Thinking through Mathematics: Book 3: Engaging students with inquiry-based learning

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Education Services Australia, 2010 - Inquiry-based learning - 104 pages
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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:

Are athletes getting better over time?

Students explore measurement and pose hypotheses about the factors influencing sporting records, as they interpret, analyse and discuss a variety of data representations.

What is the best walking school bus route in our school catchment area?

Students explore measurement, time and distance conversions, mapping conventions (including scale), and the social and environmental benefits of a healthy, safe route, appropriate for students of all ages to get to their school.

 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.


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