Week 11: Undergraduate Research

Since I decided to switch my major to elementary education, I didn't think undergraduate research would be very applicable anymore. When I heard about one of this summer's opportunities, however, I was intrigued. I would be very interested in helping to created the math lab curriculum for the local high schools. I like that it's very practical for the field I plan to enter. Although I'll be in an elementary or middle school rather than a high school, this plan appealed to me more than the more abstract and experimental ones. I've spent a lot of time with elementary school students in and outside the classroom, but never on the planning side of things. I think if I could participate in that research opportunity I would learn a lot about teaching math that I could apply in the future. I was very interested in biology in high school but since I no longer plan to double major in it, I will probably only pursue math and education research projects.

Week Eight

I have a friend who is a fan of a blog which recently featured a letter to the editor about how daylight savings time is causing global warming. The writer seemed to believe that we had negotiated for the sun to hang around our corner of the earth for an extra hour a day for eight months a year, and those extra hours we adding up. Such anecdotes give us the notion that the general public is ignorant to put it bluntly and I think college students have a tendency to develop a superiority complex over much of the adult population. When we were talking in class, however, we seem to have determined that American adults really don't need that much math by our standards, but perhaps they are lacking in certain areas. I think they need general computing skills, for balancing a checkbook, cooking, and conversions, basic algebra for problem solving, basic trigonometry for assembly and construction, and a big one is skills for interpereting statistics. As evidenced above, anecdotes are powerful, but statistics can be just as potent. When people don't understand confidence intervals, survey biases , and margins of errror, the news that 50% of 9rd graders at the local high school have below-average grades in math could send a frenzy of panicked PTA members flying at the principal. Numbers can be scary as we are bombarded with information about political polls, the DOW, and the rising prevalence of diabetes, and without some basic mathematical understanding, it's all one can do not to go crazy. Math, ironically enough from our perspective in the craziness of exams, does a lot to maintain sanity in the real world.

Math and History, Pt. II

There seemed to be a lot of books on the benefits of teaching math in history, but little evidence. I stumbled upon one study but the report contained only qualitative results. Here are some of the mathematicians I found in the various fields the article suggested, some more obscure than others: Pythagoras was a Greek religious leader, Kepler an astronomer, Aristotle a philosopher, Thales a scientist, mathematician, philosopher, and businessman, Archimedes an inventor, mathematician, physicist, engineer, and astronomer, and Charles Marie de la Condamine an explorer,mathematician, and scientist (I'd never heard of him but he was sent by the French to measure the world circumference at the equator). Most of the resources I found were for higher-level mathematics, but I found a few activities that may be practical. At
I found a worksheet on "Big Numbers" that described the origins of the name googol and an activity like one Archimedes did to guess how many grains of sand there were to determine how many candies it would take to fill a classroom. I think this would work starting about grade three. The other specific activity I found was about fractals and chaos. Though I never heard of these until last year, the activity itself is simple, a dice game to create the Sierpinski triangle, and I think it could be a fun way to get fifth graders interested in math, perhaps. It was at
http://math.bu.edu/DYSYS/chaos-game/node1.html#SECTION00010000000000000000. So basically I couldn't find any proof that integrating history is beneficial, but for better or worse I found some resources for doing so. Whereas the second activity is rather extraneous, the first activity would likely be curriculum-relevant, and an educational prelude to snack time :)

Math & History

I think that Ms. Wilson and Ms. Chavot made some interesting points in their article on the whos, hows, and whats of mathematics and including history in math lessons. It neat that they said most mathematicians we learn about didn't consider themselves such, but were astronomers or philosphers or inventors. Also interesting was the point that only a few names come up in most classes, not evenly representing all the cultures and people which developed a lot of the important tools and theorems which we regularly implement. It seems that prejudices turn up in all areas of life, even implicitly in math education. I think teaching a little about the history of mathematics as students learn the methods is a useful idea because I learn better when I understand the reasoning behind a procedure than when I merely follow instructions, and the history facts give additional frames of reference when learning to aid memorization and provoke thought. Though I don't think Wilson and Chavot offered much practical advice, the message is a good starting point for integrating this teaching method. I actually wrote the above yesterday and today my math teacher spent the majority of the period on a history lesson! Interesting timing. I liked it a lot because it was a nice change of pace but still related to our current topic, primes, and it was informative.

So I went to the elementary education major transfer information meeting on Wednesday. The guy gaves us some papers and wasn't very optimistic but I've looked at my schedule and I can still graduate on time with winter sessions. I'm going to stick with math as my concentration (we have to pick math, social studies, science, or English) since I have a lot of courses that they require for that already. I'm going to do this winter at home online and I'm going to meet with an advisor to plan for the spring. We have to take the PRAXIS, a math pretest and a math course before we're accepted, and hopefully I'll get in next summer. I find it strange that it's so complicated to get in, but that's what I want to do so I'll just take the courses I can until next year.

Week 4

A lot of VonNeumann's article was over my head, but I still picked up a few things that I thought were interesting. I learned about set theory in algebra and again this year in Discrete but I never knew there had been controversy about it. The term "intuitionism" confused me, in that the name makes it sound like a less rigorous kind of proof, but the article led me to conclude it was the more rigorous. It's definitely a challenge to learn to write proofs that break down the evidence enough to be unquestionable. It's interesting the way mathematicians settled with a certain rigor of proof, concluding it left their ideas as trustworthy as anything in an empirical science. VonNeumann got a little philosophical on me there with the comment that absolute truth outside of human existence could never be determined, which isn't exactly the kind of thing one usually mentions while proving bijections have inverses. He had an interesting take on the empirical basis of mathematics with Newton and founders, commenting that the empiricism is a thing some mathematicians find hard to accept, but which must be returned to when the practice becomes abstract and baroque (not gonna lie I had to look it up in this context- settled on convulted). Another interesting comment though was how mathematical study is relatively broad compared to other disciplines such as theoretical physics where most energy is focused on a single subject. It was neat to think of the relative freedom that mathematicians have in their research.

Week 3

It was neat to see the lab since I didn't know there was one until this class. It makes sense for the math department to have a lab so students can do labs like the one with the gold chain and to observe and determine functions in bubbles and bearings to reach practical conclusions. I'm actually in the process of changing my major to Elementary Education (with my concentration in math) so I don't think I'll end up using the lab at all actually. I was unable to attend Charles Biehl's talk but I heard that it was very interesting.