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Make room for reasoning

iMaths 8/8/16

Note: iMaths is in its final year and will be discontinued at the end of 2024. If you’re looking for a primary maths resource written for the Australian Curriculum Version 9.0, explore Maths Trek.

Studies show that reasoning can foster a deeper understanding of mathematics. That’s why we’ve put together suggestions for setting up your own ‘reasoning classroom’ – an environment where students are encouraged to explain their mathematical reasoning while using iMaths Investigations. What’s more, these suggestions help you cover the Reasoning strand of the Australian Curriculum: Mathematics. 

Elizabeth Sansome, Head of Teaching and Learning at St Paul’s Lutheran Primary School, Caboolture, Queensland¹ has researched the benefits of reasoning in the classroom. She found that reasoning allowed students to grasp maths more conceptually because they understood that maths is not governed by arbitrary rules, but by real investigation.

Sansome’s study also identified six key strategies teachers can use to enhance reasoning in maths: questioning, journaling, discussion, problem solving inquiry, planning and appropriate material use. Several of these strategies are incorporated into the following guidelines for setting up a reasoning classroom:

Establish an open-dialogue classroom culture

Students love to engage in conversation if they feel secure and comfortable and have the sense that other students will respect their views.

Warm students up with easy questions

Before introducing the main concept, build trust by asking students easy questions. This will get them talking freely without having to think too hard. 

Find out what students already know and can do

Help students recall what they have already learnt and explain that it’s okay to take risks and explore new ideas as this is the best way to learn.

Allow enough time for discussion

Incorporate discussion time into your maths lessons. If more time is spent as a class discussing ideas, less time is needed for you to demonstrate procedures or for students to learn by rote.

Encourage group work

Ideally, organise your students into groups of three because this can produce just the right balance of discussion among the group. It’s beneficial to create groups of mixed ability so that struggling students have the added support and guidance from their peers, while extension students practise their reasoning skills with peers who may lack some understanding.

Choose activities that require reasoning

Create learning opportunities that encourage students to explain, justify, compare, contrast, infer and deduce their answers.

iMaths Investigations, Problem solving tasks and Challenges have all been designed to provide everything your students need to develop reasoning skills. Even the Rubrics state the Reasoning strand criteria on which their work will be assessed.

We’ve also created targeted Communicating and reflecting questions for every Investigation. These will help you assess your students’ proficiency in reasoning by asking them to explain and justify their working. The questions are located in the Investigation teaching plan at iMaths Online.

References

1. Sansome EJ. Building teachers’ pedagogy practices in reasoning, to improve students’ disposition towards Mathematics. Master of Education (Research). Brisbane Queensland: Queensland University of Technology, 2015.↩

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