education. Before teachers preschool institutions and scientists currently have a common task - to improve all educational work and improve the preparation of children for school.
An important place should be given to teaching preschoolers the basics of mathematics. This is caused by a number of reasons: - the beginning schooling from the age of six, the abundance of information received by the child, increased attention to computerization, the desire to make the learning process more intense, the desire of parents in this regard to teach the child to recognize numbers, count, and solve problems as early as possible. The main goal is being pursued: to raise children as people who can think, navigate well in everything that surrounds them, correctly assess the various situations they encounter in life, and make independent decisions. Teaching children mathematics in preschool age contributes to the formation and improvement of intellectual abilities: logic of thought, reasoning and action, flexibility of the thought process, ingenuity and intelligence, development of creative thinking. The human brain requires constant training, exercises. As a result of exercise, a person’s mind becomes sharper, and he himself becomes more resourceful and quick-witted.
Cognitive development involves the development of children's interests, curiosity and cognitive motivation; formation of cognitive actions, formation of consciousness; development of imagination and creative activity; the formation of primary ideas about oneself, other people, objects of the surrounding world, about the properties and relationships of objects of the surrounding world (shape, color, size, material, sound, rhythm, tempo, quantity, number, part and whole, space and time, movement and rest , causes and consequences, etc.), about the small homeland and Fatherland, ideas about the socio-cultural values of our people, about domestic traditions and holidays, about planet Earth as common house people, about the peculiarities of its nature, the diversity of countries and peoples of the world.
PROBLEMS OF MATHEMATICS EDUCATION Motivational. Public underestimation of the importance of mathematics education, Overload of school and university programs technical elements and outdated content Unrealistic certification requirements for a significant part of graduates Content. Obsolescence of content and formality of studying mathematics at all levels of education. Isolation of programs from life. The content of mathematical education at all its levels continues to become outdated and remains formal and divorced from life; its continuity between levels is insufficient. The needs of future specialists in mathematical knowledge and methods, in particular based on information Technology poorly taken into account. The virtual absence of differences in curriculum and assessment requirements for different groups of students leads to low effectiveness educational process, replacing teaching with “coaching” for an exam, ignoring the actual abilities and characteristics of students’ preparation. There is a disconnect between university education. University education is divorced from modern science and practice, its level is falling, which is partly due to the insufficient integration of Russian science into the world. Personnel. IN Russian Federation There are not enough teachers and university professors who can teach mathematics in a quality manner, taking into account the educational interests of different groups of students. The existing system of teacher training, advanced training and retraining of teaching staff does not meet modern needs. The majority of graduates of pedagogical universities do not have sufficient subject (primarily in school mathematics) and practical training
AREAS OF MODERNIZATION REFLECTED IN THE SAMPLE EDUCATIONAL PROGRAM The results of mastering the program are not broken down by subject. The concept of mathematical competence is used as a set of knowledge, skills and abilities and the ability to apply them related to the field of mathematics
FEATURES OF THE SAMPLE PROGRAM Modern content of the primary mathematics and computer science course general education, reflected in the Federal State Educational Standard, is based on the fundamental concepts of mathematics and computer science: symbol, set and chain, basic operations on them, concepts of logic and algorithms. The fundamental thing is that the objects, operations, structures, actions being mastered are always, whenever possible, visual, accessible to the child’s visual perception (on paper or on the screen), and sometimes even tactile, kinesthetic (when objects materialize), and auditory. .
FEATURES OF AN EXAMPLE PROGRAM An important place in the mathematical competence formed during training in primary school is occupied by elements, the application (and thus mastery) of which traditionally begins in physics lessons. In a modern physics course, the concepts of perpendicularity, parallelism, vector (and “delaying a vector from a point”), operations on vectors (in particular, expansion of a vector along two axes), trigonometric functions (an angle less than a developed one), derivative (rate of change) are actively used. , similarities (in particular, in optics).
FEATURES OF AN EXAMPLE PROGRAM Options for constructing mathematics and physics courses: the material is introduced into the mathematics course after it is used in the physics course. Thus, its study in a mathematics course can be logically presented as “theoretical comprehension,” a system of definitions and proofs for concepts that have already been conceptually, intuitively, and visually mastered. construction of physics and mathematics courses, where applications in physics appear after completing the corresponding material in the mathematics course. the earlier study of branches of geometry that provided the "theoretical" basis for physics. This can be done both while maintaining the deductive structure of the modern (“classical”) geometry course, and simultaneously with its restructuring.
FEATURES OF THE SAMPLE PROGRAM Interdisciplinary synchronization: Primary school. The logic of mathematical reasoning, the use of names, statements about existence and universality (through which statements such as “and”, “or” are expressed) are mastered. Data structures are introduced: linear (chains) and hierarchical (trees), used in Russian and foreign languages(grammar), history, biology (classification); tables and bar charts as one of the tools for presenting data, including information about the outside world. Master the measurement and analysis of data, including those automatically obtained by digital measuring instruments, the data is visualized on a computer. Algorithms are mastered: in a visual environment - using the basic constructs of structured programming (without assignment), in a numerical environment - linear with sequential assignment: “solution arithmetic problems on questions."
FEATURES OF THE SAMPLE PROGRAM Intersubject synchronization: 5-6 cells. Rational numbers, algebraic expressions, equations, substitution of one expression into another, equivalent transformations are studied. An idea of equations that reflect laws (in particular physical ones) is formed. real world. Tasks are performed where, having a mathematical formulation of a physical law, one can express one variable in terms of others, one can find its values, having the values of these others.
FEATURES OF THE SAMPLE PROGRAM Intersubject synchronization: 7 cells. A two-dimensional Cartesian plane appears (with rational coordinates for now). Gain an understanding of functions as understood in modern mathematics, including functions defined by algebraic expressions and functions resulting from measurements made by digital sensors in physical processes (partially possible replacement with manual measurements). Theoretical and experimental curves are compared. Physical quantities, are essentially one-dimensional.
FEATURES OF THE SAMPLE PROGRAM Intersubject synchronization: 8 cells. The idea of a continuum of real numbers arises as reflecting physical reality. The acquired knowledge about the proportionality of geometric objects is reinforced and used in geometric optics. 9th grade The apparatus of metric geometry (Pythagorean theorem, distance on a plane, cosine theorem) and trigonometry (trigonometric functions of angles less than the developed one), vector algebra are mastered in parallel in the course of mathematics and their applications - in the course of physics. In a physics course, in dynamics, there is a transition from “scalar” to “vector”: speed, acceleration, force become vectors (essentially two-dimensional).
SAMPLE PROGRAM FEATURES Concept Mastery: Assessment. In the case when for names included in a mathematical (in particular, algebraic) expression, restrictions on their numerical values are known, it is sometimes possible to draw a conclusion about restrictions on the value of the entire expression. Estimate. In some situations, for example, in order to doubt the correctness of a calculation, a person makes a not obviously true, but plausible statement about the values of the intermediate results of calculations, and then about the meaning of the entire expression being calculated. Approximation. The simplest type of estimate is the estimate obtained by discarding all signs decimal notation numbers, starting from some (approximation with a disadvantage), or a similar operation that gives an “upper estimate”.
PROGRAM CONTENT Integers, rational and real numbers Measurements, approximations, estimates Algebraic expressions Equations Inequalities Functions Number sequences Descriptive statistics Combinatorics Geometry Information and methods of its representation Fundamentals of algorithmic culture Use of software systems and services Modeling Mathematics in historical development
GEOMETRY Content should be designed taking into account: the development of visual thinking, spatial imagination; formation of a mathematical vocabulary related to general cultural baggage; a unique two-thousand-year-old source and subsequent intellectual tradition, the drama of ideas into which the student has the opportunity to immerse himself, the unique beauty of geometric facts, constructions and proofs; providing each student with maximum experience in independently proving and solving construction problems; the above-mentioned task of substantiating the applications of geometry in physics; application of geometric concepts and facts in everyday and professional activities; the usefulness of solving geometric problems for the development of formulaic calculation skills, in particular, with increased (due to geometric interpretation) possibilities for monitoring the correctness of the result.
REQUIREMENTS FOR THE RESULTS OF MASTERING THE PROGRAM The requirements for the results of mastering the program record and describe the levels of mathematical competence at the end of each grade of school. The description of the results of mastering the program by grade consists of indicating new elements of competence acquired by the completion of the next grade.
REQUIREMENTS FOR THE RESULTS OF MASTERING THE PROGRAM Grade 5 Mathematical competence after grade 5 includes all elements of mathematical competence after primary school, expanded through the transition from integers to rational numbers: ordinary and decimals, the ability to use names (variables) in algebraic expressions, solving equations. 6th grade Mathematical competence after 6th grade includes all elements of mathematical competence after 5th grade.
REQUIREMENTS FOR THE RESULTS OF MASTERING THE PROGRAM 7th grade mathematical competence after 7th grade includes all elements of mathematical competence after 6th grade. The main extension is the "functional view". 8th grade The main elements of competence by the end of 8th grade are: expansion of understanding of numbers, ability to solve quadratic equations ability to work with polynomials, understanding of proportionality in geometry.
REQUIREMENTS FOR THE RESULTS OF MASTERING THE PROGRAM Grade 9 The main elements of competence by the end of Grade 9 are the ability to: construct graphs of trigonometric functions, apply the concept of derivative, recognize curves and figures defined by equations and inequalities on the plane, know and apply the properties of vectors, including in their applications in geometry and physics.
Authors: Karakozov Sergey Dmitrievich 1, Doctor of Pedagogical Sciences, Professor
Atanasyan Sergey Levonovich 2, Doctor of Pedagogical Sciences, Professor
Semenov Alexey Lvovich 3, Doctor of Physical and Mathematical Sciences, Professor, Academician of the Russian Academy of Sciences, Academician of the Russian Academy of Education
1 Moscow State Pedagogical University, 2 Moscow City Pedagogical University, 3 Moscow Pedagogical University state university
The implementation of the Concept for the Development of Mathematical Education in the Russian Federation will provide a new level of mathematical education, which will improve the teaching of other subjects and accelerate the development of not only mathematics, but also other sciences and technologies. This will allow Russia to achieve its strategic goal and take a leading position in world science, technology and economics, as well as contribute to the development and testing of mechanisms for the development of education applicable in other areas
Key ideas of the Concept for the development of mathematics education in the Russian Federation and IT education
By order of the Government of the Russian Federation, the Concept for the development of mathematics education in Russia was approved, which is a system of views on basic principles, goals, objectives and main directions of development of mathematical education in the Russian Federation.
The Concept notes that
· Information, digital civilization, knowledge-based economy require new types and levels of mathematical literacy and culture. In particular, the creation of ICT tools and tools is primarily a mathematical activity.
· The most important concepts developed in mathematics and mastered by a person in his education: proofs, algorithms, measurements and models are today universal, culturally significant, and applied far beyond the boundaries of mathematics..
Mathematics is important element national idea and Russia's competitive advantage, which should be supported by appropriate preferences.
· Every citizen and every professional must have the necessary mathematical competence, the formation of which is the task of education, starting from an early, preschool age.
· Mastering mathematics is, first of all, solving new interesting problems using precise rules. Mathematical activity is a key element of the entire system of mathematical education. Usage modern technologies and activity tools, interaction environments will help Russia regain its leading position in mathematics education.
· Each level and segment of mathematical education is necessary, including for other segments and levels of education.
· Leaders should receive special support and special freedom of professional activity.
· The professional and social activity of mathematicians, as well as mathematics teachers, their awareness and implementation of their social mission are necessary for the development of mathematical education.
· Problems with the quality of mathematics teachers should receive a systematic solution.
The implementation of this Concept will provide a new level of mathematical education, which will improve the teaching of other subjects and accelerate the development of not only mathematics, but also other sciences and technologies. This will allow Russia to achieve its strategic goal and take a leading position in world science, technology and economics, as well as contribute to the development and testing of mechanisms for the development of education applicable in other areas.
To use presentation previews, create an account for yourself ( account) Google and log in: https://accounts.google.com
Slide captions:
Concept for the development of mathematics education in the Russian Federation. Structure (forms and content) of mathematical education: 1. Preschool 2. School 3. Club 4. Olimpiadnoe 5. Vuzovskoe
Preschool mathematics education. Goals: Acquaintance with the basics of mathematical culture; Instilling interest in further knowledge of the world around us. Forms of training: Simple communication; Individual lessons.
Mathematics education at school. Primary school (grades 1-4): Education is compulsory for everyone; Unified; There is no need for specialized gifted classes; Program variations are possible.
Basic school (grades 5-7) Introduction of primary study of geometry from grade 5; Solving practical problems: logic, movement and work, problems with integers; Creating a basis for further, in-depth study of more complex concepts.
Basic school (grades 8-9) Division of classes (starting from 8) into mathematical and non-mathematical; Possibility of changing the type of class during the learning process;
High school (grades 10-11) Additional division of mathematics classes into two streams: Mathematics is the main subject of study. Mathematics is a tool for mastering a future specialty.
Math clubs, olympiads, competitions. At schools, universities and educational centers; Distance (correspondence) forms of optional work.
Conclusions. IN elementary school reduce the ideological and abstract-conceptual load, increasing the time for solving textual and practical problems; In primary and high school, save problems on solving equations and inequalities; Shift to a later time (it is better to remove) material related to probability theory, mathematical statistics, combinatorics, set theory and logic. Special attention devote to the study of geometry, a subject unique in its role in mathematical education.
“Mathematical symmetry” - Symmetry in chemistry. Translational symmetry. Symmetry in the arts. Progressive. Axial. Central symmetry. Beam (radial) symmetry. So symmetry is perhaps almost the most important thing in the Universe. Rotational symmetry. Unlike physical symmetry, mathematical symmetry is found in many sciences.
“Mathematical induction” - In the 18th century, L. Euler found that when n=5. Composite number. Before us is a sequence of odd numbers in the natural series. 1,3,5,7,9,11,13… Proof algorithm using the method of mathematical induction. The principle of mathematical induction. Every person in the world has shaken some number of hands. Prove that the number of people who shook an odd number of hands is even.
“Mathematical Sciences” - You just need to understand and see. Addition. One of the greatest mathematicians. Creator of classical mechanics. Examples in mathematics. Karl Gauss (1777-1855). Five diggers dig a 5 m ditch in 5 hours. I stand on four legs, but I can’t walk at all. Established the principle of action of liquids and gases. Isaac Newton.
"Math Games" - Basic functions. Play is one of the main types of human activity. Group games. Group. Regatta. Mathematical games are a great way not only to identify, but also to teach talented children. The game is exploration. Individual games. Development of skills and abilities necessary for research activities.
“Mathematical riddles” - Only the shavings turned white. Yes, there are four pieces in the oven, the grandchildren are counting the pies. The answer. You can’t put our mosquitoes in a row. How many sisters were there? And the cat dragged another pie under the bench. Komarik counted forty pairs, and Komar himself continued counting. My brothers helped me. The grandmother put the cabbage pies in the oven.
“Mathematical education” - The material itself makes it possible to teach a child to work intellectually. B.P. Geidman, “On school mathematical education.” I’ll talk about teaching mathematics beyond the minimum later. We need unique specialists who combine teaching skills with good mathematical training. B.P. Geidman.