2.1. Teaching Context

"I have not failed. I've just found 10,000 ways that don't work."--Thomas Edison

Integrated Math 3 is the first year of "voluntary" math for most students at my high school placement in San Jose. The school is considered low-performing, and enough students fail the required first two years of math, Integrated Math 1 and Integrated Math 2, which are a mixture of Algebra I and Geometry, to necessitate separate "repeaters" classes (as teachers in the math department call them).

The shift in demographic from Integrated 1 and 2, which reflect the predominantly Hispanic population, to Integrated 3, which includes a larger percentage of Caucasian and Asian students, is visible and worrisome in that it suggests the majority of the demographic is either unable to continue in mathematics due to grades, or otherwise deciding not to do so.

As the latest of several attempted remedies, the school switched to an A-B block schedule with the majority of classes running 100 minutes every other weekday. School begins at 7 AM and ends at 2 PM; 2-3 PM is reserved for "tutoring," but in practice not all teachers stay through that hour, and many students go home at 2 PM even when tutoring is available.

In my particular Integrated Math 3 class, my students are generally "high-achieving" juniors relative to the school population, though there are outliers. For example, the two most consistently sophisticated mathematical thoughts come from a freshman who is also accelerated in science, and a junior whose grades have been terrible for the past two years due to personal problems. Another student has been disengaged since the beginning of the year, and is failing all his classes but Guitar. As for the "average" student, she or he will pay attention most of the time but get "stuck" fairly quickly; problem-solving skills are weak, though the classroom environment my cooperating teacher and I have incubated assures that they rarely hesitate to ask for help, possibly to the detriment of those problem-solving skills.

In their list of key "strands" of mathematical proficiency, Kilpatrick et al. include strategic competence, the "ability to formulate, represent, and solve mathematical problems" and productive disposition, a "habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one's own efficacy" (2001)--in other words, flexible problem-solving strategies and the willingness to attempt them. It is these two strands that I worry about when I look at my class.

While the first two years of math are dominated by worksheets and district-mandated multiple-choice tests, Integrated 3--Algebra II with a dash of geometry--affords the teacher more freedom, with whole chapters of the textbook designated "optional." At all levels there is little coordination or collaboration between teachers. While my cooperating teacher gives me a fairly loose rein, there is still pressure to "cover" the textbook, which along with the NCTM and California standards, is our major guide to curriculum.

The class starts (optionally) with a brainteaser or "math fact of the day" (did you know that the National Security Agency hires more mathematicians than anyone else in the U.S.?), then a review of the previous day's material and outstanding questions from the homework, before moving into new material. I have often introduced new topics with a whole-class discussion highlighting some connection to previous topics or real-life applications, or an exploration that allows students to interact directly with the ideas.

However, this interaction by itself is not enough to guarantee long-term understanding or even rote retention. During the unit on data analysis, I discarded the second half of the textbook chapter, which involved calculator key-punching to find the line of best fit, in favor of having students work on their own surveys and analyze newspaper clippings in groups. While a number of students are sometimes uncomfortable with the departure from rote computation, they seemed to be more engaged than usual in the group tasks. I hope that, with this unit, they will be able to grapple with some mathematics that are both familiar (coordinate systems) yet deep enough to provide varied avenues of exploration.

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 20 May 2002