You probably know that I’m teaching math. And more than once you heard the opinion that the level of mathematical education is falling.
That’s when my children studied in the second grade, I clearly understood why the level of mathematical education in the school is falling. It is in the second grade when laying the very foundations of mathematical education, there is such a giant irreplaceable hole that you can not support by any crutches in the form of calculators.
Namely, the main problem is in the multiplication table. Look at the notebook in the cage that your schoolchildren have.
I went shopping for a 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 lot of meaningless formulas.
Well, so what is this notebook is bad? The unsuspecting parent sees that the multiplication table is on the notebook. Like, all my life on the notebooks was a multiplication table? What is not so?
And the problem is just that on the notebook is NOT a 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 may not be taken, just the basic rectangle.
First, it is a table. Secondly, it’s interesting!
No child in their right mind will consider the examples written out by the columns.
No child, no matter how brilliant he may be, can not find in the examples written out interesting chips and patterns.
Well, in general, when the teacher says, “Learn the multiplication table,” and the child does not even see the table before him-he immediately understands that mathematics is such a science where ordinary things are called somehow different and need a lot cramming, but nothing can be understood. And in general, it is necessary to do “as it is said”, and not “as it makes sense.”
Why is the “table” better?
First, there is no debris and noisy information in the form of the left part of the examples.
Secondly, you can think about it. It does not even say anywhere that this multiplication is just a table.
Thirdly, if it is constantly at hand and the child constantly comes across her, he willy-nilly begins to remember these numbers. In particular, the question “seven multiply eight”, he will never answer 55 – in fact the number 55 is not in the table and won’t be!
Only children with abnormal memory are able to remember the columns of examples. In the “table” you need to remember much less.
In addition, the child automatically searches for regularities. And he-she finds them him/herself. Even such regularities are found by children who are not yet able to multiply.
For example: numbers that are symmetric with respect to the diagonal are equal. You see, the human brain is just set to look for symmetry, and if it finds it and notices it – it’s very happy. And what does it mean? This means that the product does not change from the rearrangement of the places of the factors (or that multiplication is commutative, in simpler terms).
You see, the child notices it himself! And the fact that the person came up with himself, he will remember forever, unlike what he/she memorized or told him.
Do you remember your math examination? 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 did not write off, of course. (I exaggerate, but almost always it’s close to the truth).
And then the child sees that it is possible not to teach 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 it’s enough to recall “three by eight”. Already half the work.
And besides, it is very important that your brain does not take dry information in the form of some incomprehensible columns of examples, but thinks and analyzes.
In addition to the commutativity of multiplication one can notice, for example, another such remarkable fact. If you poke in 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 then multiplication already gets a deeper meaning than just a shortened record of several identical terms. There is also a sense for geometry – the area of a rectangle is equal to the product of its sides.
And you can not imagine how much easier to share with such a table!
In short, if your child is in the second grade, print out to him such a correct multiplication table. Hang a big one on the wall so that he would look at it when he does the lessons or sits at the computer. Or whatever he does. And print and laminate it a little (or write on cardboard). Let him carry it to school, and just conveniently keeps at hand
My children have one. And it really helped them in the second grade and still very much helps in the lessons of mathematics.
Here, honestly, immediately the average score on mathematics will increase, and the child will stop whining, that mathematics is dull. And in addition, in the future math will also be easier for your child. He will understand that you have to move your brains, and not to cram. And little that he will understand, he will also learn to do it.
And I repeat: in the examples, nothing bad is in the columns. And the amount of information in them is the same as in the “table”. But there is nothing good in such examples. This is information garbage, from which you can not find the right one yet.
Author: Kukina Ekaterina