story by Claire Miller
When mathematics teachers plan their lessons, they’re likely considering how to explain specific concepts and how they can encourage classroom discourse around particular approaches to solving mathematics problems.
But the verbal and nonverbal language teachers use, the ways they present the information and how they prompt classroom conversations with their students can have implications for how students think about themselves and approach mathematics.
Assistant Professor Daniel Edelen and colleagues at the University of Central Florida took a closer look at an ethnographic case study within an elementary mathematics classroom to highlight how teachers can recognize this impact.
Their paper, published in Investigations in Mathematics Learning, focuses on one segment of a large ethnography involving observations and audio recordings of a fifth grade teacher. In this case, they were leading a lesson on multiplying fractions.
Edelen and his colleagues studied the lesson using the lens of positioning theory, which is used to aid researchers in making sense of everyday social situations. Positioning theory has three components: a position, or the role that people play; social actions, or the verbal and nonverbal ways people communicate with one another; and the storylines, or the practiced ways that people tend to act in social situations. The researchers used this theory to identify specific social actions in one teacher’s classroom and their consequences for the opportunities students had to learn fractions during the lesson.
For example, the teacher framed multiplying fractions as “easy” a few times. This sentiment likely rang true for some students but was isolating for those who didn’t fully understand how to multiply fractions yet. This affects how students see themselves as doers of mathematics and how they perceive their classmates who understood the lesson verses those who didn’t.
“While seemingly insignificant in the moment, it has ramifications for the students and their beliefs about mathematics,” the authors wrote. “A simple shift in this [talk] turn can provide a very different storyline for the students.”
In addition, students only had an opportunity to engage with one “easy” method for multiplying fractions. Authors noted that students need to be in a position to describe their experiences with fractions, and mathematics content in general. Beginning lessons in such a way – instead of focusing solely on one approach – allows students to see themselves as mathematics experts, and shows them that their lived experiences are valued and an important tool for the lesson.
Edelen and his colleagues argue that educators who apply positioning theory to audio or video recordings from their past lessons can examine how they invite students to learn mathematics. It also helps teachers identify specific ways to be more inclusive in elementary mathematics spaces.
“The goal of this paper is to present positioning theory as a potential tool for how teaching practices impact students’ experiences in mathematical spaces,” they wrote. “Positioning theory has great potential for examining the ways students interact and the implications for students’ opportunities to engage with the content, the materials and each other in collaboratively learning.”