Three Principles of Mathematics Teaching


Principle 1: “Teaching is for learning; learning is for understanding; understanding is for reasoning and applying and, ultimately problem solving.”


Teaching is an interactive process that is focused on students’ learning. In this process, teachers use a range of teaching approaches to engage students in learning; students provide teachers with feedback on what they have learnt through assessment; and teachers in turn provide feedback to students and make decisions about instructions to improve learning.


The learning of mathematics should focus on understanding, not just recall of facts or reproduction of procedures. Understanding is necessary for deep learning and mastery. Only with understanding can students be able to reason mathematically and apply mathematics to solve a range of problems. After all, problem solving is the focus of the mathematics curriculum.


Principle 2: “Teaching should build on students’ knowledge; take cognizance of students’ interests and experiences; and engage them in active and reflective learning.”


Mathematics is a hierarchical subject. Without understanding of pre-requisite knowledge, foundation will be weak and learning will be shallow. It is important for teachers to check on students’ understanding before introducing new concepts and skills.


Teachers need to be aware of their students’ interests and abilities so as to develop learning tasks that are stimulating and challenging. This is important in order to engage students in active and reflective learning where students participate and take ownership of the learning.


Principle 3: “Teaching should connect learning to the real world, harness ICT tools, and emphasise common competencies.”


There are many applications of mathematics in the real world. Students should have an understanding and appreciation of these applications and how mathematics is used to model and solve problems in real-world contexts. In this way, students will see the meaning and relevance of mathematics.


Teachers should consider the affordances of ICT to help students learn. ICT tools can help students understand mathematical concepts through visualisations, simulations and representations. They can also support exploration and experimentation and extend the range of problems accessible to students. The ability to use ICT tools is part of the common competencies. It is also important to design learning in ways that promote the development of other common competencies such as working collaboratively and thinking critically about the mathematical solution.