Teaching Mathematics:Using research-informed strategies by Peter Sullivan (ACER)

Identify key ideas that underpin the concepts you are seeking to teach

Communicate to students that these are the goals of the teaching

Explain to the students how you hope they will learn

Write the goals on the boardProvide feedback for students

Students need to know “Where am I going?”“How am I going?”

“Where am I going to next?”

Build upon the students’ prior mathematical experiences

Create and connect students to stories that contextualise the learning

Present interesting problemsUse students’ interests to

contextualise the mathematicsBuild understandings from previous

lessons

Utilise a variety of rich and challenging tasks that allow students time and opportunities to make decisions

Encourage a variety of forms of representation

Present higher-level problems Promote discussion of alternative

solutions Require students to explain their thinking Use higher order questioning

“What do you mean when you say ___?”“Why do you think that?”

“Can you convince us that your answer makes sense?”

“Do you think that will always work?”

Interact with students while they engage in the experiences

Encourage students to interact with each other

Encourage students to ask and answer questions

Specifically plan to support students who need it

Challenge those who are ready

Use enabling promptsUse extending promptsProvide open-ended tasks

Enabling promptsEnabling prompts involve slightly lowering an aspect of the task demand, such as the formof representation, the size of the number, or the number of steps, so that a student experiencingdifficulties can proceed at that new level; and then if successful can proceed with the originaltask.

Extending promptsTeachers plan prompts that extend the thinking of students which they can pose to students who complete tasks readily. The prompts need to work in ways that do not make the students feel that they are merely getting ‘more of the same’. Extending prompts have proved effective in ensuringthat higher-achieving students are profitably engaged and their development is supported by posing higher-level problems.

Adopt pedagogies that foster communication, as well as individual and group responsibilities

Use students’ reports to the class as learning opportunities

Teacher summaries of key mathematical ideas

Pose initial problemAllow individual or group work on the

problemTeacher walks around giving

feedback and making observationsWhole class discussion with student

reportsTeacher summary of key ideas

Short everyday practice of mental processes

Practice, reinforcement and prompting of the transfer of learnt skills

Move beyond mechanical practice strategies

Use automatic practice strategies, built on understanding, so students can be procedurally fluent while at the same time having conceptual understanding