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

2.  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

3.  Write the goals on the board  Provide feedback for students Students need to know “Where am I going?” “How am I going?” “Where am I going to next?”

4.  Build upon the students’ prior mathematical experiences  Create and connect students to stories that contextualise the learning

5.  Present interesting problems  Use students’ interests to contextualise the mathematics  Build understandings from previous lessons

6.  Utilise a variety of rich and challenging tasks that allow students time and opportunities to make decisions  Encourage a variety of forms of representation

7.  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?”

8.  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

9.  Use enabling prompts  Use extending prompts  Provide open-ended tasks Enabling prompts Enabling prompts involve slightly lowering an aspect of the task demand, such as the form of representation, the size of the number, or the number of steps, so that a student experiencing difficulties can proceed at that new level; and then if successful can proceed with the original task. Extending prompts Teachers 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 ensuring that higher-achieving students are profitably engaged and their development is supported by posing higher-level problems.

10.  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

11.  Pose initial problem  Allow individual or group work on the problem  Teacher walks around giving feedback and making observations  Whole class discussion with student reports  Teacher summary of key ideas

12.  Short everyday practice of mental processes  Practice, reinforcement and prompting of the transfer of learnt skills

13.  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