Mathematics education

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods. National and international organisations regularly hold conferences and publish literature in order to improve mathematics education.

History

Ancient

Elementary mathematics were a core part of education in many ancient civilisations, including ancient Egypt, ancient Babylonia, ancient Greece, ancient Rome, and Vedic India. In most cases, formal education was only available to male children with sufficiently high status, wealth, or caste. The oldest known mathematics textbook is the Rhind papyrus, dated from circa 1650 BCE.

Pythagorean theorem

Historians of Mesopotamia have confirmed that use of the Pythagorean rule dates back to the Old Babylonian Empire and that it was being taught in scribal schools over one thousand years before the birth of Pythagoras.
In Plato's division of the liberal arts into the trivium and the quadrivium, the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. The teaching of geometry was almost universally based on Euclid's Elements. Apprentices to trades such as masons, merchants, and moneylenders could expect to learn such practical mathematics as was relevant to their profession.

Medieval and early modern

In the Middle Ages, the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian. Although it continued to be taught in European universities, it was seen as subservient to the study of natural, metaphysical, and moral philosophy. The first modern arithmetic curriculum arose at reckoning schools in Italy in the 1300s. Spreading along trade routes, these methods were designed to be used in commerce. They contrasted with Platonic math taught at universities, which was more philosophical and concerned numbers as concepts rather than calculating methods. They also contrasted with mathematical methods learned by artisan apprentices, which were specific to the tasks and tools at hand. For example, the division of a board into thirds can be accomplished with a piece of string, instead of measuring the length and using the arithmetic operation of division.
The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with The Grounde of Artes in 1543. However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in Mesopotamia, where the Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving equations like the quadratic equation. After the Sumerians, some of the most famous ancient works on mathematics came from Egypt in the form of the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus. The more famous Rhind Papyrus has been dated back to approximately 1650 BCE, but it is thought to be a copy of an even older scroll. This papyrus was essentially an early textbook for Egyptian students.
The social status of mathematical study was improving by the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by the University of Cambridge in 1662.

Modern

In the 18th and 19th 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.
During the twentieth century, mathematics education was established as an independent field of research. Main events in this development include the following:

In 1893, a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein.
The International Commission on Mathematical Instruction was founded in 1908, and Felix Klein became the first president of the organisation.
The professional periodical literature on mathematics education in the United States had generated more than 4,000 articles after 1920, so in 1941 William L. Schaaf published a classified index, sorting them into their various subjects.
A renewed interest in mathematics education emerged in the 1960s, and the International Commission was revitalized.
In 1968, the was established in Nottingham.
The first International Congress on Mathematical Education was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that, it has been held every four years.

Midway through the twentieth century, the cultural impact of the "electronic age" was also taken up by educational theory and the teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic", the emerging structural approach to knowledge had "small children meditating about number theory and 'sets'." Since the 1980s, there have been a number of efforts to reform the traditional curriculum, which focuses on continuous mathematics and relegates even some basic discrete concepts to advanced study, to better balance coverage of the continuous and discrete sides of the subject:

In the 1980s and early 1990s, there was a push to make discrete mathematics more available at the post-secondary level;
From the late 1980s into the new millennium, countries like the US began to identify and standardize sets of discrete mathematics topics for primary and secondary education;
Concurrently, academics began compiling practical advice on introducing discrete math topics into the classroom;
Researchers continued arguing the urgency of making the transition throughout the 2000s; and
In parallel, some textbook authors began working on materials explicitly designed to provide more balance.

Similar efforts are also underway to shift more focus to mathematical modeling as well as its relationship to discrete math.

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 and learning of basic numeracy skills to all students
The teaching of practical mathematics to most students, to equip them to follow a trade or craft and to understand mathematics commonly used in news and Internet
The teaching of abstract mathematical concepts at an early age
The teaching of selected areas of mathematics as an example of an axiomatic system and a model of deductive reasoning
The teaching of selected areas of mathematics as an example of the intellectual achievements of the modern world
The teaching of advanced mathematics to those students who wish to follow a career in science, technology, engineering, and mathematics fields
The teaching of heuristics and other problem-solving strategies to solve non-routine problems
The teaching of mathematics in social sciences and actuarial sciences, as well as in some selected arts under liberal arts education in liberal arts colleges or universities
Methods

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:
File:Digital carrel classroom.webp|thumb|3D sketch of desk cubicles to get computers in the classroom for computer-based mathematics, CAD, CAM, BIM, computer-aided engineering, computer programming, animation software, science software applications, and more.

Computer-based math: an approach based on the use of mathematical software as the primary tool of computation.
Computer-based mathematics education: involves the use of computers to teach mathematics. Mobile applications have also been developed to help students learn mathematics.
Classical education: the teaching of mathematics within the quadrivium, part of the classical education curriculum of the Middle Ages, which was typically based on Euclid's Elements taught as a paradigm of deductive reasoning.
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.
Relational approach: uses class topics to solve everyday problems and relates the topic to current events. This approach focuses on the many uses of mathematics and helps students understand why they need to know it as well as helps them to apply mathematics to real-world situations outside of the classroom.
Historical method: teaching the development of mathematics within a historical, social, and cultural context. Proponents argue it provides more human interest than the conventional approach.
Discovery math: a constructivist method of teaching mathematics which centres around problem-based or inquiry-based learning, with the use of open-ended questions and manipulative tools. This type of mathematics education was implemented in various parts of Canada beginning in 2005. Discovery-based mathematics is at the forefront of the Canadian "math wars" debate with many criticizing it for declining math scores.
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."
Recreational mathematics: mathematical problems that are fun can motivate students to learn mathematics and can increase their enjoyment of mathematics.
Standards-based mathematics: a vision for pre-college mathematics education in the United States and Canada, focused on deepening student understanding of mathematical ideas and procedures, and formalized by the National Council of Teachers of Mathematics which created the Principles and Standards for School Mathematics.
Mastery: an approach in which most students are expected to achieve a high level of competence before progressing.
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.
Exercises: the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding simple fractions or solving quadratic equations.
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. In traditional education, rote learning is used to teach multiplication tables, definitions, formulas, and other aspects of mathematics.
Math walk: a walk where experience of perceived objects and scenes is translated into mathematical language.