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Thinking through Mathematics - Book 1

Engaging students with inquiry-based learning

Author: Sue Allmond, Jill Wells and Katie Makar

Format: 104 pp book

ISBN: 9781742004839  SCIS No: 1448390

Publisher: Education Services Australia 2010

Audience: Teacher resource

Price: $39.95

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Mathematical inquiry challenges students to ask questions, create definitions and think very carefully about how they are going to solve a problem.

With the emphasis on mathematical reasoning, judgement and problem-solving skills, the Thinking through Mathematics series requires students to investigate questions that are open-ended and ambiguous, rather than closed and defined. The process of reasoning is reinforced as students consider the parameters of their inquiry, formulate, trial and enact a plan, and share their thinking process alongside the results.

Each book provides ten mathematical inquiry units, each posing a real-life, ambiguous question for inquiry, such as:

What is the longest paper chain that can be made from an A4 sheet of paper?

This unit explores elements of measurement, geometry and length as students determine, order and compare various lengths of flexible paper chain.

How do we know if we’re getting better at hopping on one foot?

Students collect, compare and use evidence, in the form of measurements, to substantiate a claim.


Each of the ten units follows five phases of inquiry:

  • Discover (engage with the problem)
  • Devise (create a plan)
  • Develop (implement the plan)
  • Defend (justify and communicate solutions and the decisions made)
  • Diverge (optional: explore alternative pathways)

Notes for the teacher make the process of mathematical inquiry transparent, covering the activity sequence, question prompts, key vocabulary, communicating understandings and writing meaningful reflections. ‘In Action’ sections share the authors’ experience trialling and testing these mathematical inquiries in their own classrooms, and how they develop mathematical understanding in their students.

Thinking through Mathematics provides a practical entry into inquiry-based mathematics learning which immerses students in solving authentic, complex problems.


Nicola McKinnon

“The Thinking Through Mathematics books are a very useful resource for teachers who are ready to shift from a teacher-driven to an inquiry-based, student-centred pedagogy. They provide comprehensive lesson plans for structured and guided inquiry investigations, equipping teachers with the skills and confidence to use authentic problems to make connections between mathematical concepts and real life.”

Teacher magazine

October 2010

p 73

Related resources

Other titles in this series


Thinking through Mathematics - Book 3

Engaging students with inquiry-based learning



Thinking through Mathematics - Book 2

Engaging students with inquiry-based learning


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