Educator Profile: Leading the Way Through Math's Maze

09/24/2007

By Elizabeth Lutyens, Nashoba Brooks School

Although a new member of the Nashoba Brooks faculty this year, Joel Lubin is hardly a novice. In September 2007, he will begin his 30th year of teaching middle school math, a long path paved with awards and honors. In 2000, he became the first New England teacher of middle-school mathematics to achieve National Board Certification. In 2005, he won the Edyth May Sliffe Award for Distinguished Middle School Mathematics Teaching from the Mathematical Association of America.

 
Joel's strategy for success stems from his belief in "guided discovery."  He says, "Students investigate materials first-hand, gather data, and then pore over it to see if they can discover patterns. To many students, math seems like an impenetrable maze, but when they do discoveries on their own, they explore a problem deeply and come up with methods for attacking it." As Head of the Nashoba Brooks Math Department, Joel joins with his colleagues to show students that "asking for the answer" is no way to solve problems.

Fresh from a Math Summit that he helped coordinate and host, Joel gives an example of the guided discovery approach. One of his upper grades math teaching colleagues, Kerry Stevens, presented a session on Angle Sums of Polygons, where she shared ideas with math teachers from other schools about presenting this Connected Mathematics II lesson. The session began with data-gathering work at the Smart Board and segued into teams of teachers crafting non-regular polygons  from scraps of paper. Joel is enthusiastic about this particular math program, which includes a follow-up "reflection" component after each investigation.  "This helps students as they begin reaching their own conclusions. They aren't just writing down numbers and being done with it. When you have students explain their process, you deepen their understanding."

When Joel recommends a math program, he speaks as an expert. As an adjunct faculty member of Lesley University, one of his tasks is evaluating middle school textbooks. "When I came to Nashoba Brooks," he says, "I had some notions about materials for eighth grade, my area of expertise, and I saw that teachers here also saw the power in discovery, in investigation types of programs.  Kerry and I picked Connected Math Project II, which comes highly rated." [Among the recommendations is the highest rating from The American Association for the Advancement of Science, in its review of twelve nationally available middle school mathematics curricula.]  The program is, Joel says, "a nice model. It fits well with our philosophy that the teacher is a guide, not the sole disseminator of information."

Joel continues, "This kind of discovery models for students learning that involves taking on a problem they haven't exactly seen before. We're participating in more math contests that cover a wider geographic area. We've beefed up our MathCounts team. We're giving students the opportunity to do non-routine problems, showing ways that girls can stretch themselves in math. We have a rigorous program here. We're teaching girls to be self-confident and to represent themselves in a positive way."
 
This is not only Joel's first year at Nashoba Brooks, it is also his first time teaching in a girls-only setting. As a long-time teacher in the Weston schools, Joel sees striking differences between co-ed and single-sex classrooms.  "In general," he says, "girls in co-ed classes were more tentative about problem-solving. When faced with a new problem, they were more afraid of making mistakes, and were less exploratory. Seventh and eighth grade girls can be exquisitely self-conscious, but there is less of that here, where girls are more willing to take risks. I'm reminded of Carol Dweck's attribution-theory research: when boys didn't do well, it was bad luck, and when they did well it was because they perceived themselves as smart. When girls did well they were lucky. When they didn't do well, they were 'stupid.' "
 
He continues, "Every now and then, in a co-ed situation, you find girls not wanting to be seen as too studious, but you never find that here. You do some activity with them, and they have no reluctance about saying, 'Oh, that's neat, that's great.' I don't have to give pep talks about homework or urge them to show their work. And this kind of initiative doesn't apply just to math. It's more unusual, here, to see girls who back away from possibilities of many kinds. Students have so many opportunities for leadership at Nashoba. This is a wonderful reason for a single-sex school."

Joel also notes the advantages of the wide range of ages at Nashoba Brooks.  He mentions the Big and Little Sister program and the ongoing collaboration between kindergarten and fifth grade. He was especially impressed this year to see sixth grade girls working with third grade boys during the girls' Renaissance unit. "According to Da Vinci," Joel says, "the height (which is approximately equal to the arm span) versus head length should be a ratio of eight to one, and the girls recorded the boys' measurements on a scatter chart.  It was wonderful how unself-conscious they were. This environment offers these kinds of opportunities for older and younger students to work together."

The older-younger collaborations are also a way for upper grades girls to underscore the real-life problem solving that lower grades students learn through the Everyday Math program. The math curriculum at Nashoba Brooks, kindergarten through eighth grade, functions on a continuum that is, according to Joel, "increasingly more uniform."

He says, "The NCTM [National Council of Teachers of Mathematics] standards put forth this year are called focal points-the three most important 'big' ideas in each grade level for exposure and mastery. We found, essentially, that at each grade level we meet or exceed those focal points.  It's important not to end up with a 'survey' curriculum that's a mile wide and an inch deep, but we also avoid a program that's very deep in one area and leaves gaps. We're always thinking about preparing students for their next step after Nashoba Brooks."

And for the rest of their lives. "We teach algorithms," Joel says, "but we teach in different ways, never just one way with the teacher as the central authority. The world is so full of information, so many kinds of information, and it's not possible for a teacher, an adult, to walk kids through every kind of problem they might encounter. This applies not just to math, but to everything."

Visit Nashoba Brooks School online at www.nbsc.org