Uri Treisman rocks

Uri Treisman, already well-known for his work improving the success of Calculus students, continues to impress me. (And—I had the chance to meet him last summer—he’s a nice guy.) In this talk at the WestEd Board of Directors’ 2010 Forum, Treisman talks about the work Carnegie is doing on developmental math at the college level. He makes many smart points, often backed by research and data. One of my favorite parts of his talk is that he frequently refers to actual student feedback—a radical notion, by definition.

the importance of listening to students

Good teaching is as difficult to define as other arts and the debate over how teachers should be evaluated and what it should mean is raging all over the country. While reading a paper on teacher evaluation put out by Accomplished California Teachers, I realized that, though the study is useful and the recommendations good, it misses a fundamental issue. Too often, in the discussion among professionals about teaching and learning, we neglect the voice of students.

That’s one of the reasons I like the draft study done by James W. Stigler, Karen B. Givvin, and Belinda J. Thompson, “What Community College Developmental Mathematics Students Understand About Mathematics.” In it, they try to eplore what students get wrong and what they don’t and why. They listen carefully and respectfully to students, thoughtfully writing about what they find.

One of the most profound questions that students pose when asked to solve a problem during the interview is, “Am I supposed to do it the math way, or just do what makes sense?” The question reveals a fundamental disconnect between what students experience in their lives and what they experience in the classroom. Not a revelation: the disconnect is completely consistent with my experience listening to community college students in developmental math classes. Any teacher paying attention is aware of it. However, as I read this question and the rest of the study, I began asking a series of different questions:

• Is the math we teach connected to students’ lives?
• Is the math we teach connected to our own lives?
• Are we, as math teachers, so indoctrinated into a mathematical perspective that we force the connections between math and our lives?
• Would it be beneficial to math students for teachers to call out the cultural framing that we are bringing to the subject and that we are trying to help them assume?

Clearly, I’m not going to answer the first three questions here. People make variously good and bad arguments about math’s “utility” that are usually circular, starting from the assumption that math applies to most, if not all, the natural world. Rather, I think we must continue to ask them of ourselves and of our curriculum. The question of perspective and acculturation is complex and probably unanswerable. Philosophers of science, much smarter and more capable than I (e.g., Karl Popper, Imre Lakatos, Thomas Kuhn, and Paul Feyerabend) have been arguing about it for years without full resolution.

But the last question is easier for me. Cultures around the world do math, so math seems to be a fundamentally human activity. However, that math is not usually what we’re teaching. As such, I firmly believe it is helpful for students to see that the math we teach in our classrooms is a cultural construct and not necessarily “natural”; in fact, the math in our modern textbooks is a carefully contrived version of math. It is made to appear smooth, a straight line of development from numeration, to fractions, to factoring, to graphing, to functions, to differentiation, to integration, and beyond. If students don’t see how smooth and “obvious” it all is, then it is their fault. And when the story isn’t quite so smooth, we just pretend it is — “don’t you see?”

Acknowledging the culture of math and its interplay with the other parts of our culture is an important step to demystifying math and to being intellectually honest, toward having students realize that they can bring all their intuitions, experience, and knowledge to bear on problems, both in and out of math class. At the same time, it helps remind us, as teachers, to listen to students, because their experience of math is part of what math is in our classrooms. More, their experience of math will survive us, long after we’re retired, helping to create the culture of math in the world to come.

As teachers, we have spent years mastering our content and working to be better teachers. Yet, students still sometime disparage our work and/or our chosen field of study. Working with as many students as we do, it is often hard to see what we can learn from the next batch. Truly listening to our students takes effort and focus. I frequently fail to do it well, but every time I do, I am rewarded with a better connection and a better class. Listening to our students is part of the art of teaching. We fail to listen at our own, our profession’s, and our culture’s peril.

from fish to infinity

In a New York Times opinion piece, Steven Strogatz does a great job of articulating both the power and abstraction of numbers. It’s something I try to talk about in my classes — probably with less success than Strogatz. I often use the example of shepherds keeping track of how many sheep they have by creating piles of stones. The usefulness of carrying around a number, say “24,” rather than 24 stones, to express how many sheep one has is pretty self-evident. At the same time 24 applies equally well to sheep, bombs, dollars, stones, people, and more, which presents a potentially dangerous abstraction; that is, we don’t really want to treat 24 dollars the same as 24 people.

Strogatz writes about this issue and more in the article. His goal is to discuss “the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.”

If future installments are as well done as the first, the project will be useful for the math-interested and not.

(Thanks to Alisa for the heads up.)

the eyeballing game

For the geometry/technology geek in us, there’s the eyeballing game. So far I haven’t made it to the good side of the distribution on it. (You’ll know what I’m talking about if you play.)

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.