Incorrect multiplication table

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

You probably know that I teach mathematics. And you have heard the opinion more than once that the level of mathematics education is falling.

When my children were in the second grade, I clearly understood why the level of mathematics education at school was falling. It is in the second grade, when laying the very foundation of mathematical education, such a giant irreplaceable hole appears, which cannot be supported by any crutches in the form of calculators.

Namely, the main problem is in the multiplication table. Take a look at the squared notebooks your school children have.

I went shopping for a long, long time in search of notebooks. And all the same, at all - this is the picture.

There are notebooks even worse (for high school students) on which there is no multiplication table, but there are a bunch of meaningless formulas.

Well, why is this notebook bad? The unsuspecting parent sees that the multiplication table is on the notebook. It seems that all my life there was a multiplication table on notebooks? What's wrong?

And the problem is that on the notebook NOT multiplication table.

The multiplication table, my dear readers, is this:

Sometimes the same table is even called the beautiful word "Pythagoras table". The top and left columns can be omitted, only the main rectangle.

First, there is a table. Secondly, it's interesting!

No child in their right mind would consider columnar examples.

Not a single child, no matter how brilliant he is, will be able to find interesting features and patterns in the examples written out.

Well, in general, when the teacher says: "learn the multiplication table", and the child does not even see the table in front of him, he immediately understands that mathematics is a science where ordinary things are called somehow differently and a lot is needed - a lot of cramming, but it's impossible to understand anything. And in general, it is necessary to do "as it is said," and not "as it makes sense."

Why is the "table" better?

Firstly, there is no garbage and information noise in the form of the left side of the examples.

Secondly, you can think about it. It is not even written anywhere that this multiplication is just a table.

Thirdly, if she is constantly at hand and the child constantly stumbles upon her, he willy-nilly begins to memorize these numbers. In particular, he will never answer the question "seven eight" with 55 - after all, the number 55 is not in the table at all and has never been!

Only children with abnormal memory are able to memorize columns of examples. In the "table" you need to memorize much less.

In addition, the child automatically searches for patterns. And he himself finds them. Even such patterns are found by children who do not yet know how to multiply.

For example: numbers symmetrical about the diagonal are equal. You see, the human brain is simply set to look for symmetry, and if it finds and notices it, it is very happy. And what does it mean? This means that the permutation of the places of the factors does not change the product (or that multiplication is commutative, in simpler terms).

You see, the child notices it himself! And what a person invented himself, he will remember forever, in contrast to what he memorized or he was told.

Remember your high school math exam? You forgot all the theorems of the course, except for the one that you got, and you had to prove it to the evil teacher! Well, that's if you didn't cheat, of course. (I am exaggerating, but this is almost always close to the truth).

And then the child sees that it is not possible to learn the whole table, but only half. If we already know the line for multiplying by 3, then we do not need to memorize "eight by three", but it is enough to remember "three by eight". Already half the work.

And besides, it is very important that your brain does not accept dry information in the form of some incomprehensible columns of examples, but thinks and analyzes. Those. trains.

In addition to the commutativity of multiplication, one can observe, for example, another remarkable fact. If you poke at any number and draw a rectangle from the beginning of the table to this number, then the number of cells in the rectangle is your number.

And here multiplication already acquires a deeper meaning than just an abbreviated notation of several identical terms. It makes sense for geometry - the area of a rectangle is equal to the product of its sides)

And you have no idea how much easier it is to share with such a table !!!

In short, if your child is in the second grade, print him such a correct multiplication table. Hang a large one on the wall so that he looks at it when he does his homework or sits at the computer. Or even what foolishness suffers. And print and laminate a small one for him (or write on cardboard). Let him carry her to school with him, and just keep it conveniently at hand. (it does not hurt to select the squares diagonally on such a table so that you can see better)

My children have - like this. And it really helped them in the second grade and still helps a lot in math lessons.

Here, honestly, the average score in mathematics will immediately increase, and the child will stop whining that mathematics is stupid. And in addition, in the future it will be easier for your child too. He will understand that he needs to wiggle his brains, not cram. And little that he will understand, he will also learn to do it.

And I repeat: there is nothing wrong with the column examples. And the amount of information they contain is the same as in the "table". But there is nothing good in such examples either. This is informational rubbish, from which you cannot find what you need at once.