Topic 6.
DIAGNOSTICS OF MATHEMATICAL ABILITIES OF SENIOR PRESCHOOL CHILDREN
There is a significant variety of types of giftedness that can manifest themselves already in preschool age. Among them is intellectual giftedness, which largely determines a child’s aptitude for mathematics and develops intellectual, cognitive, and creative abilities.
Children with intellectual giftedness are characterized by the following features:
- highly developed curiosity, inquisitiveness; the ability to “see” yourself, find problems and the desire to solve them, actively experimenting; high (relative to age-related capabilities) stability of attention when immersed in cognitive activity (in the area of his interests); early manifestation of the desire to classify objects and phenomena, discover cause-and-effect relationships; developed speech, good memory, high interest in new and unusual things; the ability to creatively transform images and improvise; early development of sensory abilities; originality of judgment, high learning ability; desire for independence.
The main areas of work with children with a penchant for mathematics include: determining the child’s aptitude, developing individual programs for the development of the child’s abilities, and additional education.
I want to focus on the first stage - determining the child’s aptitude for mathematics.
In view of the implementation of the Federal State Educational Standard in the educational process of preschool educational institutions, the issue of monitoring the quality of preschool education has become especially acute. It is necessary to competently approach the issue of diagnosing the levels of development of children. In the modern understanding, pedagogical diagnostics is a system of methods and techniques, specially developed pedagogical technologies, test tasks that allow us to determine the level of professional competence of teachers and the level of development of a preschool child. Its main purpose is to analyze and eliminate the causes that give rise to shortcomings in work, accumulate and disseminate teaching experience, stimulate creativity and pedagogical skill.
Purpose of diagnosis: tracking achievements in a child’s mastery of the means and methods of cognition, identifying gifted children in the field of mathematical development.
Form of organization: problem-game situations conducted individually with each child.
We have proposed several diagnostic situations: “Enter the hut”, “Restore the ladder”, “Correct the mistakes”, “Which days are missed” and “Whose backpack is heavier”.
Diagnostic situation “Enter the hut”
Goal: to identify the practical skills of children 5-6 years old in composing numbers from 2 smaller ones and in carrying out search actions.
On three huts located in a row, the numbers (6, 9,7 respectively) indicate the number of gold coins. Traces lead to the huts. Only the one who opens the door can take the coins. To do this, you need to step on the left and right footprints together as many times as the number shows. (Mark with pencil).
Teacher: Which hut did you choose? What tracks will you step on? If you want, then enter other huts?
Diagnostic situation “Correct the mistakes and name the next move”
The goal is to identify children’s ability to follow the sequence of moves, offer options for correcting mistakes, reason, and mentally justify the course of their actions.
The situation is being organized without practical action. The child watches the adult’s progress, comments on his own move, and corrects mistakes.
Teacher: Imagine that you and I are playing dominoes. Some of us made mistakes. Find them and fix them. The first move was mine (left).
As errors are discovered, the child is asked the question: “Which of us made mistakes? How can I fix them using additional chips?”
As a result, generally low results were obtained for the group. At the beginning of the school year, the use of these methods turned out to be inappropriate. The knowledge of most children is not sufficiently formed, the ability to reason and justify actions is poorly expressed. In addition, the proposed situations are not enough to diagnose all areas of children’s mathematical development.
After the diagnosis, teachers were given the following recommendations:
1. Analyze the subject-game development environment
2. Initiate the creative cognitive activity of individual children (personal participation of the teacher in children's activities, creation of gaming communities, motivation)
3. Select games and gaming materials necessary for independent mastery of the actions necessary in a given period (knowledge of the dependencies between numbers, quantities in the conditions of a serial series)
4. Practice organizing and conducting leisure activities, children's games, projects, and joint events with parents.
5. Develop your own pedagogical creative potential. (accompanied by slide)
To carry out repeated diagnostics in September, the author’s diagnostic methods of Anna Vitalievna Beloshistaya were chosen, since it was her developments, in my opinion, that are most accessible, feasible and understandable to children and teachers. The positive aspects of these diagnostic methods are their simplicity, small amount of handouts, which significantly speeds up the diagnostic procedure, especially since all types of diagnostics must be carried out during scheduled moments, and most of them, according to the instructions, are carried out individually. The author focuses on aspects of developmental learning and the personal-activity successive approach.
1. Diagnostic situation of analytical-synthetic activity
(adapted technique)
Goal: to identify the maturity of the analysis and synthesis skills of children aged 5-6 years.
Objectives: assessment of the ability to compare and generalize objects based on characteristics, knowledge of the shape of the simplest geometric figures, the ability to classify material according to an independently found basis.
Presentation of the task: the diagnosis consists of several stages, which are offered to the child one by one. Conducted individually.
Material: set of figures - five circles (blue: large and two small, green: large and small), small red square. (Slide “Circles”)
diagnostic situation
Assignment: “Determine which of the figures in this set is extra. (Square.) Explain why. (All the rest are circles.).”
Material: the same as for No. 1, but without the square.
Assignment: “The remaining circles were divided into two groups. Explain why you divided it this way. (By color, by size.).”
Material: the same and cards with numbers 2 and 3.
Assignment: “What does the number 2 mean on circles? (Two big circles, two green circles.) Number 3? (Three blue circles, three small circles.).”
Assignment rating:
Slide with a photo of a child
2. Diagnostic situation “What is unnecessary”
(methodology)
Purpose: to determine the development of visual analysis skills in children aged 5-6 years.
Option 1.
Material: drawing of figurines-faces. (slide “Faces”)
diagnostic task
Assignment: “One of the figures is different from all the others. Which? (Fourth.) How is it different?”
Option 2.
Material: drawing of human figures.
diagnostic task
Assignment: “Among these figures there is an extra one. Find her. (Fifth figure.) Why is she extra?”
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – task completed with the help of an adult
Level 4 – the child finds it difficult to answer the question even after prompting
3. Diagnostic situation for analysis and synthesis
for children 5 – 7 years old (methodology)
Goal: to determine the degree of development of the skill of isolating a figure from a composition formed by superimposing some forms on others, to identify the level of knowledge of geometric figures.
Presentation of the task: individually with each child. In 2 stages.
Material: 4 identical triangles. (slide)
diagnostic task
Assignment: “Take two triangles and fold them into one. Now take the other two triangles and fold them into another triangle, but of a different shape. What is the difference? (One is tall, the other is low; one is narrow, the other is wide.) Is it possible to make a rectangle out of these two triangles? (Yes.) Square? (No.)".
Material: drawing of two small triangles forming one large one. (slide)
diagnostic task
Assignment: “There are three triangles hidden in this picture. Find them and show them."
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – task completed with the help of an adult
Level 4 – the child did not complete the task
4. Diagnostic test.
Initial mathematical representations (methodology)
Purpose: to determine children’s ideas about relationships more than; less by; about quantitative and ordinal counting, about the shape of the simplest geometric figures.
Material: 7 any objects or their images on a magnetic board. Items can be either the same or different. The task can be offered to a subgroup of children. (slide “Yula”)
diagnostic task
Method of execution: the child is given a sheet of paper and a pencil. The task consists of several parts that are offered sequentially.
A. Draw as many circles on the sheet as there are objects on the board.
B. Draw 1 more squares than circles.
B. Draw 2 less triangles than circles.
D. Draw a line around 6 squares.
D. Color in the 5th circle.
Assignment rating:
Level 1 – task completed completely correctly
Level 2 – 1-2 mistakes made
Level 3 – 3-4 mistakes made
Level 4 – 5 mistakes were made.
During diagnostics, visual material can be provided to children in a multimedia version or on a magnetic board, if the instructions for conducting it do not require practical actions with it. The material should be colorful, age-appropriate, aesthetically designed, appropriate for the number of children.
The proposed methods No. 1 – 2 are carried out in September, as one of the stages of initial monitoring. Methods No. 3-4 – in May, to determine the result of children’s mathematical development.
Only after carrying out several diagnostics is a conclusion drawn up about the maturity of the child’s knowledge, skills and abilities, the results of which are entered into the table: (slide of an empty table)
As a result of the work carried out over the year in accordance with these recommendations for teachers to enrich the group environment in the field of mathematical development, as well as thanks to the diagnostic methods selected in accordance with the tasks of the educational educational institution in May, we came to the following results: (tables)
Analysis-synthesis | Concept of form | Initial mat. representation | |||||||
Total for the group |
As can be seen from the above data, the level of knowledge, both individually and in the group as a whole, has increased significantly. During the diagnostic process, gifted children were identified who easily coped with the situations proposed by the teacher and quickly and accurately found the right solutions.
In order to further develop the mathematical abilities of gifted children, teachers were asked to continue working with these children individually: in special moments, in joint targeted activities with the teacher in the field of mathematical development.
Bibliography:
1. Monitoring in kindergarten. Scientific and methodological manual. – SPb.: PUBLISHING HOUSE “CHILDHOOD-PRESS”, 2011. – 592 p.
2. Management of the educational process in preschool educational institutions. Toolkit/ , . – M.: Iris-press, 2006. – 224 p.
3. Formation and development of mathematical abilities of preschoolers. Toolkit. / . – M.: Arkti, 2004.
· Make sure that the child is emotionally positive about communication.
·Tasks are offered in strict accordance with the instructions.
· An assessment of a child’s mathematical development is made based on the results of several diagnostics.
· The choice of a specific diagnostic technique is made in accordance with the basic and basic general education program of the preschool educational institution.
· When summing up, you should take into account the results of short-term observations of the child, his behavior in a new game, in a creative or problematic situation.
Method of express diagnostics of intellectual abilities of children 6-7 years old (MEDIS)
E. I. SHCHBLANOVA, I. S. AVERINA, E. N. ZADORINA
Currently, a large number of schools have appeared in which education is conducted according to accelerated programs, with in-depth study of certain subjects, under special programs for gifted children, etc. In connection with this, the problem of selecting students capable of such training has arisen. Unfortunately, the solution to this problem is often arbitrary, without any psychological and pedagogical justification.
As a rule, an experienced teacher can quite competently determine a child’s readiness to enter the first grade of school and distinguish normally developed children from children with one or another developmental delay. The issue of children's readiness for school education is covered in sufficient detail in the literature.
The problem of selecting capable and gifted children requires a completely different approach to be solved. This approach should first of all take into account the complexity and versatility of the phenomenon of giftedness itself, which includes both cognitive (intellectual and creative abilities) and non-cognitive (motivational and personal characteristics) factors of development.
Therefore, first of all, it is necessary to clearly formulate the objectives of the training program for which children are being selected, and the requirements that are presented to children within the framework of this program. When making such a selection, the main attention should be paid to the interests of the child: whether studying at a given school will be optimal for his development. To resolve this issue, among many other factors, determining the level of intellectual development of the child is of great importance.
Diagnosis of the level of intellectual development of children requires a thorough and comprehensive analysis by a qualified specialist - a psychologist. However, the practical implementation of such an individual examination of each child upon admission to school is not possible. At the same time, even to make an approximate judgment about the intelligence of children, it is necessary to have a methodology that would allow one to meet a number of conditions required for diagnosing intelligence.
Among them, first of all, it is necessary to mention the standardization of tests, which allows, to a certain extent, to avoid subjectivity in the selection of tasks and ensure equal opportunities for all children. The tasks in the method must be selected in such a way that it is possible to assess different aspects of the child’s intelligence and at the same time reduce the influence of his training (“training”). In addition, the technique must be sufficiently reliable and valid with comparative ease of use and little time consumption.
The development of this methodology was carried out on the basis of well-known foreign tests of cognitive abilities - KFT 1-3 by K. Heller and co-workers. KFT tests 1-3, developed at the University of Munich and intended for gifted first-graders.
Each MEDIS form consists of 4 subtests with 5 tasks of increasing complexity. Before completing each subtest, two tasks similar to the test ones are performed in training. During this training, performing tasks together with the experimenter, the child must understand what he must do and find out everything that is not clear to him. Training tasks can be repeated if necessary.
MEDIS tasks, as in foreign tests, are presented in the form of pictures, which makes it possible to test children regardless of their reading ability. When completing tasks, the child is only required to choose the correct answer (cross out the oval under it) from several proposed ones. Before presenting the tasks, the child is shown an image of an oval, a crossed out oval under the selected picture, and a training exercise is carried out in crossing out the oval on command. All instructions and explanations are given orally by the experimenter.
First subtest aims to identifygeneral student awareness, their vocabulary. Among five to six images of objects, you need to mark the one named by the experimenter. The first tasks include the most common and familiar objects, such as "boot", and the last - rarer and lesser-known objects, such as "statue".
Second subtest provides an opportunity to assess the child's understandingquantitative and qualitative relationshipsbetween objects and phenomena: more - less, higher - lower, older - younger, etc. In the first tasks these relationships are unambiguous - the largest, the farthest, while in the last tasks the child needs, for example, to choose a picture where one object more than another, but less than a third.
The third subtest reveals level of logical thinking, analytical and synthetic activity of the child. Moreover, in tasks to eliminate the superfluous, both images of specific objects and figures with different numbers of elements are used.
Fourth subtestsent for diagnosismathematical abilities. It includes mathematical tasks for intelligence, which use various materials: arithmetic tasks, tasks for spatial thinking, identifying patterns, etc. To complete these tasks, the child must be able to count to ten and perform simple arithmetic operations (addition and subtraction) .
Thus, the variety of tasks in MEDIS makes it possible to cover different aspects of a child’s intellectual activity in minimal periods of time and obtain information both about his ability to learn in primary school and about the individual structure of his intelligence. This gives grounds for using MEDIS as the main part of a battery of methods for determining the readiness of children to learn in schools with educational programs of increased difficulty.
MEDIS can be used individually and in groups of 5-10 people. When examining children in groups, the experimenter needs the help of an assistant. The environment during testing should be calm and serious, without unnecessary tension. Each test taker must have his own test book, on the cover of which his first and last name must be indicated. During testing, monitoring of children is of great importance. In group testing, this task is performed primarily by the experimenter's assistant. This observation allows us to avoid cases of the child misunderstanding the instructions and at the same time obtain additional information about the readiness of children to learn at school and the individual characteristics of their behavior.
It should be taken into account that the group testing environment may be extremely unfavorable for some children: those with increased anxiety, confused by the new environment, etc. In such cases, it is recommended to repeat the testing using a different form of test or supplement it with an individual psychological and pedagogical examination.
All MEDIS tasks are completed without a time limit. The pace at which the experimenter reads the tasks should depend on the speed at which the children complete the tasks; it may differ in different groups. At the same time, children should not be forced to complete the task at a certain pace. Children who work quickly need 15 seconds to complete each task. Children who work slowly may need 20-25 seconds. The speed of reading tasks should not remain constant when moving from one task to another in different test parts.
When planning testing, it is important to take into account not only the time required to complete the tasks of the corresponding part of the methodology, but also the time required to distribute test materials, explain how to perform the test, and work with children on the training examples given at the beginning of each subtest. The total test time is on average 20-30 minutes.
When interpreting the results of this technique, it should be taken into account that, like any other test, MEDIS cannot serve as the only criterion for making decisions about the level of intellectual development of a child, about his selection for training in special programs, about the profile of his abilities. Test results should be considered in conjunction with other indicators: data from an interview with the child, information from parents, indicators of the child’s interests, etc.
Instructions: All test tasks are spoken no more than 2 times!
Task 1 - awareness.
1- show the rodent (correct answerin the 5th picture),
2- acrobat (4),
3- edible (2),
4- plane (2),
5- biceps (4).
Task 2 - mathematical abilities.
1- show the bed where the flowers were planted before everyone else (3),
2- a picture in which the girl stands closer to the tree than the boy and the dog (4),
3- a picture in which a duck flies the lowest, but fastest (2),
4-degree thermometer, in which the temperature is higher than the lowest, but lower than all the others (4),
5- picture where the boy runs fast, but not faster than everyone else (1).
Task 3 - logical thinking.
In all tasks it is necessary to show the “extra”.
(right answers- 3, 4, 2, 2, 5).
Task 4 - quantitative and qualitative relationships.
1- find a rectangle in which there are more than 6 sticks, but less than 12 (3),
2- We drew a row of dominoes, but forgot to draw one. Which domino do you need to take on the right to continue this row? (2),
3- choose a cube that has one more point than this cube on the left (4),
4- count the sticks in the cubes on the left. Which cube has more sticks? Show how much more (1)
5- show the plate on which the least amount of cake was eaten (3).
FULL NAME. ___________________________________________________________
Research Date ________________________________________________
MEDIS subtests | 5- high | 4- above average |
Mathematics ability is one of the talents given by nature, which manifests itself from an early age and is directly related to the development of creative potential and the desire to understand the world around the child. But why is learning maths so difficult for some children, and can these abilities be improved?
The opinion that only gifted children can master mathematics is wrong. Mathematical abilities, like other talents, are the result of a child’s harmonious development, and must begin from a very early age.
In the modern computer world with its digital technologies, the ability to “make friends” with numbers is extremely necessary. Many professions are based on mathematics, which develops thinking and is one of the most important factors influencing the intellectual growth of children. This exact science, whose role in the upbringing and education of a child is undeniable, develops logic, teaches one to think consistently, determine the similarities, connections and differences of objects and phenomena, makes the child’s mind fast, attentive and flexible.
In order for mathematics classes for children five to seven years old to be effective, a serious approach is required, and the first step is to diagnose their knowledge and skills - to assess at what level the child’s logical thinking and basic mathematical concepts are.
Diagnostics of mathematical abilities of children 5-7 years old using the method of Beloshistaya A.V.
If a child with a mathematical mind has mastered mental calculation at an early age, this is not yet a basis for one hundred percent confidence in his future as a mathematical genius. Mental arithmetic skills are only a small element of an exact science and are far from the most complex. A child’s ability for mathematics is evidenced by a special way of thinking, which is characterized by logic and abstract thinking, understanding of diagrams, tables and formulas, the ability to analyze, and the ability to see figures in space (volume).
To determine whether children from primary preschool (4-5 years old) to primary school age have these abilities, there is an effective diagnostic system created by Doctor of Pedagogical Sciences Anna Vitalievna Beloshista. It is based on the creation by a teacher or parent of certain situations in which the child must apply this or that skill.
Diagnostic stages:
- Testing a 5-6 year old child for analysis and synthesis skills. At this stage, you can evaluate how the child can compare objects of different shapes, separate them and generalize them according to certain characteristics.
- Testing figurative analysis skills in children aged 5-6 years.
- Testing the ability to analyze and synthesize information, the results of which reveal the ability of a preschooler (first grader) to determine the shapes of various figures and notice them in complex pictures with figures superimposed on each other.
- Testing to determine the child’s understanding of the basic concepts of mathematics - we are talking about the concepts of “more” and “less”, ordinal counting, the shape of the simplest geometric figures.
The first two stages of such diagnostics are carried out at the beginning of the school year, the rest - at the end, which makes it possible to assess the dynamics of the child’s mathematical development.
The material used for testing should be understandable and interesting for children - age-appropriate, bright and with pictures.
Diagnosis of a child’s mathematical abilities using the method of Kolesnikova E.V.
Elena Vladimirovna has created many educational and methodological aids for the development of mathematical abilities in preschoolers. Her method of testing children 6 and 7 years old has become widespread among teachers and parents in different countries and meets the requirements of the Federal State Educational Standard (FSES) (Russia).
Thanks to Kolesnikova’s method, it is possible to determine as accurately as possible the level of key indicators of the development of children’s mathematical skills, find out their readiness for school, and identify weaknesses in order to fill gaps in a timely manner. This diagnosis helps to find ways to improve the child’s mathematical abilities.
Developing a child’s mathematical abilities: tips for parents
It is better to introduce a child to any science, even something as serious as mathematics, in a playful way - this will be the best teaching method that parents should choose. Listen to the words of famous scientist Albert Einstein: “Play is the highest form of exploration.” After all, with the help of the game you can get amazing results:
– knowledge of yourself and the world around you;
– formation of a mathematical knowledge base;
– development of thinking:
– personality formation;
– development of communication skills.
You can use various games:
- Counting sticks. Thanks to them, the baby remembers the shapes of objects, develops his attention, memory, ingenuity, and develops comparison skills and perseverance.
- Puzzles that develop logic and ingenuity, attention and memory. Logic puzzles help children learn better spatial awareness, thoughtful planning, simple and backward counting, and ordinal counting.
- Mathematical riddles are a great way to develop the basic aspects of thinking: logic, analysis and synthesis, comparison and generalization. While searching for a solution, children learn to draw their own conclusions, cope with difficulties and defend their point of view.
The development of mathematical abilities through play creates learning excitement, adds vivid emotions, and helps the child fall in love with the subject of study that interests him. It is also worth noting that gaming activities also contribute to the development of creative abilities.
The role of fairy tales in the development of mathematical abilities of preschool children
Children's memory has its own characteristics: it records vivid emotional moments, that is, the child remembers information that is associated with surprise, joy, and admiration. And learning “from under pressure” is an extremely ineffective way. In the search for effective teaching methods, adults should remember such a simple and ordinary element as a fairy tale. A fairy tale is one of the first means of introducing a child to the world around him.
For children, fairy tales and reality are closely connected, magical characters are real and alive. Thanks to fairy tales, a child’s speech, imagination and ingenuity develop; they give the concept of goodness, honesty, broaden horizons, and also provide an opportunity to develop mathematical skills.
For example, in the fairy tale “The Three Bears,” the child unobtrusively gets acquainted with counting to three, the concepts of “small,” “medium,” and “large.” “Turnip”, “Teremok”, “The Little Goat Who Could Count to 10”, “The Wolf and the Seven Little Kids” - in these tales you can learn simple and ordinal counting.
When discussing fairy-tale characters, you can invite your child to compare them in width and height, to “hide” them in geometric shapes that are suitable in size or shape, which contributes to the development of abstract thinking.
You can use fairy tales not only at home, but also in school. Children really love lessons based on the plots of their favorite fairy tales, using riddles, labyrinths, and fingering. Such classes will become a real adventure in which the kids will take personal part, which means the material will be learned better. The main thing is to involve children in the game process and arouse their interest.
The book meets federal state requirements for the structure of the basic general education program of preschool education. It presents the planned results of mastering the “Mathematical Steps” program. The methods used for diagnosis make it possible to obtain the required amount of information in the optimal time frame. The tasks proposed in the book are designed to assess a child’s mathematical preparation for school and promptly identify and fill gaps in his mathematical development.
Diagnostics of mathematical abilities of children 6-7 years old. Kolesnikova E.V.
Description of the textbook
Ability to generalize mathematical material
Quantity and count
Connect rectangles with the same number of objects.
Tell me, which rectangles did you connect? Circle the birds that are the most numerous.
Which birds did you circle? Why?
Quantity and count
Color only the math symbols.
Ability to generalize mathematical material
Geometric figures
Draw as many leaves on each branch as there are circles on the left.
How many leaves did you draw on the top branch? Why? On the middle one? Why? On the bottom branch? Why?
Connect each twig with a card that has as many circles as there are leaves on the twig.
Which card did you connect with which branch?
Ability to generalize mathematical material
Write the numbers from 0 to 9 in order in the squares.
Color only the numbers.
Name the numbers you shaded.
Ability to generalize mathematical material
Color only the geometric shapes.
Name the geometric shapes that you shaded. Color only the quadrilaterals.
Name the geometric shapes that you shaded.
Ability to generalize mathematical material
Trace the shapes with the fewest corners.
What shapes did you circle and why? Color in geometric shapes that have no corners.
What geometric shapes did you paint?
Ability to generalize mathematical material
Magnitude
Circle the houses of the same height.
How many houses did you circle and why? Connect trees with trunks of the same thickness.
Which trees did you connect and why?
Ability to generalize mathematical material
Time orientation
Color the pictures of morning
How many pictures did you color and why?
Ability to generalize mathematical material
Listen to an excerpt from P. Bashmakov’s poem “Days of the Week.” Under each picture, write a number indicating what day of the week the girl did.
On Monday I did the laundry, on Tuesday I swept the floor, on Wednesday I baked kalach, all Thursday I looked for the ball,
I washed the cups on Friday, and bought a cake on Saturday. I invited all my girlfriends to my birthday party on Sunday.
Name the days of the week in order.
Ability to generalize mathematical material
Which picture did you connect with which and why?
Ability to generalize mathematical material
Time orientation
Match the clocks that show the same time.
What time does the clock you connected show?
Draw the hands on the clock so that they show the time that is written in the squares below them.
What time does the first clock show? Second? Third? Fourth?
Under each square, write a number corresponding to the number of circles in them.
Name the numbers in the first row, in the second. Write the “greater than” (^or “less than” signs) in the circles
Match each card with the example it matches.
Tell me which card you paired with which example.
Divide the squares into 2, 3, 4, 5 triangles.
Divide the squares into 5, 4, 3, 2 triangles.
Color the triangles so that they are all different colors.
Color in the fish, which consists of the geometric shapes drawn on the right.
Why did you paint over this fish?
Color only those geometric shapes on the right that make up the fish.
What shapes did you paint?
Write the numbers from 1 to 6 in the squares, starting from the largest nesting doll.
Write the numbers from 1 to 6 in the squares, starting from the smallest ball.
Circle the objects to the left of the bear and color the objects to the right of it.
What objects have you painted? What objects did you circle?
Color in the objects to the left of the bear and circle the objects to the right of it.
What items did you circle? What objects did you color?
Draw as many objects on the right as possible from the geometric shapes on the left.
Show with an arrow which floor each funny little person lives on. To find out, you need to solve the example he is holding in his hand.
Write the numbers in the empty squares so that when you add them you get the answer that is written at the top.
Seven children played football. One was called home. He looks out the window and counts: How many friends are playing?
Guess a riddle. Write your answer in the square.
Seven tiny kittens, Everyone eats what they are given, And one asks for sour cream. How many kittens are there?
Guess a riddle. Write your answer in the square.
The hedgehog gave the ducklings Eight leather boots. Which of the guys will answer, How many ducklings were there?
Five crows landed on the roof, two more flew to them. Answer quickly, boldly, How many of them have arrived?
Listen and complete the task from Dunno I made beads from different numbers, And in those circles where there are no numbers, Arrange the minuses and pluses, To get the given answer.
Write greater than or less than signs in the empty squares.
Write in the circle the number indicating the number that the bunny wished for. And he thought of a number that is one less than seven, but one more than five.
Answer the questions. How many ears do two mice have?
How many paws do two cubs have?
How many days are there in a week?
How many parts are there in a day?
How many months are there in a year?
Who is bigger: a small hippopotamus or a big hare?
Which is longer: a snake or a caterpillar?
Can summer come immediately after winter?
What is the name of the fifth day of the week?
Which geometric figure has the fewest angles?
Diagnostics of mathematical abilities of children 6-7 years old.
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.
Practice shows that the difficulties of first-graders are associated, as a rule, with the need to assimilate abstract knowledge, to move from acting with concrete objects and their images to acting with numbers and other abstract concepts. Such a transition requires the child’s developed mental activity. Therefore, in the preparatory group for school, special attention is paid to the development in children of the ability to navigate in some hidden essential mathematical connections, relationships, dependencies: “equal”, “more”, “less”, “whole and part”, dependencies between quantities, dependencies of the measurement result on the size of a measure, etc. Children master ways of establishing various kinds of mathematical connections and relationships, for example, a method of establishing correspondence between elements of sets (practical comparison of elements of sets one to one, using superposition techniques, applications for clarifying relationships of quantities). They begin to understand that the most accurate ways to establish quantitative relationships are by counting objects and measuring quantities. Their counting and measurement skills become quite strong and conscious. The ability to navigate essential mathematical connections and dependencies and mastery of the corresponding actions make it possible to raise the visual-figurative thinking of preschoolers to a new level and create the prerequisites for the development of their mental activity in general. Children learn to count with their eyes alone, silently, they develop an eye and a quick reaction to form.
No less important at this age is the development of mental abilities, independence of thinking, mental operations of analysis, synthesis, comparison, the ability to abstract and generalize, and spatial imagination. Children should develop a strong interest in mathematical knowledge, the ability to use it, and the desire to acquire it independently. The program for the development of elementary mathematical concepts of the preparatory group for school provides for the generalization, systematization, expansion and deepening of the knowledge acquired by children in previous groups. Work on the development of mathematical concepts is mainly carried out in the classroom. How should they be structured to ensure children’s solid learning?
In the pre-school mathematics group, 2 classes are held per week, during the year - 72 classes. Duration of classes: - 30 min.
Structure of classes.
The structure of each lesson is determined by its content: whether it is devoted to learning new things, repeating and consolidating what has been learned, testing children’s knowledge acquisition. The first lesson on a new topic is almost entirely devoted to working on new material. Introduction to new material is organized when children are most productive, i.e. at 3-5 minutes. from the beginning of the lesson, and ends at 15-18 minutes. Repetition of what has been covered is given to 3-4 minutes. at the beginning and 4-8 min. at the end of the lesson. Why is it advisable to organize work this way? Learning new things tires children out, and repeating material gives them some relief. Therefore, where possible, it is useful to repeat the material covered while working on new ones, since it is very important to introduce new knowledge into the system of previously acquired ones. In the second and third lessons on this topic, approximately 50% of the time is devoted to it, and in the second part of the lessons they repeat (or continue to study) the immediately preceding material, in the third part they repeat what the children have already learned. When conducting a lesson, it is important to organically connect its individual parts, ensure the correct distribution of mental load, and alternation of types and forms of organizing educational activities.
Methodological techniques for the formation of elementary mathematical knowledge, by section:
Quantity and count
At the beginning of the school year, it is advisable to check whether all children, and especially those who have come to kindergarten for the first time, can count objects, compare the number of different objects and determine which are more (less) or equal; what method is used to do this: counting, one-to-one correlation, identification by eye or comparison of numbers? Do children know how to compare the numbers of aggregates, distracting from the size of objects and the area they occupy? Sample tasks and questions: “How many big nesting dolls are there?” Count out how many small nesting dolls there are. Find out which squares are more numerous: blue or red. (There are 5 large blue squares and 6 small red ones lying randomly on the table.) Find out which cubes are more: yellow or green.” (There are 2 rows of cubes on the table; 6 yellow ones stand at large intervals from one another, and 7 blue ones stand close to each other.) The test will tell you to what extent the children have mastered counting and what questions should be paid special attention to. A similar test can be repeated after 2-3 months in order to identify the children’s progress in mastering knowledge.
Formation of numbers.
During the first lessons, it is advisable to remind children how the numbers of the second heel are formed. In one lesson, the formation of two numbers is sequentially considered and they are compared with each other. This helps children learn the general principle of forming a subsequent number by adding one to the previous one, as well as obtaining the previous number by removing one from the subsequent one (6 - 1 = 5). The latter is especially important because children are much more difficult to obtain a smaller number, and therefore highlight the inverse relationship.
Children practice counting and counting objects within 10 throughout the school year. They must firmly remember the order of the numerals and be able to correctly correlate the numerals with the items being counted, and understand that the last number named when counting indicates the total number of items in the collection. If children make mistakes when counting, it is necessary to show and explain their actions. By the time children enter school, they should have developed the habit of counting and arranging objects from left to right using their right hand. But, answering the question how many?, children can count objects in any direction: from left to right and from right to left, as well as from top to bottom and from bottom to top. They are convinced that they can count in any direction, but it is important not to miss a single object and not to count a single object twice.
Independence of the number of objects from their size and shape of arrangement.
The formation of the concepts of “equally”, “more”, “less”, conscious and strong numeracy skills involves the use of a large variety of exercises and visual aids. Particular attention is paid to comparing the numbers of many objects of different sizes (long and short, wide and narrow, large and small), differently located and occupying different areas. Children compare collections of objects, for example, groups of circles arranged in different ways: they find cards with a certain number of circles in accordance with the sample, but arranged differently, forming a different figure. Children count the same number of objects as circles on the card, or 1 more (less), etc. Children are encouraged to look for ways to count objects more conveniently and quickly, depending on the nature of their location. Grouping objects according to different criteria (formation of groups of objects). From comparing the numbers of 2 groups of objects that differ in one characteristic, for example, size, we move on to comparing the numbers of groups of objects that differ in 2, 3 characteristics, for example, size, shape, location, etc.
Equality and inequality of numbers of sets.
Children should ensure that any collections containing the same number of elements are denoted by the same number. Exercises in establishing equality between the numbers of sets of different or homogeneous objects that differ in qualitative characteristics are performed in different ways. Children must understand that there can be an equal number of any objects: 3, 4, 5, and 6. Useful exercises require indirect equalization of the number of elements of 2-3 sets, when children are asked to immediately bring the missing number of objects, for example , so many pens and notebooks so that all the students have enough, so many ribbons so that they can tie bows for all the girls.