Principles for the Design of Teaching - Reading Notes.

This post is my reflection on a journal article read as part of my Masters course.  I am treating it as an opportunity to think about its content while I type - and it saves my notes in a place where I can find them.

Bell, A. (1993a). Principles for the design of teaching. Educational Studies in Mathematics. 24, 5-34.

The general tenet of the article is that to design a learning activity a teacher needs to choose the situations and contexts which embodies the mathematics to be learned, then design tasks for students to work on that deeply involve the relevant concepts and relations. 

The underlying psychological principles put forward by Bell for good lesson design are:

1. Connectedness.  If what students are learning can be connected to students' existing knowledge they are more likely to retain it.  In this light the beginning of a lesson is crucial - start with a task that allows students to use their existing knowledge.
2. Structure and Content.  Structural knowledge is tied to the context in which it is learned.  Maths teachers should not assume just because a student is successful in one context that they will be able to apply it in an unfamiliar context.  So the best approach is to explore extensively the structural relations in one context and then repeat in another context making the links explicit.  
3. Feedback.  Learners should know immediately when they have correctly solved a problem.
4. Reflection and Review (of ) the process of performing the task and the new knowledge gained - labelling the new knowledge in one's memory so that it is accessible in the future.
5. Intensity  Intensive insight demanding tasks (not just memorisation!) produce long term gains.

My challenge is to translate these into practice when designing maths lessons.  The article contains a range of lessons that will be worth investigating and adapting to an appropriate level for my class.