There is no claim that the CCI is a comprehensive test of ability or skill in calculus. It is no replacement for a final exam. All questions are designed as Conceptual Understanding, and only of the most basic principles of Calculus I.
I cannot see why comparisons with results on other tests would be meaningful or how one would compare results. What is striking about the CCI results is the huge gap between Michigan (and a few other small classes) and the overwhelming bulk of the students from dozens of other schools in the US and abroad. This seems to correlate with a quite different teaching methodology, but I do not claim that it is proved what exactly has caused this enormous difference.
On 1/24/2012 8:38 AM, Robert Hansen wrote: > Actually, they do here (in the U.S.) and one can easily match that performance to the TIMSS performance here and in Shanghai. Without meaningful and whole comparisons, like comparing performance on AP exams, it will be very hard for IE to gain any traction at all. But let's move on. The University of Michigan actually uses the AP exam format for their Calculus 1 and Calculus 2 classes (115& 116). Have you tried to compare exam results that involve everything (concept, functional and problem solving skills)? Such a comparison though will not be very helpful because the curve used at UM is very pronounced. For example, in Math-116 (Calculus 2), 32% on the Final exam will garner a "C". A comparison in that environment is more like saying who is failing the least. You compared IE class performance to the stellar (and complete) performance of Shanghai and I think to be credible, you (or John) must supply us with verifiable examples of such, beyond pre and post gains on a concept inventory that really does not provide the whole picture. As an analogy, imagine if I said I created a music concept inventory for piano playing. I seriously doubt that you would accept that as an indication of success in learning to play the piano without actually seeing if the kid can play the piano. > > UM Math 115, 116 > > http://www.math.lsa.umich.edu/courses/115/Exams/index.html > http://www.math.lsa.umich.edu/courses/116/Exams/n2011fall/Final_Exam/index.html > > Bob Hansen > > > On Jan 23, 2012, at 11:59 PM, Jerome Epstein wrote: > >> The Chinese students of course do not take AP tests, and the classes I >> am referring to are university classes. >> Similarly, the large pool of IE data from U of Michigan is. . . well. . >> . university, so not AP. >> >> I am not familiar with any high school classes in calculus that use a >> strongly or totally IE approach, that would allow testing the effect of >> the teaching method on AP results. >> >> I would also emphasize that the testing we have done was specifically >> designed to test only conceptual understanding, not procedural knowledge >> (low level formulaic tasks) nor problem solving. The AP test, to the >> best of my knowledge also has a great deal of low level skill based >> material, so I don't know any way to make a comparison on the basis of >> the AP test. >> >> I have never claimed that the kind of approach I am suggesting produces >> better results on, calculating derivatives -- skills that my test does >> not measure. . . . >> >> JE >> >> On 1/23/2012 8:43 PM, Robert Hansen wrote: >>> It seems that we are getting somewhere Jerry. If these comparisons you >>> make between IE classes and noted Chinese performances are accurate >>> then we are talking 5's across the board in AP Calculus with maybe a >>> few 4's. It would help me a great deal in qualifying the successes you >>> and John speak of if you could point me to these schools and the IE >>> classes therein to witness the curriculum and the performance you >>> claim. I have loads of data on Chinese students, in Shanghai and here. >>> All I need now to complete this puzzle are these classes you speak of. >>> The AP data should be a cinch since schools normally publish stellar >>> results like that and top performing calculus students would take >>> nothing but AP calculus (BC in fact), if not simply for the challenge, >>> for the easy college credit. >>> >>> Bob Hansen >>> >>> On Jan 23, 2012, at 6:10 PM, Jerome Epstein wrote: >>> >>>> The most recent work is that students in >>>> China show gain at the same level as the Interactive-Engagement >>> students >>>> in the West. >>> [Non-text portions of this message have been removed] >>> >>> >> [Non-text portions of this message have been removed] >> >> > > > [Non-text portions of this message have been removed] > > > > ------------------------------------ > > Yahoo! Groups Links > > > >