International Journal of Research in Undergraduate Mathematics Education最新文献

In the digital age, the range of digital technologies used in mathematics education grows. Since beliefs are affective-cognitive elements that significantly determine teachers' behavior in the classroom, they are an interesting field of research in mathematics education. A review of previous research has identified different groups of beliefs about the use of digital technologies in mathematics classes. These studies are not focused on specific digital technologies. In an empirical case study that is presented in this paper, the aim was to figure out how beliefs that can be described specifically about the use of visual programming relate to general beliefs about the use of digital technologies in mathematics education. A qualitative content analysis of the reflection journals of seven undergraduate mathematics education students on their work with Scratch, a visual programming environment, in a university seminar led to the formation of ten belief categories about the use of visual programming in mathematics classes. Most of the beliefs are associated with a positive attitude towards visual programming in mathematics education. However, some beliefs could also be identified that refer to the limits and challenges of using visual programming and thus demonstrate rather negative associations. Only a few of the categories identified match the list of belief groups about digital technologies in mathematics education identified in previous research. Some possible reasons for these results are discussed and further research interests in the field of beliefs about the use of digital technologies are suggested.

We focus on the integration of STACK—a Computer-Aided Assessment (CAA) technology—in the mathematics department of a high-ranking University in the United Kingdom. We study a department-wide project where instructors were expected to implement STACK into continuous assessment tasks for (nearly) all core modules across the first two years of undergraduate study. We present this work as a departmental case study, drawing on semi-structured interviews with six novice STACK assessment designers (and module leaders), supplemented by students’ responses to an open-response feedback questionnaire, and the reflections of a co-project lead (also first author). Our thematic analysis identified four themes related to the design of STACK-based assessments by novice to STACK tutors: the process of ‘STACKification’, technical challenges, users’ perspectives on the role of CAA, and finally, variations in assessment designers’ approaches to the role of feedback. In presenting our results, we are guided by Sangwin’s (2013) design principles for mathematics assessment. We consider various technical aspects of implementing STACK-based assessments as a first-time user, and the knowledge required to do so effectively and coherently. We conclude with a series of reflections on the role of CAA in undergraduate mathematics, and the ways in which such technology can be productively integrated with established practice.

In this article we analyze how students reason about linear combinations across multiple digital environments. We present the work of three groups of undergraduate students in the Southeast United States (US) who were considered ready to take linear algebra. The students played the game Vector Unknown, reflected upon aspects of their gameplay using GeoGebra, and used that knowledge to design a level for a 3D version of the game under some constraints. We performed a grounded qualitative analysis of each student’s activity to identify key episodes of student reasoning about linear combinations using technology. Both authors reviewed the episodes and categorized them according to the type of student activity. We compared their reasoning in 2D and 3D space to understand how they made the transition and finally linked these episodes to the technology used to understand its role in building student understanding. We identify four forms of structuring space: Reasoning with Numeric Sums, Reasoning with Resultant Vectors, Reasoning with Tip-to-Tail Vectors, and Reasoning with Vectors as Points. We found that how the technology represented vectors and linear combinations influenced how students engaged in structuring space.

In recent decades, there has been rapid development in digital technologies for automated assessment. Through enhanced possibilities in terms of algorithms, grading codes, adaptivity, and feedback, they are suitable for formative assessment. There is a need to develop computer-aided assessment (CAA) tasks that target higher-order mathematical skills to ensure a balanced assessment approach beyond basic procedural skills. To address this issue, research suggests the approach of asking students to generate examples. This study focuses on an example-generation task on polynomial function understanding, proposed to 205 first-year engineering students in Sweden and 111 first-year biotechnology students in Italy. Students were encouraged to collaborate in small groups, but individual elements within the tasks required each group member to provide individual answers. Students' responses kept in the CAA system were qualitatively analyzed to understand the effectiveness of the task in extending the students’ example space in diverse educational contexts. The findings indicate a difference in students’ example spaces when performing the task between the two educational contexts. The results suggest key strengths and possible improvements to the task design.

This study investigates the impact of computational labs on students’ conceptual understanding of calculus in a one-semester Business Calculus course. The computational labs integrated Jupyter Notebook as the modeling tool. Using the Calculus Concept Inventory, quantitative analysis was performed to measure differences in conceptual knowledge between a control and experimental group based on whether the student engaged in computational labs compared to traditional classwork. Qualitative analysis was conducted to understand student perspectives about the value of participating in computational labs during the course. The qualitative data involved student reflections at the end of each lab experience. Although the quantitative analysis did not produce statistically significant results, the qualitative analysis revealed the students perceived the computational labs as beneficial regarding their understanding of the content and practical applications of the material. Notably, the students reported the labs offered a unique way to solve problems, allowed for connections to real-life mathematical situations, and helped to visualize calculus concepts. This paper describes the research project and offers practical applications of computational labs in Business Calculus courses, as well as suggestions for future research.

This paper aims at defining and exploring design principles in a distance technological setting for an educational activity for mathematics undergraduate students, devoted to the construction of basic concepts in general topology, the promotion of problem-solving processes, the development of metacognitive aspects, and, in general, the development of the students’ mathematical identity. The design exploits the production of examples and investigation of variations and invariants, exploration of problems and generation of conjectures, and an extension intertwining of the ‘inside-out’ model from the Digital Interactive Storytelling in Mathematics with the Thinking Classroom model at university education. We present a didactic activity based on the identified design principles and discuss the preliminary results of a pilot carried out with fifty mathematics undergraduate students, attending their second year of the mathematics degree.

This paper reports on the development and validation process of a new measure—the College Mathematics Beliefs and Belonging (CMBB) survey. The CMBB provides a contemporary measurement of undergraduate students’ perceptions of their mathematical practices and reasoning, beliefs about mathematics, and sense of belonging in mathematics. Primarily first- and second-year undergraduate students in five mathematics courses at a large public university in the United States completed multiple surveys to provide the data used for survey development. Confirmatory factor analysis (N = 935) along with additional psychometric evidence detailed here indicate that the CMBB is a survey with fifteen factors that adequately measure various aspects of perceived mathematical practices and reasoning, beliefs, and sense of belonging. The CMBB survey is intended for use by researchers and instructors to assess undergraduate students’ perceptions across these three domains with the aim of improving students’ experiences in college mathematics courses.

The symbol (dx) is one example of a differential, a calculus symbol that is found in multiple settings and expressions. Literature suggests that students have both many and varied conceptualizations of these differentials. For example, is (dx) a very small quantity? How small does it have to be? Is it merely notation? For our study, we interviewed ten mathematicians to determine how experts conceptualize differentials presented in multiple mathematical contexts, such as differentiation, integration, and differential equations. Using thematic analysis, we analyzed their responses and found that our interview subjects’ conceptualizations were likewise many and varied, with many different interpretations offered for the same differentials. In this paper, we present results from our study and the initial classification system that emerged from this data, while understanding that ongoing and future research may expand and deepen our initial classification system.

In this study, we investigate students’ understanding of the relation between a double integral of a continuous function over a rectangle and the corresponding Riemann sums. To do so, we explore the relation between (1) a proposed model (genetic decomposition) of mental constructions that students may do to understand the relation between Riemann sums and double integrals, (2) tasks designed to help students make these constructions, and (3) the results of semi-structured interviews with eleven students who completed the tasks. We focus on the construction differences between students who engaged in tasks designed according to the genetic decomposition and those in a previously studied lecture-based course. The study aimed to underscore the task's effect on students' learning in order to refine the genetic decomposition if needed. This study contributes a set of tasks that enable students to relate Riemann sums and double integrals. The results showed that students using the proposed materials in class and a collaborative didactical strategy provided evidence of constructing the structures proposed in the genetic decomposition. The tasks are based on a genetic decomposition, so the study also contributes by showing that it is an effective model to guide instruction. The constructions inferred from students’ work are discussed in detail and compared to those proposed in the genetic decomposition and those resulting from previous research.