A revolutionary way to teach math in the age of MCAS
When people ask Mahesh Sharma what he does for a living, he knows what their reaction is going to be. Hearing that he’s a math educator, many people tell Sharma, “Oh, I’ve never been good at math.” It’s a common complaint, one that’s becoming more worrisome as thousands of Massachusetts high school seniors face the prospect of not graduating this spring because they keep failing the MCAS math exam.
can learn math.
Sharma, who is provost and executive vice president of Cambridge College, may know more than anyone else about why so many people have a hard time learning math. He’s been studying such mental roadblocks in Asia, Europe, and the US for 35 years. And he says they’re more widespread than is generally recognized.
A tiny fraction of the population–about 2.5 percent–suffers a math learning disability akin to dyslexia that is called “dyscalculia,” he says. Like dyslexics, they have a dysfunction in the reception, comprehension, or production of certain kinds of information–in their case, quantitative and spatial information. A far larger segment of the population–perhaps 40 to 45 percent–has serious difficulties with math that can look like dyscalculia, but are the result of poor instruction or early failures.
The biggest problem, according to Sharma, is that most math teachers today still teach the way they were taught themselves–telling students to memorize formulas and procedures. “By the seventh grade, children begin to think of math as a collection of tricks,” Sharma says. In addition, he says, “many of the teachers who are teaching math themselves are afraid of math and are seeing math in a limited way.”
So what can be done? Sharma, who trains hundreds of teachers each year, has some answers. They’re not simple, but some educators say his approach could help revolutionize–or at least democratize–math education in the age of MCAS.
“He’s the math guru,” says John J. Kelley, a math and science coordinator in the Brockton public schools, who has hired Sharma to train more than 300 teachers since taking a weeklong course from him in the late 1980s, and who also teaches part-time at Cambridge College. “He makes us all believers that all children can learn because he shows the strategies that help them learn. He teaches teachers how to open those doors.”
Sharma has found five factors that affect how children learn math–and he says good teaching must incorporate all five. First, a teacher must consider each student’s level of cognitive functioning. Second, a teacher should identify the student’s “mathematics learning personality”–a concept Sharma developed that refers to how people process mathematical information–and match instruction to it. (People are either “quantitative” or “qualitative,” he says.) In addition, students need seven “prerequisite” skills to “anchor” math learning, ranging from estimation to pattern recognition, he says. And they must be led through six levels of “knowing” for each concept–from intuitive to abstract to the communications level, where students understand well enough that they can teach it to others. Finally, he says teachers should be treating math like a second language, decoding its vocabulary, syntax, and rules of translation.
Putting his theory into practice, Sharma has developed his own brand of instruction, which he calls “Vertical Acceleration.” Geared to fill gaps quickly, the model can take a middle-school student at the second-grade level and bring him up to seventh-grade in a single lesson, he says. One technique involves “cuisenaire rods,” blocks of different lengths in different colors that can represent multiplication problems visually. The model can be used to teach multiplication of whole numbers in second grade, fractions in fifth grade, and quadratic equations in middle school. Students still eventually memorize formulas and procedures, but they are more likely to understand why they work, he says.
Sharma’s approach is catching on in some local school districts that are desperate to improve the math performance of their students. “It’s a nice, easy-to-get-your-hands-around perspective,” says Ed Joyce, senior program director for secondary mathematics in the Boston public schools, who says Sharma helped “jump-start” the city’s recent efforts to reform math education. In nearby Winthrop, Sharma is doing a year of workshops with the district’s 120 teachers and aides involved with math instruction. Patty Messina, the math curriculum coordinator in Winthrop, says she already sees changes in the classroom.
“We’re not seeing flying MCAS scores yet,” says Messina. “But more important to us is, teachers seem to be more comfortable teaching math. And we hope we’re all going to be better at it.” Sharma became fascinated by math learning problems in the late 1960s shortly after coming to the US from his native India. As a college math professor, he was astounded to find many freshmen struggling with eighth-grade concepts.
Though he offers no quick fixes, Sharma’s message may be particularly appealing to anyone tired of the ongoing battles between the “traditionalists” and the “progressives” in math education. “I’m not party to these wars,” says Sharma. “I’d like to be the negotiator.”
Carol Gerwin is a former associate editor of CommonWealth.