There is a lot of discussion about whether teachers should follow lesson scripts. To me, it seems very unlikely that it would be possible, or desirable, to create a (linear) script that will encompass the complexity of classroom interactions.

I suggest that the question is not whether we should follow scripts, but rather: should lessons follow a pre-determined linear structure at all?

Or could lessons move to something more like a tutorial model, where students come to lessons having read texts and worked on problems in advance? In this model there can be no script: what is discussed is contingent on student responses.

This year, my department has been moving towards this model. We select a small number of challenging problems that encompass a given unit, or units. The problems may contain techniques or concepts that students have not been 'taught' yet.

Initially, students are expected to attempt the problems independently of the teacher's help; they are encouraged to work together on these problems, to discuss and share methods. They are encouraged to go online, or use texts, to seek information to solve the given problems.

Students then bring their (possibly partial) solutions to the following lesson, with any questions they may have. The teacher can then decide how to proceed in order to meet the needs of the students, whether this is to explain a given concept in more detail, or perhaps make connections to other areas; we are exploring the idea of

*pedagogical patterns*to assist these decisions. I will write about this in my next post.

This model has its demands. The teacher must be able to act

*in-the-moment*. They must cultivate an atmosphere where students are happy to work independently on difficult problems. They must also assess students' work carefully; reviewing student work is an integral part of the tutorial process.

However, from a teacher's perspective, the main benefit is the reduction in planning time; the plan is the selection of the problems, the anticipation of student responses, and the possible reactions to those responses.

Of more importance are the benefits to students; in the short time we have been using this approach, students are working more independently, they are producing better quality (home) work, and they are becoming more resilient when faced with difficult problems.

## A final thought

I taught for 10 years in secondary schools, and now work in a comprehensive post-16 college. One of the senses in which we are comprehensive is that we accept students onto AS maths with a grade C.

By their own admission, many of our students did not put much effort into homework over the last 11 years, and have not gained much resilience in working on difficult problems. The idea behind this approach is to attempt to change these ingrained habits, to transform students into independent learners, and ultimately to get them to a point where they have real chance of success at A-level.

I wonder, then, how these ideas might work with pre-16 students?