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Topic:
[math-learn] Re: The Moore Method
Replies:
2
Last Post:
Feb 9, 2012 12:35 AM
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Re: [math-learn] Re: The Moore Method
Posted:
Feb 9, 2012 12:19 AM
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Non-disclosure letter attached. JE
On 2/8/2012 3:40 PM, Jerome Epstein wrote: > > I am forwarding to myself at my other email: jerepst@att.net > <mailto:jerepst@att.net>, I will answer from there. . . You will get > much faster reply in the future by going direct to that email address. > > I gather you are in New York, so we might have a phone conversation or > get together some time. Feel free to call me at 718-429-3437 if you > would like to chat. > > Info on how to get either of the tests will follow. Agreement to > security conditions is required. > > Jerry Epstein > > ------------------------------------------------------------------------ > > *From:*math-learn@yahoogroups.com [mailto:math-learn@yahoogroups.com] > *On Behalf Of *kathleen Offenholley > *Sent:* Sunday, February 05, 2012 3:13 PM > *To:* math-learn@yahoogroups.com > *Subject:* Re: [math-learn] Re: The Moore Method > > Jerome, > > This is very interesting to me. What kinds of conceptual understanding > questions did you ask? I'm really curious and would love to hear more. > > I tend to think of the deep concepts behind calculus as very simple -- > but my students didn't think so. I remember an activity where I had > them each calculate the slope of the curve at a given point, then each > person plotted that one point, so that together as a class, we graphed > the derivative. It was an aha moment for many of them. > > Part of the mess, in my own opinion, is that we clog up the conceptual > understanding with lots and lots of extraneous detail. Lots and lots > of exercises in getting the limit as x approaches zero. Too much of > that before getting to the point, so to speak. Not that I am objecting > to drill and practice, not at all. But to all the extra things stuffed > in. > > Kathleen Offenholley, BMC, NYC > > ________________________________ > From: Jerome Epstein <jerepst@att.net <mailto:jerepst%40att.net>> > To: math-learn@yahoogroups.com <mailto:math-learn%40yahoogroups.com> > Sent: Sunday, February 5, 2012 12:01 AM > Subject: Re: [math-learn] Re: The Moore Method > > > > I don't know if I am just repeating on this board something that I have > already said. If so, feel free to delete this. > > I am the head of the team that developed, with NSF help, the Calculus > Concept Inventory (CCI) in a three year project that ended I think in > 2008. > > The CCI is a test of conceptual understanding (only) in first semester > calculus (no integrals). It tests only the middle level of the 3 levels > of the structure in the National Assessment of Educational Progress > (NAEP) project of some 20 years ago. The lowest level is called > Procedural Knowledge (PK) and is essentially methods of computation, the > middle level (CU) is "Conceptual Understanding" and the third is PS - > Problem Solving. > > The CCI was designed by a highly knowledgeable team of 6 researchers. > The test contains only differential calculus (and some pre-calc), and is > only designed to test CU. There are no formulaic, memorizable-solution, > items on it. > > It has been given now to about 5000 students in about 200 schools, in > about 30 states, 3 provinces of Canada, and several foreign countries in > Europe and Asia, and a recent request from South Africa. The results so > far are quite dramatic. Nearly all schools tested show results that are > stunningly poor. The test is given twice in the semester, once at the > start, and again at the end, usually as part of the final exam. The > measure of gain we use is the "Normalized Gain", better known from > physics, but other more common measures show exactly the same overall > results. > > The questions asked most faculty consider to be much too elementary -- > until they see the results. All items should be readily answerable by > any student with a modest degree of conceptual understanding. The > average scores of the classes -- with some very dramatic exceptions -- > are almost unchanged by one semester of calculus. The normalized gains > run between 0.05 and 0.25, averaging 0.15. A result of 0.15 means the > class gained 15% of the amount they could have gained if all had gotten > 100 on the post-test. The normalized gain turns out to be independent of > the pre-test score, a very interesting result. > > I have 4 schools that use a completely different teaching methodology. > Three schools were only one section of around 25 or so students. The > gain scores were much better, but too small a population to conclude > anything. Then the University of Michigan (Karen Rhea) which has a > comprehensive program across all its sections, with no lectures, all of > it "discovery" based, laboratory-type teaching. These students emerge in > a totally different world (as do the other three similar small sections > that use the same methods). The total number of students in the > Discovery-Based (Interactive-Engagement, in the terminology) classes was > about 1000. These students come out in a completely different world. The > average normalized gain came in at about 0.45, and the results compared > to the lecture based results are totally disjoint. You have 2 Gaussians > with no overlap!!! The odds against such a difference occurring in such > a large population by chance are astronomical. > > The only variable that could conceivably account for such an enormous > difference is the teaching methodology. The normalized gain turns out to > be independent of the pre-test score, and so the difference has nothing > to do with knowledge of calculus at entrance, though such a variable > would be hardly different over such a large population. > > Faculty interested in giving the test should write to me off-list at > jerepst@att.net <mailto:jerepst%40att.net>. You must agree to a set of > security conditions in order > to get the test. > > Jerry Epstein. > > On 2/4/2012 10:57 PM, Robert Hansen wrote: > > > > By teacher guidance I mean direct instruction. The teacher is not only > > involved, they are calling the shots. It is generally a mixture of > > lecture and Socratic dialog. > > > > By student application I mean that the student is calling the shots > > (the teacher may or may not be involved). This is generally a mixture > > of study, reflection, problem solving and question asking. > > > > The differentiator is who is calling the shots. > > > > By impressive amounts I mean several hours of each per week per > > subject. 50/50 would be a good start but it shifts towards the student > > since the time the student spends studying and problem solving is > > variable while the time spent by the teacher is fixed (by the class > > schedule). In any event, it takes copious amounts of both if the class > > is actually trying to succeed to the level I suggested. > > > > Bob Hansen > > > > On Feb 4, 2012, at 8:09 PM, Ed Wall <ewall@umich.edu > <mailto:ewall%40umich.edu> > > <mailto:ewall%40umich.edu>> wrote: > > > > > Bob > > > > > > To somewhat use your metaphor, what if I said something like > > "teacher and students together forge tools and begin mapping the > > terrain and application allows the student to mentally conquer that > > territory "? I am not espousing a method of teaching by the way, but > > just wondering. > > > > > > Ed Wall > > > > > > On Feb 4, 2012, at 7:54 PM, Robert Hansen wrote: > > > > > > > Well, I can clear up my message if it was wobbly. To reach the > > levels of success in these subjects required to use or teach them > > requires impressive amounts of both teacher guidance and student > > application. The guidance drives the student's mind forward into new > > territory and application allows the student to mentally conquer that > > territory. I will let Jerry summarize his view. > > > > > > > > Bob Hansen > > > > > > > > > > > > On Feb 4, 2012, at 7:30 PM, Ed Wall <ewall@umich.edu > <mailto:ewall%40umich.edu> > > <mailto:ewall%40umich.edu>> wrote: > > > > > > > >> Bob > > > >> > > > >> First is that people have always learned 'spontaneously' without, > > in a sense, teachers and they still do. I can think of many, many > > instances; however, I will admit 'learning' and 'spontaneous' are > > slippery words. Secondly I don't read Jerry as quite saying this. Yes, > > he, perhaps, leans that way and, I suppose, one could say you lean the > > other. I've always liked it sort of in the middle where one leans back > > and forth depending on the circumstances. There is a time for some > > playing around with some of the concepts at hand and there is a time > > for some 'handed down' 'accumulated' structure so as to leverage some > > of the concepts at hand. Perhaps a sort of nature 'and' nurture. > > > >> > > > >> Yes, I agree, there are probably people who are, perhaps, a bit > > 'unrealistic,' but I don't read Jerry that way. And, yes, there are > > probably people who see all this as a matter of crystal clear > > transmission, but I don't read you that way. > > > >> > > > >> Ed Wall > > > >> > > > >> On Feb 4, 2012, at 6:48 PM, Robert Hansen wrote: > > > >> > > > >>> Yes Ed, unfortunately for some it is. They don't like the > > results so they choose to believe something happy. Like believing that > > students can do problems on a board, review each other and uncover all > > we know about topology in a couple of semesters. We have been wrong > > all these years thinking that teachers are there to explain to and > > guide bright minds down these enormous and intricate paths already > > travelled. In Jerry's universe students learn spontaneously, without > > teachers. They sure don't seem to do that in this universe and you > > can't say that teachers get in their way, many of these alleged > > geniuses don't even show up for class. > > > >>> > > > >>> Bob Hansen > > > >>> > > > >>> > > > >>> > > > >>> On Feb 4, 2012, at 4:38 PM, Ed Wall <ewall@umich.edu > <mailto:ewall%40umich.edu> > > <mailto:ewall%40umich.edu>> wrote: > > > >>> > > > >>>> Nature vs nurture? Is that still controversial? > > > >>>> > > > >>>> Ed Wall > > > >>>> > > > >>>> On Feb 4, 2012, at 4:09 PM, Robert Hansen wrote: > > > >>>> > > > >>>>> Actually, I think nature produces students that understand and > > use what they have learned. Teaching only brings them up to speed. > > > >>>>> > > > >>>>> Bob Hansen > > > >>>>> > > > >>>>> > > > >>>>> On Feb 4, 2012, at 3:14 PM, Richard Hake wrote: > > > >>>>> > > > >>>>>> "Some say that the only possible effect of the Moore method > > is to > > > >>>>>> produce research mathematicians, but I don't agree. The Moore > > method > > > >>>>>> is, I am convinced the right way to teach anything and > > everything. It > > > >>>>>> produces students who can understand and use what they have > > learned. > > > >>>>>> . . . . . There is an old Chinese proverb that I learned from > > Moore > > > >>>>>> himself: 'I hear, I forget; I see, I remember. I do, I > > understand.' " > > > >>>>>> Paul Halmos (1988, p. 258) > > > >>>>> > > > >>>>> > > > >>>>> > > > >>>>> [Non-text portions of this message have been removed] > > > >>>>> > > > >>>>> > > > >>>>> > > > >>>>> ------------------------------------ > > > >>>>> > > > >>>>> Yahoo! Groups Links > > > >>>>> > > > >>>>> > > > >>>>> > > > >>>>> > > > >>>>> > > > >>>> > > > >>>> > > > >>> > > > >>> > > > >>> [Non-text portions of this message have been removed] > > > >>> > > > >>> > > > >>> > > > >>> ------------------------------------ > > > >>> > > > >>> Yahoo! Groups Links > > > >>> > > > >>> > > > >>> > > > >>> > > > >>> > > > >> > > > >> > > > > > > > > > > > > [Non-text portions of this message have been removed] > > > > > > > > > > > > > > > > ------------------------------------ > > > > > > > > Yahoo! Groups Links > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > [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] > > >
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