word problems

Another in a long line of cleverness from Savage Chickens: http://www.savagechickens.com/2009/03/teacher.html

If a word problem isn’t relevant to the teacher or the student, why are we bothering? Just because it was done to us?

i divided by zero — again and again

i divided by zero is by far my most popular post. In fact, the theme turns out to be so ubiquitous—including a band named Divided By Zero—that I can’t hope to keep up with all of it. Nevertheless, as both tribute and follow up, here’s some other images and links related to the idea:

Ben Bromberg has a nice variation of the pic I originally pulished.

Then there’s a couple of totally different pics for which I’m not certain of the source:

From there, we go toward related, but more text-based ideas:

(From DamnThoseWiffyDogs)

(From ImpactCards.com)

Finaly, there’s this ludicrous image (and comment) from lolninja.com.

links round up — 2

67% of Children Left Behind
“A new study by researchers at Rice University and the University of Texas-Austin finds that Texas’ public school accountability system, the model for the national No Child Left Behind Act (NCLB), directly contributes to lower graduation rates. Each year Texas public high schools lose at least 135,000 youth prior to graduation — a disproportionate number of whom are African-American, Latino and English-as-a-second-language (ESL) students.”
It gets worse. The link above is to a blog by Chad Orzel. Follow the link there to the report on the study.

Concept Maps
A reminder from a practicing teacher that concept maps and other “non-traditional” techniques can help students learn. The exchange in the comments is as interesting as the post itself.

Euphemism and American Violence
An insightful article on words and politics and torture and the abdication of our democratic responsibility: “‘History begins today’ was a saying in the Bush White House on September 12, 2001—repeated with menace by Deputy Secretary of State Richard Armitage to the director of Pakistani intelligence Mahmoud Ahmad—a statement that on its face exhibits a totalitarian presumption. Yet nothing so much as language supplies our memory of things that came before today; and, to an astounding degree, the Bush and Cheney administration has succeeded in persuading the most powerful and (at one time) the best-informed country in the world that history began on September 12, 2001. The effect has been to tranquilize our self-doubts and externalize all the evils we dare to think of. In this sense, the changes of usage and the corruptions of sense that have followed the global war on terrorism are inseparable from the destructive acts of that war.”

Better than Free
Smart, provocative commentary about the internet and current society and what makes things valuable from some one who clearly spends way too much time online. Doesn’t change the power or the debatable nature of his observations.

Chris Jordan Photography
I once spent a lot of time making photographs of trash and other detritus of our culture. Jordan’s work has a more arranged quality to it (mine was more about what was found), but I like it.

SAT scores and book lists
Another take on book lists.

Why Math Matters
I get this question a lot—from students, from friends, from strangers. Dustin M. Wax provides a possible answer and I thought some of you might be interested. I think there are other answers, too, and they are almost always contextual. That is, I answer the question differently depending on to whom I’m speaking and in what situation. At what I think have been appropriate times, I have said that math doesn’t matter. Not very often.

Credit goes to Scottie and Mike M. for pointing me toward these links.

late on pi day

Naturally, Savage Chickens has a lovely pi day cartoon. Who can resist these charming fowl?

(As usual, thanks to Alisa for the heads up.)

how it works

More excellent commentary on math and gender bias from xkcd.

As usual, thanks to my friend and former roomie, Alisa, for the heads up.

class of 64 followup

[Click here if you want to see the original "class of 64" post.]

The results are in for my Intermediate Algebra class:
64 students
38 passes (59%)
26 not passes (41%), including 6 drops (9%)

If we take the drops out of the base we get the following:

58 students on the roll at the end of the class
38 passes (66%)
20 not passes (34%)

10 As (17%)
13 Bs (22%)
15 Cs (26%)
8 Ds (14%)
12 Fs (21%)

(Note: the D/F percentage does not add up to the not passes percentage because the numbers have been rounded.)

First, some positives: 9% drop/withdrawal rate is pretty good, especially for a math class that is not for majors. Similarly, a 59% pass rate for those who started the class is better than the historical average for intermediate algebra sections at my college. Further, a 66% pass rate for students in the class is around the community college national average; since intermediate algebra is a pre-collegiate course, which generally have a much lower average pass rate than other courses, this pass rate is very respectable when compared to other classes like it.

On the other hand, we’re talking more than 2 of every 5 students who started my class didn’t pass. Even of those that stayed on the roll, 1 in 3 didn’t pass. That is not acceptable to me. My assumption is that every student who tries and who doesn’t have some life crisis during the semester should pass.

A surprise was waiting for me in the demographics: the pass rate for women (21/32) is almost identical to that of the men (17/26). That’s surprising because in the past, women have done better in my classes than men. The racial breakdown is, unfortunately, more predictable. 78% of white students passed, with white women passing (7/8) significantly more than white men (4/8). The gender disparity in white students was made up for by the Latinas, six of whom passed out of nine, as compared to Latinos (4/8)—59% overall pass rate for Latina/os. Only one-third of my African American students passed (1/1 men and 1/5 women), while 70% of Asians passed, split evenly between men and women.

The $64/64-student-question: Could I have made a difference with some of the students who didn’t pass if I had fewer students in the class? My heart says yes. The numbers tell a different story—aside from the new gender parity, the results are very similar to most of my classes. This leads me to three possible explanations:

• Because of conscious and/or unconscious factors, I make grade distributions turn out about the same regardless of the number of students.
• There are other systematic and/or structural issues that lead to similar outcomes no matter the number of students in the class.
• I can teach 64 students as effectively as 34 students.

I don’t know which of these, or what combination of them, explains this semester’s results. And whatever the case, the issue becomes one of workload. In effect, I taught two sections of intermediate algebra during the last semester. The fact that they happened to be in the same room at the same time did little to mitigate the number students’ names and stories I needed to know or the amount of papers, quizzes, and tests I graded every night. The wear and tear on me, the number of late nights or very early mornings, the anxiety from always having the grading hanging over my head—all this is not sustainable.

I’m back to the conclusion that I can’t let it happen again—not if I want to survive semester after semester and year after year and continue to enjoy the same or better success. And fewer students would give me more time to work on other parts of my teaching, improvements that might help some of those students that are currently not passing.

So, how will I prevent classes from getting so large while still giving students the power to choose to be in my class? I don’t have an answer about which I’m entirely happy. Next semester, I’m going to experiment with a modified version of my system, whereby coming to class and doing the homework moves students up the waiting list; I will cut off the roll somewhere around 40 or 45. Still too many.

We are working in a system of scarcity—in this case educational—in which those that can afford to pay can get more attention, more support, and more access to higher paying jobs; those that can’t afford to pay, rarely get the same attention, support, or anything else. We continue to recreate this system. My little attempt to move away from a scarcity model worked in that the students who stayed in the class succeeded at the similar levels to those in other classes. But the personal cost is too high. Individuals can’t do it alone. It will take institutions, governments, and societies to move away from a scarcity model to one of access and plenty. I am hopeful, but not optimistic, about the possibilities for this kind of change to ever happen. Hoping and working for change, sometimes paying a personal price that is too high and sometimes not, is all I know to do.

moebius transformations

This video is a brilliant and (aside from the cheesy color scheme) beautiful depiction of moebius transformations and their connection to the Riemann sphere. For those of you that don’t know what I’m talking about, just watch it and enjoy.

Thanks to Fred T. for the heads up.

carnival of math #18

JD2718 is dedicated and thoughtful and seemingly tireless. He’s put up the current version of the Carnival. There are some good articles. Check it out.

quadratic grafitti

In the tradition of i divided by zero, I bring you this picture courtesy of Charles Hope, via Ms. Choat. My friend and colleague, Mary, immediately thought of someone potentially risking their life to stand in the road and write the quadratic equation. There are worse things than math for which to risk your life.

math as a civil right

Check out Julie J. Rehmeyer’s post on Robert Moses, mathematical literacy, and civil rights. Rehmeyer focuses on being informative, not editorial—unlike your’s truly.