Gain Pain Ratios
A way of learning about fractions seemed to appeal to my Phase 2 budding master-criminal.
It involved estimating the Gain and the Pain of doing different things.
For example, the gain from eating cake came out at 10, while the pain was 1, so a ratio of 10:1. Definitely worth doing. But the discussion quickly turned to other things and different conditions. For example, what about watching telly or cutting the hedge? Was that more or less gain, more or less pain? What about stuff like the disapproval of your parents? etc
We ended up doing this on a piece of paper for a range of different things and comparing the fractions we got. This way we could decide what was best and what was worst, and what to concentrate on if we could only do a few of the things on the list.
We were laughing about it, so the final step was see how parental disapproval might affect the results. To simulate a time when things were a bit fraught at home, we added 5 disapproval points to pain or 5 brownie points to gain (depending on what the choice was), and that produced a different list of things to concentrate on.
Effectively we'd done a sort of cost-benefit analysis, something I'm pretty sure she's often busy doing anyway.
[Interesting side note: studies (e.g. [1]) show that people literally calculate the tangent of an angle when they catch a ball.]
For the school
What was striking about this was not just that the game seemed to naturally appeal to an 8 year old mind, but that the gain and the pain were so blatantly subjective. Normally in cost-benefit analysis you use objective measures as much as possible so that you can't be accused of bias. If we'd used Ofsted scores as part of our analysis, for example, we'd have come up with quite different gain:pain ratios.
But actually, that would just reflect another bias - Ofsted bias, perhaps the sort of thing the school was set up to challenge. Since it's all relative anyway, and the trick is to be consistent (as in feedback monitoring), why not let your biases just shine through? As long as things are generally moving uphill, and you can demonstrate that they are, an alternative index might be a useful thing for everyone.
