This is a post intended only for members of BATS and other related professionals. Thanks in advance for any light you can shed on this problem.


It’s always nice when you find a way to improve your teaching and your business at the same time. I think a good way to do this is to publish your core methods.  Crucially, though, you have to do it in a way that simple enough that anyone can understand it, but detailed enough that anyone can also see that there’s something to it.

I’d like your help today thinking through one such method, and crucially what to name the pieces of this method.

The system

The basic idea is that math mistakes can be grouped into one of three different categories, and that each category has its own “fixes” that work best.  The marketing power here is in distinguishing my methods from that of others.  The educational power is in helping people see right from the start ways in which they might make better progress if they focused on different things.

Here are the categories into which I claim all math mistakes can be grouped:

  • Category 1 is “I can’t believe I made that mistake!”  In this case, you knew everything you needed to know, and you just didn’t execute correctly. This could be “I misread the question” or “I had a brain fart” or “I was operating at less than full capacity (e.g. I was tired)”, among other things.
  • Category 2 is “I just didn’t know enough math.”  In this case, you either don’t understand what the problem is asking, or else you do, and it’s clear that there’s a method for solving, but you’ve never seen that method and don’t have enough information to figure it out.
  • Category 3 is “I couldn’t put it all together.”  You read the question correctly, you brought your “A-game,” and you know all the math you need.  But you can’t quite bring it together into a solution.  There’s a leap you need to make, and you just can’t figure out which direction to jump in, in order to get there.

So, what should I call these categories?

  • In a related method first developed together with Justin Sigars (of, we called them carelessnessknowledge, and hard questions, respectively.
  • Later, I changed them to thoroughness, knowledge, and synthesis.
  • Most recently I’ve been using attentionmath fluency (or mastery, depending on the day), and creativity.

And how should one decide?

Beside the question of what to call them is the meta-question of how to decide.  What makes a good naming scheme?

Please comment below.

Anything you have to say, I’m eager to hear.  Thanks so much!



See for the resolution of this discussion. Again, thanks so much for helping to clarity this small but vital issue.