Teaching children to solve maths problems is a matter for the teacher, but even parents should not stand aside if their child is “hampered” in this matter. One math textbook will not be full. After all, if you teach a child to solve problems independently in grades 1–3, then he will click like seeds not only in math, but also in physics, chemistry, geometry, etc. And most importantly, this skill will be useful to a child in life!
In the article How to teach a child math we wrote in detail what 4 parts each task consists of and what needs to be done first of all, so that the child will understand what they want from him and how to answer the question of the task. Having understood the problem solving algorithm, the child will be able to solve almost any task on his own, even though they all seem so different.
The main types of math problems: a brief summary
Small educational program,
Consider the most common types of tasks in primary school.
1. Simple addition and subtraction tasks
This group includes several tasks, but for all there are general recommendations:
- Solved in one action.
- Sometimes it is convenient to make an equation.
- On their example, the child should learn how to perform a short record.
- If a short condition is not enough, draw a picture. If the drawing did not help, show on specific objects and perform actions with them.
- Accurately understand that “+” is to add, increase, and “-” to reduce, subtract, subtract.
- Well remember the components of arithmetic operations:
addend + addend = sumdecremented – subtracted = difference
- Understand the difference between the words “became” and “left.” Clearly understand what it means to “on … less,” “on … more.”
- It is important to understand and remember: in order to find ON, HOW MUCH a single number is more or less than another, it is necessary to subtract less from a larger number.
- It is important to understand and remember: to find an unknown addend, you need to subtract the known addend from the sum.
- It is important to understand and remember: in order to find the unknown diminishing, add the difference to the deductible.
- It is important to understand and remember: to find the unknown deductible, you need to subtract the difference from the value to be reduced.
Tasks with an indirect question
These are the most insidious tasks from this group. Read the condition carefully and see why.
In the parking lot at the first entrance of 7 cars. This is 2 cars more than in the parking lot at the second entrance. how many cars parked at the second entrance.
2. Composite addition and subtraction tasks
These tasks are solved by two or more actions.
There are several solutions:
- on actions with explanations;
- on actions with questions;
In solving such problems, the main thing is:
- find the most important and make a brief record;
- decompose this task into several simple ones and draw up a plan for solving it;
- remember the main thing: according to two data we find the third.
3. Tasks on understanding the meaning of multiplication and division actions
- It is important to remember the names of the components of actions and understand their meaning:
1st factor x 2nd factor = productdivisible: divisor = quotient
- The child must understand that the 1st factor shows WHAT the number repeats and the 2nd factor indicates that it repeats ONCE.
This is very important for correct recording in tasks, otherwise it will be nonsense.
You can find tips on how to teach your child to consciously relate to multiplication and division in our article How to teach children to quickly count: math to school. If you have problems with solving multiplication problems, hand it back a little, fix the awareness of this arithmetic operation.
4. Simple multiplication and division problems
- It is very important to understand and remember the difference “in”, “on”.
“How many times” or “how much”? The preposition “on” is addition or subtraction, and “in” is multiplication or division.
- It is important to understand and remember: to find out how many times one number is greater or less than another, you need to divide a larger number into a smaller one.
5. Composite tasks for all 4 arithmetic operations
6. Tasks for price, quantity, cost
7. Tasks for movement
This is a separate broad topic, back to it later.
Typical errors in solving problems
Error number 1. The child inattentively read the condition of the problem.
It often happens that errors arise from inattention. So often happens in problems with an indirect question. The child looks at the numbers, everything seems logical, but … not true.
For example: “Masha has 8 candies, which is 2 less than Katya’s. How many candies do Katya have?
The child sees “2 less” and makes a “logical” conclusion that we must take away. You can take away from a large number
How to fix the error. Immediately deal with the condition, will help a brief record.
Error number 2. The child made a mistake in the decision.
When there are several unknowns in the problem, the decision is made difficult, it is required to perform not one action, but to invent a whole chain of reasoning.
How to fix the error. To begin with, we will determine what data we lack. We decide on the actions. We find the necessary numbers (we remember the rule: we find the third by the two unknowns), we substitute them and answer the question of the problem.
Error number 3. Wrong record of the answer.
Often the child writes the wrong explanation.
How to fix the error. It is necessary to carefully read the question of the problem. Understand once and for all that the answer begins with a number, and then we write what needs to be found (we rewrite the wording of the problem question).
Creative approach to solving problems
- Teach your child to reason.
- Create tasks with extra or missing data.
Let the child himself cross out the extra, those data that do not affect the decision.
- Give a condition, and let the child himself come up with an answer.
- Let the child himself make up the reverse task.
- Come up with several tasks for one solution.
- Figure out how to solve the problem in another way and explain it.
Hope for school, but don’t make it yourself
Let’s look at pedagogy and “decipher” the thoughts of clever and deserved, based on today’s realities.
Back in 1867 K. Ushinsky he said: “For good teachers, it’s like this that the arithmetic problem is together an entertaining story, a lesson in agriculture or home economics, or a historical or statistical topic and an exercise in the language.”
- The student must be placed in such conditions so that he is at the epicenter of events,
Not always the tasks in the school textbook “inspire” modern students. For many, the condition is not clear for one simple reason: the child has no idea what is being said. For example, the problem of milk production and cans with milk, and the city “put in” and a cow in my eyes did not see, not that tons of milk in cans. Or in the task such values are used that are unreal in life – this makes perception difficult,
The task of parents is to help the child understand the condition. In any way: draw though, dance though.
- To solve problems you need to be creative.
Interest causes the child to be active, and activity in turn enhances attention.
In everyday life, we now and then have to solve problems. Attract a child, ask questions, ask for advice. For example, the theme of repair. Calculate room footage; calculate the right amount of paint, knowing the consumption per square meter; buy linoleum, knowing the length and width of the room; calculate which metric area is more profitable if there is a floor covering with a width of 2, 5 meters and 3 meters so that there will be less residue and at a price that is more profitable. Buy fabric for tailoring bed linen, knowing the size of the mattress. There are lots of examples! And it works much more efficiently than the “soulless” task in the textbook, which is completely unattached to life and does not cause an emotional response.
- When solving life tasks, a child, in addition to everything else, develops observation, speech, a working mood appears, creative abilities and independence develop.
After a while, you will notice that the child combines information in various ways, easily compiles tasks himself, finding ideas in the world around him, and not sucking it out of his finger.
- When the child is asked to create their own problem, you need to monitor the content and the solution. The task must be meaningful and expedient.
For example, one should not allow such “blunders” as “I ate 13 yellow pears and 20 green apples. How many fruits have I eaten? ”The task loses its meaning if it is cut off from life.
- From the task it is necessary to go for example, and not vice versa.
Children do not think in the abstract, but in concrete images. Example 12-6 does not mean anything, but the situation when out of 12 people 6 already bought tickets to a football match is another matter. Then the child will answer without hesitation that the remaining six are very risky, you need to hurry, otherwise the tickets may not be enough and you will have to sit at the TV, instead of actively chanting in the stands in support of your favorite team.
Lebedintsev in his book “Introduction to Modern Mathematics” wrote: “The influence that can be taught in numeration and in general mathematics on the mental development of children is directly dependent on the material that we use in teaching; if abstract exercises in actions and cunning tasks with conditions devoid of internal communication and, essentially, far from life, prevail in the educational material, then, practicing students on such material, we may also develop their formal skills in calculations and , perhaps, we will refine their mind for solving different rebuses and puzzles, but by no means will we make them more capable of correct thinking in life or of any field of knowledge … ”.
French teacher Jean mose I was also sure that “forcing a child to begin with an abstract rule and then to offer him tasks is to go against the development of the human mind …”.
Practical tips on solving problems from real moms
What we Ushinsky, Lebedintsev and Mose, ask those who are “from our sandbox.” How do they help their children solve math problems, what “works”, what techniques in practice have proven their effectiveness and helped to improve performance.
Tatiana, mother of students 4 cells. and 6 cl.
“I know that speed problems are especially difficult for children, so I began to prepare my boys for this from the 1st grade. When we drove to our grandmother in Pinsk, we talked about speed, we noticed time, we counted how many kilometers we drove, looked at the signs and figured out how much time we would have if we would go at the same speed and how much if Dad would go with another one. In general, I was very surprised when my boys at the speed of the problem solved as nuts. I realized that in my childhood there was a lack of a practical idea of what was said in the tasks. ”
Olga, mother of a student of 1 grade. and student 4 cl.
“The older one is not good friends with tasks)) Almost always comes for help. I try to work out an algorithm for the solution, but I often rest on “too lazy to think.” If absolutely “plug”, we draw the scheme. There are absolutely no time for additional tasks, and the daughter herself will definitely not be dealing with them)) Sometimes there are tasks with an incorrectly posed question, you have to help with the wording of the answer.
Junior to sit behind the math is very difficult. In those rare moments when it comes to tasks, he solves them in his mind and gives an answer verbally). ”
Veronica, mother of students 2 cells. and 4 cl.
“Junior solves problems without problems, but he hates drawing diagrams for them and writing explanations. The older one goes to elective in mathematics, he does his homework at home. ”
Katerina, mother of a student of 2 cells. and female student 5 cl.
“The son does an excellent job himself. He draws such schemes, that I am sometimes in shock)). If a daughter appeals for help, I try to simplify the task condition to understandable images, and then she herself guesses how to solve a complex model. ”
Tatiana, mom student 5 cl.
“Most often we resort to drawing. Right here as by the condition … we sit down and draw as it is. So to say, visibility helps. The cyclist left … then we draw a little man on a bicycle, the city from which he left, etc.)))) If the boat goes with the flow, we draw the sea, the waves)))))) , in fact, there were no questions either. See by the condition that they ask – and write the answers near each action. ”
Natalia, mother of a student of 5 cells.
“I had to explain the fractions using the example of broken pencils, torn pieces of paper. Visiting at that moment was a friend-designer, he decided to visually explain to his son the problem. I usually resort to drawing help. In the tasks for speed / time / distance, the whole stories were drawn: who went where and on what, whom he met on the way and at what moment. Sometimes the solution of problems turned into a cartoon, one draft is usually not enough. The whole family solved tasks several times: the mother was separate from the father, then they compared the results and each one explained to the child her “most rational and simple” way. As a rule, men have their own logic)), my decision is usually different from my father’s. “
Dear readers! Share in the comments your findings and difficulties in solving problems in mathematics with children. We will understand it many times together and help with tips and useful articles on topics that interest you.