Re: the quality of knowledge

From: Herman Family (celcaps_at_frontiernets.net/without_any_s/)
Date: 08/11/04 

Date: Wed, 11 Aug 2004 04:11:41 GMT

It appears we have hit upon one of the great problems in teaching. We
teach facts and strategies, but when it comes to synthesis the students are
by definition on their own. The other great problem is that we teach the
details of subjects, but these are only the outer facts of an underlying
concept and philosophy. We test on the facts, but often miss the subject
completely. We don't give the big picture, we just study the brush marks
and hope it all makes sense in the end.

One of my favorite paradoxes is that "to teach" requires another being "to
learn", and that without the "learning" there is no "teaching" no matter how
much lip flapping goes on.

One of the gentle tricks I've learned in teaching is to make a lot of
mistakes. We often get up in front of the class and do our lectures so
perfectly that the students are used to just writing things down. Next
lecture, when you get to an example, start to work it out, make an error,
continue to work with the error for about another 5 or 6 steps. Perhaps
continue even to the end of the problem with the error, and "discover" that
something is wrong. Announce that there is an error, and get help from the
class to find it.

This does a few things. Firstly, it lets the students work the problem out
for themselves. Secondly, and more importantly, it lets them know that even
a great wizard as yourself makes errors, so if mere students goof up it's
ok. It also makes them think, instead of just record.

A second method is to ignore all the simple examples and go for a
big,complicated one. One which makes your hair stand on end. It takes the
same principles to solve (ok, it takes a couple more principles, but not
many more)

2x+3 = 3(x^2+2x) - (((2x + 1) + 3x) * 6x) + (8x + 4)
as it does 2x+3 = 4x+2
except for two details. The first is that the problem is bigger, causing an
immediate stress on the student. This activates the brain to remember the
event better and to learn the material better. The second is that it
applies all the principles together and many times, giving lots of
reinforcement and examples of the rules working together. I don't use small
examples except for the very first ones to show very specific rules. The
third, probably the reason I do it, is to hear the gasps from the students
as they realize that they will have to solve this half board monstrosity.
The great part is that in two or three minutes we solve the problem together
and it gives them a real sense of accomplishment.

Another method is to relate each item to something in everyday life in a
uniform manner (only works on some topics). This allows them to "borrow" a
knowledge structure that they already have, and use it for problem solving
in the new field.

There is also a need for open ended problems. We live in an open reality
world, but expect students to answer closed reality questions. Give them
questions with no "right" answer. Ask for their strategies and general
ideas on how to solve it. Don't bog them with the details on these
questions, let them use just the concepts. Make them think big for a
change.

Michael

"Renata Ruiæ" <renata.ruict@zd.htnet.hr> wrote in message
news:cfb3bf$fvr$1@bagan.srce.hr...
> Thank you on answering me!!
>
> I see that under quality of knowledge you consider understanding, which
you
> divide in memorizing, witch is necessary, and ability to synthesise.
>
> I usually think of understanding as ability to apply facts on new
situation,
> new task, anything not given in classroom.
> But, it seems to me that understanding is only part of quality. I have
> pupils that understand but are so afraid to think critically or to do
proper
> synthesis.
>
>
> "Herman Family" <celcaps@frontiernets.net/without_any_s/> wrote in message
> news:8c%Rc.2472$c12.1483@news02.roc.ny...
> >
> > "Renata Ruiæ" <renata.ruict@zd.htnet.hr> wrote in message
> > news:cf9lci$sb7$1@bagan.srce.hr...
> > > Hi.
> > > I'm Renata Ruiæ, chemistry teacher in high school from Croatia. I'm
> > > researching what is the quality of knowledge and it is not easy to
find
> on
> > > WOS, ERIC or Google.
> > > Anyway, I'm interesting how scientists and teachers, professors decide
> > what
> > > is the quality of knowledge
> > > in common working situation.
> > > So, if you are willing to help me, send me answers on this questions:
> > > 1) What is the quality of knowledge? What are the
> > > indicators of the quality of knowledge?
> > > 2) Do you assess knowledge quality to your students or
> > > assistants?
> > > 3) If you do, how you measure this?
> > >
> > >
> > > Thank you for your time!!
> > >
> > > P.S. Please add your working place shortly ( elementary school, high
> > school,
> > > university, institute, laboratory or ....)
> > >
> > >
> > You have raised some very good questions which are often not raised
> enough.
> > I suppose you could mean a few different things:
> > A. You could mean how well students understand material
> > B. You could refer to some measure of how valid a set of facts and
truths
> > are.
> >
> > I'll answer A. I'm a firm believer in giving tests to students to make
> sure
> > that they understand that they must learn material, to find out where
they
> > are weak, and to reward them for being strong in an area. By using the
> > results of the tests, I tune the class material to make sure that all
the
> > material is more understandable. My typical class at a college
consisted
> > of a few minutes of review, a few question quiz, and then new material.
> > The review session might very well have material which the class was
weak
> on
> > in the quiz the prior day. Some topics can be reviewed for several
> periods.
> >
> >
> > I divide understanding into two categories: rote and synthesis. Rote
> would
> > refer to the students just spitting back what is given to them. It's
the
> > first level of knowledge, and is somewhat reflective of their memory.
> > Synthesis requires them to use that knowledge to go beyond what has been
> > explicitly taught. There are many levels of this. I've used a more
> > advanced testing, or projects to assess the synthesis levels.
> >
> > All this has been at university or community college levels.
> >
> > Michael
> >
> >
>
>

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