Past Presentations

Abstract/Description: In this study we investigated how a small sample of students used variational reasoning while discussing ordinary differential equations. We found that students had flexibility in thinking of rate as an object, while simultaneously unpacking it in the same reasoning instance. We also saw that many elements of covariational reasoning and multivariational reasoning already discussed in the literature were used by the students. However, and importantly, new aspects of variational reasoning were identified in this study, including: (a) a type of variational reasoning not yet reported in the literature that we call “feedback variation” and (b) new types of objects, different from numeric-quantities, that the students covaried.

Abstract/Description: The Pathways to College Algebra curriculum aims to build concepts that cohere with the big ideas in Calculus, and initial results suggest improved readiness for Calculus by students who have taken a Pathways class. However, less is known about how Pathways might influence students’ initial understanding and reasoning about calculus concepts. Our study examines similarities and differences in how Pathways and non-Pathways students initially understand and reason about the calculus concept of the limit. Our findings suggest that Pathways students may engage a little more in quantitative reasoning and in higher covariational reasoning, and have more correct and consistent initial understandings. Further, the Pathways students were explicitly aware of how their Pathways class may have benefited their understanding of limits.

Abstract/Description: We explore issues related to responsive teaching by presenting excerpts of whole-class discussion and considering the degree of responsiveness within each excerpt as it relates to the collection of instances of student thinking that had been shared thus far.

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.

Abstract/Description: We present six aspects of curricular reasoning and illustrate the interactions among teachers, students, mathematics, and curriculum materials using data from Grade 8 teachers as they planned and enacted geometric transformation lessons. We discuss differences across teachers with varying backgrounds and consider how teachers’ curricular reasoning can influence students’ opportunity to learn mathematics.

Abstract/Description: The transition from the static perspective of right triangle trig ratios to the dynamic perspective of circular trig functions, and from measuring angles in degrees to measuring angles in radians, can generate roadblocks and misconceptions. In this session we will examine a sequence of tasks that reveal, rather than obscure, trigonometric ideas. Participants will engage in tasks that develop the following CCSSM concepts for students: (1) defining radians as a proportionality constant, prior to defining radians as an arc length on a unit circle; (2) using the unit circle to generalize the definitions of the trigonometric functions and to establish trig identities, rather than focusing on memorizing "special angles" which can hinder students' understanding; (3) modeling contexts with trig functions, rather than just sketching graphs.

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.

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.

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.

Abstract/Description: The Comprehensive Mathematics Instruction Framework (CMI), developed by the Brigham Young University Public School Partnership, captures the research and best practices of the CCSSM standards and the NCTM Principles to Actions and makes these ideas accessible to practicing and preservice mathematics teachers. By 
organizing these principles and practices into a Teaching Cycle, a Learning Cycle and a Continuum of Mathematical Understanding, teachers can attend to learning progressions, formative assessment and teaching practices that support construction of conceptual understanding and procedural fluency on a foundation of student thinking. Mathematics Vision Project (MVP) is an example of a curriculum created using the CMI Framework. In this session, participants will be introduced to the CMI framework and its implementation through classroom vignettes where student thinking is elicited by tasks from the MVP curriculum designed to promote conceptual, procedural and representational understanding.