Mathematics in primary school is not just numbers. It is the foundation on which logic, engineering, and even artificial intelligence stand. If a child does not understand what a number is or does not learn the multiplication table in third grade, they will struggle their whole life. But how to make sure that a child does not hate mathematics but loves it? Let's figure it out with examples, games, and the horrors of Soviet textbooks.

What is studied in 1-4 grades

The primary school mathematics curriculum is standard. In first grade — numbers, counting to 10, addition and subtraction within this decade. One-step problems. In second grade — counting to 100, crossing over the decade, multiplication table for 2-5, two-step problems, concepts of "perimeter" and "area" of simple figures.

In third grade — the entire multiplication table, division with remainder, multiplication and division of multi-digit numbers by a single-digit number, fractions (initial concepts), units of time, length, mass, speed. In fourth grade — multi-digit numbers (up to a million), operations with them, equations, fractions (comparison, addition and subtraction with the same denominators), percentages (beginning), problems of movement in pursuit and head-on.

It seems simple. But it is in primary school that algorithmic thinking is laid. If a child does not understand how multiplication is constructed, they will never understand how an integral works. Therefore, you cannot ignore "This is just simple."

Why do children hate mathematics at school

It's not the children who hate. Children love to count when it's about candies or toys. They hate the method of presentation. Boring examples in columns where you have to rewrite 30 identical actions. A teacher with a harsh voice who scolds for a mistake. The fear of "not understanding correctly." A perfect storm.

The second reason is parents who press. "You must solve it for five," "look at your neighbor, she managed, but you didn't." The child begins to associate mathematics with danger and shame. The brain blocks logic to protect itself.

The third reason is the lack of visual aids. The textbook says: "3 + 5 = 8." But what are these numbers? Three apples and five pears are already more interesting. But teachers often save time on pictures.

The fourth reason is the transition through the decade in second grade. This is a stumbling block. The child does not understand why 27 + 5 = 32. Instead of explaining it on counting sticks, teachers force them to simply memorize the algorithm. And children become dumber.

How to explain addition and subtraction with crossing over the decade

The secret is in counting with sticks or buttons. Take 27 buttons. Count 10, tie a rubber band — this is a decade. Tie another 10 — the second decade. There are 7 buttons left. Now add 5 buttons. Add 3 to 7 to make another decade. Now we have 3 decades and a remainder of 4 buttons. 27+5=32. The child sees. Understands. Remembers forever.

You can use a mind map: draw a line from 0 to 100. Go 5 steps to the right from 27. 28, 29, 30, 31, 32. Then train without a drawing.

For subtraction — reverse counting. 32 - 5 = 27. Go 5 steps to the left from 32. 31, 30, 29, 28, 27.

The main thing is not to rush. One topic can take a week. Better slowly but with understanding than quickly with memorization.

Multiplication table: how to learn without tears

Piaget's table is a curse of primary school. But there are ways to make it easier. The first is visualization. Draw a square 10x10. Write the product in each cell. The child sees symmetry. For example, 5x4 and 4x5 are the same, this reduces the amount of memorization by half.

The second is poetry. "Three on three — nine, this must be checked by everyone." "Twice two — four, this is known in the whole world." You can come up with your own.

The third is cards. On one side is the example "3x4", on the other side is the answer 12. The child checks themselves. Game: who will collect 10 cards faster.

The fourth is songs. There are plenty of multiplication tables in rap on YouTube. The child absorbs rhythmically.

The fifth is object counting. 3x4 is three times taking four candies. The child counts. It's delicious and understandable.

Important: do not learn the entire table at once, but in blocks. First on 2, then on 3, then on 4. A break of one to two days between blocks. And repetition: mix old examples with new ones.

Fractions in primary school: when to start

In first grade, fractions are not discussed. But in second-third grade, you can introduce the concept of half (1/2) and a quarter (1/4) on a pizza or cake. Cut a circle into 2 equal parts — each half. On 4 — a quarter. The child understands at once.

By fourth grade, fractions with different denominators are introduced for comparison. Again, in practice: two-thirds or three-quarters of a cake — which is bigger? Cut circles with different denominators, overlay transparent films. It's visible with the eyes.

Addition of fractions with the same denominators is the addition of pieces of the same cake. 1/4 + 2/4 = 3/4. Easy. For different denominators in fourth grade, only the simplest cases (1/2+1/4=3/4) are given with the help of a drawing.

Do not require from a fourth grader to abstractly reduce to a common denominator. This will kill love.

Logic problems: how to develop thinking

Mathematics in primary school is not just counting, but also logic. Problems of the type "Three sparrows were sitting on one branch, two flew in, then one flew away. How many are left?" develop the sequence of actions. It's better to have problems with extra data so that the child learns to filter out unnecessary. "There are 3 apples, 2 pears, and 1 banana in a vase. Nastya ate 2 apples. How many fruits are left?" — extra about pears and bananas.

Logic puzzles with a star: "How many ends are on 3 and a half sticks?". Or "There are 10 sticks on the table. Two boys take turns taking 1 or 2 sticks. Who will win?". This is already strategy.

The best way is chess, checkers, Sudoku for children. Do not impose, but play together. A math circle is also good, but not before 8 years old.

Typical mistakes of parents and teachers

Mistake number one: shout "You don't understand? This is elementary!". For a child, it is not elementary. Their brain has not yet formed neural connections. Your "elementary" is the result of 30 years of practice.

Mistake number two: forcing to solve many identical examples. Better 5 times with explanation than 50 automatically. Automation will come later.

Mistake number three: comparing with others. "Petja has already solved it, but you haven't." Compare only with yourself: "Yesterday you made a mistake in this, but today — not, good job."

Mistake number four: ignoring mistakes. A mistake is not a failure, but a hint where there is a gap. Analyze the mistake together. Ask: "What do you think, why did it come out 7 instead of 8? Let's recalculate."

Mistake number five: pressing time. "Solve it in 5 minutes." Anxiety kills thinking processes. Give as much as needed, but don't drag on.

Mistake number six: making mathematics a routine. Don't do examples after school if the child is tired. Better to play "store" (where change has to be counted). Or weigh fruits and compare the weight.

Games and applications for mathematics

On paper: "Battlefield" with coordinates (develops the coordinate system). "Tank" on a checkered field (movement along vectors). "Mathematical bingo" — a number falls out, you close the answer.

Outdoors: counting cars, clouds, steps. Measuring distance with steps. Comparing the height of trees. Weighing stones on homemade scales.

In the kitchen: recipes — half a cup of flour, a quarter of a teaspoon of salt. Portions: you need to treat 5 guests, and 15 cookies — how many each?

Applications (without links): "Mathematics and Numbers for Children", "Counting App", "Multiplication Table in Games". The main thing is to dose it, not more than 20 minutes a day.

Important: no applications before bedtime. The brain should switch.

What to do if a child is mathematically incompetent

True mathematical inability (dyscalculia) occurs in 3-7 percent of children. This is not laziness, this is a brain feature. Symptoms: cannot understand that 4 is greater than 3, even if shown buttons. Confuses the numbers 6 and 9, 2 and 5 constantly. Cannot count objects to 10, even counting with fingers. Does not memorize the multiplication table, despite long training.

If this is your case, go to a neuropsychologist and a child psychiatrist. Dyscalculia cannot be cured, but it can be corrected. The child will be given a lenient program, possibly released from the second foreign language. Do not blame yourself and him. This is not a sin. This is a diagnosis.

But more often, "inability" is the result of intimidation or poor teaching. Change teachers, change the approach, study with a tutor who uses games. The result may surprise.

Mathematics and life: why it is needed for a child

They will grow up — they will count their salary, taxes, discounts in stores. Take a loan or not. Compare prices per kilogram. Understand whether the "two for the price of one" promotion is profitable. But this is not the main thing. Mathematics teaches structured thinking. Do not panic in front of a difficult task, but break it down into parts. Look for patterns. Check yourself. These are skills for life.

Therefore, do not say "mathematics is boring". Say "mathematics is magic that helps predict the future". And the child will believe it. And love it.
© elibrary.org.uk

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