Optimisation (9860)
When studying quadratic functions/calculus, do too many of your students find 'optimisation questions' hard? Have you ever wondered why? The booklet you can download here is the unit of work that supports the ideas presented in a number of workshops during 2011 and 2012 that outlined why students find the ideas hard. Basically, traditional teaching-and-doing approaches fail to focus on what is really happening: the measurement on one dimension and the subsequent calculation of other dimensions. Also, algebraic simplification turns out to be the devil - the patterns in the symbols are lost and so generalisation is not 'seen'! The approach in the booklet supports the idea of each student developing a calculation and then comparing and contrasting to it other's calculations - it is in this that the symbolic patterns appear and the generalisation literally reveals itself. The 9860 .g1m file features animate-able versions of many of the problems presented in the booklet, offering a reinforcement of generality at work. The included document will assist you to access these constructions.