Let’s assume that math is already going hard, creaking, in a child’s elementary school. It’s hard and boring to add and subtract, let alone anything more complicated. New topics just won’t sink in. Writer and mother of three Ksenia Buksha tells you from her own experience how to help your child learn math and how teaching area of a triangle.

Breaking Down Difficulties

There are no kids in grades 1-5 who can’t do math. But there are children with specific difficulties that can and should be overcome. Let’s think about why a child has difficulty in math.

Here are the possible options or combinations of options.

Doesn’t count well, doesn’t have counting skills. Not very familiar with numbers.
Can’t go into the essence of the task set, has difficulty understanding what to do. He/she tries all the variants (“Is this wrong? Then I will try to divide”, “Three times as much – do we need plus or minus here?”).
Learns a template solution, but cannot refine it. Faced with the slightest change of conditions, falls into a stupor.
Unable to read complex texts. As a result, does not understand either the rules or the text of the task. If things are explained to him on the fingers, he is able to solve them right away.
She does not have the concepts in her head. He hardly understands them and quickly forgets. Such a child can hear an explanation a hundred times of what “X” (the unknown) is, but still not understand it.
The visual representational skill is not developed. He or she cannot imagine, draw a schematic picture or “see in his or her mind”.
Short attention span: understands everything, but makes a lot of mistakes, especially in the long complex examples.
As you can see, math breaks down into many different skills. Once we figure out what the problem is, we can solve it. I apologize in advance to teachers and guidance counselors: I’m just a parent, and my thoughts on this are just a private opinion, although I try to justify it.

Waiting for the ability to think abstractly to mature

A neurotypical child’s brain does not mature to abstract and generalize immediately. For some it happens earlier and for others later. For example, not all children can relate number and quantity. For very many even in the 2-3rd grade, there are only “15 apples”, and just “15” is not there. Some of them need to be told about cognates word meaning.

At the same time, they somehow get used to operating with numbers, and the gap in basic understanding is not very noticeable until it comes to a little more complicated things. For example, it is difficult for them to understand why it can not be “one and a half” in the answer to the question “How many diggers? And when they start with percentages or speed and distance problems, it gets really hard.

It’s worth getting back to the specifics. Perhaps to understand fractions, you need to say “watermelons in the numerator, boys in the denominator; 21 watermelons went to 42 boys – each had half a watermelon. Even in fifth grade, almost all concepts can still be grounded to specifics.

Developing Counting Skills

Just learning to count is boring. All kinds of number games can help us. For starters – difficult walkers with 2-3 dice (when one move maximum – 18 points, not 6), then – a variety of games in dice, where you have to count points.

The simplest game I know is “one”: players take turns rolling one die (or two, or three), trying to get to a hundred points. The series is interrupted when a player rolls at least one 1, in which case his points for the series are burned, and you have to be smart to stop in time.

I highly recommend dice poker. This game has a series of combinations, each of which must be discarded in three tries. These attempts can be accumulated. Players take turns making the moves; the one who completes all the combinations first wins. In addition to the simple skill of folding points, poker gradually develops a subtle understanding of randomness and probability, calculated risk and chance. Even a six- or seven-year-old can learn to play this kind of poker.

To practice division and multiplication, my daughter and I talked about numbers as “relatives.” For example, number 72 has a very large “family”: it has “babies” 24 and 36 and “grandchildren” – 2, 3, 4, 6, 12, 18. But number 37 has no “family”, it is simple. But if you “marry” it with another “single” – 41, they get 78 together, now you can “have children and grandchildren. It’s a good way to learn the multiplication table.

Learning to see and visually summarize the problem

In order to be good at schematizing, you need to be able to highlight exactly what is important to the problem, and represent it schematically in a picture. First we learn to emphasize the main thing. These are the famous “what’s extra?” games, which can also have several answers. Watermelon, stork, apricot, grape-what’s extra? It depends on the reason.

The Peterson textbook has wonderful problems cluttered with a lot of unnecessary data or deprived of necessary conditions. In the task, the author asks you to find and highlight only those conditions that are needed to solve it, and if they are not – indicate what is missing. Having learned to see the problem, you can move on to schematization.

Many children don’t understand why they have to draw schemes for tasks and why it is easier. It is because these schemes are ready-made. But on what principle are they built? Why, for example, it doesn’t matter how long the train is, if it goes from A to B? How do you draw “3 hours”? And “all the pears planted by the boys”?

You can draw diagrams of different tasks together, and then offer your child to come up with similar ones. There are such tasks in the textbooks as well, but there are few of them. For some, this difficulty in general determines the whole relationship with mathematics, and in general with the ordering of data, abstraction, generalization, search for solutions.

Sharpening the logic.

Logic is one of the tools everyone needs. There are no people who have no aptitude for logic; there are those who don’t have it. It’s like knowing how to wield a screwdriver: anyone with hands can learn. You can judge for yourself how iron-fisted your logic is. I love this wonderful test.

A person with logic can’t be fuddled by any propaganda or advertising, he can’t be confused by an unscrupulous bank, and he’s much better at navigating the world around him.

With children you can start with simple syllogisms, which sometimes sound ridiculous, but lead to an understanding of very important things. For example, after hearing the maxim “boys don’t cry” from someone, a child might clarify, “some or all?”

If children don’t go through the concept of set, it is worthwhile to draw “circles” together with them (it is not necessary to introduce all the concepts at once) and to solve corresponding problems: here are the boys, here are the cats, and here are the ones named Vasya. Where are the boys whose name is not Vasya? Where are the girls? Where’s the cat Barsik?

Developing our imagination

Imagination is necessary for everything to do with math and logic. (I don’t even write “oddly enough,” because it’s not odd at all.) Especially the ability to think in images.

I really like the game where parent and child take turns asking each other “graphic riddles” that have no exact answer. Each draws a series of obscure geometric shapes or combinations thereof (a dot in a triangle, lightning and a circle, several circles, tangents…), and the other completes them so that a picture emerges. The wittier the solution, the more fun both players have.

There are many ancient and new games in which you need to add patterns of parts and fragments of the egg (a columbo egg), a square, differently colored faces of the cube ( “Build a pattern”). There are also three-dimensional sets, such as “Pentamino. We are not talking about doing tasks, although all of these sets can be used as such, but it is about creativity with the available details and the ability to see an image.

And you can also cut out the snowflakes, finish drawing symmetrical butterflies and little men, come up with ciphers, draw mazes and maps. All this is the development of mathematical imagination.

Teaching a child to deduce what exactly he doesn’t understand (metacognition)

I’ve written about it more than once, both in connection with math and with essays. In a nutshell, metacognition is the ability to “understand how I think,” to “know exactly what I don’t know,” to be aware of one’s own thought process. This is what is almost never taught at school, and sometimes even spoils an already developed ability. It is assumed, after all, that there are simple and complex ways of solving this or that problem. Often there are, but sometimes it’s much more valuable to be able to go on your own and check yourself out step by step: “Is this the way to do it? Am I right?”

Collaborative reasoning (and I don’t mean math) is valuable both because it brings the child and the parent closer together, and because we show how the thinking process goes. It doesn’t have to be smooth and automatic. It has dead ends, unexpected twists and turns. “Our initial assumption is wrong, which means you have to take not Road 1, but Road 2.” By the way, this will also come in handy in school math when you need to understand the proofs of theorems. After all, it’s only good to remember what you went through with your own mind, when you can repeat someone else’s reasoning and know every turn in it.