Let's not twist things further Ed. I do not think Jerry supplied any results to refute or even attempted to refute my candidates, which were students scoring 5's on the AP calculus exam. And it would be silly to refute that as I will explain. There are students who are quite successful in math and calculus and physics, otherwise what are even chasing? Something that doesn't even exist in the first place? I work at a company with 5000 engineers and new ones are hired regularly as old ones leave and in that group I see many people who have been quite successful in these subjects. They came from somewhere. And most of them, especially in the last 10 years or so, took AP classes. Are we saying that they came from the group that did poorly on AP exams?
Jerry said that most students that pass calculus don't even know what calculus is. I agree with him. I wasn't talking about that group and the Jerry wasn't talking about students scoring 5's on AP exams. I put the bar high enough so that any more quibbling would be silly.
I have read and studied a great deal of the data John (and Hake) have pointed me to. And I have looked, as much as possible, at the scant "live" examples of IE that they have pointed me to.
My simple request for something real, like showing me top students practicing I.E. is born of all that review. The "research" John keeps pointing me to is ruined by a fundamental (and absurd) flaw in the design of the experiment. Essentially, an I.E. class is set up next to a traditional class and an inventory test is taken at the beginning and end (by each class). And then the results are compared. Actually, rather than comparing the results directly and absolutely, they are obfuscated by converting them to "normalized gain" prior to the comparison. But that isn't the flaw I was talking about. The flaw is that an inventory test is no substitute for a full blown calculus or physics exam. Who would form an hypothesis that IE classes are better than traditional classes and then not set out to prove it with full blown traditional exams? You can't make a claim and then redefine how you test the claim as well. To make the claim that IE is better than traditional you have to face the music and test it using full blown exams, not fragments of an exam.
However, John and Jerry claim that inventory exams are a sufficient rubric to make that claim. Well, that sounds like another hypothesis to me and if true, easily proven. All you would have to do is give those IE students full blown traditional exams and see if they succeed. I have proof that inventories alone are not a sufficient rubric. I took the released results of AP calculus AB and BC for 2003 and 2008 and I compared the performance on each and every problem. I ranked the problems according to how well the students did against how well they did on the exam in whole. In other words, if students scoring a "1" on the whole exam got problem #12 right 50% if the time and problem #6 right only 5% of the time then #12 is easier than #6. Essentially, it is like IRT but in reverse. What I found was that conceptual problems ranked a little higher than rote problems (like what is the derivative of sin(2x)) but lower than full problems, like given two functions what is the area between them and then at the far end were the free response multi part problems, where you actually do math. I have performed this analysis with TIMSS and PISA as well. These problem rankings are surprisingly immutable regardless of any demographic grouping you can come up with. In other words, regardless of country, school, race, gender, economic status or anything, if you pick two students that each got 50% on the exam, they will have gotten mostly the same problems right and the same problems wrong.
So you see, I have been busy. You can believe my analysis or not but that is irrelevant. I never asked John or Jerry to prove their first hypothesis that IE students do better on inventory exams. I already know their answer because I reviewed the data they (and Hake) provided me before. I asked them to prove their SECOND hypothesis, that inventory exams are a sufficient rubric to make the claim that IE is better than traditional. And if you have been following this discussion, you know their answer, they don't have one. In 20 years of touting the benefits of IE it seems to never have occurred to them that the only way people will accept their claim is with a toe to toe comparison. And it should be very easy, if their claim is true that is.
What I see happening here is this. My world (I am not a teacher) consists of people (and when I was younger, fellow students) that were and are quite successful at these subjects. John and Jerry though are teachers and their worlds consist of every student and their definition of pedagogy is in that image while my definition of it is in the image of an aspiring student. I am actually open minded but analytical and critical as well. All essential qualities required to find the truth. I have even given IE points for being a better pedagogy for students that do not aspire to the subject. Mezur himself said that traditional methods work for students that want to figure things out but they do not work for students not so inclined. I agree! But you lose me right after that when you say "Therefore, we should teach all students with methods geared toward those that do not try to figure things out." Huh? Why?
We are talking about two very different groups of students. One group is simply not aspiring to the subject at hand and the other group is. The mechanics of teaching the second group to their full potential is going to be very different than the first. When I present new ideas to my peers I do not start the meeting by handing out toys to help them understand the big ideas in what I am about to say. I simply go to the whiteboard and write and speak. And it is quite natural, and efficient. But we are in that second group. And if you go way back in our lives you will find that we developed this "urge" to figure things out early on and it evolves into full blown reasoning with its Socratic dialog quite naturally. And this urge is not what we commonly call "curiosity". Common curiosity is very brief and without this developed urge it has no real effectiveness and only satisfies the moment. This urge I speak of is never satisfied. Teaching students without that urge is obviously going to be an entirely different phenomena (and outcome) than teaching students with it.
On Jan 26, 2012, at 11:23 PM, Ed Wall wrote:
> 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 . > > Ed Wall > > > 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 >> >> >> >> >> > > > > ------------------------------------ > > Yahoo! Groups Links > > >