> 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! :)
Linda Coutts e-mail address: firstname.lastname@example.org Coordinator Elementary Mathematics Columbia Public Schools Voice: (314) 886-2233 1206 E. Walnut St FAX: (314) 886-2078 Columbia, MO 65201