Math Matters: Closing the Gap on Mathematical Quandaries

Standard assessments across the nation have yet to show that students are getting any closer to a better understanding of math. A more in-depth look at math education today reveals that the problem goes far beyond just finding the right answer.

In classrooms across the United States, teachers, students, and society are being bombarded by what Harvard Graduate School of Education Senior Lecturer Katherine Merseth calls, "math wars"--an ongoing battle over how to teach and assess mathematics.

On Thursday, November 17, Merseth met with HGSE students to discuss why people are afraid of math and how to change this. Based on Merseth's 1993 essay, "How Old is the Shepherd?" which examines math misconceptions, students discussed problems facing math educators today.

"Why are there so many math-phobic teachers and students?" Merseth said. "What are we going to do about it?"

Math educators see students being stifled by a fear of giving a wrong answer. The notion that there is only one answer in math and, consequently, only one method to arrive at an answer is equally paralyzing for students.

Mike Fauteux, a student in the Learning and Teaching master's program, pointed out that there is a pre-existing subjective view that there's only one way to do math. As a result, the more traditional approach to teaching math does not always mesh with what some consider a more "warm and fuzzy" approach, he said.

However, what educators are discovering is that the old way, which is steeped with rules, may not necessarily be the best method for children.

Math educators see students being stifled by a fear of giving a wrong answer. The notion that there is only one answer in math and, consequently, only one method to arrive at an answer is equally paralyzing for students.

For example, elementary school students often find mathematics is fraught with confusion. Merseth pointed out that there are several ways people tell time from saying quarter past two to 2:15 p.m., and even military time. How can you explain such rationale to a first grader? "Time is one of the most abstract concepts," Merseth said.

Even teaching the difference between fractions like 1/3 and 1/4 can also be confusing. After learning to count, a child knows that three is smaller than four, but 1/3 is also larger than 1/4. How can a teacher explain to young children the specific reason for this?

When Merseth asked HGSE students to divide a fraction, getting the answer wasn't the problem. However, few students could explain exactly how they arrived at an answer beyond a memorized rule they had learned as children.

In order to fully understand math, students need to know the concept. Merseth said that part of the problem for teachers becomes a society that only knows math through a series of rules. If a teacher only knows the rule and not the rationale, it becomes difficult to actually teach a child math. Then, children often create their own reasons for an answer. "Children make up their own rules and procedures," Merseth said. "Their answers aren't random. They have a reason."

Perhaps the biggest challenge for math educators is not only training teachers differently, but changing society's beliefs on how math should be taught. While Merseth acknowledged significant changes in the math curriculum, she pointed out that the changes required new methods of teaching to completely work.

Adjunct Lecturer Paul Natola agreed that professional development is a key issue in conquering math education and cited a need for mandates and systematic changes.

According to Merseth, some of the challenges standing in the future of math education include changing the way the culture perceives math, improving teacher's understanding of the subject matter, and listening more closely to the students.

Students cited a need for teachers to link math more to the real world, provide more opportunity to listen to students, and allow students to develop a more self-correcting ability.

"There's no mystery of what has to happen," Merseth said. "We just don't have it [math] in our society."