It addresses an issue I’ve troubled myself over before.
For all of the naysaying about the validity of the study, it rings true to me.
How do I get my kids to see the connection between these two problems:
1) You have a piece of string that is 17 inches long. You cut it into four pieces. How long is each piece?
2) The base of a dog house is 17 square feet. If the dog house is four feet wide, how long is it?
Completely different physical concepts – exactly the same abstraction. How do I effect the transfer?
One of the studies in the paper looked at this. For students that learned from either one or two concrete examples, there was almost no transfer of knowledge to a new scenario. For students that were present with 3 distinct cases, there was some improvement over the other two groups.
The group that learned the rules in an abstract symbolic fashion first transferred the knowledge far more easily than either of the other groups.
A further study (not reported in the Times article) addressed a common teaching strategy: What happens if you teach them the abstraction, but after you give them an example to give them an idea of what it’s about?
It turns out that the group that had a concrete example first had more difficulty transferring the knowledge to a new domain. Something about the concrete connection made it difficult to envision new situations. (The article didn’t make this direct comparison, but it appears that, from the data, that the concrete/general methodology is still a step above just teaching pure concrete examples.)
A further study addressed one of my personal teaching techniques: the compare and contrast. Students were given two different concrete representations, and then asked to find commonalities between the two. This technique actually did yield some results. Bimodal results. Some students (44%) actually learned how to transfer the knowledge, while others (51%) did not.
So, how does this inform my teaching?
Maybe not much. Because of our spiral model of standards, most of my students will have seen most of the material before, presented with concrete examples. I’m not painting on a blank canvas – I’m adding to 8 or 9 years of work by vastly differing painters before me. I don’t get to present an idea in the abstract, and only then make connections to concrete examples.
On the other hand, the idea of transfer is critical to the gaining of abstraction. I think part of my summer curriculum (busy as it will be with a brand new subject to teach next year) will be to examine every concept for transferability, and focus on that.
I’m not sure this is the right answer. There could be flaws in the research that I’m not aware of. (It certainly has more rigor than most education research I’ve seen, though.) I may be drawing the wrong conclusions. But if I want my students to be strong in their later education, they’ll need to be able to transfer what the get in my room to something else.
I need to make sure that can happen.