International Journal of Research in Undergraduate Mathematics Education最新文献

Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is essential to consider instructional resources’ use and perceived potential to contribute to students’ understanding. This case study considers how four instructors selected and used digital and physical resources in multivariable calculus and their motivations for doing so. We use the teaching triad of sensitivity to students, mathematical challenge, and management of learning to consider the reasons for resource adoption, studying how these instructors think about the resources they use. We also consider how instructors, students, and resources are reported to interact in multivariable calculus. Findings suggest that the instructors’ concern for students’ learning and their conviction that visualization is crucial in multivariable calculus moved them to explore and adopt different resources, especially ones that were free and easy to use. However, visualization was not the only spatial literacy aspect considered. As the instructors gained more experience with the instructional resources they were using, they reported adopting more student-centered use of these resources that allowed them to do more than facilitate visualization during a lecture. The resources began serving as referents for students as they communicated and reasoned about tasks with the instructor as well as among themselves.

This study describes the effects of a small pedagogical intervention in first semester calculus at an engineering college; it is a collaboration between two lecturers: a pure mathematician and a mathematics education researcher, who wished to learn about the effects of self-work (i.e., students solving problems on their own during class) on students' exam achievements, self-efficacy, and students' written communication. Students were given mastery experiences of self-work and feedback in three out of five classes. In all five classes, students were given in-class quizzes with peer instruction. Data was collected in multiple forms: quiz results, questionnaires, exam questions, and reflections; both quantitative and qualitative analysis methods were used. The findings show self-work increases students’ engagement and self-efficacy and slightly improved students’ achievement in class and on the final exam grade. Moreover, it positively influences students' learning experience. There were nonconclusive findings for improvement in the quality of students' written communication in the final exam. Self-work can be easily incorporated, even in coordinated courses with a common syllabus and a large lecture, without requiring instructors to make big changes to their lecture style. Effects of self-work should be further studied.

The COVID-19 pandemic shifted higher education online, drawing attention to synchronous learning and instruction on digital communication platforms. Learner-centered teaching practices in the tertiary level, such as mathematical discussions, have been shown to benefit student learning. The interactions involved in online synchronous mathematical discussions have been studied less. Most research taps into these aspects drawing on students’ academic outcomes and reflective interviews. This study explores instructional practices as they unfold online, with a focus on student-instructor and student-student interactions. We zoom-in to online synchronous teaching and learning processes on a popular communication platform by analyzing Linear Algebra tutorials in the first pandemic year. Using the commognitive framework, we characterize instructional interactions with the construct of a learning-teaching agreement. The analysis resulted in three interactional patterns, where in all cases, the tutorial transformed at some point to the one dominated by the instructor.

This work investigates how students interpret various eigenequations in different contexts for (2 times 2) matrices: (Avec {x}=lambda vec {x}) in mathematics and either (hat{S}_x| + rangle _x=frac{hbar }{2}| + rangle _x) or (hat{S}_z| + rangle =frac{hbar }{2}| + rangle) in quantum mechanics. Data were collected from two sources in a senior-level quantum mechanics course; one is video, transcript and written work of individual, semi-structured interviews; the second is written work from the same course three years later. We found two principal ways in which students reasoned about the equal sign within the mathematics eigenequation and at times within the quantum mechanical eigenequations: with a functional interpretation and/or a relational interpretation. Second, we found three distinct ways in which students explained how they made sense of the physical meaning conveyed by the quantum mechanical eigenequations: via a measurement interpretation, potential measurement interpretation, or correspondence interpretation of the equation. Finally, we present two themes that emerged in the ways that students compared the different eigenequations: attention to form and attention to conceptual (in)compatibility. These findings are discussed in relation to relevant literature, and their instructional implications are also explored.

As interest in the implementation of active learning practices grows, so too does the body of literature illustrating negative experiences of these practices among some populations of students. These trends necessitate a critical inquiry into how students with identities that are traditionally marginalized in mathematical spaces differentially experience active learning practices. We leverage critical quantitative theories to analyze how shifts in precalculus and calculus students’ math affect are mediated by intersectional race-gender identities and the active learning instructional practices of math engagement, peer collaboration, instructor inquiry, and participation. Drawing on a dataset of over 30,000 U.S. student survey responses, we found that experiencing high levels of all four practices increased math affect for all student identity groups in our dataset. Considering each individual practice revealed variation of students’ affective changes based on race-gender identities, such that not every individual practice benefited every student identity group. These findings emphasize the value in promoting the collective high use of multiple active learning practices, coupled with more in-depth understandings and attention to how these individual practices can differentially impact students.

Given the important role graduate teaching assistants (TAs) play in undergraduate students’ learning, we investigated what TAs identified as students’ difficulties from students’ written work, their plans to address them, and implementation of their plans in class. Since the difficulties that TAs identified in general matched errors that students made, we analyzed what TAs identified in terms of literature on error handling. We examined levels of specific details of students’ work involved in TAs’ identifying, planning, and teaching. Our results show that (a) TAs often did not identify the most frequent errors students made, which reflected well-documented difficulties from the literature, (b) the errors TAs identified were mainly procedural in nature, (c) specific details of students’ work were mainly included in procedural errors, and (d) the level of specificity of students’ work was generally consistent but showed some drops when going from identifying to planning, then to teaching. Our results highlight interesting questions for future research and could be used as resources to design professional development that helps TAs use students’ errors in teaching to promote students’ learning.

Our study investigated the impact of active learning on student learning in a large, first-year, multi-section Calculus for Life sciences course(s). Two cohorts of students in control (traditional lectures) and experimental (active learning) conditions were compared based on achievement on identical test items, administered in a supervised in-person environment. We additionally held focus groups to ascertain student perspectives on active learning. Findings suggest that in both sets of cohorts, students in experimental conditions performed better, on average. Further, students felt that learning this way supported the development of transferable skills, such as work habits, self-directed learning and metacognition. We contend that with the combination of these results, in addition to our context and design, this study offers new evidence and insights into the impact of active learning in tertiary mathematics. We argue that, when implemented properly, active learning methods can improve student performance, even in large-enrollment and multi-section mathematics classes.

Mathematics education research is increasingly focused on how students’ movement interacts with their cognition. Although usually characterized as embodiment research, movement research often theorizes the body in diverse ways. Ingold (Making: Anthropology, archaeology, art and architecture, 2013) proposes that thinking and knowing emerge from the entwined, dynamic flows of human and non-human materials in a process called making and, following Sheets-Johnstone (The primacy of movement (Vol. 82), 2011), contends that humans think in movement. The study that this paper draws on employs Ingold’s making to study students’ movement during mathematical problem solving. In this paper I also recruit Laban’s movement elements (Laban & Ullmann, 1966/2011) as a framework to describe and analyse how the body moves in space and time and to incorporate the often-forgotten dynamic qualities of movement. This paper investigates the movement of a small group of tertiary students as they engage with a mathematical prompt (a task in Abstract Algebra), using thick description, to answer the questions: (1) How do students think mathematically in movement? (2) How do Laban’s elements help inform research into students’ movement? Through the lens of Laban’s movement elements, my analysis demonstrates that students think mathematically in movement. These findings suggest that mathematics educators may be overlooking valuable instances of students’ mathematical thinking and knowing: the thinking and knowing in movement which may not be available through verbalizations or artefacts. Although thinking in movement does not fit a traditional conceptualization of undergraduate mathematics, which privileges written communication heavily reliant on notation, to understand students’ mathematical cognition more comprehensively, mathematics educators need to reconsider and appreciate students’ mathematical thinking in movement.