**Mathematics education** is the practice of teaching and learning mathematics, as well as the field of scholarly research on this practice. Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice.

### History of mathematics education

Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.

The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with *The Grounde of Artes* in 1540.

In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.

In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic, became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age.

By the twentieth century mathematics was part of the core curriculum in all developed countries.

### Objectives

At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included:

- The teaching of basic numeracy skills to all pupils
- The teaching of practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry) to most pupils, to equip them to follow a trade or craft
- The teaching of abstract mathematical concepts (such as set and function) at an early age
- The teaching of selected areas of mathematics (such as Euclidean geometry) as an example of an axiomatic system and a model of deductive reasoning
- The teaching of selected areas of mathematics (such as calculus) as an example of the intellectual achievements of the modern world
- The teaching of advanced mathematics to those pupils who wish to follow a career in Science, Technology, Engineering, and Mathematics (STEM) fields.
- The teaching of heuristics and other problem-solving strategies to solve non-routine problems.

Methods of teaching mathematics have varied in line with changing objectives.

### Standards and methods

Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils.

In modern times there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In England, for example, standards for mathematics education are set as part of the National Curriculum for England, while Scotland maintains its own educational system.

In North America, the National Council of Teachers of Mathematics (NCTM) has published the *Principles and Standards for School Mathematics*. In 2006, they released the *Curriculum Focal Points*, which recommend the most important mathematical topics for each grade level through grade 8. However, these standards are not nationally enforced in US schools.

The method or methods used in any particular context are largely determined by the objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following:

**Conventional approach** – the gradual and systematic guiding through the hierarchy of mathematical notions, ideas and techniques. Starts with arithmetic and is followed by Euclidean geometry and elementary algebra taught concurrently. Requires the instructor to be well informed about elementary mathematics, since didactic and curriculum decisions are often dictated by the logic of the subject rather than pedagogical considerations. Other methods emerge by emphasizing some aspects of this approach.
**Classical education** – the teaching of mathematics within the classical education syllabus of the Middle Ages, which was typically based on Euclid’s *Elements* taught as a paradigm of deductive reasoning.
**Rote learning** – the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning. A derisory term is *drill and kill*. Parrot Maths was the title of a paper critical of rote learning. Within the conventional approach, rote learning is used to teach multiplication tables.
**Exercises** – the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding vulgar fractions or solving quadratic equations.
**Problem solving** – the cultivation of mathematical ingenuity, creativity and heuristic thinking by setting students open-ended, unusual, and sometimes unsolved problems. The problems can range from simple word problems to problems from international mathematics competitions such as the International Mathematical Olympiad. Problem solving is used as a means to build new mathematical knowledge, typically by building on students’ prior understandings.
**New Math** – a method of teaching mathematics which focuses on abstract concepts such as set theory, functions and bases other than ten. Adopted in the US 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 critiques of the New Math was Morris Kline’s 1973 book *Why Johnny Can’t Add*. The New Math method was the topic of one of Tom Lehrer’s most popular parody songs, with his introductory remarks to the song: “…in the new approach, as you know, the important thing is to understand what you’re doing, rather than to get the right answer.”
**Historical method** – teaching the development of mathematics within an historical, social and cultural context. Provides more human interest than the conventional approach.
**Standards-based mathematics** – a vision for pre-college mathematics education in the US and Canada, focused on deepening student understanding of mathematical ideas and procedures, and formalized by the which created the *Principles and Standards for School Mathematics*.

(From Wikipedia, the free encyclopedia)

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