While certainly not a novel idea, the use of manipulates as a means to provide access to mathematical concepts is gaining considerable popularity nationwide. And while this is to be lauded, certainly, it should not be viewed solely as an option for those pupils struggling to grasp the concepts before them. Quite the opposite in fact. Those pupils ‘who grasp mathematical concepts with relative ease’ have as much to gain from their use as anyone else in the classroom!
Take for instance this photograph...
While the each of the concepts on show may not necessarily be pitched at National Curriculum expectations, I think it’s a good example of how manipulatives can be used to generate mathematically rich discussion and allow the concepts themselves to leap from the page (table).
By simply asking pupils what the next term in each sequence is or what the formula for calculating the nth term might be (in words initially of course) we can offer challenge our pupils no end.
Yet, if we ask, which is the odd one out, then the potential connotations go way beyond that which we can predict (though we should be prepared for some common/predictable occurrences).
(*An alternative image perhaps)
On three occasions I posed this question to a group of adults and each time came a curveball answer I hadn’t considered but which was as mathematically valid as those I had.
The underlying point being that regardless of your expectations or view how the conversation will go, your pupils will be encouraged to discuss what they already understand, what they observe and can be directed towards a greater, deeper understanding as the conversation continues.
Of course, the examples here require some not insignificant prior knowledge but could I see myself posing this question to Year 5 or 6 pupils? Yes and it’s something I aim to explore over the coming weeks and years.
Kieran
@Kieran_M_Ed