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Creativity and 'feeling' needed to solve novel maths problems

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We used to believe that you’re either creative or you’re good at maths, as it turns out to be really good at maths you have to be very creative too as intuitive non-cognitive thought processes are vital to solving mathematical problems.

A focus on creative thinking in maths and a different approach to teaching it in schools may help to reverse the trend away from studying maths. Teachers might change the way they approach their classes and emphasise the role of creativity in problem solving.

Acknowledging the crucial role of 'feeling' in solving maths problems and freeing students from the constraints of systematic and analytical-only reasoning processes has the potential to revolutionise maths learning and teaching.

“People have told you that feeling interferes with solving a problem, but what nobody has told you is that in the absence of feeling you won’t solve the problem,” Dr Carol Aldous of Flinders University says.

In her research, Aldous gave novel maths problems from the Australian Mathematics Challenge to 405 students to measure the role that creativity plays in solving problems, she found that “while it is possible to solve a problem straight from a feeling, solving a truly novel problem while relying solely on cognitive processes is not possible.”

Australia’s secondary school students have been enrolling in maths less and performing more poorly for decades

“Current approaches to teaching and learning, which target only conscious aspects of thinking, neglect other possible approaches … particularly non-conscious aspects of thinking.

“Teachers must be able to foster among their students the use of non-cognitive processes as well as the usual cognitive processes,” Aldous writes. "Feeling can provide a 'source of direction' to navigate students through problem solving. Teachers'need to alert students to their inner resources, found by attending to feeling in its deeper sense.'

“No curriculum for schools and universities is complete without reference to … problem solving and creativity, yet problem solving and being creative are not easily taught or learnt.”

Being creative involves a variety of processes, but generally involves utilising both conscious and non-conscious parts of the self and working to increase their interaction. “This interaction may involve oscillating between states of focused or defocused attention, switching between visual-spatial and analytical forms of reasoning, or moving between moments of thinking and feeling.”

From Aldous, C.R. (2019). Unlocking Creativity in Solving Novel Mathematics Problems: Cognitive and non-cognitive perspectives and approaches, Routledge.

Image by Susanne Nilsson under flicr cc attribution license

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