Post on 18-Jan-2016
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