Teaching children math must be one of the great challenges that teachers face in their daily mission of acting as a belt of knowledge transmission. And is that explaining mathematics requires skills, abilities and knowledge so that the children's brain is able to understand and use the abstract language, numbers, letters and symbols, which are used in mathematics.
For example, the other day he asked us for little help for a math problem that said, more or less, like this:
A tomato manufacturer has 180 kilograms (kg) of tomatoes and uses 36 bags of 5 kg to transport them all. How many bags would you have to use if the bags were 15 kg?
Apparently in class they still don't know how to divide by two figures so to solve the problem we start to make a table to help you think and imagine, That capacity for abstraction! What would happen to the bags if they triple the capacity.
And in the three-row table with two columns we write in the first two cells the 180 kg of the total tomatoes. Below we write the capacity of the bags, 5 kg in one cell, and 15 kg in the next. In the last row we draw the number of bags needed, in the first cell, the 36 bags and in the second, in the second we started thinking.
And that's where it shows that Mathematics requires abstraction, effort, thought, dedication, concentration and strength so as not to despair on how to solve the problem. I read the other day an interview with Cecilia Christiansen, the best math teacher in Sweden 2011, that children like to do and do and that over time understand what they do. While girls want to know and know first before doing. In both cases Professor Cecilia said that all children come to understand the concepts of mathematics.
What we did in this problem was to try to explain with a drawing that if the capacity of the bag was increased, the number of tomatoes that could be put in each bag would increase so that fewer bags would be necessary. In this specific case, one third of the number of bags.
So what had to be done was to divide the initial number of bags by three, a division of the simplest and that we did not take anything to do. Thus we fill the last cell with the number 12 which is the total number of 15 kg bags to be used to carry the 180 tomatoes.
Apparently I had to explain the problem in class to the child and told what she had learned, practically by heart, and what we used to illustrate this article:
Tripling the capacity of the bag ensures that one third of the initial number of bags is used
The teacher congratulated him, although I fear that he realized that he had acquired too much abstraction for a nine-year-old girl.
And is that teaching mathematics requires that children increase their capacity for abstraction and that is achieved by repeating, explaining, working, striving and surpassing. And no, now we can't give up knowing math and we have to go beyond teaching multiplication tables in a memorial way. It is a subject, mathematics, which should not be ashamed to know but not to know, know and handle it fluently.
