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## Understanding vs. Doing

At a session I facilitated today, I was going over our old (1996) curriculum as compared to our revised (2010) curriculum.  Many of the outcomes are similar, but the big difference is in the wording of the outcomes.  I asked the participants to compare the two below.

1996

13. Use the Pythagorean relationship to calculate the measure of the third side, of a right triangle, given the other two sides in 2-D applications.

2010

2.  Demonstrate an understanding of the Pythagorean theorem.

The outcomes get at essentially the same thing.  In my opinion, though, the big difference is in the word “understanding” in our 2010 curriculum.  Back in 1996, we don’t appear to have been too concerned about whether or not the students understood it, as long as they could do it.  I threw this thought out in my session, and one person challenged it and said that they were the same thing.  He insisted that a student couldn’t do something unless that student actually understood it.

I disagreed, and he claimed I was arguing semantics (which I had to look up later).  I had to move on, but I certainly thought about what he had said on my flight home.  In the end, though, I stand by my original assertion.  I think that too often we ask kids to “do” things in math class without really trying to get at understanding.  Some kids imitate our algorithms, score well on tests, without having a true understanding of the math involved.

I tried to think of a real-world example of this distinction, and so far the best one I have come up with is as follows.  I know that if I push the gas pedal on my car, it will move forward (if I put that stick thing in the spot marked “D”, which I assume stands for “Go”).  This is something I am confident I can do.  I do not, however, have any understanding as to why the car goes forward or what is going on to make that happen.  I do it without any understanding at all.

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### One Response

1. At first glance, the 96 version looks to be a very specific objective. One could take this one step further and map this objective to a grading criteria. So for example, in Sweden I could map this objective to “G” grading criteria – which maps to Bloom’s knowledge and comprehension cognitive domains. So the 96 version is very restrictive in terms of implementation.

No objective contains the word “understanding”. However, it might be used to specify course goals or standards. The 2010 version looks as though a layer of abstraction has been
implemented. Now the teacher and/or school can construct the conceptual layer by specifyin the specific objectives. One of those could be the 1996 version objective stated for PThm.

Thus, a teacher could define a new objective such as: Prove the Pthm. Again in Sweden, this could be mapped to MVG grading criteria, which maps to Bloom’s highest cognitive domains.

I agree, if a student can acheive the 96 version objective – that does not necessarily demonstrate understanding. However, if one can assess across all cognative domains, then it helps to provide a better picture of the students understanding.

Personally, one thing I look for is a student who is able to teach a concept AND is able to teach this concept from various perspectives. A experienced teacher knowledgeable in their subject area UNDERSTANDS the concept. That is my end-state picture of what understanding is.

Wow I can’t beleive I just hunt and pecked this waiting for my flight. Good Luck with the 2010 version and take advantage of it to push your students towards enduring undertsanding.