Mathematics education

Mathematics education is an important part of learning in schools today. It involves how teachers teach, how students learn, and how researchers study the best ways to share mathematical knowledge. This field looks at many different ideas, theories, and methods to help everyone understand math better.

A child calculating with his fingers (2006)

People all over the world, including national and international organisations, work together to improve how math is taught. They hold meetings and publish literature to share new ideas and findings. This helps make sure that students everywhere get the best possible education in mathematics.

Objectives

Mathematics education aims to help students learn many different skills and concepts. Some of the goals include teaching basic counting and number skills to everyone. It also teaches practical math like adding, subtracting, and understanding shapes to help students in everyday life, such as when seeing charts or percentages online.

Other goals are to introduce more complex ideas early on, show how math can be a logical system, and prepare students who want to study science or engineering. Math is also taught to help solve tricky problems and is used in many different subjects and careers.

Methods

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.

The way math is taught depends on what the school wants students to learn. There are many different methods used to teach math:

Games can motivate students to improve skills that are usually learned by rote. In "Number Bingo," players roll 3 dice, then perform basic mathematical operations on those numbers to get a new number, which they cover on the board trying to cover 4 squares in a row. This game was played at a "Discovery Day" organized by Big Brother Mouse in Laos.

Computer-based math: Using special math software as the main tool for calculations.
Computer-based mathematics education: Teaching math using computers and mobile apps.
Classical education: Teaching math as part of an old education style from the Middle Ages, using a famous book called Elements by Euclid.
Conventional approach: Teaching math step-by-step, starting with arithmetic, then geometry, and algebra.
Relational approach: Using math to solve everyday problems and connecting it to current events.
Historical method: Teaching math by looking at how it developed over time in different cultures.
Discovery math: A way of teaching math by letting students explore and discover ideas through problems and activities. This method started in Canada in 2005.
New Math: A teaching method that focuses on abstract ideas like sets and different number bases. It was popular in the US for a time but faced criticism.
Recreational mathematics: Using fun math problems to make learning math more enjoyable.
Standards-based mathematics: A plan for teaching math in the United States and Canada that aims to help students understand math ideas deeply.
Mastery: Making sure students are very good at a math topic before moving on to the next.
Problem solving: Teaching students to think creatively and come up with their own ways to solve unusual and challenging math problems.
Exercises: Practicing math skills by doing many similar problems, like adding fractions or solving equations.
Rote learning: Teaching math by repetition and memorization, often without deep understanding.
Math walk: A walk where students describe what they see using math words and ideas.

Content and age levels

Different levels of mathematics are taught at different ages in various countries. Sometimes, students may take advanced classes earlier than usual.

In elementary school, children learn about whole numbers and arithmetic, including addition, subtraction, multiplication, and division. They also study comparisons and measurement, fractions, patterns, and basic geometry.

A mathematics lecture at Aalto University School of Science and Technology

In high school in the US, algebra, geometry, and analysis are usually taught as separate courses. In many other countries, these topics are integrated into one ongoing course each year. Some countries offer different math options based on what students plan to study after high school. For example, in South Africa, students can choose between Mathematics, Mathematical Literacy, and Technical Mathematics. Science students often study calculus and trigonometry by age 16–17 and more advanced topics like integral calculus and complex numbers in their final year.

At the college level, science and engineering students typically study multivariable calculus, differential equations, and linear algebra. Mathematics majors go deeper into pure and applied mathematics, including topics like differential geometry, set theory, and topology. Applied mathematics covers areas such as partial differential equations and numerical analysis. Business and social science students usually take courses in statistics and probability, while liberal arts students might study topics like number theory, logic, and applications of mathematics to other fields.

Standards

In the past, each school or teacher decided what level of math students should learn. Today, many places have set rules for math learning as part of their school plans. For example, England has its National Curriculum, and Scotland has its own system. Many countries have special groups that decide these rules.

Some studies show that students who take more math classes do better on tests. Because of this, some areas now ask students to take three years of math instead of two. Groups like the National Council of Teachers of Mathematics have made suggestions for what math topics are most important for each grade. In the United States, many states use the Common Core State Standards, but each state can choose whether to follow them.

The Programme for International Student Assessment (PISA) checks how well 15-year-old students around the world do in reading, science, and math. It started in 2000 with 43 countries and happens every three years to help improve education.

Research

Paul Ernest talked about important topics to study in learning math. These include how math is taught, what students learn, and how teachers help students understand math.

Research shows that good teaching gives students chances to really learn. Teachers can help by setting clear goals and giving students tasks that let them think and solve problems. Two key ideas are helping students understand concepts and letting them work with tricky math ideas. This helps students learn better, even if they get confused at first.

Good ways to check how students are learning include special activities that help teachers see what students know and giving helpful feedback. Homework that lets students practice old lessons or get ready for new ones works best. For students who find math hard, working with friends, using pictures, and talking about their thinking can help a lot.

Learning algebra takes time. Kids need to understand ideas before they learn symbols. Many think letters always mean unknown numbers, which can be confusing. It also helps to connect math to different cultures and backgrounds so all students feel included. Learning to teach math well includes learning from students and focusing on their thinking.

History

Ancient

Elementary mathematics was an important part of education in many ancient places, including ancient Egypt, ancient Babylonia, ancient Greece, ancient Rome, and Vedic India. Usually, only boys who were wealthy or from important families could go to school.

One of the oldest math books we know about is the Rhind papyrus, which is about 3,600 years old.

Pythagorean theorem

People in Mesopotamia used a rule that matches the Pythagorean theorem over 4,000 years ago, teaching it in schools long before a famous thinker named Pythagoras was born.

In the way Plato divided learning, math was part of a group called the quadrivium, which included arithmetic and geometry. Geometry lessons often used a book called Elements written by Euclid. Tradespeople like builders and shop owners learned practical math for their jobs.

Medieval and early modern

Illustration at the beginning of a 14th-century translation of Euclid's Elements

In the Middle Ages, math was not very respected because it was linked to trade and business. Even so, it was still taught in European universities, but seen as less important than studying nature, ideas, and good behavior.

The first modern math books in English and French were written by Robert Recorde in 1543, called The Grounde of Artes. Before that, people in Mesopotamia were doing multiplication and division almost 6,000 years ago. We have pieces of paper from Egypt called the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus that show their math skills. The Rhind Papyrus is from about 1650 BCE, but it may be a copy of an even older book. It was like a textbook for Egyptian students.

By the 1600s, math was becoming more respected. Schools such as the University of Aberdeen and the University of Oxford started special positions for teaching math.

Modern

During the 1700s and 1800s, as cities grew because of the Industrial Revolution, knowing basic math became very important for everyday life. In new schools for everyone, math became a key subject for young children.

By the 1900s, math was a main part of school in all advanced countries.

The 1900s saw math education become its own area of study. Important moments include:

In 1893, a special position for math teaching was created at the University of Göttingen, led by Felix Klein.
In 1908, the International Commission on Mathematical Instruction was started, with Felix Klein as its first leader.
By 1941, there were over 4,000 articles about teaching math in the United States.
In 1968, a center for math education was set up in Nottingham.
The first meeting about world math teaching happened in Lyon in 1969, with more meetings every four years.

Since the 1980s, there have been efforts to change the usual math curriculum to include more balanced topics and focus on how math relates to the real world.

Organizations

Many groups work together to help teach math better. Some of these groups are the Advisory Committee on Mathematics Education, the American Mathematical Association of Two-Year Colleges, and the Association of Teachers of Mathematics. Others include the Canadian Mathematical Society, the National Council of Teachers of Mathematics, and the OECD. These organizations hold meetings and share ideas to improve how math is taught in schools around the world.