Wednesday 16 April 2014

Desirable learning behaviours

There is some fantastic research about how we should go about learning mathematics or numeracy.  In a nutshell: Everything you think you know – IS WRONG!
Comforting for tutors huh.

Here’s the skinny.

The strategies learners use to learn mathematics can be categorised as either ‘desirable’ or ‘non-desirable’.
Non-desirable strategies include:
  •       Memorisation
  •      Single-strategy problem solving
  •      Repetition
  •      And my personal favourite: listening

Now there are a lot of reasons these approaches suck – the main being that these strategies are effectively useless in regard to understanding mathematics – despite their persistence in the education zeitgeist.

The reason these are not effective can be summed up in two words – passive learning.  Learning is an active process of making meaning and connections about and between ideas and concepts.  As my old lecturer used to say ‘the brain is not a data collecting machine but a meaning making machine’.  The strategies above are generally considered ‘passive’ and facilitate only ‘shallow level processing’. 

Mathematical success requires understanding.  If a learner believes and then actually tries to use these four strategies they are doomed to poor academic performance.  At best they may experience some short term success, but they are destined for failure.  It ain’t good.

Desirable strategies include:
  •      Elaboration
  •      Strategic problem solving
  •      Collaboration
  •      Connection making

These strategies are considered to engage learners in ‘deep level processing’ and have consistently been shown to produce incredible results.  In a latter post I am going to go into detail about what ‘elaboration’, ‘collaboration’ and ‘connection making’ mean and look like in practice.  There is some description of strategic problem solving here.  But the basic idea is that they all require ‘mental action’ by the learner. 

Now for a brief thought.  Is developing mathematical skills synonymous with developing learners strategic learning repertoires?   

What message do we as educators send to learners about preferable behaviours?  Do we implicitly send the message that if learners will listen, concentrate and practice they will learn? 

If so, we are setting learners up for failure - again.  If I could sum up all this research in five words it’s these. 

Nobody learns maths by listening.

Provocative?  More soon…


  1. It would seem to me that learning maths via the for keys you suggest sets you up for life then. Those same strategies are what is required for all luff learning aren't they? Is it simply neural pathways being developed regardless of what they are used for?

    1. Please excuse the ridiculous predictive text...that's what you get for emailing in the car!

    2. I love 'luff' learning! Also like that I get someone commenting!

  2. A strong correlation between the desirable strategies and academic success in general. The strategies here are the best for maths but good learners have a repertoire of strategies as part of a whole self-management process. I'm not sure about the neural pathways but it would make sense if they become part of normal behaviour. They are also the product of strong meta-cognitive thinking (how will I think about this and what will I do?).

    It seems that traditional education isn't setting up people to be life-long learners but rather passive consumers.