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1. Considering the Alignment Between Teachers' Conceptions of Justification and Their Visions for Equitable Instruction

   Bieda, Kristen; Staples, Megan; Coherty, Kristin; Anthonypillai, Serena; Matthews-Johnson, Alicia; Hwang, Jihye (October 2023, Psychology of Mathematics Education - North American Chapter)

   Lamberg, Teruni; Moss, Diana (Ed.)

   The process of proving, and more broadly conceived “reasoning and sense-making,” has received a great deal of attention in mathematics education research over the past three decades. Recently, scholars have argued for the importance of justification as a learning and teaching practice. As teachers work toward realizing goals for more equitable classroom environments, little is known about whether teachers’ conceptions about mathematical practices, such as justification, reflect an understanding of how students’ engagement in those practices can support more than just mathematical achievement. In this paper, we present findings from our analysis of interviews with 10 secondary mathematics teachers engaged in participatory action research to explore connections, and potential disconnections, between teachers’ conceptions of justification and their visions for equitable instruction. 

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2. Considering the alignment between teachers’ conceptions of justification and their visions for equitable instruction

   Bieda, Kristen; Staples, Megan; Doherty, Kristin; Anthonypillai, Serena; Matthews-Johnson, Alicia; Hwang, Jihye (October 2023, Proceedings of the forty-fifth annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, vol. 1)

   Lamberg, Teruni; Moss, Diana (Ed.)

   While proving, and more broadly conceived “reasoning and sense-making,” have received a great deal of attention in mathematics education research over the past three decades, recently scholars have argued for the importance of justification as a learning and teaching practice. As teachers work toward realizing goals for more equitable classroom environments, little is known about whether teachers’ conceptions about mathematical practices, such as justification, reflect an understanding of how students’ engagement in those practices can support more than just mathematical achievement. In this paper, we present findings from our analysis of interviews with 10 secondary mathematics teachers engaged in participatory action research to explore connections, and potential disconnections, between teachers’ conceptions of justification and their visions for equitable instruction. 

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3. CONSIDERING THE ALIGNMENT BETWEEN TEACHERS’ CONCEPTIONS OF JUSTIFICATION AND THEIR VISIONS FOR EQUITABLE INSTRUCTION

   Bieda, K; Staples, M; Doherty, K; Anthonypillai, S; Matthews-Johnson, A; Hwang, J (November 2023, Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lamberg, T; Moss, D (Ed.)

   While proving, and more broadly conceived “reasoning and sense-making,” have received a great deal of attention in mathematics education research over the past three decades, recently scholars have argued for the importance of justification as a learning and teaching practice. As teachers work toward realizing goals for more equitable classroom environments, little is known about whether teachers’ conceptions about mathematical practices, such as justification, reflect an understanding of how students’ engagement in those practices can support more than just mathematical achievement. In this paper, we present findings from our analysis of interviews with 10 secondary mathematics teachers engaged in participatory action research to explore connections, and potential disconnections, between teachers’ conceptions of justification and their visions for equitable instruction. 

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4. A Model of How Student Definitions of Substitution and Equivalence May Relate to Their Conceptualizations of Algebraic Transformation.

   Wladis, C.; Sencindiver, B.; Offenholley, K.; Jaffe, E.; & Taton, J. (January 2022, Proceedings for the 12th Congress of the European Society for Research in Mathematics Education (CERME12))

   Cho, Sung Je (Ed.)

   This empirical paper explores students’ conceptions of transformation as substitution equivalence by linking it to their definitions of substitution and equivalence. This work draws on Sfard’s (1995) framework to conceptualize conceptions of substitution equivalence and its components, equivalence and substitution, each on a spectrum from computational to structural. We provide examples of student work to illustrate how students’ understandings of substitution, equivalence, and substitution equivalence as an approach to justifying transformation may relate to one another. 

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5. Design Educators’ Conceptions of Prototyping in Engineering Design Courses

   Ali, Hadi; Lande, Micah (June 2019, ASEE Annual Conference proceedings)

   This is a research study that investigates the range of conceptions of prototyping in engineering design courses through exploring the conceptions and implementations from the instructors’ perspective. Prototyping is certainly an activity central to engineering design. The context of prototyping to support engineering education and practice has a range of implementations in an undergraduate engineering curriculum, from first-year engineering to capstone engineering design experiences. Understanding faculty conceptions’ of the reason, purpose, and place of prototyping can help illustrate how teaching and learning of the engineering design process is realistically implemented across a curriculum and how students are prepared for work practice. We seek to understand, and consequently improve, engineering design teaching and learning, through transformations of practice that are based on engineering education research. In this exploratory study, we interviewed three faculty members who teach engineering design in project-based learning courses across the curriculum of an undergraduate engineering program. This builds on related work done by the authors that previously investigated undergraduate engineering students’ conceptions of prototyping activities and process. With our instructor participants, a similar interview protocol was followed through semi-structured qualitative interviews. Data analysis has been undertaken through an emerging thematic analysis of these interview transcripts. Early findings characterize the focus on teaching the design process; the kind of feedback that the educators provide on students’ prototypes; students’ behavior while working on design projects; and educators’ perspectives on the design course. Understanding faculty conceptions with students’ conceptions of prototyping can shed light on the efficacy of using prototyping as an authentic experience in design teaching and learning. In project-based learning courses, particular issues of authenticity and assessment are under consideration, especially across the curriculum. More specifically, “proportions of problems” inform “problem solving” as one of the key characteristics in design thinking, teaching and learning. More attention to prototyping as part of the study of problem-solving processes can be useful to enhance understanding of the impact of instructional design. Challenges for teaching engineering design exist, and may be due to difficulties in framing design problems, recognizing what expertise students possess, and assessing their expertise to help them reach their goals, all at an appropriate place and ambiguity with student learning goals. Initial findings show that prototyping activities can help students become more reflective on their design. Scaffolded activities in prototyping can support self-regulated learning by students. The range of support and facilities, such as campus makerspaces, may also help students and instructors alike develop industry-ready engineering students. 

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