Teaching Mathematics:Using research-informed strategies by Peter Sullivan (ACER)
Identify key ideas that underpin the concepts you are seeking to teachCommunicate to students that these are the goals of the teachingExplain to the students how you hope they will learn
Write the goals on the boardProvide feedback for studentsStudents need to know Where am I going?How am I going?Where am I going to next?
Build upon the students prior mathematical experiencesCreate 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 decisionsEncourage a variety of forms of representation
Present higher-level problemsPromote discussion of alternative solutionsRequire students to explain their thinkingUse higher order questioningWhat 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 experiencesEncourage students to interact with each otherEncourage students to ask and answer questionsSpecifically plan to support students who need itChallenge those who are ready
Use enabling promptsUse extending promptsProvide open-ended tasksEnabling 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 responsibilitiesUse students reports to the class as learning opportunitiesTeacher 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 processesPractice, reinforcement and prompting of the transfer of learnt skills
Move beyond mechanical practice strategiesUse automatic practice strategies, built on understanding, so students can be procedurally fluent while at the same time having conceptual understanding