Rigid maths views equal a problem
Teachers have a rigid belief system, akin to "religious fundamentalism", that maths is a boring, solitary activity involving testing, strict rules and right and wrong answers, according to researchers.
And that fundamentalism is the main barrier to delivering rich and stimulating maths lessons in Scottish schools, they add.
But the same University of Dundee academics believe they have found a way to help primary teachers escape this mindset.
Despite attempts over the years to improve the quality of maths lessons in Scotland, the Dundee research shows most still feature some form of teacher-led demonstration, followed by pupils practising skills and procedures using a commercially-produced scheme.
To combat this, the Developing Mathematical Thinking in the Primary Classroom project, funded by the Scottish government, gave 24 primary teachers the opportunity to reflect on their current teaching and try something new.
At the start of the six-month course, which began last September, participants carried out an audit of their maths teaching and then developed an action research plan for a small-scale project designed to develop mathematical thinking in their classrooms.
One teacher looked at the effects of carrying out open-ended investigations in maths; another looked at the impact of teachers' questioning skills on mathematical thinking.
Before starting the course, 65 per cent of participants said they were "good at maths" and 73 per cent that they were "confident about doing maths". At the end of the project both these figures had risen to 93 per cent and there was "a distinct move from the fundamentalist viewpoints held by many of the participants".
At the beginning of the course, almost 80 per cent thought maths was "about certain truth" - this dropped to 20 per cent. Likewise, the 75 per cent who thought maths was "about testing" dropped to just over 30 per cent; and the 55 per cent who thought maths was about "right and wrong" answers fell to less than 15 per cent.
Only 15 per cent of participants reported that they found maths boring before the course; this figure dropped to 7 per cent.
By the end, 100 per cent of participants thought that maths was interesting (up from roughly 90 per cent); about multiple solutions (up from roughly 90 per cent); about creative reasoning (up from just over 70 per cent) and enjoyable and fulfilling (up from almost 80 per cent).
Developing Mathematical Thinking in the Primary Classroom can be taken as a module worth 30 credits at the University of Dundee
Doing more problem solving was on the school improvement plan at Auchterhouse Primary in Angus - so the headteacher of the small, rural school, Peter Ferguson, and both its teachers, Amanda McIntosh and Donna Simpson, signed up for the Developing Mathematical Thinking in the Primary Classroom Project at the University of Dundee.
After the first workshop, Mr Ferguson sat in the university's quad with his head in his hands and contemplated dropping out.
"I was so upset by my own teaching," he said. "I had been one of those people who for many, many years had spent endless hours doing tasks but not relating that to the world in which we live. I realised if it could not be understood in a realistic context it was pointless."
But as the course progressed, Mr Ferguson realised some of the good practice being talked about was evident in his 50-pupil school. That has now been built upon and, while textbooks have not been abandoned entirely, teachers aim to cultivate a genuine understanding in their pupils of maths in context.
"We want a generation of children who understand and love maths rather than just do it because it has been set by a teacher," said Mr Ferguson.