Multiplication table (5 photos)

You have often heard the opinion that the level of mathematics education is falling. In the second grade, when laying the very foundation of mathematical education, the main problem arises - in the multiplication table. Look at the checkered notebooks that your schoolchildren have, all of them - this is the picture.

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

Well, why is this notebook bad? An unsuspecting parent sees that there is a multiplication table on the notebook. It seems like you’ve had multiplication tables on your notebooks all your life? What's wrong?

But the problem is that the notebook does NOT contain the multiplication table.

The multiplication table, my dear readers, is this:

Sometimes this same table is even called the beautiful word “Pythagorean table”. You don't have to take the top and left columns, just the main rectangle.

Firstly, this is a table. Secondly, she is interesting!

No child in his right mind would look at examples written out in columns.

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

Well, in general, when the teacher says: “learn the multiplication table,” and the child doesn’t even see the table in front of him, he immediately understands that mathematics is a science where ordinary things are named somehow differently and you need a lot - a lot of cramming, but it’s impossible to understand anything. And in general, we must do it “as it is said,” and not “as it makes sense.”

Why is “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’s not even written anywhere that this multiplication is just a table.

Thirdly, if it is always at hand and the child constantly bumps into it, he willy-nilly begins to remember these numbers. In particular, he will never answer the question “seven eight” with 55 - after all, the number 55 is not and never was in the table!

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

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

For example: numbers that are symmetrical relative to the diagonal are equal. You see, the human brain is simply tuned to look for symmetry, and if it finds and notices it, it is very happy. And what does it mean? This means that the product does not change when the factors are rearranged (or that multiplication is commutative, to put it more simply).

You see, the child notices this himself! And what a person came up with himself, he will remember forever, unlike what he memorized or was told.

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

And then the child sees that he can’t learn the whole table, but only half. If we already know the line of multiplication by 3, then we do not need to remember “eight by three,” but just 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. is training.

In addition to the commutativity of multiplication, one can notice, for example, another remarkable fact. If you point 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 takes on a deeper meaning than just an abbreviated notation of several identical terms. It also makes sense for geometry - the area of a rectangle is equal to the product of its sides)

You have no idea how much easier it is to divide with such a table!!!

In short, if your child is in second grade, print out this correct multiplication table for him. Hang a big one on the wall so he can look at it when he does his homework or sits at the computer. Or suffers from some other stupidity. And print and laminate a small one for him (or write on cardstock). Let him carry it to school with him, and just keep it conveniently at hand. (it wouldn’t hurt to highlight the squares on such a table diagonally to make it easier to see)

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

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

And I repeat: there is nothing wrong with the examples in columns. 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 garbage, from which you will not be able to find what you need right away.