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Improving Secondary Preservice Mathematics Teachers’ Attention to Student Mathematical Thinking

Presenters: Dawn Teuscher, Brigham Young University and J. Matt Switzer, TCU
Location: AMTE 2021, Virtual
Abstract/Description:
The activities that teacher educators prepare for preservice teachers should be intentional in their purpose for improving teaching practices. We report on a video database activity that our preservice teachers engaged in and their improvement in attending to student mathematics.

Examining Teachers’ Reasoning for Their Instructional Decisions

Presenters: Porter Nielsen and Dawn Teuscher, Brigham Young University
Location: AMTE 2021, Virtual
Abstract/Description:
Teachers’ instructional decisions are important to students’ mathematics learning as they determine the learning opportunities for all students. We will discuss 8th-grade teachers’ reasoning for their instructional decisions in the context of geometric reflections and orientation of figures.

Establishing Student Mathematical Thinking as an Object of Class Discussion

Presenters: Blake E. Peterson, Brigham Young University; Shari Stockero, Michigan Tech University, Laura R. Van Zoest, Western Michigan University, and Keith R. Leatham, Brigham Young University
Location: AMTE 2021, Virtual
Abstract/Description:
To productively use student mathematical thinking, it must be 1) made clear and 2) established as the object of discussion. The nuances of these two aspects of the teaching subpractice, Make Precise, will be discussed through examples from the data.

Using a Public Record to Anchor Whole-Class Mathematical Discussion

Presenters: Laura R. Van Zoest, Western Michigan University; Carlee E. Madis, Western Michigan University, Blake E. Peterson and Keith R. Leatham, Brigham Young University and Shari Stockery, Michigan Tech University
Location: AMTE 2021, Virtual
Abstract/Description:
We share our research on uses of a public record to support whole-class discussions, show examples of revising a public record in real-time to support the discussion, and consider how this information can be used in developing well-prepared beginning teachers.

Students’ Reasoning About Multivariational Structures

Presenters: Steven Jones and Haley Jeppson, Brigham Young University
Location: PMENA in Mazatlan, Mexico and virtually
Abstract/Description:
Covariation and covariational reasoning are key themes in mathematics education research. Recently, these ideas have been expanded to include cases where more than two variables relate to each other, in what is termed multivariation. Building on the theoretical work that has identified different types of multivariation structures, this study explores students’ reasoning about these structures. Our initial assumption that multivariational reasoning would be built on covariational reasoning appeared validated, and there were also several other aspects of reasoning employed in making sense of these structures. There were important similarities in reasoning about the different types of multivariation, as well as some nuances between them.

Students’ “Multi-sample Distribution” Misconception about Sampling Distributions

Presenters: Steven Jones and Kiya Eliason, Brigham Young University
Location: PMENA in Mazatlan, Mexico and virtually
Abstract/Description:
The sampling distribution (SD) is a foundational concept in statistics, and simulations of repeated sampling can be helpful to understanding them. However, it is possible for simulations to be misleading and it is important for research to identify possible pitfalls in order to use simulations most effectively. In this study, we report on a key misconception students had about SDs that we call the “multi-sample distribution.” In this misconception, students came to believe that a SD was composed of multiple samples, instead of all possible samples, and that the SD must be constructed by literally taking multiple samples, instead of existing theoretically. We also discuss possible origins of this misconception in connection with simulations, as well as how some students appeared to resolve this misconception.

Articulating the Student Mathematics in Student Contributions

Presenters: Laura R. Van Zoest, Western Michigan University; Shari Stockero, Michigan Tech University; Keith R. Leatham and Blake E. Peterson, Brigham Young University; and Joshua M. Ruk, Western Michigan University
Location: PMENA in Mazatlan, Mexico and virtually
Abstract/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. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers’ abilities to notice and productively use student mathematical thinking during instruction.