Six key principles for effective teaching of mathematics are outlined in Peter Sullivan’s Teaching Mathematics: Using research-informed strategies (2011). These principles draw on work from a range of researchers in this field, including Good, Grouws and Ebmeier (1983); Hattie (2009); Swan (2005); Clarke and Clarke (2004); and Anthony and Walshaw (2009).
The six principles are articulating goals, making connections, fostering engagement, differentiating challenges, structuring lessons, and promoting fluency and transfer. Explore teaching strategies aligned to the principles below.
Principle 1: Articulating goals
Identify key ideas that underpin the concepts you are seeking to teach, communicate to students that these are the goals of the teaching, and explain to them how you hope they will learn (Sullivan, 2011).
Having a clear learning goal when planning a lesson or sequence of lessons ensures that learning activities are targeted towards the goal.Read more
Principle 2: Making connections
Build on what students know, mathematically and experientially, including creating and connecting students with stories that both contextualise and establish a rationale for the learning (Sullivan, 2011).
Culturally responsive pedagogies
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.Read more
It is well known that girls tend to be under-represented in higher level mathematics classes. How teachers talk and interact with their students is key to overcoming this.Read more
Principle 3: Fostering engagement
Engage students by utilising a variety of rich and challenging tasks that allow students time and opportunities to make decisions, and which use a variety of forms of representation (Sullivan, 2011).
Principle 4: Differentiating challenges
Interact with students while they engage in the experiences, encourage students to interact with each other, including asking and answering questions, and specifically plan to support students who need it and challenge those who are ready (Sullivan, 2011).
Principle 5: Structuring lessons
Adopt pedagogies that foster communication and both individual and group responsibilities, use students’ reports to the class as learning opportunities, with teacher summaries of key mathematical ideas (Sullivan, 2011).
Principle 6: Promoting fluency and transfer
Fluency is important, and it can be developed in two ways: by short everyday practice of mental processes; and by practice, reinforcement and prompting transfer of learnt skills (Sullivan, 2011).
Spaced, interleaved and retrieval practice
These are three strategies that can be used to increase student retention and recall of their learning.Read more
Metacognitive skills are those that students need to be able to reflect on their own learning, set goals for themselves, monitor their progress and make improvements to move forward.Read more