I went to a retirement party this evening, finding my way there with GPS. I’ve been very slow getting my phone to do that for reasons I won’t get into; but when I got into my car to go home, I realized I would need my GPS again. In the past, I followed Mapquest maps to my destination and barely needed to glance at them to remember how to get home. But with GPS, I had no reason to pay attention to where I was turning or how long I went straight. To me this was further confirmation that what I am seeing in my students is exactly what so much research is telling us: explorations or “discovery learning” tends to be far more memorable and transferable than direct instruction.
I’m aware (and have read) many studies and opt eds that argue students need to be taught new information explicitly and directly. When I have had deep conversations with anti-discovery educators, though, I have found much of the disagreement has to do with definitions and limitations. How much is a student is supposed to struggle to figure out something that can be explained in seconds? As with anything else, common sense is needed to balance the pedagogical strategies: fitting the method with the content.
Direct instruction proponents do not necessarily believe it is wise to train students to expect us to force-feed them information by repeating direct instruction over and over. Nor does it seem productive to have students rehearse scripted procedures until they are burned into a memory bank without being able to transfer them into realistic contexts. On the other hand, I do not believe any discovery proponents expect students to derive all the Laplace transforms.
It makes sense to me that my lectures are more like GPS: efficient but not likely to stick and transfer. That doesn’t mean that I won’t tell students how to enter a function into their calculators, but it does mean I expect them to make many connections through reading and exploring toward logical next steps. If you are interested in getting started on a few discovery-type math lessons without going whole hog, plug into my other site, “Got it ->Get it Transfers.”