TM4T Techniques 2.1.3 - Planning - The Rocks Problem
This is a simple problem, and it may be quite familiar to some teachers. Lamentably, though, I am going to waffle on about it a bit. This is because we aren't just interested in the answer, we are interested in the thought process we follow in tackling the problem.
Here is a picture of the problem: the black thing on the left represents an empty jar - the challenge is to fit all the odd-shaped objects on the right into the jar
Let's look at how an average teacher might tackle this problem. They would probably start with the bits which seemed to occupy the least space, like this:
Yes, that seemed to work didin't it? By the way, if you're wondering why teachers tend to take this particular approach, it is because most other people do too. They are also encouraged by how well this approach works, and continue to fill in the bits which seem to occupy the least space.
Yes, this looks OK. Definitely on the right lines. Crack on with the next few objects.
Nearly finished now. We'll just bung the last bits in....
Oh bugger. There is, in fact no way to fit these last few pieces into the jar and close the lid. We've done all that work, and it was all for nothing. How frustrating.
I'm sure you've all figured out that this is a metaphor, right? We're not talking about objects and jars, we're talking about fitting tasks, activities and events into our schedules. We're also talking about the thought process which leads people to plan the bits of their lives which are easily plannable, and tackle the big ugly bits last. There is of course some logic in this, but before we look at an alternative approach, let's look at another version of this problem (a really short one, I promise).