30 Design Strategies and Tactics from 40 Years of Investigation
Appendix: Further information and examples
Replacement units
Many of the new teaching materials that have proved most creative and effective were and are delivered in the form of units that support a few days to a few weeks of innovative teaching. (See Gradual change)
Here we simply list a few that have been widely used and have links that make them accessible.
Mathematics Assessment Project
MAP website
100 formative assessment lessons for students age 11-17, designed to probe students' capabilities and move their thinking forward. Two thirds of the lessons focus on concept-development, the others on modelling and problem solving.
Links to materials:
- Mathematics Assessment Project
- https://www.map.mathshell.org/lessons.php
Bowland Maths
Bowland Maths website
A collection of 'case studies' of 'real world' problems of a great variety of kinds, designed for 14-15 year old students to tackle in small groups over 4 to 5-lessons.
Examples include Alien Invasions, Reducing Road Accidents, How risky is life?
Links to materials:
- Bowland Maths
- https://bowlandmaths.org.uk
Testing Strategic Skills
These materials are described in more detail under Gradual Change.
- Problems with Patterns and Numbers introduces, over three weeks teaching, non-routine problem solving in pure mathematics
- The Language of Functions and Graphs introduces, over three weeks teaching, modelling real world situations with graphs and, in Unit B, with algebra
Link to PPN materials
Link to LFG materials
Links to materials:
- TSS – Problems with Patterns and Numbers
- https://www.mathshell.com/materials.php?series=tss&item=ppn
- TSS – The Language of Functions and Graphs
- https://www.mathshell.com/materials.php?series=tss&item=lfg
Numeracy through Problem Solving
Link to Numeracy throug Problem Solving materials
Five modules each support three-week small-group modelling projects on the following situations, guided primarily by student booklets:
- Design a Board Game – discover the elements of board game, design, make and test one
- Produce a Quiz Show - on devising and running an in-class game show.
- Plan a Trip: agree a destination across the class, plan, carry out, and evaluate the trip
- Be a Paper Engineer – on the design of pop-up cards and gift boxes
- Be A Shrewd Chooser – on learning to make sensible consumer decisions.
Each module has four phases: explore the domain; decide on a design; realise it; test it.
Links to materials:
- Numeracy through Problem Solving
- https://www.mathshell.com/materials.php?series=numeracy
Other sources
NRICH website
There are many interesting individual lessons on the web mostly involving investigation. Sources include nRich and journals of professional associations like Mathematics in Schools and Mathematics Teaching.
Links to materials:
- NRICH
- https://nrich.maths.org/