Presentation of elements of the concept of mathematics education in the classroom. Motivational problems of mathematics education


Concept for the development of mathematics education in the Russian Federation The main goal of the Concept: to bring Russian mathematics education to a leading position in the world. The task of the Russian pedagogical community is to ensure that mathematics in Russia becomes an advanced and attractive field of knowledge and activity, and that obtaining mathematical knowledge becomes a conscious and internally motivated process.




MOTIVATION Low academic motivation of schoolchildren is associated with: – public underestimation of the importance of mathematics education, – overload educational programs, as well as evaluation and teaching materials technical elements and outdated content - with a lack of programs that meet the needs of students and the actual level of their preparation. Concept for the development of mathematics education in the Russian Federation


Goals of mathematics education The priorities of mathematics education are the development of abilities to: logical thinking, communication and interaction on a wide range of mathematical material (from geometry to programming); real mathematics: mathematical modeling(building a model and interpreting the results), applying mathematics, including using ICT; finding solutions to new problems, forming internal representations and models for mathematical objects, overcoming intellectual obstacles. Particular attention to independent decision tasks, including new ones that are at the limit of the student’s capabilities, were and remain important feature domestic mathematical education.


The subject content of education will include everything more elements applied mathematics, computer science, " computer mathematics» (including those created to describe and study the processes of thinking, communication, and human activity); Mathematical (like all educational) activities will increasingly take place in a (digital, electronic) information environment that ensures interaction between participants educational process, access to information sources, recording the progress and results of the educational process, the possibility of their automated analysis and external observation


Mathematics in general education For each child, his “corridor of proximal development” must be individually designed. The concept of “a child incapable of mathematics” should lose its meaning and disappear from the vocabulary of teachers, parents, schoolchildren and society.


Concept for the development of mathematics education in the Russian Federation Preschool and primary education: – creation of conditions conducive to the development of logical-mathematical and communicative abilities; – use of mathematical, logical and strategic games, subject and screen competitions. Basic school: – variety of applications; – computer tools and models. High school: identify three streams that provide basic mathematical competence for students, a broad general cultural program of mathematical training; – in-depth study mathematics.


Schools, kindergartens, institutions additional education children, higher and additional vocational education should be centers of mathematical culture in society: accessible, vibrant mathematics should be present in the information environment of urban spaces, premises and sites, educational methodological complexes should include material for parents to work with their child. Mathematics in general education


Students with low academic results, with “accumulating ignorance” from socially disadvantaged families, with disabilities health, those who missed classes due to illness should be provided with constant tutor support, which will allow them to return “to the main stream.” This is important both for increasing the guaranteed minimum of mathematical competence in society and for increasing the effectiveness of learning for the bulk of students. Mathematics in general education

PROBLEMS OF MATHEMATICS EDUCATION Motivational. Public underestimation of the importance of mathematics education, Overloading of school and university programs with technical elements and outdated content. Unrealistic certification requirements for a significant part of graduates. Content-based. 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. There is virtually no difference in curricula oh and certification 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 and higher education. There is a disconnect between university education and modern science and practice, its level is falling, which is partly due to insufficient integration Russian science to 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. Graduates pedagogical universities the majority 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 AN EXAMPLE PROGRAM The modern content of the mathematics and computer science course of primary 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 THE SAMPLE PROGRAM Important place Mathematical competence developed during primary school education includes elements whose application (and thus mastery) traditionally begins in physics lessons. IN modern course physicists actively use the concepts of perpendicularity, parallelism, vector (and “delaying a vector from a point”), operations on vectors (in particular, decomposition of a vector along two axes), trigonometric functions(angle less than the unfolded angle), derivative (rate of change), similarity (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 passing 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 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 unfolded 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 an estimate obtained by discarding all decimal places of a number, starting with a certain one (approximation with a disadvantage), or a similar operation that gives an “upper estimate.”


PROGRAM CONTENT Whole, rational and real numbers Measurements, approximations, estimates Algebraic expressions Equations Inequalities Functions Number sequences Descriptive statistics Combinatorics Geometry Information and methods of its presentation 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 by moving 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 at the end of grade 9 are the ability to: construct graphs of trigonometric functions, apply the concept of derivative, recognize curves and figures, given by equations and inequalities on the plane, know and apply the properties of vectors, including their applications in geometry and physics.


I. The importance of mathematics in modern world A quality mathematics education is necessary for everyone to lead a successful life in modern society. Without high level mathematical education, it is impossible to complete the task of creating innovation economy, implementation of long-term goals and objectives of the socio-economic development of the Russian Federation. Increasing the level of mathematical education will make more full life Russians in modern society will meet the needs for qualified specialists for knowledge-intensive and high-tech production.


II. Problems of development of mathematics education 1. Problems of a motivational nature: - low educational motivation of schoolchildren associated with public underestimation of the importance of mathematics education; - outdated content and lack of training programs that meet the needs of students and the actual level of their training. 2. Problems of a substantive nature: - the content of mathematical education continues to become outdated and remains formal and detached from life; - the needs of future specialists in mathematical knowledge are not sufficiently taken into account; - replacing training with “coaching” for an exam.


II. Problems of development of mathematics education 3. Personnel problems - Graduates educational organizations higher education pedagogical orientation for the most part do not meet the qualification requirements, professional standards have little experience pedagogical activity and experience in applying pedagogical knowledge.




III. Goals and objectives of the Concept Objectives: - modernization of the content of mathematics education curricula at all levels (ensuring their continuity); - ensuring that there are no gaps in basic knowledge for each student; -ensuring the availability of publicly available information resources necessary for the implementation of mathematics education curricula; -improving the quality of work of mathematics teachers; - support for leaders in mathematics education; -providing students who are highly motivated and exhibit outstanding mathematical abilities with all conditions for the development and application of these abilities; - popularization of mathematical knowledge and mathematical education.


IV. Main directions for the implementation of the Concept 1. Preschool and primary general education: The system of mathematics education curricula with the participation of the family should provide: primary education– a wide range of mathematical activities for students in the classroom and during extracurricular activities, material, information and personnel conditions for the development of students using mathematics


IV. Main directions for the implementation of Concept 2. Basic general and secondary general education Mathematics education should: - provide each student with the opportunity to achieve the level of mathematical knowledge necessary for further successful life in society; -provide each student with developing intellectual activity at an accessible level; - to provide the number of graduates required by the country, whose mathematical support is sufficient to continue education in various directions and for practical activities, including teaching mathematics.


IV. Main directions for the implementation of Concept 2. Basic general and secondary general education It is necessary to provide each student with the opportunity to achieve compliance with any level of training, taking into account his individual needs and abilities. The possibility of achieving a high level of training should be ensured by the development of a system of specialized educational institutions and specialized classes, a system of additional education for children in field of mathematics. Need to stimulate individual approach and individual forms of work with lagging students, primarily involving teachers with extensive experience.


IV. Main directions for the implementation of Concept 5. Mathematical education and popularization of mathematics, additional education For mathematical education and popularization of mathematics, the following is provided: - Ensuring state support for the accessibility of mathematics for all age groups of the population; - creating a public atmosphere of a positive attitude towards the achievements of mathematical science and work in this field; -Providing continuous support and improving the level of mathematical knowledge. Additional education system: mathematical clubs, competitions, distance learning in mathematics, interactive museums of mathematics, mathematical projects on Internet portals, professional mathematical online communities.



“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. On four legs I’m standing, but I can’t walk at all. Established the principle of action of liquids and gases. Isaac Newton.

"Math Games" - Basic functions. Game is one of the main types human activity. Group games. Group. Regatta. Math games – great way not only identifying, but also training 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 pedagogical skill with good mathematical background. B.P. Geidman.

CONCEPT OF THE DEVELOPMENT OF MATHEMATICS EDUCATION IN THE RUSSIAN FEDERATION

Approved

by government order

Russian Federation



Problems of development of mathematics education:

  • Low motivation of schoolchildren and students, which is associated with
  • undervaluation of mathematics education
  • overloading of programs with technical elements
  • outdated content;

3. Personnel. In Russia there are not enough teachers and university professors who could teach mathematics with high quality.


Purpose of the Concept

bring Russian mathematical education to a leading position in the world.

Mathematics in Russia should become an advanced and attractive field of knowledge and activity, and acquiring mathematical knowledge should be a conscious and internally motivated process.


  • preserve the merits of the Soviet system of mathematics education and “overcome serious shortcomings”;
  • ensure that there are no gaps in basic knowledge for each student using modern technologies educational process;
  • modernize the content of training programs based on the needs for specialists in various fields;
  • improve the quality of work of mathematics teachers (from school to college);
  • strengthen material and social support for mathematics teachers;
  • formulate among students and teachers the following attitude: “there are no children incapable of mathematics”;
  • stimulate individual forms of work with lagging students, involving teachers with extensive experience, etc.

Main directions of implementation of the Concept

  • Preschool and primary general education
  • V preschool education– students’ mastery of forms of activity, primary mathematical concepts and images used in life;
  • in primary general education – ensuring students’ mathematical activity both in class and in extracurricular activities (primarily solving logical and arithmetic problems, constructing algorithms in a visual and gaming environment).

2. Basic general and secondary general education

  • provide each student with the opportunity to achieve the level of mathematical knowledge necessary for further successful life in society;
  • provide each student with developing intellectual activity at an accessible level, using the inherent beauty and fascination of mathematics;
  • provide the number of graduates required by the country, whose mathematical preparation is sufficient to continue education in various directions and for practical activities.

In basic general and secondary general education, it is necessary to provide for the preparation of students in accordance with their needs for the level of preparation in the field of mathematics education.

It is necessary to stimulate an individual approach and individual forms of work with lagging students, first of all, attracting teachers with extensive experience.


As a result of the implementation of the concept, levels of mathematics education will be introduced:

  • the first level - for a successful life in modern society;
  • the second level - for the professional use of mathematics in further studies and professional activities;
  • third level - for further preparation for creative work in mathematics and related scientific fields.

3. Vocational education

must provide the necessary level of mathematical training for the needs of mathematical science, economics, scientific and technological progress, security and medicine.

4. Additional professional education

training of scientific and pedagogical workers of educational organizations of higher education and scientific workers.


Implementation of the Concept

  • 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.
  • The implementation of this Concept will contribute to the development and testing of mechanisms for the development of education applicable in other areas.

Action plan for the implementation of the Concept for the development of mathematics education in Bogucharsky municipal area in 2016.

Event name

Workshop for mathematics teachers

We assume. duration of the event

Venue

May 2016

Meeting of the Russian Educational Institution for Mathematics Teachers on the topic: “Implementation of the Concept for the Development of Mathematics Education in the Russian Federation: Everyone Needs Mathematics”

Analysis of the quality of teacher mathematics education

MKOU "Bogucharskaya Secondary School No. 1"

June 2016

Development of an educational institution plan to improve the quality of mathematics education for students

MKOU "Bogucharskaya Secondary School No. 1"

July 2016

MKU "Department of Education and Youth Policy"

RMO meeting:

a) “Problems of mathematical education in the light of Unified State Exam results, OGE"

b) “Examination of work programs in mathematics”

August 2016

General educational institution

August 2016

MKOU "Bogucharskaya Secondary School No. 1"

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