The subject of mathematics is everything that this science studies, expressed in the most general form.
Education scholars are mainly concerned with tools, methods and approaches that facilitate learning in general. However, research in mathematics education, known on the European continent as didactics or pedagogy of mathematics, has today become a vast field of study with its own concepts, theories, methods, national and international organizations, conferences and literature.
History
The elementary subject of mathematics was part of the education system in most ancient civilizations, including Greece, the Roman Empire, the Vedic Society and, of course, Egypt. In most cases, formal education was only available to male children of fairly high status or we alth.
In the history of the subject of mathematics, Plato also divided the humanities into trivium and quadrivium. They includedvarious fields of arithmetic and geometry. This structure was continued in the structure of the classical education, which was developed in medieval Europe. The teaching of geometry is almost universally distributed precisely on the basis of the Euclidean elements. Apprentices in professions such as masons, merchants and lenders can look forward to studying such a practical subject - mathematics, as 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 unchristian. Although it continued to be taught in European universities, it was considered subordinate to the study of natural, metaphysical and moral philosophy.
The first modern arithmetic sample program in the subject of mathematics (starting with addition, then subtraction, multiplication and division) originated 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 in universities, which was more philosophical and de alt with numbers as concepts rather than methods of calculation.
They also bordered on the theories learned by artisan apprentices. Their knowledge was quite specific to the tasks at hand. For example, dividing a board into thirds can be done with a piece of string instead of measuring the length and using the arithmetic operation of division.
Later times and modern history
Soci althe status of mathematical education was improving towards the seventeenth century, when a chair of the subject was established at the University of Aberdeen in 1613. Then, in 1619, geometry was discovered as a taught discipline at Oxford University. A specialized chair was established by the University of Cambridge in 1662. However, even an exemplary program in the subject of mathematics outside of universities was a rarity. For example, even Isaac Newton did not receive an education in geometry and arithmetic until he entered Trinity College, Cambridge, in 1661.
By the twentieth century, science was already part of the core curriculum for mathematics 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 was focused on "working with specialized problems in arithmetic", the emerging structure type had knowledge, made even young children think about number theory and their sets.
What subject is math, goals
At different times and in different cultures and countries, numerous goals were set for mathematics education. They included:
- Teaching and mastering basic counting skills for absolutely all students.
- Practical math class (arithmetic, elementary algebra, plane and solid geometry, trigonometry) for most kids to practice craft.
- Teaching abstract concepts (such asset and function) at an early age.
- Teaching certain areas of mathematics (for example, Euclidean geometry), as an example of an axiomatic system and a model of deductive thinking.
- The study of various fields (such as calculus) as an example of the intellectual achievements of the modern world.
- Teaching advanced math to students who want to pursue careers in science or engineering.
- Teaching heuristics and other problem solving strategies to solve non-routine problems.
Great goals, but how many modern schoolchildren say: “My favorite subject is math.”
Most Popular Methods
The methods used in any given context are largely determined by the goals that the respective education system is trying to achieve. Mathematics teaching methods include the following:
- Classical education. Studying the subject from simple (arithmetic in elementary grades) to complex.
- A non-standard approach. It is based on the study of the subject in the quadrivium, which was once part of the classical curriculum in the Middle Ages, built on Euclidean elements. It is he who is taught as paradigms in deduction.
Games can motivate students to improve skills that are usually learned by heart. In Number Bingo, players roll 3 dice, then perform basic math on those numbers to get new values, which they place on the board in an attempt to cover 4 squares in a row.
ComputerMathematics is an approach based on the use of software as the main tool for computing, for which the following subjects have been combined: Mathematics and Computer Science. Mobile apps have also been developed to help students learn the subject
Traditional approach
Gradual and systematic guidance through the hierarchy of mathematical concepts, ideas and methods. Starts with arithmetic and is followed by Euclidean geometry and elementary algebra, which are taught simultaneously.
Requires the teacher to be well-informed about primitive mathematics, as decisions on didactic and curricula are often dictated by the logic of the subject rather than by pedagogical considerations. Other methods emerge, emphasizing some aspects of this approach.
Various exercises to strengthen knowledge
Strengthening math skills by doing lots of similar type of tasks like adding improper fractions or solving quadratic equations.
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 reach a high level of competence before progressing.
New item in the modern world
A math teaching method that focuses on abstract concepts such asset theory, functions and foundations, and so on. Adopted in the US as a response to a challenge to early Soviet technological superiority in space, it became contested in the late 1960s. One of the most influential critics of modern times was Maurice Kline. It was his method that was one of the most popular parodic teachings of Tom Lehrer, he said:
"…in the new approach, as you know, it's important to understand what you're doing, not how to get the right answer."
Problem solving, Mathematics, Counting
Cultivate ingenuity, creativity and heuristic thinking by presenting students with open, unusual and sometimes unsolved problems. Problems can range from simple verbal challenges to international math competitions such as the Olympics. Problem solving is used as a means to create new knowledge, usually based on students' previous understanding.
Among the mathematical subjects studied as part of the school curriculum:
- Mathematics (taught grades 1 to 6).
- Algebra (7-11).
- Geometry (grades 7-11).
- ICT (computer science) grades 5-11.
Recreational math is introduced as an elective. Fun challenges can motivate students to study a subject and increase their enjoyment of it.
Standards Based
The concept of preschool mathematics education is focused on deepening students' understanding of various ideas and procedures. This concept is formalizedThe National Council of Teachers who created the "Principles and Standards" for the subject at school.
Relational approach
Uses classic themes to solve everyday problems and relates this information to current events. This approach focuses on the many applications of mathematics and helps students understand why they need to learn it, as well as how to apply what they have learned to real situations outside the classroom.
Content and age levels
Different amounts of mathematics are taught according to how old the 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.
In general, students in these science programs learn calculus and trigonometry at age 16-17, as well as integral and complex numbers, analytic geometry, exponential and logarithmic functions, and infinite series in their final year of high school. Probability and statistics may also be taught during this period.
Standards
ThroughoutFor most of history, math education standards were set locally by individual schools or by teachers based on merit.
In modern times, there has been a shift towards regional or national standards, usually under the auspices of broader school mathematics subjects. In England, for example, this education is established as part of the National Curriculum. Whereas Scotland maintains its own system.
A study by other scholars who found, based on nationwide data, found 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 in this academic discipline.
For example, an in-depth study of the subject was supplemented during the course in mathematics by solving problems of a lower level, creating a “diluted” effect. The same approach was applied to classes with a regular school curriculum in mathematics, "wedging" into it more complex tasks and concepts. T
Research
Of course, today there are no ideal and most useful theories for studying the subject of mathematics at school. However, it cannot be denied that there are fruitful teachings for children.
In recent decades, much 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 moststrong outcomes and achievements of recent experimentation and testing is that the most significant feature of effective teaching has been to provide students with "opportunities to learn". That is, teachers can define expectations, times, types of math assignments, questions, acceptable answers, and types of discussions that will affect the ability of the process to implement information.
This should include both skill effectiveness and conceptual understanding. The teacher is like an assistant, not a foundation. It has been noticed 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 teaching in this direction are explicit attention to concepts and enabling students to deal 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 making connections between facts, procedures, and ideas (this is often seen as one of the strengths of mathematics teaching in East Asian countries, where teachers typically devote about half of their time to making connections. At the other extreme is the United States, where there is practically no imposition in school classes).
These relationships can be established by explaining the meaning of procedure, questions, comparing strategies and problem solving, noticing how one task is a special case of another, remindingstudents about the main points, discussing how different lessons interact and so on.
