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.