“Some of our findings were surprising in that they challenge some popularly held beliefs about what makes a teacher effective. For example, style of organization for mathematics teaching was not a predictor of how effective teachers were. Whole-class ‘question-and-answer’ teaching styles were used by both highly effective and comparatively less effective teachers. Similarly, individualized work and small-group work were used by teachers across the range of effectiveness. At the school level, setting across an age group was used in schools with both high and low proportions of highly effective teachers. The same published mathematics schemes were used by highly effective and comparatively much less effective teachers. Our findings also raised questions about the sort of mathematical knowledge teachers need in order to be effective. Despite what might be expected, being highly effective was not positively associated with higher levels of qualifications in mathematics. The amount of continuing professional development in mathematics education that teachers had undertaken was a better predictor of their effectiveness than the level to which they had formally studied mathematics.”