Discourse

Teachers' Responses to Instances of Student Mathematical Thinking with Varied Potential to Support Student Learning

Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support learning. This study investigated teachers’ responses to a common set of instances of SMT with varied potential to support students’ mathematical learning, as well as the productivity of such responses.

Author/Presenter: 
Shari L. Stockero
Laura R. Van Zoest
Ben Freeburn
Blake E. Peterson
Keith R. Leatham
Year: 
2020
Short Description: 

This study investigated teachers’ responses to a common set of instances of student mathematical thinking (SMT) with varied potential to support students’ mathematical learning, as well as the productivity of such responses.

Teachers' Orientations Toward Using Student Mathematical Thinking as a Resource During Whole-Class Discussion

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations.

Author/Presenter: 
Shari L. Stockero, Keith R. Leatham, Mary A. Ochieng, Laura R. Van Zoest & Blake E. Peterson
Year: 
2020
Short Description: 

The purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction.

Conceptualizing Important Facets of Teacher Responses to Student Mathematical Thinking

We argue that progress in the area of research on mathematics teacher responses to student thinking could be enhanced were the field to attend more explicitly to important facets of those responses, as well as to related units of analysis. We describe the Teacher Response Coding scheme (TRC) to illustrate how such attention might play out, and then apply the TRC to an excerpt of classroom mathematics discourse to demonstrate the affordances of this approach.
Author/Presenter: 
Laura R. Van Zoest
Blake E. Peterson
Annick O. T. Rougée
Shari L. Stockero
Keith R. Leatham
Ben Freeburn
Year: 
2021
Short Description: 

We argue that progress in the area of research on mathematics teacher responses to student thinking could be enhanced were the field to attend more explicitly to important facets of those responses, as well as to related units of analysis. We describe the Teacher Response Coding scheme (TRC) to illustrate how such attention might play out, and then apply the TRC to an excerpt of classroom mathematics discourse to demonstrate the affordances of this approach. We conclude by making several further observations about the potential versatility and power in articulating units of analysis and developing and applying tools that attend to these facets when conducting research on teacher responses.

Clarifiable Ambiguity in Classroom Mathematics Discourse

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Author/Presenter: 
Blake E. Peterson
Keith R. Leatham
Lindsay M. Merrill
Laura R. Van Zoest
Shari L. Stockero
Year: 
2020
Short Description: 

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Articulating the Student Mathematics in Student Contributions

We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contribution.

Author/Presenter: 
Laura R. Van Zoest
Shari L. Stockero
Keith R. Leatham
Blake E. Peterson
Joshua M. Ruk
Year: 
2020
Short Description: 

We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contribution.

Think Alouds: Informing Scholarship and Broadening Partnerships through Assessment

Think alouds are valuable tools for academicians, test developers, and practitioners as they provide a unique window into a respondent’s thinking during an assessment. The purpose of this special issue is to highlight novel ways to use think alouds as a means to gather evidence about respondents’ thinking. An intended outcome from this special issue is that readers may better understand think alouds and feel better equipped to use them in practical and research settings.

Author/Presenter: 
Jonathan David Bostic
Lead Organization(s): 
Year: 
2021
Short Description: 

Introduction to special issue focusing on think alouds and response process evidence. This work cuts across STEM education scholarship and introduces readers to robust means to engage in think alouds.

Gathering Response Process Data for a Problem-Solving Measure through Whole-Class Think Alouds

Response process validity evidence provides a window into a respondent’s cognitive processing. The purpose of this study is to describe a new data collection tool called a whole-class think aloud (WCTA). This work is performed as part of test development for a series of problem-solving measures to be used in elementary and middle grades. Data from third-grade students were collected in a 1–1 think-aloud setting and compared to data from similar students as part of WCTAs. Findings indicated that students performed similarly on the items when the two think-aloud settings were compared.

Author/Presenter: 
Jonathan David Bostic
Toni A. Sondergeld
Gabriel Matney
Gregory Stone
Tiara Hicks
Lead Organization(s): 
Year: 
2021
Short Description: 

This is a description of a new methodological tool to gather response process validity evidence. The context is scholarship within mathematics education contexts.

An Examination of Credit Recovery Students’ Use of Computer-Based Scaffolding in a Problem-Based, Scientific Inquiry Unit

In this study, we investigated how high school credit recovery students worked in small groups and used computer-based scaffolds to conduct scientific inquiry in a problem-based learning unit centered on water quality. We examined how students searched for and evaluated information from different sources, and used evidence to support their claims. Data sources included screen recordings, interviews, scaffold trace data, and scaffold entry quality ratings. Findings indicate that many students struggled to use the scaffolding and did not fully respond to scaffold prompts.

Author/Presenter: 
Brian R. Belland
D. Mark Weiss
Nam Ju Kim
Jacob Piland
Jiangyue Gu
Lead Organization(s): 
Year: 
2019
Short Description: 

In this study, we investigated how high school credit recovery students worked in small groups and used computer-based scaffolds to conduct scientific inquiry in a problem-based learning unit centered on water quality.

Supporting Sense-making with Mathematical Bet Lines

This article presents an instructional strategy called Mathematical Bet Lines that was designed to promote classroom discourse and sense-making for all students, in particular English Language Learners.  Introduced in Project AIM (All Included in Mathematics), a 40 hour professional development program focused promoting meaningful mathematical discourse, the Mathematical Bet Lines strategy supports comprehension of story problems by having students articulate to themselves and others their predictions regarding what is happening in the problem as it is revealed one sentence at a time.  With

Author/Presenter: 
Lara Dick
Tracy Foote White
Aaron Trocki
Paola Sztajn
Daniel Heck
Kate Herrema
Year: 
2016
Short Description: 

This article presents an instructional strategy called Mathematical Bet Lines that was designed to promote classroom discourse and sense-making for all students, in particular English Language Learners.

Resource(s): 

Launching a Discourse-rich Mathematics Lesson

Facilitating meaningful mathematical discourse is dependent on the launch of the lesson where teachers prepare their students to work on the task.

Author/Presenter: 
Aaron Trocki
Christine Taylor
Tina Starling
Paola Sztajn
Daniel Heck
Year: 
2015
Short Description: 

This article discusses the use of the Think Aloud strategy at the beginning of a lesson to model to students both the type of thinking that develops conceptual understanding, as well as how to share one’s thinking.

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