Math Forum Discussions

Linda Coutts

Posts: 11
Registered: 12/6/04

Re: where's the math? (was Re: 5th Grade Activity)
Posted: Apr 20, 1995 11:41 AM

Plain Text

On Wed, 19 Apr 1995, Cathy Brady wrote:

> Playing devils advocate for a moment....
>
> Other than for topology students in grad school, where is the mathematics
> in exploring mobius strips and hexaflexagons?

->Cathy, that's a good question and I will give you my opinion of
where the mathematics is within the exploration of Moebius strips and
hexaflexagons ( which really are a Moebius strip in another "form"). If
you are looking for number crunching, which I really don't think that you
are, then the exploration may not serve your purpose. Even though I was
not necessarily looking for number relationships during the exploration,
the students used number in order to describe what they found and what
they predicted might happen before they cut the Moebius strips and loops.
A few weeks earlier I had been invited to the fourth grade classrooms at
this building to work with equivalent fractions. When I arrived at the
door for the math club, several of the fourth grade students recognized me
and said are we going to do fractions again? I said "NO, I have something
different planned for you today." Well, to my surprise as they began
describing their "creations" fractions were what they used to describe the
relationships between the original Moebius strip or loop and the resulting
band. So even though, I wasn't necessarily looking for those
relationships, the students saw them and they were there. (And I knew
they were there. I learned a long time ago that if I go into an activity
looking for specific answers, I can get them, but that doesn't mean that I
am observing student learning. You might want to read some of Cathy
Fosnot's work about helping student clarify their thinking for further
info along this line.) So mathematically, I found out that these students
were able to use mathematics to describe their world. That to me is
certainly one indication of mathematical power. If that was all I found
out during this experience, I would have been satisfied. However, there
was much more going on with the exploration.

My purpose for having the students explore the Moebius strip was to
provide them with an opportunity to look at something from another
perspective. (By the way, this would not be the students only
opportunity). Mathematics for us, beside including command of number and
number operations, includes opportunities to:
* communicate and share thoughts and reasoning involving
mathematical process(es)
* relate mathematics to real-life situations
* exercise flexibility in exploring mathematical ideas and be
willing to seek and try alternative methods for solving problems
* persevere in a mathematical task

>
> Mobius strips and hexaflexagons are great "gee wiz" activities, but I
> wonder if they are on the same order as baking soda/vinegar volcanoes
> (don't teach much except possible misconceptions).
> I'd like to put together some activities for facilitators to do with
> visitors on the museum floor, but I want to be able to answer the
> facilitators when they ask "why is this Math?"

Cathy, I understand your concern for "gee wiz" activities, and if
that is all they are for, then, I have a similar concern.

As far as putting together some activities for facilitators to do
with visitor on the museum floor, I suggest that the facilitators ask
themselves where is the math? Earlier on this listserv, I believe, there
was a good discussion about what the "definition" of mathematics is. To
me mathematics is a study of patterns and realtionships for both beauty
and the study of our world. I know that even with my gobal definition of
mathematics, the view is still narrow according to other peoples view.

Soemthing that has helped me to evaluate mathematical activities
are the criteria Marilyn Burns offers in her writings. (I don't have a
copy of the criteria in front of me, so some of the following may be
paraphrased. Sorry to those of you who know the criteria by heart.)

*1. The activity *must* cause the student to think. (there
was a great deal of thinking going on during this activity.
The thinking was not only a result of my questioning, but more
importantly the students questioning.)

*2. The activity has mathematical significance. That's where
you are questioning me. Within my definition of mathematics and
the disposition I would like to foster in our students, the
exploration of Moebius strips is a worthwhile mathematical task.

*3. The activity is achievable to the least knowledgeble and a
challenge for the most knowledgeble. This is the most difficult criteria,
in my opinion. My exploration of the Moebius strip, allowed for
all to enter the activity and leave the activity with more
knowledge than they had before.

>
> If you dare to answer my question, add the word "so?" to your explanation
> and continue until the "so?" question no longer seems appropriate.

I hope that I have answered your questions. By the way, I'm the one
you gave the ribbon to in Boston, thanks! :)

later.....

Linda Coutts e-mail address: lcoutts@mail.coin.missouri.edu
Coordinator Elementary Mathematics
Columbia Public Schools Voice: (314) 886-2233
1206 E. Walnut St FAX: (314) 886-2078
Columbia, MO 65201