Because I love Pepsi, and who doesn’t love old school Michael?

I’m a math major so I am not really seeing this topic coming up as
part of a lesson plan or part of normal in-class discussion per se. Yes, there are all sorts of mathematical
things you could do with this magic “44oz” number: how many smaller cans would
have to be consumed to equal that amount; how much pop the average American
consumes in a day; what is the recommended daily soda intake maximum (a quick
internet search will reveal its “zero”).

None of this is really the point of the discussion though. I wouldn’t feel like I was being honest with
my material to go this route. I would be
making an attempt to be “relevant” without actually addressing the core of the
topic. Our Willingham reading in EDUC
606 directly cautioned against this sort of lesson planning (as I interpreted
it anyway).

That doesn’t mean this topic has no relevance to math.

For discussion sake, let’s pretend my class is in NYC (would be
awesome!). Let’s pretend my students
roll into class one day roaring about Czar Bloomberg and his pending edict on
soda consumption.

Although I am a math teacher, I love the humanities and philosophy in
particular (although admittedly, due to my educational background, my experience
is limited). I decide to tackle this
issue in my math classroom. All year we
have been learning about methodical ways to solve mathematical problems. Let’s take ‘em to the streets. No more numbers. Let’s use the same tools and ideas to solve
real world problems (or at least form intelligent opinions).

First, like any good math student, we need to clearly write out what
the problem is. I would probably have my
students work in small groups to come up with an initial question/problem
statement. Then, as a larger group, we
would agree on a statement. If we
couldn’t find agreement, then I would possibly do the next steps as separate
groups.

In encouraging Intellectual Character in my students, I remind them
that while their ideas are important, they are only the starting point. Just like in math, we need solid data and
proven tools to solve problems. We need
to analyze the problem in front of us objectively to know what to do with it. In Step Two I would direct the students to the
internet to research data and op-ed pieces from various media outlets like the
New York Times, The New Yorker, health websites, etc. I might have them work individually or in
groups to go after different types of data.

The biggest mental exercise I would encourage in this step? I would tell them I don’t want their opinion
anymore. I want other people’s ideas and
data from respected sources. Math is not
a subjective discipline. Data research
should not be either if you are truly trying to find a right or best answer.

Note: Perfect anti-example (made that word up):
People posting political memes on Facebook when they know nothing about the
real issues and have not done objective research. While I would teach my students that everyone
has the right to express their opinion, it is only the informed opinions that
elicit worthwhile change…and rarely can informed opinions be condensed into Internet
memes.

Step 3. So we have some
objective data now. Does our problem
statement change or stay the same? I would
encourage discussion on this…do we need to reformulate? Can we clarify our problem statement? The better we can define our terms, the more
likely we are to agree on the terms, and the more likely we can either reach a
resolution, or reach an agreement to disagree.
It is the lack of definition, or agreement on definition, of terms that
lies at the root of most problems.

Step 4. Time to think
big. Any equation in a math class is the
result of a need that occurred at some point in history. We have the Pythagorean Theorem because
Pythagoras (more likely others before him) had a need to more quickly calculate
the hypotenuse of a triangle. We have
Integration in Calculus because there was a need to figure out how acceleration
was related to velocity. So why do we
have laws in this country? Who gets to
make the laws and why? I would drive my
students up to the macro level to understand the purpose of governments. If I was feeling really ambitious, I might
even break out some Plato, Thomas Hobbes, John Locke, and others for varying
perspectives on government. If we can
answer these questions about laws and the purpose of government, they might
give us clues to solve this problem.

And that’s really all math is anyway: looking for clues and utilizing
proven tools to solve problems.

Caveat: I fully acknowledge that social problems are not math
problems. There is no social equivalent
of y=mx+b. Often social issues are
extremely complex and no complete answer exists. That doesn’t mean that mathematical concepts can’t
be applied. Mathematical concepts are
just another tool, another way to think about something. At the very least, we might get a clearer
understanding.

There are a lot more steps I could take if I wanted. At this point in the lesson (likely due to
time constraints) I would try to bring my students back to the original problem
statement. We have objective data on the
issue. We have some history about laws
and governments in general: why we have them, who gets to make them, etc. Now what can we say about this issue? This is where the debate would come. And it would be fun and I would thoroughly
enjoy it…hopefully my students would too!

Lastly, I would remind my students that we are privileged to be able
to have such a debate. It is uncommon in
history. We live in a country where we
have collectively decided that no one person or group is above the law or below
the law. We live in a country that, while
certainly not flawless, strives to respect the law on both the lawmaker and
law-abider sides.

As passionate as we get about our politics, we can’t ever forget
that. Our respect for the law and those
we have put in authority should trump petty disagreements.

I am especially intrigued by the intersection of mathematical and societal laws. It seems like students having to sort this out and differentiate between the two categories might be a higher cognitive challenge. Indulge me a minute here. At first glance I would say that mathematical versus societal laws is a matter of descriptive versus prescriptive: the former describe what does happen, while the latter establish what must or should happen. So never the twain shall meet: they are mutually exclusive.

ReplyDeleteOn second thought, though, societal laws are not completely arbitrary either. Concerning the issue of on-line etiquette, some of us have argued in these blogs that there is a very distinct etiquette on Facebook, for example, and one which sprang up fully armed and all at once. The FB etiquette is descriptive, like math rules, insofar as it imitates how people act. They are prescriptive to the extent that one reaps the consequences, good or bad, of negotiating the etiquette system to the degree of success or failure that one does. In a sense, then, societal laws describe how things are done, like math.

The mathematics of the Soda Ban and the underlying problem of sucrose toxicity seem like a big math formula, a formula that is out of whack. The human being factored by quantity sugar equals an irrational number. (I know: “Stick to Latin.”) Anyway, maybe the formula is something more like this: H x S = H (human times sugar should = human). But it doesn’t equal human: it equals a human plagued by a spectrum of ailments. And the physiological imbalance is describable mathematically (involving the ratio of sugar molecules vs. fat cells, etc.).

I really like the sound of needing “solid data and proven tools to solve problems”. You “want other people’s ideas and data from respected sources”. Math, you point out, “is not a subjective discipline”. And data research should not be either. In a certain sense, every academic discipline is science. In Germany, I have noticed, one operates in terms of Literaturwissenschaft or ‘literary science’, which to most English scholars is an oxymoron, a contradiction unto itself. But any critic, especially from Erasmus onward, is expected to ground their findings in fact, even if it’s text interpretation. Maybe “subjective discipline” is an oxymoron.

But disciplines like philosophy and poetry analysis do seem subjective by the look of them. What I think is really going on there, though, is a scientific or objective look at subjectivity. My feelings about these issues resonate very much with yours. What is the value, at the end of the day, of a “reflective piece”? My answer is that the extent to which it is pure opinion is the extent to which it is a waste of time. Opinion, as I understand the Greeks on this, is unfounded belief. What I think I share with you is a concern that students acquire and retain factual knowledge—not just the ability to process cognitively. The pendulum may have swung back a bit too far in the direction of reflection, creativity, and critique. Without real knowledge of facts—be they historical, poetological, or mathematical—reflection is worthless.

My favorite sentence in your comments "What I think is really going on there, though, is a scientific or objective look at subjectivity."

ReplyDeleteI think this sums up what I would like to see in my students. It is impossible to remove subjectivity from issues like this, nor do I think we should. Our society will allow you to exist with only your opinions. I would want to teach my students to start with the objective, and work to the subjective.

I had a great professor once tell me very simply, "Start with what you know and work to what you don't." What we "know" by definition should be objective. What we "don't know" by nature, will be subjective.

I really like your approach to the lesson plan. I was trying to think about how other disciplines would implement this lesson plan (My content area is English). I also really liked how you related it back to Intellectual Character. You blended math and the humanities in a way that would make me (who struggled with math) excited to learn.

ReplyDelete"And that’s really all math is anyway: looking for clues and utilizing proven tools to solve problems."

This is a great way to think about math. Again, for a person who struggled with math in school, I would have really appreciated having a teacher like you that would be able to relate the math content to my humanities inclined brain.