unhappy with the "Education System" in our societies, we think it should be doing something it was never designed to do.
Accept it as it is, if you want to have truly educated people, don't send them to school, teach them at home, in the park, in the car, at the beach, at the shops, on a bike ride, give them meaning to what they are learning, and most importantly, give them space and time to contemplate and sort it all out in their own heads. Then and only then, there will be truly educated people in our society.

I would love to hear just what you know about Peter's personal anger.