Past Presentations

Abstract/Description: "Work on the teaching and learning of definite integrals has expanded significantly in recent years, with the specific conceptualization "adding up pieces" being a promising foundational meaning for integrals. Yet, work in this area has largely focused on student understanding and reasoning, with only small attention to the detailed work of how task-based learning over an entire unit of integration could support students in coming to develop these understandings. This poster presents an outline of a learning trajectory for a unit on integration based on adding up pieces and how students come to learn the individual parts that make up the larger integral concept.

Abstract/Description: Four groups of mathematics teacher educators share the ways they are exploring the creation, organization, and use of public records of student mathematical thinking--physical and visual representations of student mathematics that are publicly accessible to all participants within a classroom.

Abstract/Description: Student teaching has long been plagued by a lack of coherence and sustained institutional and research support. In this working group participants will identify challenges and share strategies to support efforts to improve secondary mathematics clinical practice.

Abstract/Description: Abstract: Studies have shown a correlation between religious ideologies and racist beliefs. Less is known about how people are bringing their religious ideologies to make sense of and participate in discussions about racism and other systems of oppression. In this paper, we analyze the discourse used a small set of White prospective and practicing mathematics teachers in response to a question about how their religious beliefs influenced their perspectives on race. This analysis reveals that current White discursive frameworks may not reveal important components of discourse used by Christians discussing race, racial differences, and racism. Therefore, we turn to Bakhtin’s theoretical perspective on language and discourse to make sense of the participant data. We explore the religious teachings of The Church of Jesus Christ of Latter-day Saints focusing on how the meaning of “we are all children of God” is developed through church curricula, the scriptures used by its members, and the teachings of the Church’s leadership. In other words, we unfold the possible dialogic relationships among contexts, speakers, and words associated with derivations of the phrase “we are all children of God” in The Church and its members. We use this unfolding to show how the ventriloquation of “we are all children of God” operated in contexts about racism to illuminate messiness in prospective and practicing teachers’ use of their religious ideologies in making sense of racism.

Abstract/Description: Students who are learning to work with equations in algebra need to understand the structural conventions for equations, i.e., the norms for writing, organizing, and interpreting equations in a problem solution. Little research has been done to identify the structural conventions for equations that are prominent in middle school mathematics. In this study, we examined two middle school curricula to identify the structural conventions used in the materials. We found two main structure—lists of equations and strings of equations—and identifiied conventions for reading and writing these structures.

Abstract/Description: Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing “conventions” that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting related, derived graphical objects (e.g., the graphs of a function and its inverse or the graphs of a function and its derivative) on the same set of axes. We show problems that arise from this convention in different mathematical content areas when considering contextualized functions and graphs. We discuss teaching implications about introducing such related graphical objects through context on separate axes, and eventually building the convention of placing them on the same axis in a way that this convention and its purposes become more transparent to students.

Abstract/Description: We describe a framework for characterizing students’ graphical reasoning, focusing on providing an empirically-based list of students’ graphical resources. The graphical forms framework builds on the knowledge-in-pieces perspective of cognitive structure to describe the intuitive ideas, called “graphical forms”, that are activated and used to interpret and construct graphs. As part of the framing for this work, we provide theoretical clarity for what constitutes a graphical form. Based on data involving pairs of students interpreting and constructing graphs we present a list of empirically documented graphical forms, and organize them according to similarity. We end with implications regarding graphical forms’ utility in understanding how students construct graphical meanings and how instructors can support students in graphical reasoning.

Abstract/Description: Productive use of student mathematical thinking is a critical yet incompletely understood dimension of effective teaching practice. We have previously conceptualized the teaching practice of building on student mathematical thinking and the four elements that comprise it. In this paper we begin to unpack this complex practice by looking closely at its first element, establish. Based on an analysis of secondary mathematics teachers’ enactments of building, we describe two critical aspects of establish—establish precision and establish an object—and the actions teachers take in association with these aspects.