“If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?” ~St. Augustine aka Augustine of Hippo (354-430), *De Magistro ch X, 23.*

I had the opportunity to teach accelerated algebra during summer school this year – a class full of twenty-one 10-13 year olds who wanted to move a year ahead in math, and so they chose to spend five hours a day for six weeks of the summer in a classroom. It was a great experience in many ways but one of the things I noticed was how often the students would say things like “just tell me the formula!”. The students were, generally, very good at math – but not always so good at answering my favorite question, “Does your answer make sense?”

This reliance on formulas is something that drives me a little bit batty, and something I hope to work on this year is finding new ways to teach that don’t rely on me writing down formulas and students copying them. I want students to figure the formulas out – to be able to get to the answer the long way if they forget a formula on an assessment, to understand why the formula works the way it does and how to use it correctly. Coming from a physics background, something that I find particularly useful is the idea of dimensional analysis and I hope to have a chance to introduce it to my students this year, too, as a further aid to understanding.

I think St. Augustine was on to something all those many years ago…

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I agree that this is one of the challengesofworking with accelerated students,orreallyany students who are “good at doing school.” one thing that has been helpful to me is encouraging students to create their own formulas. It’s a total win-win: they get a formula, they understand their formula on a really deep level, and a lot of math is learned both in creating the formula and when they compare and contrast their formulas and show how they created them.

I like this idea too! I often have students create their own algorithm after we have explored for awhile, but then we come up with the formal algorithm/formula at some point too.