Teaching older preschoolers to solve arithmetic problems
Bibliographic description:
Avsyukevich, N. I. Teaching older preschoolers to solve arithmetic problems / N. I. Avsyukevich, I. A. Bashkatova. — Text: direct // Questions of preschool pedagogy. - 2016. - No. 3 (6). — P. 103-105. — URL: https://moluch.ru/th/1/archive/41/1258/ (access date: 01/18/2022).
... Arithmetic, especially arithmetic problems, has always been recognized as having another exceptional role in learning, namely the development of intelligence and ingenuity.
A. I. Markushevich
By the time they enter school, children should have acquired a relatively wide range of interrelated knowledge about set and number, shape and size, and learn to navigate in space and time.
In the process of mathematical and general mental development of children of senior preschool age, special attention is paid to learning to solve and compose simple arithmetic problems. In kindergarten, preparatory work is carried out to develop children's confident calculation skills in adding and subtracting single-digit numbers and rapid mental calculations with two-digit numbers in order to prepare them for learning in primary school. If in school calculations are taught by solving examples and arithmetic problems, then in the practice of preschool institutions it is customary to introduce children to arithmetic operations and the simplest calculation techniques based on simple problems, the conditions of which reflect real, mainly play and everyday situations. The condition of the problem indicates the connections between the given numbers, as well as between the data and the required ones. These connections determine the choice of arithmetic operation.
Having established these connections, the child quite easily comes to understand the meaning of arithmetic operations and the meaning of the concepts “add”, “subtract”, “get”, “remain”. By solving problems, children master the ability to find relationships between quantities.
At the same time, tasks are one of the means of developing logical thinking, ingenuity, and ingenuity in children. In working with tasks, the skills of analyzing and synthesizing, generalizing and concretizing, revealing the main thing, highlighting the main thing in the text of the problem and discarding the unimportant and secondary are improved.
Simple tasks , i.e. tasks that can be solved with one action, are usually divided into the following groups:
The first group includes simple problems in which children learn the specific meaning of each arithmetic operation, i.e., which arithmetic operation corresponds to a particular operation on sets (addition or subtraction). These problems involve finding the sum of two numbers and finding the remainder.
The teacher forms ideas about the operations of addition and subtraction, and at the same time introduces children to the signs “+”, “-”, “=”. Thus, children gradually move from actions with concrete sets to actions with numbers - solving arithmetic problems and becoming familiar with notating the model of arithmetic operations using mathematical symbols.
Already in the 2nd-3rd lesson, where visual material was used, children are asked to solve oral text problems. To master the algorithm of action, exercises in independently composing tasks are useful.
4 + 2 = 6
The second group includes simple problems, when solving which it is necessary to comprehend the connection between the components and results of arithmetic operations. These are tasks to find unknown components:
a) finding the first term from the known sum and the second term.
b) finding the second term using the known sum and the first term.
c) finding the minuend from the known subtrahend and difference.
d) finding the subtrahend from the known minuend and difference.
These problems help reinforce knowledge of the structure of a problem and develop the ability to find the appropriate arithmetic operation. To help children remember numerical data better, cards with numbers, and subsequently with signs, are used.
9–3 = 6
The third group includes simple problems related to the concept of difference in ratios:
a) increasing the number by several units.
b) decreasing the number by several units.
In these problems, arithmetic operations are, as it were, prompted by the very conditions of the problem. A ratio greater than one requires the child to increase, count, add, a ratio less than one requires decrease, subtraction.
Depending on the visual material used to compose the tasks, they are divided into dramatization tasks and illustration tasks. Each type of these tasks has its own characteristics and reveals certain aspects to children, and also contributes to the development of the ability to select the necessary life, everyday, and play material for the plot of the task, and teaches them to think logically.
The peculiarity of dramatization tasks is that their content directly reflects the life of the children themselves, that is, what they just did or usually do. In dramatization tasks their meaning is most clearly revealed. Children begin to understand that the problem always reflects the specific lives of people.
The ability to think about how the content of a problem corresponds to real life contributes to a deeper knowledge of life and teaches children to consider phenomena in diverse connections, including quantitative relationships.
Problems of this type are especially valuable at the first stage of learning: children learn to compose problems about themselves, talk about each other’s actions, pose a question for solution, therefore the structure of the problem using the example of dramatization problems is most accessible to children.
A special place in the system of visual aids is occupied by tasks - illustrations. In these tasks, with the help of toys, space is created for a variety of plots. These tasks develop imagination, stimulate memory and the ability to independently come up with problems, and therefore lead to solving and composing oral problems.
Pictures are widely used to illustrate problems. The main requirements for them are simplicity of plot, dynamism of content and clearly expressed quantitative relationships between objects.
The teacher himself can create a picture task. These visual aids help to understand the meaning of an arithmetic problem and its structure.
After children have formed ideas and some concepts about an arithmetic problem, about the relationships between numerical data, between the condition and question of the problem, you can move on to familiarize yourself with the transformation of direct problems into inverse ones . This helps to better understand the specifics of each type of task. The teacher explains: any arithmetic problem can be transformed into a new one if the resulting required is considered one of the data of the new task, and one of the data of the transformed task is considered the desired one.
An example task for teaching children to solve problems in their heads.
The teacher hangs cards with tasks - pictures on which the conditions of four tasks are presented using depicted objects and arithmetic signs.
3 pears - 1 pear
2 pears+1 pear
2 berries+1 berry
3 berries - 1 berry
Choose from four picture problems the one whose solution will correspond to the given value.
1 task. The value is set to 3 pears. Which picture task is appropriate? What action should you perform in this task?
Task 2. The value is set to 2 berries. Which picture task is appropriate? What action should you perform in this task?
3 task. The teacher offers to find among the laid out picture cards those that correspond to the answer.
4 task. Try to come up with similar problems using picture cards. Children come up with the condition of the problem, tell how it should be solved, and, using cards with numbers and arithmetic signs, post the answer in an empty cell of the picture card.
An example task for introducing children to problems involving the relation “more (less) by several units.”
Problem: “Mom put 2 spoons of sugar in the car’s cup of tea, and 1 spoon more sugar in dad’s big cup. How many spoons of sugar did mom put in dad’s cup?” What is this problem about? Repeat her condition. What is asked in this problem? What needs to be done to solve the problem? There are 2 spoons of sugar in a Mashina cup - this is the first set. How many spoons of sugar are in dad's cup is unknown. This is the second set. But it is known that Dad’s cup has 1 spoon of sugar more than Masha’s cup. We need to determine the amount of sugar in the second set. There is as much sugar in dad's cup as in the first set, and one more spoon. What action will we use to solve the problem? How do we answer the problem question? Write down the solution to the problem in your notebooks using numbers and arithmetic symbols.
Familiarization with simple and inverse problems increases cognitive activity and develops the ability to think logically.
Key terms
(automatically generated)
: task, child, spoon of sugar, daddy's cup, arithmetic task, action, what action, what picture task, visual material, example task.
Report on the topic: “Types of arithmetic problems used in working with preschoolers.”
Municipal preschool educational institution
"Child Development Center No. 12 of the Sovetsky District of Volgograd"
Report on the topic: “Types of arithmetic problems used in working with preschoolers.”
The teacher completed it first
qualification category:
Ilyina S. V.
Volgograd, 2017
In the process of mathematical and general development of preschool children, a significant place is occupied by teaching them to solve and compose simple arithmetic problems.
Arithmetic problem
is the simplest mathematical form of displaying real situations that are both close and understandable to children and which they encounter every day. There is every reason to believe that this to some extent explains the high interest of students in solving arithmetic problems.
Proper training in solving arithmetic problems does a lot for the development of a child’s logical thinking. When solving problems, children must learn to reason, prove, and justify their actions.
It is important that the content of the task corresponds to real life, as this fosters a thoughtful attitude towards facts and teaches them to critically analyze them.
However, despite the fact that computing activities are of interest, and the problem itself is given a significant place in the curriculum in kindergarten, many preschoolers experience significant difficulties in solving arithmetic problems. When solving problems, children focus mainly on external, unimportant connections and relationships between numerical data in the condition of the problem, as well as between the condition and the question of the problem.
Understanding the simplest arithmetic problem requires analyzing its content, isolating its numerical data, understanding the relationships between them and, of course, the very actions that the child must perform.
It is especially difficult for preschoolers to understand the question of the problem, which reflects the mathematical essence of the actions. It is the question of the problem that directs the child’s attention to the relationships between numerical data.
Teaching preschoolers to solve arithmetic problems leads them to understand the content of arithmetic operations (add-add, decrease-subtract). In order for them to master basic methods of computational activity, preliminary work is necessary, starting from the middle group, aimed at mastering knowledge about the relationship of substitute objects with the number of objects in a given group, the use of substitute signs (number cards, counting material), the ability to highlight objects from groups, divide objects into groups.
In the practice of preschool institutions, it is customary to introduce children to arithmetic operations and calculation techniques based on simple problems that reflect the actions of the children themselves. This contributes to a gradual awareness of the meaning of constantly used terms: add, subtract, turn out, remain, i.e. awareness of the meaning of arithmetic operations. Mastering the simplest task requires analyzing its content, isolating numerical data, understanding the relationships between them, and, therefore, those actions that must be performed.
