Presentations

Has it been a challenge to implement class discussions into your lessons? When you send students to work at vertical whiteboards, is it more of a disaster than a delight? Are small group activities in your classroom a stressful struggle or a teacher triumph? If you are struggling to implement some of these pedagogical moves into your teaching, establishing effective norms with your students may be helpful. Small group activities, class discussions, and working at whiteboards can be successful learning tools when we have established classroom norms that support our pedagogical goals. Join us as we share new research about how to establish norms in a mathematics classroom. Learn how to introduce norms, refine them, and reinforce them throughout the school year.

While students often begin school with a single, operational meaning for the equal sign, they need to develop an additional three meanings to be successful in creating and using equations in school mathematics. In this presentation, we provide a model for expert understanding of the equal sign and describe how to help students in each of the grade bands PK-2, 3-5, 6-8, and 9-12 move along the path to expert understanding. We illustrate this progression with tasks in each grade band that you can use to help your students improve their understanding of the equal sign.

Abstract/Description: Past research on students' understanding of the equal sign has focused largely on two meanings: operational and relational. In this poster, we introduce two additional meanings for the equal sign and describe the findings of a textual analysis of four middle school curricula that shows all four meanings are used in secondary mathematics. Based on our findings, we conclude that growth in expert use of the equal sign is characterized by the adoption of additional meanings and a gradual increase in one's ability to use the contexts in which equations are embedded to determine which meanings of the equal sign are being used. We present a model of an expert conception of the equal sign that consists of three fundamental understandings regarding the meanings for and uses of the equal sign.

New mentor teachers need to develop new knowledge, skills, and understandings as they transition from teaching mathematics to supporting student teachers in learning-to-teach activities. In a series of collaborative experiences, new mentor teachers learn how to extend practices of teaching mathematics to create learning-to-teach activities. Mentor teachers formed support networks by participating in these collaborative experiences.

For PSMTs, learning to notice elements of mathematics lessons involves shifting perspectives from a student-learner to a teacher of mathematics who can navigate the complexities of teaching. PSMT-led debriefings after peer teaching is one activity that teacher educators can implement for PSMTs to learn how to shift lenses.

Have you ever had students ask, "Wait, what are we talking about?" during a whole-class mathematics discussion? The quantity of ideas that surface in the midst of a discussion where students are engaged in mathematical sense making may create difficulties for some students to track the discussion. We will discuss strategies to ensure that students always have a clear understanding of what object they are to focus on and how they are to engage with that object as a sense-making discussion evolves.

During a class discussion about a student contribution, have you had another student share a mathematical idea not related to the topic under discussion? What do you do when this happens? How can you avoid this? In this talk, we share strategies for keeping the class focused on the student contribution under discussion.

Come learn how to take better advantage of public records (the physical representations of ideas we capture on the board) to help scaffold joint sense making of mathematics in the classroom. Learn how to efficiently capture students' ideas, organize them in meaningful ways, and purposefully reference the public record you create.

Some go-to teacher practices work well in certain situations but can actually be counterproductive in others. Learn about three such practices: collecting information from the class, asking a student to clarify their contribution, and asking students to revoice their peer's contribution, including examples of both productive and counterproductive uses of each practice. Leave with ideas for how to leverage these practices and others to nurture opportunities for students to shine.

Teaching Practice and Classroom Activity In this exploratory study, we analyzed one mathematics teacher’s annotations of a transcript of their teaching. The teacher was prompted to annotate the transcript for actions that contributed to or hindered their enactment of a complex teaching practice. We analyzed these noticings to explore what we could learn about the teacher’s understanding of the practice, and then what these understandings revealed about our own conceptualization and communication of the practice. Our approach to analyzing teacher noticing illustrates how the study of noticing can contribute to advancing researchers’ understanding not just of teachers’ noticing but also of the phenomena they are noticing.

Navigating and Negotiating Identity: "Children of God" in Latter-day Saint Scriptural and Prophetic Discourse Creating and shaping culture, religious or otherwise, happens through language. Seemingly small discursive utterances impact how people view themselves others, particularly when repeated over time. This paper addresses how the concept of being a “child of God” has been conceptualized and used rhetorically in Latter-day Saint scriptural and prophetic discourse to both fortify and dismantle boundaries between groups and individuals. Our paper builds on work by Kate Johnson, Emma Holdaway, and Amy Saunders Ross which highlighted how “children of God” was used both within Latter-day Saint discourse and discourse about race. It also builds upon Daniel Becerra’s work on theological anthropology (i.e. human nature as it relates to God) in Latter-day Saint scripture. Our examination is at once historical and literary. It is historical in the sense that it traces the evolution of thought regarding this concept from its first appearance in the book of Genesis, throughout the LDS scriptural canon, and to its most recent public use at the October 2023 General Conference of The Church of Jesus Christ of Latter-day Saints. Our examination is literary in that we also examine the rhetorical deployments to understand the culture shaping work it is intended to accomplish. For example, uses of “children of God” might focus attention to people’s divine worth, to the creation of their physical bodies, or to their moral character. We note in particular how the phrase has been used to navigate and negotiate identity among humans based on race, ethnicity, gender, sexual orientation, and faith commitments. We conclude by describing some implications for scholarly and theological discourse that contributes to the work of reconciliation and inclusion.

Important work has created approaches to calculus based on crucial quantitative reasoning. For integration, however, the major topic of u-substitution has generally not been fully detailed in these paradigms. This paper presents a study where students were taught u-substitution from a quantitative perspective based on a three-part quantitative structure: differential quantity, integrand quantity, bounds quantity. The students reasoned about the quantitative conversions in flexible ways, and used various quantitative relationship types in their reasoning. However, reasoning about the differential quantity was difficult, and a new type of “collapse” metaphor was identified. By the end, the students had all developed a good quantitative basis for u-sub.

Research has shown how crucial quantities-based meanings are for calculus concepts. While past work has developed important quantitative approaches to integration, the major topic of u-substitution typically has not been fully detailed in these paradigms. This theoretical paper extends this past work to clearly define and elaborate u-substitution through a quantitative perspective. We use conceptual analysis based on quantities, starting with a concrete example of a solar panel producing energy. We abstract from this example to define u-substitution as a transformation from one quantitative relationship, via nested multivariation, to another quantitative relationship. We also detail a three-part structure within this transformation.

As teachers make curricular decisions they must often choose between different instructional options each with their own advantages and disadvantages. Such choices may cause tension as teachers consider how such options will align with instructional goals as well as outside factors.

The Curricular Reasoning Model explains how teachers reason about the role of the four classroom elements: mathematics, curriculum, teacher, and students. Data collected from secondary mathematics student teachers gives insight into how the Curricular Reasoning Model and accompanying self -assessment survey assist them in making intentional decisions during planning. Novice and pre-service teachers benefit from reflecting on which curricular reasoning aspects they engage with and which ones they overlook during planning. The Curricular Reasoning Model also provides teachers with an organizing structure to prioritize their decisions during planning.

Abstract/Description: Noticing activities are abundant in teacher education. We will discuss an implicit methodology used by many that may mask key details about teachers' professional noticing skills. We will engage in two activities to demonstrate the importance of interrelating noticing skills.

Abstract/Description: We will discuss findings from employing a methodology to study student teachers interrelated professional noticing skills, differences in findings when studying professional noticing as individual skills, and share implications for developing preservice mathematics teacher educators professional noticing.

Abstract/Description: Mathematics teachers rely heavily on their curricular reasoning (CR) when making decisions regarding curriculum. In this session, we highlight the Instructional Pyramid model for CR and discuss approaches teacher educators can use to enhance teachers' CR.