In the current climate of compliance, lessons are driven by learning objectives. Students' thinking is supposed to converge on pre-determined "content" with the teacher as modeller of the required knowledge and student as imitator. This structure does not encourage the emergence of creative and independent learners who can monitor and regulate their own performance.
In classrooms of guided inquiry, on the other hand, students are encouraged to pose questions from a statement provided by the teacher, to discuss and justify mathematical tools that could be used to better understand the stimulus, and to make decisions on approaches the class will employ. At times of inquiry, students find "content" far more meaningful than in traditional numeracy lessons.
Some of us are trying to break out of the strategy's stranglehold.
Teachers, in my experience, respond to open debate about alternative models of teaching and learning, not to being told what to do.
Andrew Blair. Head of mathematics. Varndean school. Balfour Road, Brighton