Math Forum Discussions

Jerry Epstein

Posts: 63
Registered: 12/3/04

Re: [math-learn] Re: The Moore Method
Posted: Feb 9, 2012 12:19 AM

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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]
> > > >>>>>
> > > >>>>>
> > > >>>>>
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> > > >>>>> Yahoo! Groups Links
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> > > > Yahoo! Groups Links
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