Re: motivating * knowing the subject

[John Clement <clement@HAL-PC.ORG>]

> I wrote:
> > > Teaching is maybe 10% knowing the subject matter and 90%
> > > motivating the students.  They could have gotten the subject
> > > matter from books.
>
> ... which was more-or-less OK in context, but won't withstand
> detailed scrutiny.
>
> John Clement wrote:
> ...
> > Incidentally there have been several studies that showed that
> students learn
> > much more when the teacher has better mastery of the subject.
> So content
> > mastery is actually a very large factor.
>
> Good point.  The percentages I gave are not right in general.
>
> Interestingly, changing the percentages doesn't fix the problem.
>
> The key word here is "factor" (in contrast to "term").  That is,
> motivating_the_students (M) and subject_area_knowledge (K) are
> !!multiplicative!! not additive.  Both are required;  neither will
> make up for a lack of the other.  We have
>   success ~ M*K
> (not M+K) so the idea of percentage is not directly applicable.
>
> ================
>
> If we now make the (questionable) assumption that things are
> differentiable, we obtain
>   d(success) ~ M dK + K dM
> which is additive, so percentages might apply in particular cases.
>
> I suspect the 90%/10% numbers made sense to me only because of
> my narrow experience -- I've taught only in situations where I
> was very much in command of the subject, so the "K dM" term was
> dominant for me.  In contrast, if you made me a major-league
> baseball pitching coach, or asked me to teach sculpture, I'm sure
> I would get a brutally keen reminder of the importance of knowing
> the subject.

Actually nothing in education follows a simple equation, and I would propose
that motivation probably, as with teacher subject competence has a
threshold, and above that the effect of motivation is probably not that
great.

1. For example a student who has no motivation will learn nothing and
probably fail.
2. On the other hand my data clearly shows that highly motivated students
often do not achieve good gain unless they also have the requisite thinking
skills.
3. Some moderately motivated students do achieve good gain, and would have
gotten excellent grades if they had handed in all the work.
4. Some students can still learn with zero teacher subject competence by
doing work on their own, but most will not.
5. Pedagogy has a large influence, and probably the largest influence on
gain in understanding, once other thresholds are satisfied.  Students do
learn some even in conventional courses, or by themselves so there is
probably not much of a threshold there.
6. The level of student thinking is a big factor.

Let us look at the factors.
Normalized Hake gain in a conventional course goes from 0 to 20,25%.  This
is probably highly dependent on teacher content knowledge and student
motivation.  However in reformed courses gain goes from 25%-70% with one
data point I know of at 80%.  My research shows that the maximum gain is
roughly equal to the raw score on the Lawson test x 10.  When students score
10/12 they can get 100% gain.  But when they score 4/12 the maximum is about
40%.

According to Priscilla Laws HS teachers test with similar scores on the
FCI/FMCE.  College teachers make the same number of mistakes, but they are
just distributed differently.  Teacher subject competence in HS/college
physics would not seem to be much of an issue.  I suspect that she has
mainly tested the more competent teachers, so there is probably a number of
less subject competent teachers out there say 10%.

Motivation really also has 2 parts.  The first part is willingness to do at
least some of the work, and the other part has to do with attitudes about
how to do the work.  This first type of motivation is a prerequisite.  The
second type has a huge influence on gain.  The MPEX (Redish) and the VASS
(Hallouin, Hestenes) can be used to evaluate the latter with a bit of the
former.  The MPEX generally goes down in most physics courses, except for
workshop style courses.  The VASS can be used a good predictor of final
grades.

This leaves us with a very messy formula.  However the 3 things that seem to
be the largest contributors toward good normalized gain is pedagogy,
attitude about how to tackle the course, and the thinking skill.  Instructor
subject competence and other attitudes (likes, dislikes) are probably
threshold effects with a small influence once the threshold is reached.  One
factor that has not been mentioned actually falls under pedagogy.  The
correct pedagogy is probably dependent on instructor competence in using it.
Real Time Physics labs, for example, have been made somewhat instructor
independent so they should have a beneficial effect in all cases, but the
biggest benefit will come when the instructor provides the correct support.

I would like to also address the homework issue.  While student reluctance
to do homework has always been with us and the impassioned call for more
homework resonates in all of us, the facts are a bit different.  Standard
homework produces little gain in conceptual understanding, and excessive use
of back of the chapter problems can produce lower understanding.  Studies
have shown that challenging homework is often done incorrectly so mistakes
are reinforced.  Many members of this list can remember how they did those
challenging problems and learned from them.  But remember for each of us
there were 20 students who did not do the problems well, find them fun, or
learn from them.  Yes, some homework does improve gain, but the actual
improvement is small compared to correctly using reformed pedagogy on formal
operational thinkers.  Having helped my daughter with a lot of her math
homework, these facts come into focus.  Many students, especially those on
this list, benefited from a few problems to practice algebra skills, but a
large number of problems were not necessary.  However my daughter waded
through hours of math every night doing every single problem in the book.
She resisted my attempts to get her to reason about why things worked
because that meant she might be up till 2 AM doing all the problems.  She
was being force to routinely do the work without having been given the
opportunity to think about it.  The pedagogy of just lecturing and pushing
was clearly the wrong strategy.

Anyone who would like to pursue how motivation, and pedagogy can work
together should read some of Beichner's papers about his scaleup project.
Remember we are the people who did the 40 difficult problems in one sitting
because we wanted to, and were capable of it.  Average students, especially
Tina's are totally different.

John M. Clement
Houston, TX