“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,” she said.

Aldous gave novel maths problems from the Australian Mathematics Challenge to 405 students to measure the role that creativity plays in solving problems.

The results were conclusive: “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. 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. Teaching maths and science could be presented as an opportunity for experiencing “joy, beauty, and wonder”.

“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.”

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.