That's a picture of some blueberry muffins I made on Monday - taste good, look good I was very pleased. Pleased until I started thinking: what am I pleased about? That they came out well I guess, but what was my input? I followed a recipe which is, by its very nature, an algorithm so would I have known what the problem was if something had gone wrong? Probably not.Which brings me back to the question: what am I pleased about? It seems to me that I'm pleased that the muffins 'worked' after I blindly followed some instructions - sure I recognised some of the ingredients but did I understand what was going on? Not really. This got me thinking about mathematics teaching. How often do our students blindly follow recipes to be pleased when the right thing appears? How often are they able to see what the problem is in their working? How often can they tell when a solution doesn't fit with the problem? These are all things which we should be considering when we are teaching mathematics - is the understanding there?
I'm hungry...off to get a muffin!
