According to Dr Carol Aldous of Flinders University, there is strong evidence that intuitive, non-cognitive thought processes – including creativity and emotion – are vital to solving mathematical problems.
Dr Aldous gave novel maths problems from the Australian Mathematics Challenge to 405 students to measure the role that creativity plays in solving problems. “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,” she said.
“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.”
With Australian secondary school students enrolling in maths less and performing more poorly than in past decades, Dr Aldous’ research offers hope that a focus on creative thinking in maths, and a different approach to teaching maths in schools, may help to reverse this trend. She suggests that teachers change the way they approach their classes and emphasise the role of creativity in problem solving.
“Current approaches to teaching and learning, which target only conscious aspects of thinking, neglect other possible approaches,” she said, “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,” Dr 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.”
She added that no curriculum for schools or universities was complete without referencing 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.”
Dr Aldous believes that 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.