20160514 TAKE AND GIVE:

Sorry, another big scare.

The British edition of Huffington Post reported an Internet sensation. I feel free to quote because the article mostly quotes the sources. Here it is, complete with the headline.

Year 2 SATs: Maths Question Aimed At Six And Seven-Year-Olds Is Completely Stumping Parents

Parents are claiming it’s too hard for their kids.

Parents are puzzled over a maths question that is aimed at Year 2 pupils taking their SATs exams.

Mum Louise Bloxham tweeted a photo of the task that involved working out how many people were on a train.

The question states: “There were some people on a train. 19 people get off the train at the first stop. 17 people get on the train.

“Now there are 63 people on the train. How many people were on the train to begin with?”

I gave the problem to TLG. In the middle of her 7th year, she is not a British 2nd year student of math, she is an American kindergartener learning to count to 20. Immediately, she started subtracting 17 from 63. Then she added 19. She messed up the computations - OK, there were the reasons for this - but her thinking was correct.

The parents' tweets quoted by HuffPost drew a familiar picture. In the age of free mandatory education, the majority of citizen perceive learning as a punishment. They hate school, then math, then - and most of all - algebra. How dare they ask our kiddies an algebra question?

No doubt, school is reaping what it sow, and it could not care less. Mandatory (or, more correctly, compulsory) education is a monopoly run on artificial sweeteners and fear.

Yet there is a math lesson in this story. Everybody assumed that the problem required equation, and equation is much-loathed algebra.

I had mentioned several times in this blog that I do not teach TLG equations. She simply knows how to solve them because she learned the operations of increment and decrement using X-bag.

Unlike addition and subtraction, increment and decrement are reversible, and not only conceptually so. I taught TLG the fully reversible algorithm of addition of shnumbers, on which she built her numerical carrying and borrowing skills.

Once TLG had gotten the problem, she started reversing the operations. This understanding was woven into the fabric of her mental arithmetic.

Increment and decrement are very useful for teaching. I will invoke them again and again.

I created this blog on 5/11/2016. Currently, I am uploading the preexisting content from my website at http://defmath.com.

20160501 THE BIG SCARE:

How I discovered unteaching.

The common method of teaching arithmetic is demotivating and debilitating. Guess, when schools will be allowed to teach children to walk, they will do it one step a year. I'll probably live to see how exciting it will be.

Not being able to stand the educational misery, I taught several first graders long numbers and addition. I was afraid to do it in the US, so I allowed the American school to make a math hater out of my oldest American child. With my second American child I did it again, and it helped.

The second child was seriously distressed. Looking for the least traumatic method, I borrowed a toy from my lessons with her little sister — the one I call the little girl or TLG. The toy worked surprisingly well, and soon I became using it to teach a four years old elementary math.

I am not an ambitious parent, and I had other things to do. I just fell into path dependence. I started playing with TLG when she was learning to speak. I had to keep teaching her after she turned four. My experience with her toy and her big sister suggested the most obvious way to go.

With TLG, my messy DYI teaching grew into a solid method. I started telling this story in SHNUMBERS, but found it too long for a demo. Eventually, I created STEREO LEARNING to tell it through animation.

The algorithms of long positional counting and addition shown in STEREO LEARNIG are standard for decimal counting frames. Every American school and many families have them and think they are just toys.

Like all abaci, the decimal counting frames gave rise to extremely popular and robust information technology. They coexisted with calculations on paper and easily outlived mechanical calculators. I suspect, in some countries people still use them.

For several important reasons, I would not rely on counting frames for teaching young kids positional arithmetic. Fortunately, I realized that another very common toy - a pegboard - could do the job much better.

With TLG's big sister, I did not pay attention to numeral words and phrases. I thought they were more English than math. TLG wanted to learn them and enjoyed this knowledge. To her it was empowering.

It so happened that, by the time TLG entered preschool, she could name and handle billions and trillions. She did not remember the bigger names. Neither did I.

With two American schoolchildren at home, I had to learn a thing or two about American education. I knew that cognitive development of young Americans was standardized in several contradicting ways, and that school was enforcing conformity to the standards. Understandably, teachers were not very eager to pull forward the students who were falling behind. With TLG I learned that teachers were very good at smothering the knowledge that should not be there.

Once TLG came home from preschool and proudly told me that she learned to count to 20. I asked her if she could count to anything bigger. She said she could not. I asked her what number goes after 20. She said it's 21, took a pencil and happily added up two 10 digits numbers. She loved doing this too.

I did not pay attention until this happened again. And again.

TLG's narratives were becoming elaborate. I talked to her, demonstrated to her her abilities and asked her to remember that she could count to any number. Sadly, I started noticing her emerging fear of big quantities.

Once again, TLG came home and told me that she knew how to count to 40. She said her big sister - a third grader as far as I remember - was allowed to count to one thousand, and her big brother must be able to count to one million.

The power of American educators appeared unsurmountable. I could not believe how easily they manipulated TLG. I talked to her again, very bluntly. Hadn't I done this, America would win another standard mind.

Miraculously, TLG understood that school was not teaching and should not be taken seriously. From time to time, I ask her what is the biggest number she can count to. She confirms that there is no limit to counting.

I wish I could tell that TLG is now free from fear. In the background, the school keeps doing its job. The next teacher is coming up soon. From time to time, I have to remind TLG that usually the bigger numbers are just more of the same.

I've seen four American preschools. Two of them were private and pretty benign. LIke, you know, we are not a garage daycare, he rent the premises, we hire the teachers, we are an academy, no less. Pay us more. We teach your children colors and shapes. Where else can they learn them? Not that I cared about colors and shapes, but I wanted my Russian kids to grow Americans.

TLG had attended two preschools closely affiliated with the local elementary school, and they were different. Apparently, they were charged with supplying standardized human material, and it was worse than I thought. Only the kindergarten started teaching the numbers to 20.