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When mathematics educators work towards making mathematics more relevant, they often think about including more real-world applications into mathematics lessons. But what happens when a lesson is devoid of real-world contexts? In what ways can students find it relevant? This study explores how high school students perceived relevance when they were asked to describe their experiences during decontextualized mathematics lessons. Students highlighted how they found certain characteristics of the lessons to be useful in their learning and how they perceived relevance through different feelings experienced in the lessons. This, in turn, broadens our understanding of what relevance means to students. [For the complete proceedings, see ED630210.]

This paper explores how a professional learning community (PLC) redesigns high school mathematics lessons towards a shared commitment. We describe the nature of a PLC's collective curricular vision to illuminate how teachers can come to new understandings as a group in order to shift the ways students experience mathematics. Using the curricular noticing framework (attending, interpreting, and responding), we analyzed the meetings of a PLC with six teachers as they individually presented lessons to be redesigned with a focus on the group's shared commitment. Findings indicate three ways ideas were introduced that led to expansive responses, which suggests this analytic approach could identify ways in which a PLC can work towards new curricular decisions. [For the complete proceedings, see ED630210.]

By highlighting the curriculum modifications that lead to maintaining, or enhancing, the mathematical quality of an algebra lesson introducing the substitution method for solving systems of equations from an algebra textbook, we present an analysis of how a teacher and her students impact how the mathematical ideas unfold across the lesson and how they are experienced. Using a narrative-based analytical approach to write the stories of the written and enacted lessons, we found key similarities and differences in the lessons. In comparing the mathematical plots, we found evidence of how the teacher and students alter the unfolding story with the incorporation of more jamming than seen in the text and more questions developed based on the students' needs and their responses. [For the complete proceedings, see ED630210.]

How can we design mathematical lessons that spark student interest? To answer this, we analyzed teacher-designed and enacted lessons that students described as interesting for how the content unfolded. When compared to those the same students describe as uninteresting, multiple distinguishing characteristics are evident, such as the presence of misdirection, mathematical questions that remain unanswered for extended time, and a greater number of questions that are unanswered at each point of the lesson. Low-interest lessons did not contain many special narrative features and mostly had questions that were answered immediately. Our findings offer guidance for the design of lessons that can shift student mathematical dispositions. [For the complete proceedings, see ED629884.]

Students studying geometry at the secondary level are expected to read diagrams in different ways than those in elementary school. In this paper, we present an analysis of the changes in diagrammatic expectations by comparing the geometric diagrams found in Grade 1 U.S. textbooks with those in U.S. high school geometry textbooks. This work included developing and using a coding scheme that recognizes dimensions of reading a diagram geometrically, including the type of object represented, use of deduction, use of mental redrawing, interpretation of markings, and the necessity of the diagram. The way in which elementary and secondary students are expected to interpret diagrams was shown to change along several of these dimensions, posing potential learning barriers for students. We end our paper with a discussion of what our results mean for the learning of geometry. [For complete proceedings, see ED581294.]

Efforts to enhance the aesthetic impact of mathematics lessons must account for the role of teachers in shaping the unfolding mathematical content of their enacted lessons. In this paper, we draw from Dietiker (2015) to describe differences in the mathematical stories of the enacted lessons of two veteran teachers teaching the same lesson. We identify connections between these differences and the variations in student experiences as illustrated by visible student reactions. [For the complete proceedings, see ED583608.]

This paper explores the construct of curricular noticing, defined as the act of teachers making sense of the complexity of content and pedagogical opportunities in written or digital curricular materials (Dietiker, Amador, Earnest, Males, & Stohlmann, 2014), and reports the results of four exploratory studies aimed to examine the Curricular Noticing framework. Taken together, these studies capture work done with 62 PSTs in elementary and secondary mathematics methods courses at four universities. Findings illuminate what PSTs attend to in curriculum materials and how they interpret and respond to these materials. Irrespective of level (i.e., elementary, secondary) and materials, PSTs can learn to notice aspects of curriculum materials in order to make decisions about what to do and how to do it, and activities within methods courses can facilitate this development. [For the complete proceedings, see ED583989.]

Students' aesthetic and affective responses are interrelated and both central to mathematics learning. This working group will continue the conversation begun in 2022 to explore the connection between the affective and aesthetic dimensions of mathematics education, and how connecting these dimensions can help to understand how students experience mathematics. The goals of this working group are to evaluate the state of the field, build shared terms, and identify research questions for further inquiry. [ABSTRACT FROM AUTHOR]

The positive relationship between students' attitudes toward mathematics and mathematics achievement is well documented. Yet there is a worsening problem of low appeal of mathematics especially at the secondary level. Therefore, in this paper we focus on three high school students who report a strong dislike of mathematics. By analyzing student surveys, interviews, and lesson observation data, we examined how some mathematical lessons improved these students' experiences (i.e., their aesthetic dimensions). We found that while student preferences varied, each student was interested in lessons that centered them as sense-makers and in which the content unfolded with suspense. Such lessons led to positive aesthetic responses such as surprise, curiosity, and satisfaction. Thus, lessons can be designed in which even students with the most negative views of mathematics can find mathematical concepts interesting. [ABSTRACT FROM AUTHOR]

In recent years, mathematics lessons addressing social justice have been increasingly published and taught, but little is known about how mathematical and social content unfolds within them. In this study, we interpret five secondary social justice mathematics lessons (SJMLs) as stories and analyze the questions that arise within them. We found that most of these lessons began and ended with a focus on social matters, while shorter mathematical questions arose in the middle of the lessons. However, the lessons varied in terms of what proportion of the questions overall were focused on social or mathematical thinking. Finally, we found that narrative devices were used in several lessons when the focus transitioned from social issues to mathematics, or vice versa. This way of thinking about lessons could enable the design of SJMLs that meaningfully integrate social and mathematical thinking. [ABSTRACT FROM AUTHOR]

How does the design of lessons impact the types of questions teachers and students ask during enacted high school mathematics lessons? In this study, we present data suggesting that lessons designed with the mathematical story framework in order to elicit a specific aesthetic response ("MCLEs") have a positive influence on the types of teacher and student questions asked during the lesson. Our findings suggest that when teachers plan and enact lessons with the mathematical story framework, teachers and students are more likely to ask questions that explore mathematical relationships and focus on meaning-making. In addition, teachers are less likely to ask short recall or procedural questions in MCLEs. These findings point to the role of lesson design in the quality of questions asked by teachers and students. [ABSTRACT FROM AUTHOR]

In this study, we explore the relationships between the types of student exclamations in an enacted lesson (e.g., “Wow!”) and the varying dramatic tensions created by the unfolding content. By analyzing student exclamations in six specially-designed high school mathematics lessons, we explore how the dynamic tension between revelations of mathematical ideas at the moment and what is yet to be known connects with the aesthetic pull to react by the student. As students work through novel problems with limited information, their joys and frustrations are expressed in the form of exclamations. [ABSTRACT FROM AUTHOR]

Students' aesthetic and affective responses are interrelated and both central to mathematics learning. This new working group will bring together researchers as a community to explore the connection between affect and aesthetic, and how this connection can help to understand how students experience mathematics. The goals of this working group are to evaluate the state of the field, build shared terms, and identify research questions for further inquiry. [ABSTRACT FROM AUTHOR]

Curricular coherence has been emphasized by leaders in mathematics education as it enhances deeper understanding by enabling students to see connections between mathematical ideas. Although there are different forms of curricular coherence, the coherence of lesson has received considerably less attention. Little is known about what constitutes coherent lessons or how to measure the degree of coherence. Using the data from a larger study in which lessons are intentionally designed for coherence, we propose a tool for examining lesson coherence and describe characteristics of the lessons with different levels of coherence. [ABSTRACT FROM AUTHOR]

Secondary students do not often have positive experiences with mathematics. To address this challenge, this paper shares findings of a design-based research project in which a mathematical story framework was used to design mathematically captivating lesson experiences (“MCLEs”). We provide evidence that designing lessons as mathematical stories shows promise. That is, students reported improved experiences in MCLEs when compared to randomly-selected lessons. The MCLEs also impacted the students’ descriptions of their experience. [ABSTRACT FROM AUTHOR]