Maybe the experience with the calculus Concept Inventory is relevant here.
The CCI is a test of conceptual understanding (only -- not procedural knowledge not problem solving, using the lingo of the Federal studies).
The CCI has now been given, pretest and post-test, to about 5000 students in some 20 states, 3 provinces of Canada, and several foreign countries. While this test is not typical of all tests in school, it is surely a set of relevant knowledge and understanding. The test was carefully designed by a national team to specifically test only the most basic understandings, things that most instructors would consider too basic for their students.
Students in specific "Interactive-Engagement" method classes (little or no lecture, lots of group work, all emphasizing depth of conceptual understanding of the most basic concepts that faculty always assume THEIR students surely understand). Students receive a pre-test at the start of a calculus course -- and about 1/3 of the items are answerable with only a pre-calculus background -- and a post-test at the end. The measure of gain used is the normalized gain used by Hake and others in physics. Analysis with other common measures of gain show exactly the same thing.
The test results divide the population into two sets who are in different worlds -- two Gaussians with no overlap. The population that has experienced standard lecture based teaching is lower than the students who have experienced so-called "Interactive Engagement" teaching by two standard deviations. The effect of the teaching methodology is simply enormous and, we believe, cannot possibly be accidental or coincidental. The most recent work is that students in China show gain at the same level as the Interactive-Engagement students in the West.
While further work is of course needed, and the interpretation of the results is not yet totally clear, the effect is without doubt huge.
On 1/23/2012 9:17 AM, Robert Hansen wrote: > > "The argument that IE has not worked is specious, because it has not > really been tried." > > But wouldn't that apply equally to the argument that it does work? > > I have looked at the (IE) class at MIT in considerable detail. At > least it tries to retain a notion of rigor but I am not seeing any > transformation there. Clearly, the non IE version remains the path of > choice for those seeking the depth we are used to and that these > Chinese (and other emerging countries) are showing. Depth I might add > that is unmistakable in an interview. Are there other IE classes out > there that I should be looking at? That is a much as I can do to look > at your theory. It isn't like these students are showing up at my > door, because as you said, they don't exist yet. > > What would interest me really is a high school class, using IE that > you think is equal to our high school physics class, or at least the > way I described it. I would like to see that curriculum, the text and > the tests. That is the only way I can be sure that your coverage is > complete. the math in the course should begin with algebra (2) and > progress through calculus. Over two years. I would like to see such a > course. > > Bob Hansen > > [Non-text portions of this message have been removed] > >
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