I've been reading this conversation as it has progressed and thought I'd make a comment or so and put forth a speculation.
I think I read Bob Hansen as saying he'd like to see some correlation of traditional 'success' (and while I believe he has some candidates in mind for this term, they seem to be up for debate) with the interesting results Jerry has noted. However, I really am doubtful much of anything will necessarily convince those who don't want to be convinced. Further, I rather doubt that those who don't want to be convince are going to take John up on reading and trying. However, strangely enough I am starting to see sort of a Kuhnian paradigm surfacing with regards a number of folks who were randomly anti. There is still skepticism but it has become grudgingly nuanced.
I've been thinking about some related matters for some time under the guise of what is often termed 'studying.' My remembrances of the halcyon days of physics or calculus education that Bob is referring to is that 'motivation' was, in a sense, visible in one's performace of studying. My past and current remembrances of 'foreign' students is that this is part and parcel of them also. With this in mind, some work by Ericson and FS Ellett, 2002, Education Policy Analysis Archives might be relevant (whether you read or not is up to you - smile). They look at all this studying (more or less at the collegiate level) and construct a hierarchical typology of those who engage in studying ranging from the student who values an intellectual discipline for its own sake (out of love, one might say) to those students who study an intellectual discipline for ?strongly external? reasons (the possibility of garnering, one might say, big bucks). In between, among other possibilities, are those who, for instance, orient strongly towards some career choice. They note that it is very difficult to tell from outward performance who is what or where. Nothing very earthshaking here although they argue the situation - which was never populated heavily at the upper levels - has moved rapidly downward. I do know that when I talk to the high scoring AP Calculus student a very very few of them are, before, after, and during, little interested in calculus, per se. They take calculus to satisfy requirements, get into Engineering, etc. This isn't bad, by the way and, as I mentioned, traditional measures of performance don't distinguish within the hierarchy. However, how about intellectual 'love' for calculus (smile). It seems that along the way to developing an 'affection' for calculus, you might need or might find it useful to develop a sort of intellectual intimacy, a sort of conceptual understanding. Perhaps the CCI and similar others measure such intimacy (smile) and the beginning of what has been termed internal motivation (which many be
On Jan 25, 2012, at 3:23 PM, Jerome Epstein wrote:
> I think it is a bit more complex than that. I think that a lot of > students who score well on traditional tests also do very poorly on > tasks where basic conceptual understanding is needed. > > JE > > On 1/25/2012 11:01 AM, Robert Hansen wrote: >> I don't think anything I have said is counter to those observations. I never said that all students of traditional classes are successful. My statement is that almost all students scoring a 5 (which is like 65%-70%) on an AP calculus exam are successful. The reason so many students succeed in traditional classes (or any classes for that matter) yet are not actually successful, is grade inflation. It is just not in our nature to fail a student that has worked hard all year. It's easy if they don't show up or goof off the whole year, but we can't do it if they tried all year. I doubt even I could do it. That is why it is so important to me to see comparisons of high performance on comprehensive exams. >> >> Bob Hansen >> >> On Jan 25, 2012, at 9:00 AM, John Clement wrote: >> >>> I find this to be a bit funny, because I have seen so many students who have >>> gone through a first year traditional calculus course and can't use it. >>> They can't write a simple integral nor a simple algebraic equation. My son >>> got good grades in calculus, but still didn't seem to understand it. As a >>> result he couldn't apply it. He could do the mechanics, but not much else. >>> What is even worse I have seen students who passed calculus, but still >>> didn't exhibit the ability to do proportional reasoning. And the type of >>> courses they passed were all traditional using traditional texts. >>> >>> They simply did not understand the concepts behind Calculus. They could >>> sometimes recognize the name of a math principle, but recognizing that they >>> needed to use it did not seem to happen. >>> >>> John M. Clement >>> Houston, TX >>> >>>> And my point is simply that since it isn't a comprehensive >>>> assessment of Calculus then it cannot be used to compare the >>>> effectiveness of IE to non IE classes. The only way to make a >>>> useful comparison between IE and non IE is to use a >>>> comprehensive exam. There is a lot more to owning calculus >>>> (or physics) than owning an inventory of basic principles. My >>>> impression of IE is that it works better in first year >>>> terminal classes than traditional methods that are geared >>>> toward full ownership. In other words, if someone is trying >>>> to be a nurse but has to take calculus (because the college >>>> says so) as their last ever math class, then IE might be a >>>> useful alternative to a real calculus class that is geared >>>> towards students that actually need and use calculus. >>>> >>> >> >> >> [Non-text portions of this message have been removed] >> >> >> >> ------------------------------------ >> >> Yahoo! Groups Links >> >> >> >> > > > ------------------------------------ > > Yahoo! Groups Links > > > > >