Research In Undergraduate Mathematics Education Research Articles

Using Data to Sustain and Measure Student Success Initiatives

This is a follow-up to an earlier case study [Faudree, J. 2021. Courage by experiment, rescue by data. PRIMUS. 31(3–5): 483–491.] describing one Math Department's attempt to improve pass rates in Calculus I by implementing the recommendations from national studies of successful calculus programs [Bressoud, D. and C. Rasmussen. 2015. Seven characteristics of successful calculus programs. Notices of the American Mathematical Society. 62(2): 144–146; Rasmussen, C., J. Ellis, and D. Zazkis. 2014. Lessons learned from case studies of successful calculus programs at five doctoral degree granting institutions. In Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education, pp. 999–1005. Denver, CO.]. This article, along with the earlier one, provide concrete, detailed strategies for promoting departmental change. We describe how the collection and analysis of baseline data has formed the backbone of a sustained, department-driven effort to improve outcomes for undergraduate students and one that weathered the pandemic. For context, our public university is the major research institution of the state, but it is also open-admissions, small (7500 undergraduates) and physically isolated. The effort described here started in 2016 with few resources: no faculty with expertise in mathematics education at the post-secondary level, no support from administration, and no external funding.

Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about inquiry-oriented instruction relative to vertices of the instructional triangle (content, students, and instructor). Through this lens, we analyze conversations of twenty-five mathematicians who elected to attend a workshop on inquiry-oriented instruction at a large national mathematics conference. Identifying differences in talk between two breakout groups, we argue that deeper mathematical engagement in task sequences designed for students supported deeper engagement in students’ mathematical reasoning and engendered reasoning about instruction that was more frequently accompanied by rationale based in mathematics or students’ reasoning about mathematics. Importantly, deeper mathematical engagement was observed when the discussion facilitator prompted participants to engage through a mathematical lens rather than an instructional lens.

Connecting the Stakeholders: Departments, Policy, and Research in Undergraduate Mathematics Education

The Mathematical Association of America’s Precalculus to Calculus: Insights and Innovations Conference brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we report on major themes that arose from the discussions at this conference, contextualized with research findings and policy recommendations. We aim to shed light on where the priorities of departments, policy, and researchers are aligned and where they are not. In doing so, we hope to support efforts to enact and sustain change in undergraduate mathematics education through connections and communication.

Pre-service Teachers’ Mental Constructions of Concepts in Matrix Algebra

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers through a structured activity sheet. The aim was to explore their mental constructions of matrix algebra concepts and how they concur with a preliminary genetic decomposition. The study is underpinned by APOS theory (action–process–object–schema). The findings revealed that the mental constructions made by pre-service teachers in most cases concur with the preliminary genetic decomposition. In terms of APOS theory, the responses revealed that most pre-service teachers were operating at action and process stages, with few operating at the object stage. It was observed that the schemata for basic algebra and real number are necessary for the conceptual development of matrix algebra, and that familiarity of the correct use of terminology and notations promotes the earning of matrix algebra. On the basis of the detailed response analysis, modified genetic decompositions are proposed for the matrix order concept, matrix transpose concept and for matrix operations.

수학개념 형성단계에 대한 모델과 적용사례 - 분수체 형성 추상화 단계

Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student`s personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.

Research on undergraduate mathematics education: A South African perspective.

Research on undergradute mathematics education is a relatively new field that originated less than 20 years ago in the United States of America (USA), and that is known under the acronymn RUME (Research in Undergraduate Mathematics Education). In South Africa researchers in this field form a small but strong group that originated at the University of Pretoria. In this article a brief overview is firstly given on the international increase in interest and activities in this research field. Secondly the research field is viewed from a South African perspective. Examples of research projects are discussed, as well as the career path that leads to research in this field. Finally local activities and existing international ties are considered. The aim of this article is to give a South African overview of the research field and activities, hoping to motivate and stimulate research in this important and growing field.

Research in undergraduate mathematics education

Research in undergraduate mathematics education (RUME), the study of teaching and learning of college mathematics, is a new area of research in mathematics. Information to support this discipline is found in publications from all over the world, in the form of monographs, reports, research guidelines and resource manuals, as well as journal articles. Researchers in RUME require access to materials that are specific not only to their field, but also to the broader literature of mathematics, education, learning theories, instructional strategies, alternative assessment techniques, cognitive development and human behavior. This annotated bibliography is designed to be a template for a comprehensive and up‐to‐date collection of RUME resources. World Wide Web (Web) locations for many of the items are provided, as are descriptions of several Web sites that present information of interest to RUME researchers.

Affective Variables and Mathematics Education

to general feelings such as liking/disliking of mathematics, nor is it meant to exclude perceptions of the difficulty, usefulness, and appropriateness of mathematics as a school subject. There are several ways affective variables are related to mathematics learning. It is likely that a student who feels very positive about mathematics will achieve at a higher level than a student who has a negative attitude toward mathematics. It is also likely that a high achiever will enjoy mathematics more than a student who

Reliability of Grading Work in Mathematics

Reliability of Grading Work in Mathematics