The subject of mathematics is all that this science studies, expressed in the most general form.
Scientists in the field of this education mainly deal with such tools, methods and approaches that facilitate learning in general. However, studies in the field of mathematical education, known on the European continent as didactics or pedagogy of mathematics, today have turned into a vast field of study with their own concepts, theories, methods, national and international organizations, conferences and literature.
History
The elementary subject of mathematics was part of the educational system in most ancient civilizations, including Greece, the Roman Empire, the Vedic society, and, of course, Egypt. In most cases, formal education was available only to male children with a fairly high status or income.
In the history of the subject of mathematics, Plato also divided the humanities into the trivium and quadrivium. They included various fields of arithmetic and geometry. This structure was continued in the structure of classical education, which was developed in medieval Europe. Teaching geometry is almost universally distributed precisely on the basis of Euclidean elements. Pupils of professions such as masons, traders and lenders can rely on the study of such a practical subject - mathematics, since it is directly related to their profession.
During the Renaissance, the academic status of mathematics declined because it was closely associated with trade and commerce and was considered somewhat non-Christian. Although she continued to be taught at European universities, she was considered subordinate to the study of natural, metaphysical, and moral philosophy.
The first modern arithmetic sample program in the subject of mathematics (starting from addition, then subtraction, multiplication and division) arose in Italian schools in the 1300s. Spreading along trade routes, these methods were developed for use only in trade. They contrasted with the Platonic mathematics taught at universities, which was more philosophical and related to numbers as concepts, rather than calculation methods.
They also bordered on theories learned by artisan students. Their knowledge was quite specific for the tasks. For example, dividing a board into thirds can be done using a piece of string instead of measuring length and using the arithmetic division operation.
Later times and modern history
The social status of mathematical education improved by the seventeenth century, when the department of the subject was created at the University of Aberdeen in 1613. Then, in 1619, geometry was discovered at Oxford University as a taught discipline. A specialized department was created by the University of Cambridge in 1662. However, even an exemplary program in mathematics outside universities was rare. For example, even Isaac Newton did not receive education in the field of geometry and arithmetic until he entered Trinity College, Cambridge, in 1661.
By the twentieth century, science was already part of the main curriculum of the mathematics subject in all developed countries.
In the 20th century, the cultural influence of the “electronic age” also influenced the theory of education and teaching. While the previous approach focused on “working with specialized problems in arithmetic,” the emerging structural type possessed knowledge and made young children think about number theory and their sets.
What subject is mathematics, goals
At different times and in different cultures and countries, many goals were set for mathematical education. They included:
- Learning and mastering basic counting skills for absolutely all students.
- A lesson in practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry) for most children so that they can engage in craft.
- Learning abstract concepts (such as set and function) at an early age.
- The teaching of certain areas of mathematics (for example, Euclidean geometry), as an example of the axiomatic system and model of deductive thinking.
- The study of various areas (such as calculus), as an example of the intellectual achievements of the modern world.
- Teaching advanced mathematics to those students who want to pursue a career in science or technology.
- Training in heuristics and other strategies for solving problems for solving non-standard problems.
Wonderful goals, but how many modern schoolchildren say so: "My favorite subject is mathematics."
Most popular methods
The methods used in any particular context are largely determined by the goals that the relevant educational system is trying to achieve. Mathematics teaching methods include the following:
- Classical education. Studying a subject from simple (arithmetic in elementary grades) to complex.
- Custom approach. It is based on the study of the subject in quadrivium, which was once part of the classical curriculum in the Middle Ages, built on Euclidean elements. It is he who is taught as a paradigm in deduction.
Games can motivate students to improve skills that they usually learn. In Number Bingo, players roll 3 dice, then perform basic mathematical operations on these numbers to get new values, which they place on the board, trying to cover 4 squares in a row.
- Computer mathematics is an approach based on the use of software as the main calculation tool, for which the following subjects were combined: mathematics and computer science. Mobile applications have also been developed to help students learn this subject.
Traditional approach
Gradual and systematic leadership through a hierarchy of mathematical concepts, ideas, and methods. It starts with arithmetic and is accompanied by Euclidean geometry and elementary algebra, which are taught simultaneously.
It requires the teacher to be well informed about primitive mathematics, because decisions on didactic and curriculum are often dictated by the logic of the subject, rather than pedagogical considerations. Other methods appear, highlighting some aspects of this approach.
Various exercises to strengthen knowledge
Strengthening mathematical skills by performing a large number of tasks of a similar type, such as adding irregular fractions or solving quadratic equations.
The historical method: teaching the development of mathematics in an epochal, social and cultural context. Provides more human interest than the usual approach.
Mastery: The way in which most students must achieve a high level of competency before progressing.
A new subject in the modern world
A math teaching method that focuses on abstract concepts such as set theory, functions and foundations, and so on. Accepted in the United States as a response to the challenge of early Soviet technical superiority in space, it began to be challenged in the late 1960s. One of the most influential critics of the new era was Maurice Kline. It was his method that was one of the most popular parody teachings of Tom Lerer, he said:
"... in the new approach, as you know, it is important to understand what you are doing, and not how to get the right answer."
Problem solving, math subject, subject count
The cultivation of ingenuity, creativity and heuristic thinking by setting students open, unusual, and sometimes unresolved problems. Tasks can vary from simple verbal to international mathematical competitions, such as, for example, the Olympics. Problem solving is used as a means to create new knowledge, usually based on a previous understanding of students.
Among the math subjects studied in the framework of the school curriculum:
- Mathematics (taught from grades 1 to 6).
- Algebra (7-11).
- Geometry (grades 7-11).
- ICT (computer science) grades 5-11.
Entertaining math is introduced as an optional. Fun tasks can motivate students to study the subject and increase their enjoyment.
Standards Based
The concept of preschool mathematical education is focused on enhancing students' understanding of various ideas and procedures. This concept is formalized by the National Council of Teachers, which created the "Principles and Standards" for the subject in the school.
Relational approach
Uses classic themes to solve everyday problems and associates this information with current events. This approach focuses on the many areas of application of mathematics and helps students understand why they need to study it, and also shows how to use their knowledge in real situations outside the classroom.
Content and age levels
Different quantities of mathematics are taught according to how old a person is. Sometimes there are children for whom a more complex level of the subject can be taught at an early age, for which they are enrolled in a physics and mathematics school or class.
Elementary mathematics is taught in the same way in most countries, although there are some differences.
Most often, algebra, geometry and analysis are studied as separate courses in different years of high school. Mathematics is integrated in most other countries, and topics from all its fields are studied there every year.
Basically, students studying these scientific programs learn differential calculus and trigonometry at the age of 16–17 years, as well as integral and complex numbers, analytical geometry, exponential and logarithmic functions, and infinite series in the last year of their high school. Probability and statistics can also be taught during this period.
Standards
For most of history, standards for math education have been set at the local level by individual schools or teachers, depending on their performance.
Nowadays, there is a transition to regional or national standards, usually under the auspices of wider school subjects of mathematics. In England, for example, this education is established as part of the National Curriculum. While Scotland maintains its own system.
According to a study by other scientists who found, based on national data, it turned out that students with higher scores on standardized math tests took more courses in high school. This has led some countries to revise their teaching policies for this subject.
For example, an in-depth study of a subject was supplemented when taking a course in mathematics by solving problems of a lower level, creating a “diluted” effect. The same approach was used for classes with the usual school curriculum in mathematics, “wedging” more complex tasks and concepts into it. T
Research
Of course, to date, the ideal and most useful theories for studying mathematics at school do not yet exist. Nevertheless, it cannot be denied that there are fruitful teachings for children.
In recent decades, a lot of research has been done to find out how these many theories of information integration can be applied to the latest modern learning.
One of the strongest outcomes and achievements of recent experiments and tests is that the most significant feature of effective learning has been the provision of “learning opportunities” for students. That is, teachers can determine expectations, time, types of tasks in the subject of mathematics, questions, acceptable answers and types of discussions that will affect the ability of the process of introducing information.
This should include both skill effectiveness and conceptual understanding. The teacher as an assistant, not the basis. It is noted that in those classes in which this system was introduced, students often say: "My favorite subject is mathematics."
Conceptual understanding
The two most important features of training in this direction are the explicit attention to concepts and the provision of opportunities for students to cope with important problems and difficult tasks on their own.
Both of these features have been confirmed through a wide range of studies. Explicit attention to concepts involves establishing links between facts, procedures, and ideas (this is often seen as one of the strengths in teaching mathematics in East Asia, where teachers usually devote about half their time to establishing links. The other extreme is the USA, where in school classes there is practically no imposition).
These relationships can be established by explaining the meaning of the procedure, questions comparing strategies and problem solving, noting how one task is a special case of another, reminding students of the main thing, discussing how different lessons interact and so on.