Maths is complicated and needs hard thinking but should be more accessible to all pupils, even the bottom sets, an Oxford University researcher told maths students and teachers in Edinburgh last weekend.
"Teachers and learners together need to change their habits," Anne Watson stated. Too many teachers focused on what students "can't" do, rather than what they could do with more help.
Dr Watson said that primary teachers and secondary specialists should not just do the basics with those who traditionally opted out of maths. The full curriculum, including aspects such as simultaneous equations, should be open to all.
Her remarks come two weeks after inspectors found important or major weaknesses in attainment at S1-S4 in two out of five secondaries. Gains in early stages of primary are not sustained in later primary and early secondary.
Dr Watson said that every teacher had to believe that all their students could do better at maths. "Less able children do think harder than other children because it's harder for them, but no one is helping them how to think better," she said.
A project in one disadvantaged Oxfordshire school had shown what was possible. "The thinking was that maths is complicated and requires hard thinking, so we are going to help the learners do the hard stuff. We are not going to water down mathematics so that it is terribly, terribly easy.
We are actually going to help these people enter the world of maths," she said.
Teachers had used puzzles and practical approaches to engage weaker students and encourage them to work out their solutions, using the same thought processes and strategies employed by more able students.
A key element was time to think, a particularly important factor for those who find maths hard, Dr Watson told the conference, run by the Edinburgh Centre for Mathematical Education.
John Hibbs, a former maths inspector south of the border and Open University lecturer, said that students were "frightened" of the subject and called for a maths makeover. Many children came into maths classes not expecting to learn in "an ethos of failure" and that was down to the school.
Some schools made it easier than others to learn maths. "At least if they are not having fun, they are not bored to death," Mr Hibbs said.
Puzzle it out
A good starter for all ages. A die is rolled to generate nine numbers. The numbers are placed in three groups of three and added together, the target sum being 1,000. It works particularly well when teams compete with each other. For example, nine rolls produce 4, 2, 4, 5, 1, 1, 4, 6, 2. Just by taking them in order we get 424 + 511 + 462 = 1,397. It is possible to get closer than that by juggling the numbers.