Students often are not aware of how they participate in classroom discussions. They may not realize that they are not sharing “space” when they interrupt, talk too much, talk too little, ignore lower-achieving peers or fail to question or challenge a higher-achieving peer.
A new study in The Elementary School Journal proposes a novel way to raise awareness: Take video of classroom or small-group discussions and share that video with students. Researchers say when students see themselves on video it not only increases awareness of individual behavior but also of norms for high-level discourse.
“Mathematics discourse, particularly the practice of students reasoning aloud or explaining their thinking, is often a new experience for students who enter learner-centered classrooms that emphasize communication of mathematical thinking,” the researchers write. “Socialization into this type of learning environment often takes considerable time for some students as they adjust to revised classroom norms.”
The researchers note that “Though video playback is not typical practice and requires the willingness of teachers to use such a method, the quality of participation cannot improve without substantial reflection on the part of both teachers and their students.”
Small-group discussions are more problematic than whole-class discussions because teachers are not on hand to make sure everyone gets a chance to speak. One of the important roles math teachers play when they facilitate discussions or discourse in their classrooms is to make “space” for low-achieving students to participate in the dialogue, according to the study.
Researchers studied interactions among low-achieving and high-achieving students in a 6th-grade math class by analyzing video of 9 whole-class instructional task discussions and 2 small-group discussions among 4 girls, 2 low-achieving students (Heidi and Rachel) and 2 high-achieving students (Patty and Marie). These 4 students were interviewed immediately after discussions on 2 instructional tasks and 1-3 days later after they viewed a video clip of the small-group discussions.
Researchers made the following observations about “space-making” and “meaning-making” behaviors during small-group discussions:
- To claim or waive space in discussion students used a variety of behaviors such as thinking aloud, seeking clarification, blurting out ideas and interrupting one another.
- Patty and Marie, the high-performing girls, tended to discuss math tasks with each other rather than with Heidi and Rachel, the 2 low-performing girls. When Heidi shared her thinking with the group, Marie and Patty sometimes conversed privately. Asked by the interviewer why she favored interacting with Patty rather than Heidi and Rachel, Marie said, “Sometimes they don’t get what we’re thinking.”
- While the high-performing girls may have better understood the math tasks, their explanations were often vague and confusing. Heidi and Rachel complained that Marie and Patty used pronouns which made their comments difficult to follow. Many teacher interactions with Marie and Patty involved revoicing their vague explanations of the tasks.
- Heidi and Rachel often asked their higher-achieving peers for clarification, while Marie and Patty never asked for clarifications from Heidi. Rachel’s interactions with the group were characterized by excessive help-seeking. She felt that her participation largely depended on whether the other students’ contributions were clear and easy to follow.
- Pacing was another issue in the interactions. Heidi found it nearly impossible to check or evaluate Patty and Marie’s claims because her thinking lagged behind theirs, limiting her ability to make contributions to the discussion. She would plead with them to “hang on” but they would move ahead choosing answers with group consensus.
- Patty told the interviewer that if she didn’t interact with, or help Heidi or Rachel, it was because she found it frustrating and fruitless if not counterproductive. When she explained her thinking to others she said became confused. “So I just like going on my own track instead of explaining things to people because once I, I have this thing where if I explain it to someone where I know it really well, sometimes it drops out of my head and then I don’t understand it anymore.”
“This study’s findings question the presumption that higher-performing students often provide more detailed and easier-to-understand explanations of their mathematical thinking than their lower-performing peers,” the researchers write. “These findings challenge the assumption that because of compatible language use, children may find it easier to understand the explanations of their peers than the explanations provided by their teacher.”
The students were all more intent on finding answers and moving to the next problem than on explaining their thinking to their peers. Both low- and high-performing students tended to favor abbreviated, decontextualized, computational explanations aimed at revealing answers rather than thinking processes, the researchers write. One student acknowledged that “knowing it in your head” and “explaining it in words” are fundamentally different abilities.
The researchers make the following recommendations to teachers to ensure that both high achievers and low achievers have opportunities to participate in math discussions:
- Find ways to encourage students to reflect on how they are participating (or not participating) in math discussion and how they are interacting with their peers.
- How you group students of different ability levels is a complicated issue. One way to help lower-performing students participate more in small groups is to specifically assign tasks or roles that they can perform well to raise other students’ expectations of them.
- Help high-performing students to craft clearer and more precise explanations of thinking processes. Encourage lower-performing students to demand clear explanations from their peers.
“Low- and High-Achieving Sixth-Grade Students’ Access to Participation During Mathematics Discourse,” by Brian Lack et al., The Elementary School Journal, 2014, Volume 115, Number 1, pp. 97-123.