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A Characterization of Student Mathematical Thinking that Emerges During Whole-Class Instruction: An Exploratory Study

Presenters: Laura R. Van Zoest, Western Michigan University; Keith R. Leatham, Brigham Young University; Okan Arslan, Mehmet Akif Ersoy University; Mary A. Ochieng, Western Michigan University; Joshua M. Ruk, Western Michigan University; Blake E. Peterson, Brigham Young University; and Shari L. Stockero, Michigan Technological University
Location: PMENA Conference in Greenville, South Carolina
Abstract/Description:
This exploratory study investigated 164 instances of student mathematical thinking that emerged during whole-class instruction in a high-school geometry course. The MOST Analytic Framework provided a way to categorize these instances according to their Building Potential—that is, the potential for learning to occur if the student thinking of the instance were made the object of consideration by the class. The variations in the building potential of student thinking revealed in the study highlight the complexity of teaching, and the need to support teachers in identifying and appropriately responding to instances with different levels of Building Potential.

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

Presenters: Shari L. Stockero, Michigan Technological University; Ben Freeburn, Western Michigan University; Laura R. Van Zoest, Western Michigan University; Blake E. Peterson, Brigham Young University; and Keith R. Leatham, Brigham Young University
Location: PMENA Conference in Greenville, South Carolina
Abstract/Description:
We investigated teachers’ responses to a common set of varied-potential instances of student mathematical thinking to better understand how a teacher can shape meaningful mathematical discourse. Teacher responses were coded using a scheme that both disentangles and coordinates the teacher move, who it is directed to, and the degree to which student thinking is honored. Teachers tended to direct responses to the same student, use a limited number of moves, and explicitly incorporate students’ thinking. We consider the productivity of teacher responses in relation to frameworks related to the productive use of student mathematical thinking.

Covariation Graphing Practices: The Change Triangle

Presenters: Daniel Siebert and Konda Luckau, Brigham Young University  
Location: PMENA Conference in Greensville, South Carolina
Abstract/Description:
Using a sociocultural lens to study graphing, we investigate the graphing practices of an experienced function-based algebra teacher to see how she uses the change triangle to support students reasoning about covariation and rates of change. We describe the elements of a change triangle and the ways the teacher attends to and reasons with these elements and multiple copies of the change triangle to enact a variety of practices as she completes common tasks related to functions and their graphs.

Secondary Student Teachers’ Ability to Respond to Student Mathematical Thinking

Presenters: Dawn Teuscher, Brigham Young University and J. Matt Switzer, TCU
Location: AMTE Conference, Orlando, Florida
Abstract/Description:
We share findings from an analysis of eight preservice secondary mathematics teachers’ noticing of student mathematical thinking while student teaching. We focus on how they responded to student mathematical thinking and discuss differences among student teachers.