"Now I'm Starting to Wonder": What Is the Role of Listening as Young Mathematicians Persevere With Complex Problems and Revise Their Ideas?

• In Event: Teacher as Listener: Empirical and Philosophical Perspectives on the Roles of Teacher-Listening in Supporting Democratic Learning Environments

Abstract

1. Objectives/purpose: Effective mathematics teaching and learning engages students in complex problems that promote reasoning and sense-making through discussion (NCTM, 2014). Such discussions, often incorporating argumentation (Wood, Williams, & McNeal, 2006), can provide appropriate challenge to students and require young mathematicians to engage in productive struggle, perseverance in solving, and often revision of their assertions. This purpose of this analysis is to better understand the complexities of listening as students engage in ambitious forms of mathematical discourse.

2. Theoretical framework: This analysis draws on a sociocultural perspective (Vygotsky, 1987/1934) and a conceptual framing of three types of listening, evaluative, interpretive, and hermeneutic (Davis, 1996, 1997), in order to interpret the listening interactions in a fourth grade classroom as students defend their conjectures about whether the following statement is true or false: 80 ÷ 4 = 80 ÷ 2 + 80 ÷ 2

3/4. Methods and data sources: This analysis focuses on a 20-minute episode of discussion. Situated in a high-needs, poverty impacted urban classroom, the discussion was selected as an exemplary model of mathematical speaking and listening. The following research questions guided the analysis:
• What does the teacher listen for in order to support students to lean into and through moments of perseverance and revision during mathematical discussion? How does the teacher’s listening shape students’ listening?
• How does listening to classmates’ ideas support student’s persistence with and revision of mathematical ideas?
What is the role of listening when it comes to ensuring that moments of discontinuity (English, 2013) in learning are productive (Kapur & Bielaczyc, 2011) when learning mathematics?

5. Results: At a turning point toward consensus in the discussion, a student who originally defended “true”, hears his classmate’s argumentation for why the statement is false. After listening, he says, “Now I’m beginning to wonder.” He begins to revise his claim, adding, “I think [Biffy] might be right. So, I’m starting to think it is false.”

A turn-by-turn analysis of the discussion provides a revelatory case of student and teacher listening during moments of collaborative sense-making. Findings reveal that the way the teacher tactfully (English, 2013) leaned into confusion, struggle, and disagreement, by listening for student understanding and evolving conceptions and her use of intentional moves that opened up opportunities for students to hear classmate’s ideas, played a significant role in supporting students to persist and revise their assertions. Also, hearing classmates’ ideas, and listening in order to understand, supported students to persist and revise, however, robust classroom norms were in place to support such practices. Finally, complex tasks play an essential role in creating opportunities for meaningful mathematical listening.

6. Scholarly significance: This analysis contributes to literature in mathematics education by carefully considering the constructive role of struggle, persistence, and revision of ideas in learning and education (Kapur, 2014). Analysis of these questions contributes to our understanding of the role of listening in mathematics education as well as in moral education as it pertains to participating in democracy (Dobson, 2014).

Authors

• Allison Beth Hintz, University of Washington - Bothell

• Andrea R. English, University of Edinburgh

• Kersti Tyson, University of New Mexico