Matt Wallace

There is great power in math; most students just don’t know how to harness it.

“Most students have no understanding about how useful math can be to them. Too often, they see math as a challenge, rather than an opportunity,” said Matt Wallace, a PhD student in math education. Math taught well serves as a “bridge” from a subject often dreaded to one that empowers students to think conceptually and more deeply about the role math plays in a variety of fields, according to Wallace.

Traditionally math assessments have focused on close-ended answers and procedures with student mastery assessed through quizzes and testing. One result is that teachers feel pressure to teach to the test.

“This approach can reduce the typical math class to test preparation only. Assessment serves many purposes, but test scores should not be the main focus,” said Wallace.

Instead, he argues the future of math instruction lies in contemporary methods which encourage students to reason, find patterns, and explore possible solutions to real world problems. Reform-based assessment methods focus on advancing learning, not just measuring it, so tasks involve problem solving, multiple solutions and strategies, and communicating mathematical ideas. There are a variety of activities and the process is about teachers and students building on prior knowledge. As students gain a genuine understanding of math, research shows that test scores increase as well, according to Wallace.

“Professionals who use math, such as engineers, aren’t following rote procedures but solving problems,” said Wallace. “Students, who learn about math as a concept, have a richer and deeper understanding of the fluidity of math and how it functions. Exploration and creating our own understanding of math becomes an assessment in and of itself.”

However, a lot of professional development for teachers comes in the form of kits or day-long workshops with little to no follow up, which according to Wallace “is a problem because many of these ideas are quite foreign to teachers. Without sustained and math-specific professional development, many contemporary ideas get used in traditional ways. For example, a teacher may give students an open-ended task where they are asked to explain a pattern and use it to make predictions (reform-based), but grade the task as correct/incorrect (traditional).”

Wallace, who received the prestigious Spencer Dissertation Fellowship, is researching how pre-service math teachers in reformed-minded programs learn and deal with the challenges of teaching in a system which still values traditional teaching and assessment methods.

Wallace recognizes that the process is not easy. Math is the most highly scrutinized subject taught at the K-12 level, so it can be hard to overcome more hurdles on top of that. “Pre-service teachers have a lot on their plates, and you are asking them to do something that they have no idea what it will look like in practice,” said Wallace.

Wallace, who wants to be a math teacher educator, hopes his research will not only help him better know the challenges at every stage of pre-service preparation, but also help him understand how to prepare pre-service teachers and shape their assessment practices.

As Wallace explained, student teachers come in with their own experiences as math students (often taught in very traditional ways) and their own notions about how math ought to be taught. Their evolutionary process has many stages that can either help or hinder them in their attempts to apply reform-based methods.

“We need to understand the challenges within that process before we can ever hope to get them to embrace more contemporary methods,” said Wallace.

For example, pre-service teachers are not always placed with reformed-minded mentor teachers, and there can be a lot of tensions between what pre-service teachers are learning, what they are seeing, and what they are being asked to do. New teachers, then, may leave their respective programs with  reform-based theories and little practical understanding of how to apply them in the classroom.

In the end, Wallace concedes, “Student teachers have to see it for themselves. Until then, they have to truly believe this method of teaching works. It can be difficult for new teachers because at the end of the year they know they have to get those results. Sometimes, it just has to be a leap of faith.”