There have been many reformers offering ideas for improving numeracy in our schools. Many of them advocate the use of specific commercial resources or explicit lesson plans – in short they offer recipes for teachers and schools to follow. The quietly spoken Alistair McIntosh (formerly Associate Professor at the University of Tasmania, Australia) avoided this path – yet identified some key ingredients of successful mathematics teaching. To create a narrative thread through his suggestions he nominated concepts starting with “C”.
For McIntosh the basic principles for improving numeracy teaching included;
· Conceptual understanding (rather than simple procedural competence).
· Connecting new mathematical concepts to known concepts and also to the “real world”.
· Communicating – students need to be able to describe, explain, justify, convince, hypothesise and prove.
· Consolidating – ideas need to be revisited, used in practical settings, implanted in games where possible, required skills need to be developed and establish in the mind. This should not be confused with rote learning or memorisation tasks.
· Coordination – teaching is more effective if it is consistent, both within a classroom and within a school – especially at adjacent grades.
· Community of learners – as society changes so does the relevance of the curriculum. As a result teachers need to be aware of what is relevant, how technological and social advancement make new methods of teaching possible and of course, the needs of the learner need to be considered. So teachers are learning, not necessarily new numeracy concepts, but how to present and apply them in the real world.
· Curriculum – McIntosh supports the views expressed in the NCTM Principles and Standards for School Mathematics - the mathematics curriculum should be well articulated,
focus on important mathematics,
and is much more than just a collection of activities.
I’ve taken the liberty of presenting some of the ideas in McIntosh’s brief paper in video form.
This presentation is a condensed version of McIntosh’s ideas. The full paper can be accessed here.
The strength of McIntosh’s ideas is their simplicity – he has provided a lens through which we can view our programs. By considering and including these aspects in our practice we can make progress towards improving numeracy in our schools.