The first thing you notice about Andrew Smith’s math class is that he isn’t teaching it. Yet his students seem to be learning a lot.
The Beach Elementary second-graders are scattered into half a dozen small groups, intently doing math lessons. Using playing cards, dice and geometric tracing tools, they figure out fractions, diagram trapezoids and create number groupings, all with each other’s help.
“There’s three parts here and one part here, so what’s the fraction?” Eli Howland asks Brooke Derosia, who’s traced three small trapezoids inside a larger one. “One out of three,” she says, and writes down 1/3.
So goes Math Workshop, a new program designed to make students their own mathematicians. Second-grade teachers Smith, Amanda TenBrink and Darcy Oberdorfer say the approach is producing remarkable results, both in what students are learning and how they do it.
“The beauty is you walk in here and there’s a sense of calmness,” Smith says of his 26 students quietly working. “They’re driving their own learning. I’m not the source of information anymore. Their fellow mathematicians really are the source.”
Not that he is disengaged. The exercises are based on pre- and post-tests measuring students’ mastery of various concepts, and Smith holds small-group sessions for those needing extra help. But the students themselves are some of their best teachers.
“I really feel comfortable when people help me and get me through things,” Brooke Derosia says after working with Eli. “You learn something new every day.”
A New Way of Teaching and Thinking
The Beach second-grade teachers began using the approach late last school year after being frustrated by their students’ lack of progress. Looking for alternatives, they studied a similar program at Ada Elementary in Forest Hills. They also read the book “Math Exchanges,” a small-group teaching method by Kassia Omohundro Wedekind, and heard her speak last fall.
The results have been dramatic, the teachers say.
“The work they’re doing on a daily basis is just amazing,” Smith says. “Kids are blowing the (test) assessments out of the water.”
But Math Workshop places more emphasis on students’ thought process than on their answers. Pupils systematically learn to analyze a story problem, figure out what’s important and what’s not, and decide different ways they could solve it.
“It’s really powerful for the kids to know, ‘It’s okay to change my thinking,’ and not worry about having a right answer right away,” says Darcy Oberdorfer, a fourth-year teacher at Beach.
“Do you want to change your thinking?” is a phrase teachers use to help students correct their calculations. They teach students to use one of three different methods — abstract (equations), concrete (physical objects) or representational (drawing objects or shapes) – then check their work with a second method.
Just how much students gain academically from the method will become clearer next year when they take third-grade standardized tests. But for now,Smith says, “It is just about the pride and joy we get every day … from knowing these kids really are mathematicians.”
Allison Camp, a math consultant for Kent ISD, says the workshop approach fosters the critical analysis required by the new Common Core State Standards.
“It is just a small movement right now,” Camp says, noting teachers in Northview and Caledonia also use it. “But I am hoping to grow it because I think it could make a big difference for teachers and students who are working to reach the rigorous expectations of the Common Core.”
Promising Results, Motivated Students
So far it’s going well. All 27 of Oberdorfer’s students have met or exceeded the test standards on their current study unit. She says her students carry the methods over into other classes, adding, “It’s all building that community where we want to collaborate and help each other.”
She, Smith and TenBrink have made presentations on Math Workshop at Grand Valley State University’s Math in Action conference and to the Cedar Springs school board.
“I thought it was a new way of doing a basic thing that we all learned the hard way,” says board President Brook Nichols. “It really felt like the kids were really excited about it and the teachers were too.”
Faith Fraser says her second-grade twins, Travis and Emily, have come a long way thanks to the workshop.
“When they first started this year, they needed our assistance,” Faith says. “Now they’re saying, ‘We don’t need your help with it. We know how to do it.'”
Students say working together and using tools like plastic blocks make math fun.
“It’s my favorite subject,” says Matthew Vaughn, sprawled on the floor and drawing geometric shapes with a plastic template.
“It’s like a puzzle,” says his work mate, Gracey Newman. “I like making puzzles a lot.”
Not that it all comes easily. It is math after all.
“It’s a challenge sometimes,” concedes Eli Howland. But he adds, “It’s like, when I finish the challenge, I feel good – because I did it.”
Kassia Omohundro Wedekind discusses “Math Exchanges”