From the editor - What does it mean to be functional in mathematics?
I suppose, if you are a teacher of mathematics, then your attention will be drawn to the mathematics of the things that happen around you. Here are three things that my attention has been drawn to recently – as you read the stories you may want to consider their relevance to functional mathematics.
My husband has now fully recovered from his heart attack. A year ago he was in A & E. So scary. It’s strange how you remember some bits so vividly. The excellent doctors asked the fantastic nurse to administer 0.5mg of a clot-busting drug – she got out her phone. What?! 3mg of the drug was dissolved in 10ml of a saline solution and she was working out how much solution to give…
We have recently had our bathroom tiled. It looks fantastic. The wall tiles are 60cm x 30cm and the floor tiles are 30cm x 30cm. It would be impossible to line up the wall and the floor tiles exactly so I thought my eye might be drawn to the inconsistency of the arrangement. I asked the tiler if he could lay the floor tiles so that the edges of the tiles were at 45º to the wall. He turned a shade of green and said we would have to negotiate a different price... Why is that so hard? He has still cut every tile…
There was a great recipe in the newspaper a couple of weeks ago to make cheese. Really simple instructions – mix equal quantities of goat's milk yoghurt (4% fat) and ordinary yoghurt (2% fat). Add a bit of salt. Suspend in a muslin bag to drain off the whey. Leave for 36 hours. Hey presto – cheese. My husband is very conscious of fat in the diet (see Story One) so was overjoyed – 3% fat – cheese I can eat. Or is it?
So do these stories have a bearing on what it means to be functional in mathematics? How would they score in the functional skill assessment areas of complexity, familiarity, independence and technical demand?
I think there is a degree of complexity in each of the stories. That’s what makes them interesting for me. While proportionality is a big idea in mathematics, using a ‘nasty’ multiplier or a two step problem using a unitary method makes the situation complex. The tiling problem goes beyond some peoples’ intuitive feel for shape. And what is it I am finding a percentage of to make decisions about cheese?
These situations have a high degree of familiarity to me – they were my stories. They may not be familiar to learners but could they engage with these situations? Could learners generate their own ‘stories’ to work on?
It is hard to comment on independence in this context, but giving pupils exposure to mathematical problems within the supportive atmosphere of the classroom would encourage them to be able to show more independence in tackling problems in real life.
None of these stories include very difficult mathematics, do they? The technical demand is low. If the three concepts were given as straightforward questions they would not be very difficult – would they? Proportional reasoning, spatial awareness/tessellation and percentages: ideas commonly encountered in mathematics.
So how are we preparing pupils to be functional in mathematics? Have we got our own mental picture of what functionality in mathematics would look like? I will certainly keep referring back to these stories as I develop my ideas of functionality and give learners the opportunity to engage with complex yet every day mathematical situations. Why not tell us what you are doing?