> ----------
> From: Lillie Crowley[SMTP:lillie@POP.UKY.EDU]
> Reply To: Lillie Crowley
> Sent: Thursday, October 28, 1999 7:57 AM
> To: Jane Sieberth; mathedcc@archives.math.utk.edu
> Subject: Re: [MATHEDCC] Why Johnny can't read.
>
> I intended my original response to go to the entire list, and I think I
> sent it only to Nancy. Here it is:
>
> Charles is absolutely correct. This business of doing a zillion examples,
> making certain that there's an example done in class that covers every
> possible variation on a problem type, actually complicates things rather
> than make them more transparent to the student. It's not (IMHO) simply
> the
> point of diminishing returns that kicks in; rather, the student is
> encouraged to see each variation as a new type of problem, and makes it
> vastly more complicated to compress it and make it part of his/her
> conceptual structure.
>
> And we compound this phenomenon by repeating the process every time
> there's
> a new topic. Each topic acquires lots and lots of sub-topics or
> variations, each of which the student is tempted to treat as an entirely
> new problem to be learned.
>
> Lillie
>
> p.s. this is what I'm working on for my dissertation research.
>
>
> At 09:32 PM 10/27/99 -0400, Jane Sieberth wrote:
> >This one fascinates me, too. I'd love to see a research study on this.
> >Jane
> >
> >Nancy Sattler wrote:
> >
> >> Maybe we should collect information and do a study?
> >> Nancy
> >>
> >> -----Original Message-----
> >> From: owner-mathedcc@archives.math.utk.edu
> >> [mailto:owner-mathedcc@archives.math.utk.edu]On Behalf Of Lindsey, Dr.
> >> Charles
> >> Sent: Tuesday, October 26, 1999 9:12 AM
> >> To: mathedcc@archives.math.utk.edu
> >> Subject: RE: [MATHEDCC] Why Johnny can't read.
> >>
> >> Another anecdote: several years ago, I was teaching two sections of
> Calculus
> >> I one semester, and I decided to try an experiment. In one class i
> spent
> the
> >> usual one or two full days going over these problems; in the other I
> did
> one
> >> example and assigned everything else for homework. Result? no
> significant
> >> difference in test performance.
> >>
> >> Now, this was not a carefully controlled experiment, but it does
> suggest an
> >> interesting hypothesis: that the "point of diminishing returns" for
> class
> >> time spent on these type of problems is reached very quickly. Those
> that
> >> will get it, will get it after one or two examples; those that don't,
> will
> >> most likely not become proficient even if you spend a month on it. If
> true,
> >> this has significant implications for the way we conduct our classes.
> >>
> >> I have a second hypothesis that the difference between the groups
> correlates
> >> closely with *general* reading comprehension skills (as opposed to the
> >> specific tactics that we teach for word problems), but have not tested
> this
> >> yet. I think these hypotheses would make a good dissertation topic for
> some
> >> erstwhile grad student in education...
> >>
> >> Chuck Lindsey, Ph.D. clindsey@fgcu.edu
> >> Director of General Education
> >> Associate Professor and Program Leader, Mathematics
> >> Florida Gulf Coast University
> >> 10501 FGCU Blvd South
> >> Fort Myers, FL 33965-6565
> >> Phone: (941) 590-7168 FAX: (941) 590-7200
> >> http://itech.fgcu.edu/faculty/clindsey
> >>
> >> > -----Original Message-----
> >> > From: Bret Taylor [SMTP:bret@IAG.NET]
> >> > Sent: Monday, October 25, 1999 9:42 PM
> >> > To: mathedcc@archives.math.utk.edu
> >> > Subject: [MATHEDCC] Why Johnny can't read.
> >> >
> >> > Anybody remember that book? Popular about 25 years ago.
> >> >
> >> > Well, I'm gonna write a sequel: Why Johnny can't do math.
> >> >
> >> > And the reason will be, Johnny can't read.
> >> >
> >> > I've been reading with interest some of the wonderful posts here that
> were
> >> > spawned with the thread started a few days ago. Vern, Martha, and
> several
> >> > others (sorry, I don't remember all the names) have made very good
> points
> >> > about students seeming lack of ability and desire to do any critical
> >> > thinking. And Martha mentioned that the problem may even get worse
> as
> the
> >> > level of math increases.
> >> >
> >> > Permit me to give another anecdotal stroy to support this. I'm
> teaching a
> >> > Calc I class. We are presently doing optimization problems. If the
> >> > students are given an equation they can (fairly well) find maxes,
> mins
> and
> >> > points of inflection and distinguish between them (algebraically and
> >> > graphically). But understanding what they mean with respect to a
> "real
> >> > world problem" is a completely different story. This class is having
> more
> >> > trouble than any other I have ever taught in finding the proper
> equation
> >> > to
> >> > model the problem.
> >> >
> >> > And today, one problem completely befuddled them. A standard max/min
> >> > problem: How long a pipe can be carroed down a hall that has a right
> >> > angle
> >> > in it. I told them to do it for homework. (We had spent two days on
> >> > applications problems in class.) One student asked me to work it
> today.
> >> > I
> >> > asked for help and no one had a clue. They saw the diagram in the
> book,
> >> > showing the pipe touching both outside walls of the hall and the
> inside
> >> > corner. They knew the length of pipe was a funciton of theta. But,
> the
> >> > problem asked to find the maximum lentgth of pipe. So, they wanted
> to
> >> > find
> >> > the length of pipe as a function of theta and then find the value of
> theta
> >> > that maximized the length. When I showed them that theta equalling
> 90
> >> > degrees or zero degrees the maximum length for the pipe was infinite,
> they
> >> > thought we had solved the problem and that it was a pretty stupid
> problem.
> >> > When I asked them to read the problem again and explain what was
> wrong
> >> > with
> >> > our thinking, they couldn't.
> >> >
> >> > I honestly believe the their problem was more a reading comprehension
> >> > problem than a mathematical comprehension problem. Not a single
> person in
> >> > the class could explain to me what the problem was actaully asking.
> Even
> >> > when I asked them if they had ever tried to move a piece of furniture
> (or
> >> > a
> >> > ladder or a bed frame) out of a room into a hall could they see this
> was
> >> > that type of problem, they had difficulty seeing it.
> >> >
> >> > We worked the problem, and they never really understood that the
> minimum
> >> > vlaue of the length of the pipe was the maximum length of pipe that
> could
> >> > be
> >> > carried down the hall and turn the corner.
> >> >
> >> > I've been using this type of problem for 15 years and don't ever
> remember
> >> > this much of a struggle trying to explain it before. I'm convinced
> the
> >> > problem is primarily a reading comprehension problem and also a lack
> of
> >> > desire to try and understand the problem. The problem said find the
> >> > maximum
> >> > length, so we had to find a relatvie maximum. Simple.
> >> >
> >> >
> >> >
> >> > Bret Taylor "It matters not the subject taught,
> >> > Lake-Sumter Community College nor all the books on all the
> shelves.
> >> > Leesburg, FL What matters more, yes most of all,
> >> > John 3:3^3+3 is what the teachers are themselves."
> >> > John Wooden
> >> >
> >> >
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> >
> >
> >
> >--
> >Jane Sieberth
> >Franklin University
> >201 South Grant Avenue
> >Columbus, OH 43215
> >
> >email: sieberth@franklin.edu
> >phone: (614)341-6269
> >fax: (614)224-4025
> >
> >
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> *************************************************************
>
> Lillie R.F. Crowley
> Professor, Mathematics
> 138 Moloney Building
> Lexington Community College
> Cooper Drive
> Lexington, KY 40506-0235
>
> (606) 257-4872 x 4115 Phone
> (606) 257-4988 Fax
> lillie@pop.uky.edu e-mail
>
> http://www.uky.edu/LCC/MATH/Crowley
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