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1. Instructor-Student Interactions in Geometry Courses for Secondary Teachers: Results from A National Survey

   Herbst, P; Jeon, S; Ko, I (December 2024, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, S; Katz, B; Moore_Russo, D (Ed.)

   We report preliminary results of selected questions from a national survey of instructors of geometry courses for secondary teachers about the nature of instructor-student interactions. Survey responses (n= 118) are used to indicate six latent constructs describing aspects of instructor-student interaction that in turn quantify hypothesized characteristics of two didactical contracts, which we call inquiry in geometry and study of geometry. We found that instructors whose highest degree is in mathematics education are less likely to rely on a study of geometry contract than instructors whose highest degree is in mathematics. Also, instructors who have previously taught high school geometry are less likely to lecture. 

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2. Investigating problem-posing during math walks in informal learning spaces

   https://doi.org/10.3389/fpsyg.2023.1106676  

   Wang, Min; Walkington, Candace (March 2023, Frontiers in Psychology)

   Informal mathematics learning has been far less studied than informal science learning – but youth can experience and learn about mathematics in their homes and communities. “Math walks” where students learn about how mathematics appears in the world around them, and have the opportunity to create their own math walk stops in their communities, can be a particularly powerful approach to informal mathematics learning. This study implemented an explanatory sequential mixed-method research design to investigate the impact of problem-posing activities in the math walks program on high school students' mathematical outcomes. The program was implemented during the pandemic and was modified to an online program where students met with instructors via online meetings. The researchers analyzed students' problem-posing work, surveyed students' interest in mathematics before and after the program, and compared the complexity of self-generated problems in pre- and post-assessments and different learning activities in the program. The results of the study suggest that students posed more complex problems in free problem-posing activities than in semi-structured problem-posing. Students also posed more complex problems in the post-survey than in the pre-survey. Students' mathematical dispositions did not significantly change from the pre-survey to post-survey, but the qualitative analysis showed that they began thinking more deeply, asking questions, and connecting school content to real-world scenarios. This study provides evidence that the math walks program is an effective approach to informal mathematics learning. The program was successful in helping students develop problem-posing skills and connect mathematical concepts to the world around them. Overall, “math walks” provide a powerful opportunity for informal mathematics learning. 

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3. Sensemaking opportunities provided by college chemistry instructors

   https://doi.org/10.1039/D5RP00139K  

   Desi, Desi; Roehrig, Gillian; Schuchardt, Anita (January 2026, Chemistry Education Research and Practice)

   Studies have shown that students often struggle to solve quantitative science problems because they fail to make connections between mathematical equations and associated scientific phenomena. This struggle has been attributed to instructors providing limited sensemaking opportunities that connect science and mathematics sensemaking. Our prior research on college instructors teaching population growth shows that the types of sensemaking elicited varied and were organized in different ways. This case study extends the research by exploring sensemaking opportunities about mathematical equations provided by three instructors teaching Gibbs free energy. This study also examines different levels of connection between sensemaking types within and across the science and mathematics dimensions and analyzes factors (i.e., pedagogical approaches, equation types) that might shape the types of sensemaking that were provided. The Sci-Math Sensemaking Framework was used to identify sensemaking opportunities provided by three instructors during the lessons and a comparative case study approach was employed. Findings showed that while each instructor provided both science and mathematics sensemaking opportunities, they had distinct ways of sequencing their sensemaking even when teaching the same scientific phenomenon using mathematical equations. Mathematics sensemaking was mostly presented separately from science sensemaking, with only a few instances of connected sensemaking occurring in instructors’ lessons, albeit at varying levels. When instructors expose students to connected science and mathematics sensemaking, they model for students how to use resources from two different disciplines to understand scientific concepts or solve quantitative problems. We provide evidence to show that levels of connection between sensemaking types within science and mathematics dimensions reflect distinct approaches to developing more robust scientific explanations or to working with equations. Based on these case studies, we suggest that instructors’ equation choices and pedagogical approaches support specific types of sensemaking and levels of connection between sensemaking opportunities. 

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4. Mathematics Graduate Student Instructor Observation Protocol (GSIOP): Development and Validation Study

   https://doi.org/10.1007/s40753-019-00106-4  

   Rogers, Kimberly Cervello; Petrulis, Robert; Yee, Sean P.; Deshler, Jessica (December 2019, International Journal of Research in Undergraduate Mathematics Education)

   This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions particularly relevant for students’ development of conceptual understanding, called the Mathematical Classroom Observation Protocol for Practices (MCOP^2). Instrument validation involved content input from mathematics education researchers and upper-level mathematics graduate student instructors at two universities, internal consistency analysis, interrater reliability analysis, and structure analyses via scree plot analysis and exploratory factor analysis. A Cronbach-Alpha level of 0.868 illustrated a viable level for internal consistency. Crosstabulation and correlations illustrate high level of interrater reliability for all but one item, and high levels across all subsections. Collaborating a scree plot with the exploratory factor analysis illustrated three critical groupings aligning with the factors from the MCOP2 (student engagement and teacher facilitation) while adding a third factor, lesson design practices. Taken collectively, these results indicate that the GSIOP measures the degree to which instructors’ and students’ actions in undergraduate mathematics classrooms align with practices recommended by the Mathematical Association of America (MAA) using a three-factor structure of teacher facilitation, student engagement, and design practices. 

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5. STEM Excellence and Leadership Program: Increasing the Level of STEM Challenge and Engagement for High-Achieving Students in Economically Disadvantaged Rural Communities

   https://doi.org/10.1177/0162353217745158  

   Ihrig, Lori M.; Lane, Erin; Mahatmya, Duhita; Assouline, Susan G. (March 2018, Journal for the Education of the Gifted)

   High-achieving students in economically disadvantaged, rural schools lack access to advanced coursework necessary to pursue science, technology, engineering, and mathematics (STEM) educational and employment goals at the highest levels, contributing to the excellence gap. Out-of-school STEM programming offers one pathway to students’ talent development. Using a concurrent triangulation mixed-methods research design, this study was conducted to evaluate the experiences of 78 high-achieving students and their 32 teachers, participating in an extracurricular, school-based, STEM talent development program for rural students from economically disadvantaged communities. Findings suggest that students and teachers expressed satisfaction with program participation and that they thought more creatively and critically about their work. Results also showed that students’ perceptions of the mathematics and science activities were significantly different, which informs ways to improve programming for future high-achieving, rural students. These findings expand the literature supporting the use of informal STEM education environments for underserved gifted populations to increase engagement in and access to challenging curricula. 

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