Raising achievement matters because it makes people richer and healthier, according to formative assessment guru Dylan Wiliam.

He told a national numeracy conference last week that every year of education added one-and-a-half years of life.

Routine cognitive skills were the fastest-disappearing from the workplace - but the only 21st-century skill that mattered was the ability to act intelligently when faced with something you had never seen before, he told delegates at the Edinburgh event, organised by Learning and Teaching Scotland and HMIE.

Professor Wiliam, who taught maths before specialising in educational research and teacher education, said that formative assessment appeared to be the most successful way of preparing students for the challenges they faced.

Assessment was the bridge between teaching and learning; it was the only way teachers could relate what they did to what pupils were learning.

He stressed the need for teachers to give constructive feedback: even those who no longer gave grades, but gave comments instead, too often fell into the trap of saying what was wrong with the last piece of work rather than explaining how the next could be better - post-mortems instead of diagnoses.

Instead of testing pupils at the end of a unit, teachers should do it three-quarters of the way through - and then plan the final few lessons to address any problems thrown up by the test.

“Find time to work with your colleagues to get ‘good’ questions,” he told the audience of primary and secondary teachers from across Scotland. “Good” questions would illustrate how well pupils had understood a lesson; leaving it to the marking stage to find out whether or not a pupil had understood was a “refuge of last resort”.

“Marking is what you do because you didn’t manage to put your learning back on track.”

Teachers who batted out a series of questions were playing “serial table-tennis” and should instead be playing basketball with their pupils: pose a question to one student, pause, pounce on another with a related question and then bounce a follow-up question to yet another student.

When a child replied that he or she didn’t know an answer and the teacher put the question to another pupil, the teacher was being lazy, he said. Instead, the teacher should say: ‘OK, I’ll ask a few other people and come back to see what you think’. That way, the child had to listen and think about the question.

The most powerful revision tool, he said, was to get pupils to write their own test question with the right answer. “Train students to pose questions. No one usually asks a question, because they don’t want to look stupid,” he said.

“But if you put pupils into a group and ask them to devise questions, that is more effective.”

A LITTLE AND OFTEN WHEN DEVELOPING NUMERACY

Dyce Academy, along with three other Aberdeen secondary schools, was commissioned by Learning and Teaching Scotland to produce numeracy materials to share with other teachers (they are expected to be available next term).

Ian McLean, principal teacher of maths at Dyce, chose to concentrate on finding interactive ways of developing pupils’ understanding of fractions, decimals and percentages.

He had never heard Dylan Wiliam speak about formative assessment until last week’s numeracy conference, but found that much of his own work on margin games and loop games chimed with the professor’s ideas - particularly when asking pupils to create their own and review each others’ questions.

Mr McLean believes in the principle of “little and often” when it comes to developing numeracy. He devised “margin games” - a series of mental maths calculations involving fractions, decimals and percentages - as a warm-up routine at the start of the lesson for his S1-2 classes.

Next, he asked them to design their own margin games. Working in pairs, each pupil had to devise a game and check the one produced by their partner. The student then copied the game onto card. Pupils were formed into groups of three or four and played each game in turn. They were then asked to review them and write comments. When problems were identified, the game was returned to the author for correction. Comments ranged from “Question didn’t make sense, for example, % 10 x” to “Could have been harder”.

His next task for pupils was to devise a “loop game” - a circular sequence of 12 mental maths questions which form a loop (right), with the answer being written at the top of the next card in the sequence, above the question. The results were “impressive”, says Mr McLean.

“The games produced were more effective than before. Pupils expressed considerable satisfaction about the process they were engaged in. Understanding of desired ‘targets’ also appeared very good.”

The overall aim was to find “a more active way to get kids involved in their own learning” and it seems to have worked. Pupils were engaged and even the “trickier customers” behaved well in class.

Find 90% of 20 - 18

Write 24% as a decimal - 0.24

Find 13 of 90 - 30

What is 25% as a fraction in its simplest form - 14

Find 40% of 30 - 12%

Find half of 82 - 41

Write 11% as a fraction - 11100

Write 41% as a decimal - 0.41

Find 10% of 50 - 5

Find 23 of 9 - 6

Write 7% as a fraction - 7100

Write 6% as a decimal - 0.06.