30 Design Strategies and Tactics from 40 Years of Investigation

Appendix: Further information and examples

Hugh Burkhardt and Daniel Pead

Bookmark for top

‘The Sandwich Model’ and other PD tactics

Bowland Maths PD
Thumbnail for Bowland Maths Professional Development

Link to materials

We want teachers to embrace social constructivism, ‘connectivist’ learning, open investigations, metacognition, discussion & reflection; we talk about changing the role of the teacher from oracle to facilitator - then we sit teachers in a lecture theatre and have an expert talk to them about these things!

The practices we want to foster in the classroom can also be applied to professional development and teacher training. The professional development modules produced for Bowland Maths embody several approaches to this:

Bookmark – Section 1

‘The Sandwich model’ – learning by doing

Structure of a Bowland PD unit
Thumbnail of Bowland unit page

Link to materials

All of the Bowland Maths PD modules take this structure. Each module is based on three sessions, a week or two apart:

  1. structured teacher-group discussion of the target issue, with lesson preparation
  2. each teach that lesson in their class
  3. structured group consideration of what has been learned
Bookmark – Section 2

Teachers engage with student activities

Teachers working on an estimation problem
Thumbnail for Teachers working on an estimation problem

Link to materials

Start the session by having the teachers actually take part in some exemplar student activities – this is easier with more open problem-solving and/or discussion-based activities that are less trivial than traditional exercises. As well as being a good ‘ice-breaker’, this can raise teachers’ awareness of the subtleties of some of these activities. Here, three teachers find that the often-used ‘Fermi estimate’ task of ‘How many people can stand on a football pitch’ may not be as easy as it sounds:

Bookmark – Section 3

Realistic classroom videos

Bowland PD classroom video
Thumbnail for     Bowland PD classroom video

Link to materials

Sessions make frequent use of videos showing the techniques in use in the classrooms. A key feature here is realism – “Perfect” videos are easy for teachers to reject with “that would never work in my classroom”. The Bowland classroom videos were unscripted, with carefully selected extracts, lightly edited. They feature regular teachers trying out new types of lesson for the first time, and reflecting on the results. The videos were not presented as “best-practice” exemplars – teachers participating in the PD were free to question and criticize what they saw, and discuss how it could be adapted to their own situation.

The Bowland Maths materials drew on aspects of the Professional Development materials from Improving Learning in Mathematics: https://www.stem.org.uk/elibrary/collection/2934

The resources from these two projects were adapted for use in other projects: