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1. Instructional interventions and teacher moves to support student learning of logical principles in mathematical contexts

   Roh, K.H.; Dawkins, P.C.; Eckman, D.; Tucci, A.; Ruiz, S. (August 2023, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, S.; Katz, B.; Moore-Russo, D. (Ed.)

   This study explores how instructional interventions and teacher moves might support students’ learning of logic in mathematical contexts. We conducted an exploratory teaching experiment with a pair of undergraduate students to leverage set-based reasoning for proofs of conditional statements. The students initially displayed a lack of knowledge of contrapositive equivalence and converse independence in validating if a given proof-text proves a given theorem. However, they came to conceive of these logical principles as the teaching experiment progressed. We will discuss how our instructional interventions played a critical role in facilitating students’ joint reflection and modification of their reasoning about contrapositive equivalence and converse independence in reading proofs. 

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2. Inservice teachers’ attributions for mathematical success.

   Cross Francis, D.; Jessup, J.; Yavuz, S.; Franklin, J.; Pierce, S.; Gustaveson, A.; Jacobson, E. (October 2023, Proceedings of the 45nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Beliefs teachers hold influence the judgments they make about their students, and opportunities they provide for engaging them in rigorous mathematics. While math-related beliefs have been widely studied, less is known about teachers’ attributional beliefs (i.e., beliefs about people’s actions or behaviors) for mathematical success. In this study we investigated in-service elementary teachers’ stated beliefs about mathematical success. Findings show that teachers attribute mathematical success to factors that are both internal and external to the student. Although teachers explicitly stated that race and gender were not factors, many used descriptors that served as proxies for students’ demographic markers. 

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3. Poetry writing to enhance conceptual understanding of mathematical models and approaches for inventory management

   Akcali, Elif; Belay, Saron G.; Williams, Jade. (June 2023, 2023 ASEE Annual Conference & Exposition)

   To enhance conceptual understanding of mathematical models for inventory management, we developed poetry-writing assignments for a required, upper-level undergraduate course in an industrial and systems engineering program. Specifically, two poetry-writing assignments were incorporated into an inventory and supply chain system design and control course. The first assignment, due one week before the first term exam, asked students to write a poem about a concept, model or topic related to deterministic inventory modeling. The second and assignment, due one week before the second term exam, asked the students to write a poem about a concept, model or topic related to stochastic inventory modeling. The students were also asked to respond to several open-ended questions on their approach to writing the poems and their assessment of the impact of these poetry writing on improving their conceptual understanding of the underlying mathematical models. Data was collected in Spring 2022 semester. The student written-poetry will be analyzed for correctness and to identify misunderstandings or gaps in understanding. In this paper, we will present our findings from the content analysis of student-written poetry and our preliminary findings on the effectiveness of poetry-writing assignments to enhance conceptual understanding of mathematical models for inventory management. 

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4. Factors that influence student mathematical dispositions

   Riling, M.; Dietiker, L.; Gibson, K.; Tukhtakhunov, I.; Ren, C. (January 2018, Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Why do secondary students in the US consistently and increasingly report a lack of interest in mathematics? Lack of interest in mathematics has been well documented in TIMSS responses; students dissatisfaction with mathematics more than doubled by 2011, when 40% of 8th graders reported not liking math, up from 18% as 4th graders in 2007. And, sadly, the trend appears to be worsening; in 2015, 47% of 8th graders indicated not liking math, up from 22% as 4th graders. In order to positively impact student attitudes towards mathematics, it is important to understand factors that may influence secondary students’ relationship with the discipline. This poster presents findings from an exploratory study of student disposition toward mathematics. We designed an online survey to learn about students’ relationship with mathematics, including experiences and settings that contribute to both positive and negative feelings about the subject. We surveyed 275 students, grades 9 to 12, in 11 classes in three schools in three New England districts. Though not randomly chosen, this sample allows us to examine student attitudes across a variety of contexts. We asked students about their feelings towards mathematics over the years, as well as which aspects of class they most enjoyed or disliked. Finally, we included items from the TRIPOD survey (Wallace et al., 2016) and the 2015 NAEP survey, which allows us to compare our sample with the national sample. Initial results indicate that student view their teachers and the topics of study as the central factors influencing their enjoyment of mathematics class. We found a correlation between responses that math is boring and that it is not relevant. Students who like math and those who do not reported different class activity preferences. For example, students who like math reported disliking watching a video in class, while students who dislike math reported disliking learning something new. Both groups of students (those who like math and those who do not) dislike math class when they have to present work to classmates, but hold positive views of solving puzzles and working with other students. Technology seems to appeal equally to both groups. Students who reported disliking math also look forward to playing competitive games. We saw no evidence that gender or race corresponded to students’ level of appreciation math. Finally, students reported liking math class less in high school than in middle school. Identifying factors that influence secondary student mathematical dispositions can inform curriculum designers seeking to improve mathematical attitudes. Future studies can learn if new curricular designs can change student relationships with mathematics to reverse recent trends. 

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5. Work in Progress: Promoting the Transfer of Math Skills to Engineering Statics

   https://doi.org/10.18260/1-2--44334  

   De_Rosa, Alexander; Reed, Teri; Arndt, Angela (June 2023, ASEE Conferences)

   Students often face difficulties in transferring concepts, knowledge and skills between their courses. This difficulty is especially true of the fundamental math and science courses that are often taught outside the major of the student and without engineering context. At the same time, graduating engineers are moving into an increasingly interdisciplinary workplace that values the ability to work broadly across a range of contexts. More work is needed to better prepare students to adapt their knowledge and skills to new situations and to demonstrate how the various courses and concepts within their curricula relate. In this study, we ask students, teaching assistants and faculty to “think aloud” through their solution to a statics problem that requires mathematical knowledge to be transferred in order to be solved. Two faculty, two teaching assistants and seven undergraduate students are interviewed as they think aloud through the problem. Interview transcripts and solutions to the statics problem are then examined for themes and patterns in responses in order to draw conclusions about the challenges different populations face in transferring knowledge and solving such problems. Observations indicated that students could apply simple integration skills to find the area of a shape when given a curve describing its shape, but could not use integration to find the centroid. The participants did however recall being taught how to calculate centroids in the past and discussed a lack of usage of this skill causing their inability to recall it correctly. Student participants in general displayed simple approaches to problem solving based on reading the problem statement rather than following an engineering approach starting with governing equations. A potential barrier to problem solving success was identified in the varying symbols used by different research participants which could lead to a lack of understanding if these symbols are not clearly explained and defined in a classroom setting. Future work will further examine these themes, as well as developing prompts and activities to promote knowledge transfer and problem solving success. 

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