With each issue, Trib+Edu brings you an interview with experts on issues related to public education. Here is this week's subject:
Sarah Powell is a University of Texas assistant professor in the Department of Special Education. After teaching kindergarten, Powell worked at Vanderbilt University as a project coordinator of grants related to word problem solving and computation for elementary students. Her dissertation focused on providing instruction about the equal sign to students with mathematics difficulties. During two years as an assistant professor at the University of Virginia, she designed and implemented randomized control trials related to non-symbolic understanding of mathematics, manipulative use and explicit mathematics vocabulary instruction for students with mathematics difficulties.
Editor's note: This interview has been edited for length and clarity.
Trib+Edu: What led to your math education research?
Sarah Powell: I was an elementary education major in college, and thought I wanted to be an elementary school teacher. I ended up in a master's program where I had the opportunity to work in a department of special education on a research program where we were in a kindergarten and first grade classroom, working with teachers testing out a program to see if peer tutoring in mathematics was a beneficial strategy.
The program was written to incorporate lower performing students into general classroom activities, but it was used at the general classroom level. We learned that not only the lower-performing students benefit from peer tutoring but the higher-performing students benefit as well. During that time, I was spending time in classrooms, which I love, working with children but also learning how research can inform what teachers are doing in the classroom.
I ended up then going to teach, and I used some research programs in my own classroom. I then had the opportunity to work at the university full time, developing these research programs. I like that idea because when you are a classroom teacher, you might have 15, 20 or 25 students in your class. But when you are writing research programs and determining their effectiveness, then those programs can be used by teachers across the United States. You’re not just influencing the math education of 20, but maybe the education of thousands of students. As someone who would call myself a teacher first, I am still able to teach through this research paradigm.
I worked on other programs at Vanderbilt and spent two years as an assistant professor at the University of Virginia. There we developed three programs for teachers to use in first and second grade for students that were having difficulty with math symbols. Since I’ve been here at Texas, I’ve been working on assessments to understand how students interpret math symbols and the difficulty that might create for them. Next year, we will be developing intervention modules that we will test in local schools in the Austin area and those will be available for teachers to use.
Trib+Edu: How did the problem with math symbols become the focus of your research?
Powell: When I was doing my dissertation project, I also took a class in the department of psychology where education psychologists were using the equal sign symbol. They determined kids do not interpret the equal sign correctly, which seems so trivial but can have really big implications. In school, we give students so many problems that look like two plus two equals blank, and you put an answer. Many early students interpret the equal sign to mean they need to write an answer or they need to add them up.
The equal sign does not mean that, it means you need to balance two sides of an equation. Psychologists were using this to see how quickly children can change their thinking about a concept that they are thinking about incorrectly to a way that they are thinking about it correctly. They would do these one-day experiments where they would come in to a classroom and assess equal sign knowledge, teach the students about the equal sign as a balance and the kids would do really well after. A lot of the research was from educational psychology, and it made me wonder if students with math difficulty also misunderstand the equal sign.
I developed a little project with that and we have done five or six subsequent studies and seen every time that students in the elementary grades think the equal sign means to add things up or write an answer. You can change that with instruction. We’ve developed little programs that teachers can use to talk about the equal sign. Now I’m starting to think about other symbols, like the inequality symbols, the greater-than and less-than sign. It is amazing that for students, one little misinterpretation can create some pretty far reaching difficulties. It is not just students with disabilities and difficulties, it is a lot of students.
Trib+Edu: What prompts this misunderstanding for students?
Powell: I did a textbook analysis about four years ago. One of the things textbooks almost always do is present equations where the equal sign is in the second to last position of the equation. When students see thousands of equations that are in that exact same format, the students just think the equal sign means to do something, to write an answer. Rarely do textbooks give students the opportunity to solve an equation like blank equals nine times nine. The equal sign is just in a different position.
Textbooks in the mathematics curricula that are used in classrooms don’t give opportunities for students to think about the equal sign in any other way than to write an answer. When we look at teacher editions of textbooks, rarely do teachers provide instruction on the equal sign. You might see it in kindergarten or first grade when students are introduced to the plus sign, and told it means to add, and the equal sign which means to write an answer, which is an incorrect definition of the equal sign.
We actually found some textbooks that provided incorrect definitions, but that might be the only time a teacher is encouraged to talk about those symbols with the students. By lack of exposure to different types of equations and lack of instruction from the teacher, the students are not getting an opportunity to think about the equal sign in a different way. It becomes really important when students get to the middle school grade and they have to balance two different sides of an equation.