Dear Parents and Carers,

Over the year Ms O’Connor, Mr Armstrong and

Mrs Jellis have been engaged in Professional

development conducted by the Victorian

Academy of Teaching and Leadership. This

program has supported our school team to

investigate, analyse and strengthen current

approaches to mathematics learning, teaching

and leadership at the classroom, team and school-wide levels.

A focus of this course has been how we approach the teaching of mathematics through problem solving.

Being able to wrestle with and solve problems is an essential proficiency for learners to become the ‘active and critical citizens in a technological world.’ Someone who develops as a problem solver has more than just skills and strategies for solving problems, they develop, dispositions such as persistence, curiosity, risk-taking, resilience, look-from-another-angle and try-another-way. They learn to think through a problem systematically and logically like mathematicians and to be calm and unflustered in the face of something they do not yet understand (because they’re confident that with persistence and effort, or via the support of others, they will eventually crack the problem open and experience the thrill of overcoming a personal or collective challenge). Teachers know they have landed on just such a problem when the students refuse to give in and reject out of hand the very idea of being given the solution.

Tasks should be challenging

Learning is most effective when students are engaged in higher order thinking as they work on tasks appropriately challenging for them. A task or problem is considered challenging if students do not initially know how to proceed, have not been told the steps by the teacher, and are expected to make decisions on solutions or solution strategies for themselves. Many mathematics concepts are difficult to understand – at least initially – and students benefit when they persist with concepts and tasks that include:

Concentrating
Applying themselves
Believing they can succeed
Connecting effort with learning.

Tasks designed to foster such actions are termed ‘challenging’ because they allow for the possibility of sustained thinking, decision-making and some risk-taking by students.

In Summary, the main characteristic of a challenge is when students do not know how to solve the task, and work on that task before receiving any teacher instruction. Other features of appropriately challenging tasks are that they:

Build on what students already know
Take time
Engage students, so that they are interested in the task and see value in persisting with it
Focus on important aspects of mathematics – as identified or implied in relevant curriculum documents
Use simple words, possibly drawing on relevant contexts or stories
Foster connections within mathematics and across domains of thinking
Foster choice and a sense of control by having more than one correct answer of more than one solution pathway.

A particular barrier for teachers can be students’ reluctance to take the time to engage with a task, as they can resent being expected to struggle with ideas. However, teachers work at finding ways to support students through such reluctance, rather than simplifying the tasks to avoid the struggle.

Kind regards

Jennifer O’Connor

Assistant Principal.

Taken from the works of Peter Sullivan and Van de Walle

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