Learning Patterns

Are there patterns to learning in Maths? Are these different in different subjects?

Patterns and pattern languages are used to think about writing computer software that works quickly. I’ve noticed that when students are learning (say) directed numbers in Maths, the adding and subtracting is learned fine, and then the rules for multiplying and dividing. Mixed problems can be sorted using varied examples. But then they have to solve problems with multiplying out brackets – application of the multiplying and then the adding rules on a single problem – and there is nearly always some relearning needed.

My pattern would be something like

Context: students applying directed numbers to symbolic algebra
Problem: they need to switch between the multiplying rules where the sign of the answer can be inferred from the signs of the terms to adding where the size of the like terms being collected matters
Solution: Remind students of the rules in a familiar context – quick examples using numbers. Add the directed numbers table on the right hand part of the whiteboard for easy reference

A concrete example of what I’m on about is the Writer’s Circle patterns page on the c2 wiki – but that looks more like a lesson plan or set of rules. Conservation Economy Net has a nice looking mind map come pattern language for sustainable development.

Keith Burnett 2004 - 2010