In the course of my research, I came across the project shown here, as represented by the accompanying video. In the video, they show (and tout) the value of their approach to developing pattern recognition around mathematics. Further, they argue that it’s superior to the typical rule presentation and practice. And I can buy that, but with many caveats that I want to explore.
So it’s clear that we learn by abstracting patterns across our experiences. We can provide models that guide, but ultimately it’s the practice that works. An extreme example is chicken-sexing (mentioned in the transcript); determining the gender of new-born chicks. Here, no one can articulate the rationale, it’s merely done by attempts and correct/incorrect feedback! And the clear implication is that by having learners do repetitive tasks of looking for patterns, they get better at it.
And, yes, they do. But the open question is what is the learning benefit of that. Let’s be clear, there are plenty of times we want that to happen. As I learned during my graduate studies, pilots are largely trained to react before their brains kick in: the speed at which things happen are faster than conscious processing. When speed and accuracy is important, nay critical, we want patterned responses. And it does work for component skills to more complex ones in well-defined domains. But…
When we need transfer, and things are complex, and we aren’t needing knee-jerk responses, this doesn’t work. I would like to train myself to recognize patterns of behavior and ways to deal with them effectively, for instance (e.g. in difficult presentation situations, or negotiations). On the other hand, in many instances I want to preclude any immediate responses and look for clues, ponder, explore, and more.
The important question is when we want rote performance and when we don’t . Rote ability to do math component skills I’m willing to accept. But I fear a major problem with math instruction in schools is about doing math, not about thinking like a mathematician (to quote Seymour Paper). And I don’t want students to be learning the quadratic equation (one of Roger Schank’s most vivid examples) instead of how math can be used a problem-solving tool. The nuances are subtle, to be sure, but again I’m tired of us treating learning like color-by-numbers instead of the rocket science it should be.
Look, it’s great to find more effective methods, but let’s also be smart about the effective use of them. In my mind, that’s part of learning engineering. And I’m by no means accusing the approach that started this discussion of getting it wrong, this is my own editorial soapbox ;). There’s much we can and should be doing, and new tools are welcome. But let’s also think about when they make sense. So, does this make sense?