Turning the Tables
By Gena Mangiaratti, staff writer
Reprinted with permission from the June 11 Daily Hampshire Gazette
EASTHAMPTON — About 30 or so math teachers from across the Valley sat in clusters of desks in an Easthampton High School classroom on an early spring day. They talked in hushed voices. The instructor for this after-school workshop, Christine von Renesse, associate professor of mathematics at Westfield State University, had asked them to make a list of the most common mathematical misconceptions among their students.
They wrote these misconceptions on giant lined paper on their shared work table. Among the ideas they jotted down:
- If you divide a number by zero the answer is infinity.
- You can only count as high as the number of fingers you have.
- If you add a number to another number, it’s always a bigger number.
- If you divide a smaller number by a larger number, you get a negative number.
- If you multiply two numbers you always get a bigger number.
The purpose of this exercise, according to von Renesse, of Williamsburg, was to focus teachers on observing their students as a way to help them understand the way they think. Just because students are in the same grade level, for example, does not mean they all have the same mathematical ability. This gathering has drawn not only elementary and high school teachers, but college instructors as well, which von Renesse believes will help participants develop a fuller understanding of how students learn and build on mathematical concepts.
She noted that some of her students at Westfield State still need help with understanding fractions. And, she said, this is why it is crucial that teachers have a full understanding of not only the concepts they teach in their classes, but the ideas imparted to students before and after the grade levels they teach.
Her goal in this workshop is to show teachers how the concepts they teach connect with other grade levels.
This workshop is one of a series of five sessions offered by the Western Massachusetts Mathematics Partnership to 50 local educators this spring. The educators came from 11 school districts to participate in the program, which included monthly classroom-style workshops where teachers were encouraged to mentor and teach one another. At these gatherings, which ran from January through May, participants explored algebraic thinking across grade levels and discussed strategies to teach to the standards of the state Common Core.
The program was founded in 2011 by Mount Holyoke College faculty member Lenore Reilly and Sue Thrasher, the now-retired director of partnership programs for Five Colleges Inc. Its goal is to help educators come up with the best ways to teach mathematical concepts across grade levels, said Marla Solomon, director of Five Colleges partnership programs.
The $300,000 in start-up funding from the National Science Foundation and additional funds from Five Colleges made it possible for teachers to not only attend these workshops for free, but for each participant to receive a $250 stipend, according to Solomon.
There were two sets of the workshops — one at Easthampton High School and the other at the offices of Five Colleges in Amherst — to give teachers on both sides of the Connecticut River better access.
At the recent session at Easthampton High School, teachers from grades kindergarten through college sat in groups of four or five. When it came time to present to the larger group their lists of misconceptions, one member from each group held up the large lined paper, while others talked about their group’s findings.
Shirley Gilfether, Easthampton’s director of curriculum, laughed about the misconception that you can’t count higher than the fingers on your hand, noting that shoes would have to come off to get to 20. This prompted Matthew Pace, seventh and eighth grade math teacher from Pioneer Valley Performing Arts Charter School to note that students would need partners to count to 40. This provoked laughter from the crowd.
But there were many serious moments as well — and plenty of opportunities for teachers to pair up as they worked out a variety of math problems.
What teachers learned
Workshop participants say there is value to be gained in once again sitting squarely in the student’s seat.
“It’s important for teachers to be lifelong learners, and not to say, ‘Oh, I’m the expert, I know everything,’ ” Mary Cowhey, Jackson Street School math teacher said in a telephone interview after the workshop. “Teaching requires a certain amount of humility, and doing this kind of work helps us see that we’re learners as well as teachers.”
Also in an interview after the workshop, Margaret Betts who teaches first grade at the Maple Elementary School in Easthampton, said she found herself trying to solve a math problem for a fellow participant, which is a dynamic she has observed between students in her class.
At those moments, she said she would ask herself, “How can I help those kids — like I’m going to right now help myself — to stop doing this and not be so presumptuous to think they need to lead the way?”
Cowhey, of Northampton, said she liked hearing how math concepts learned in the younger grades play a role in upper level maths. For example, she learned that a solid understanding of fractions in elementary school can play into learning calculus in high school.
“A lot of what I am gaining from this work is just seeing how all the pieces fit together — how those skills and concepts deepen over time,” said Cowhey.
Betts said she liked doing math problems.
“Math doesn’t come as naturally in our world” when compared to subjects like reading and writing, she said. For example, while she might write a letter to the editor of the newspaper, she’s less likely to work on complicated calculus problems, she noted.
As for von Renesse, she said in addition to teaching new mathematical concepts, she also aims to arm participants with new teaching strategies such as using hands-on activities and discussions rather than lecturing.
“I really want the teachers just to learn to listen to their students,” she said.
Solomon said the partnership hopes to expand its offerings through another grant from the National Science Foundation for $7.5 million.
The partnership will hold an all-day summer institute July 2 open to area teachers. Time, place and topics to be discussed are to be announced. For more information, Solomon can be reached at email@example.com or by phone at 542-4018.