loading purchase support website google preview sample pages
item image

Thinking through Mathematics - Book 2

Engaging students with inquiry-based learning

Author: Sue Allmond, Jill Wells and Katie Makar

Format: 104 pp book

ISBN: 9781742004822  SCIS No: 1427960

Publisher: Education Services Australia 2010

Audience: Teacher resource

Price: $39.95

Audience year level

support website


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:

How many television advertisements will a typical Year Four student watch in a year?

Students collect and compare multiple data types, deciding on appropriate representations for the comparison of data sets, to make useful judgements.

Is a daily goal of 10 000 steps achievable?

Students plan and explore the distance and time needed to walk 10 000 steps, using written calculations, proportion, distance and time conversions in the context of a healthy daily goal.

 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 1

Engaging students with inquiry-based learning


Similar learning area


Asia Counts: Secondary

Numeracy and studies of Asia



Maths in the Making 3 (Ages 10-12)

Creative activities using everyday resources