Teachers are expected to foster critical and creative thinking in their students, in every subject area. But how and why do this with maths?
1. Encourage students to figure out the answers, rather than telling them
2. Tasks about mathematical reasoning produce more lightbulb moments
Mathematical reasoning tasks encourage students to generate as many examples as possible. Teachers can encourage students to analyse them, and notice the patterns. What are the similarities? What are the differences? What conjectures can they test?
"[They’re] connecting their understanding and their knowledge … they’re putting it all together and figuring bigger things out through reasoning” (Year 3/4 teacher).
That’s when the magic can happen as students experience the joy of discovery.
By figuring out a maths problem on their own, students become genuinely engaged in mathematics. And for teachers, that means more light bulb moments in the classroom.
3. Foster collaboration and communication through group tasks and teacher prompts
“Convince me” is one of the challenging prompts that you can use to promote collaboration when students are working on reasoning tasks in pairs or reporting to the whole class.
Students communicate their thinking in many ways – through drawings, talking, gesturing and using mathematical symbols.
"The kids were constantly having to explain, because they work with partners. [It] meant they could think out loud, you could always hear them justifying, thinking about other reasons why things won’t work, or the reasons why things do work…" (Year 3/4 teacher)
4. Like it or love it: it’s a part of the curriculum
5. A rubric to help primary teachers assess three key areas
In collaboration with primary teachers, we have developed a rubric to formally assess three key reasoning actions: analysing, generalising and justifying.
Teachers can use this rubric to record observations or analyse written work and use their findings for planning.
"I quite like [the reasoning rubric] because it’s making me learn what they should be doing. I'm thinking maybe I should be encouraging them to verify the truth of what they’re saying more" (Year 5 teacher)
"I could use that language [in the reasoning rubric] to help write reports and [plan] what they need to do next." (Year 5 teacher)
6. Problem-solving and reasoning are two different things
Investigating real-world problems requires creative and critical thinking from students. But problem solving should not be confused with reasoning.
Students are thinking creatively when they interpret the problem and make choices about how to solve the problem. They think critically when justifying their interpretation of the problem and evaluating their solution.
7. Creative and critical thinking are fundamental skills for the future
We can't predict the jobs we need to prepare children for, but we do know the skills that will equip them for success. According to Australia’s Chief Scientist these are creative and critical thinking.
In work, and in life, problem solving is a pretty important skill. So too is critical thinking. It’s what helps us explain things clearly, and back up our ideas.
In mathematics, this starts by teaching problem solving and reasoning, and it’s accessible to every year level.
"I haven’t done as much for maths reasoning because I’ve always thought it’s more of a high school thing and I haven’t really thought about it being in primary, but now I'm realising it can [be]" (Year 5 teacher)
Australian Association of Mathematics Teachers (AAMT) Inc. (2016). Top Drawer.
Vale, C., Bragg, L. A., Widjaja, W., Herbert, S., & Loong, E.Y. (2017). Children’s mathematical reasoning: Opportunities for developing understanding and creative thinking. Australian Primary Mathematics Classroom, 22(1), 3-8.
Vale, C., Widjaja, W., Herbert, S., Loong, E. & Bragg, L.A. (2017). Mapping variation in children’s mathematical reasoning: The case of ‘What else belongs?” International Journal of Science and Mathematics Education, 15(5), 873-894.
Loong E. Y-K, Vale, C., Herbert, S., Bragg, L. A., Widjaja, W. (2017). Tracking change in primary teachers' understanding of mathematical reasoning through demonstration lessons. Mathematics Teacher Education and Development, 19(1), 5-29.