Past Presentations

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.

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.

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.

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.