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Engaging Maths: Higher Order Thinking with Thinkers Keys

Engaging maths: Higher

All students should be encouraged to engage with higher order thinking tasks. This book uses a critical and creative thinking tool called Thinkers Keys, adapted to be specifically mathematical.

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Reasoning

Mathematics is reasoning.

It was created by reasoning and depends on reasoning for its further development as well as its usefulness.

Reasoning is one of the four proficiencies in the national curriculum, which describes it as a capacity for logical thought and actions. Reasoning develops throughout the curriculum and there are identifiable milestones. You can download a summary of Some Milestones in the Development of Mathematical Reasoning.

Mathematics content knowledge is important, but it should be taught and learned in a way that emphasises the process skills, or proficiencies. Then students will not only gain content knowledge but will also learn to think as young mathematicians. They will be well prepared for future learning as well as very competent in using mathematical processes in everyday life.

Reasoning is not problem solving.

You can download Problem Solving versus Reasoning which is a summary drawn from the Australian Curriculum: Mathematics showing how reasoning is different from problem solving.

Big ideas

There are a number of big ideas that underpin the concept of mathematical reasoning.

Good teaching

Reasoning is taught well when it is embedded in all mathematics classes.

Assessment

There are many audiences for the assessment of reasoning, including students, parents and teachers, as well as state and national bodies.

Activities

Student activities that appear in other parts of the drawer have been collected here.

Downloads

All downloadable files, such as student worksheets, teacher notes, activity templates and video transcripts, are available here.

Acknowledgements

The reasoning drawer is based on In Teachers’ Hands – Reasoning, a project of the Mathematical Association of Victoria in 2011. A/Prof. Judith Mousley was responsible for the conceptual design of the drawer and wrote most of the material.