This is why place values are important and why it is always better to have relational understanding than just instrumental understanding. =D ========================================================== The kind of learning which leads to instrumental mathematics consists of the learning of an increasing number of fixed plans, by which pupils can find their way from particular starting points (the data) to required finishing points (the answers to the questions). The plan tells them what to do at each choice point, as in the concrete example. And as in the concrete example, what has to be done next is determined purely by the local situation. (When you see the post office, turn left. When you have cleared brackets, collect like terms.) There is no awareness of the overall relationship between successive stages, and the final goal. And in both cases, the learner is dependent on outside guidance for learning each new ‘way to get there’. In contrast, learning relational mathematics consists of building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point. (I say ‘in principle’ because of course some of these paths will be much harder to construct than others.) This kind of learning is different in several ways from instrumental learning. ~ Richard Skemp, Mathematics Teaching, 77, 20–26, (1976) https://youtube/watch?v=xkbQDEXJy2k
Posted on: Mon, 17 Nov 2014 02:46:36 +0000