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.

İLKÖĞRETİM MATEMATİK ÖĞRETMENLERİNİN LİSANS EĞİTİMLERİ BAĞLAMINDA MESLEKİ KARİYERLERİNE İLİŞKİN GÖRÜŞLERİ

Bu çalışmanın temel amacı, ilköğretim matematik öğretmenlerinin lisans eğitimleri bağlamında mesleki kariyerlerine ilişkin görüşlerinin alınmasıdır. Bu amaca ulaşmak için çalışma grubunun belirlenmesi, veri toplama kaynakları ve verilerin analizi süreçlerinde nitel yöntem esas alınmıştır. Çalışma grubunda, resmi orta okullarda görev yapan toplam 13 matematik öğretmeni bulunmaktadır. Araştırmada veri toplama aracı olarak dört ayrı form kullanılmıştır. Sonuç olarak matematik öğretmenlerinin lisans eğitimleri bağlamında mesleki yeterliklerine ilişkin görüşleri incelendiğinde öğretmenlik meslek bilgisi ve mesleki doyum anlamında güçlü hissettikleri, bürokrasi, eğitim-öğretim süreci ile sosyo-ekonomik durumlar bağlamında mesleki zorluk yaşadıklarını ifade etmişlerdir. Lisans eğitimlerinin mesleğe hazırlanmada yetersiz olduğunu bu durumu özellikle mesleklerinin ilk yıllarında hissettiklerini belirtmişlerdir. Lisans ders içeriklerinin matematik öğretmenlerinin mesleki yeterliklerini artırabilmesi adına daha çok uygulamaya dönük ve alan eğitimi dersi ağırlıklı olmasını, öğretmenlik uygulaması derslerine sadece dördüncü sınıfta değil ara sınıflarda da yer verilmesi gerektiğini vurgulamışlardır. Araştırma sadece çalışma gurubundaki öğretmen görüşleri ile sınırlıdır. Bu nedenle matematik öğretmenlerinin yetiştirilmesinde görev alan tüm paydaşlarla öğretmenlerin mesleki yeterlikleri üzerine çalışmalar, değişen lisans programların etkililiğine ilişkin boylamsal çalışmalar yapılabilir.

Queer of Color Justice in Undergraduate Mathematics Education

Queer of Color Justice in Undergraduate Mathematics Education

A linear algebra quiz game as a supplementary learning tool in tertiary-level

This article presents a study investigating the use of games in undergraduate mathematics instruction, with a specific focus on students’ perspectives regarding post-instructional quiz games. The study explores students’ opinions on the implementation of a linear algebra quiz game as a supplementary learning tool. A survey was administered to 78 students to examine their perceptions of the game’s usefulness in preparing for their linear algebra examinations. Students reported high levels of attention and interest while engaging with the game and described it as fun, dynamic, exciting, and beneficial for reviewing linear algebra concepts. The findings suggest that quiz games can be a valuable addition to undergraduate mathematics education, fostering student engagement and providing an enjoyable and effective means for reinforcing course material.

Influence of Internet Addiction on Pre-Service Mathematics Teachers’ Learning and Motivation in Nigerian South-West Universities

The widespread use of the internet has led to a growing concern about the impact of internet addiction on pre-service Mathematics teachers' learning. This paper investigates the impacts of internet addiction on the learning and professional development of pre-service Mathematics teachers. The population covers the undergraduate Mathematics education students from public universities in south-west Nigeria. The sample was randomly selected from 100 to 400 levels while the sample size was 200 pre-service teachers across the levels from one selected university. A well-structured questionnaire was used to get data from pre-service Mathematics teachers on internet addiction. This study employed a descriptive and inferential research design to create responses to the research questions. The data collected were analysed using mean and standard deviation for the two research questions while Pearson Product Moment Correlation Coefficient was used to test the hypothesis raised. There is a significant relationship between internet addiction and Mathematics learning. This yields a positive result that, the students who access the internet more frequently learn more effectively and highly motivated in learning Mathematics. It was suggested that the internet can be a useful tool for learning but must be used responsibly. However, addressing internet addiction through education, prevention, and intervention efforts should be integrated into the teacher education program to support pre-service mathematics teachers in developing healthy internet use habits and maintaining high levels of motivation to learn.

Enhancing Measurement Education in Schools: A Study on the Efficacy of STAD (Student Teams Achievement Division) in Undergraduate Mathematics Education

Enhancing Measurement Education in Schools: A Study on the Efficacy of STAD (Student Teams Achievement Division) in Undergraduate Mathematics Education

Problem-Based Learning Approach for Developing Learning Management Skills in Undergraduate Mathematics Education

This study explores the effectiveness of problem-based learning (PBL) activities in developing learning management skills among mathematics education students. The research was conducted with 30 participants selected from a public university in Thailand using a cluster sampling method. A holistic rubric with a rating scale of 1 to 5 was employed to assess learning management design and teaching implementation. The results indicate that PBL significantly enhanced students’ learning management skills, with mean scores of 77.90 (82% of full mark) for learning management design and 56.90 (81.29% of full mark) for teaching implementation. Overall, the participants achieved a mean score of 134.80 (81.70% of full mark), demonstrating the effectiveness of PBL in fostering comprehensive learning management abilities. Moreover, participants expressed high satisfaction with the PBL approach, as evidenced by a mean satisfaction score of 4.54 (S.D. = 0.48) on a 5-point Likert scale. The study contributes valuable evidence supporting the integration of PBL in teacher education curricula, with implications for both academic and pedagogical contexts. Policymakers are encouraged to consider incorporating real-world problem-solving experiences in all teacher education classes, and further studies can explore the long-term effects of PBL on students’ teaching practices.

A Framework for Facilitator Actions in Professional Development That Support Mathematicians’ Instructional Change

In this work, we discuss the development of descriptive actions that facilitators take in semester-long online professional development geared at supporting instructional change at the undergraduate level. Current work in undergraduate mathematics education includes various large-scale projects aimed to support individuals or departments in reforming their instruction to align with recommendations from professional organizations and existing mathematics education research standards. One research area that has recently grown is the use of online synchronous environments to form collaborations to support the inclusion of student-centered instruction in mathematics. This paper discusses the actions that facilitators take in these collaborative environments and highlights how these actions supported the overall goal of the semester-long online faculty development.

Factors that influence student engagement with technology-enhanced resources for formative assessments in first-year undergraduate mathematics

Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students’ successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement.

When learning stumbles upon identity and affect: a loaded student–student collaboration in linear algebra

In undergraduate mathematics education, students’ collaborations have gained a reputation as a ‘good’ learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. In this study, I take a close look at a twenty-minute-long interaction between two first-year students who engaged in a sequence of routine problems about dot products presented in a computer-based learning-support system. The commognitive analysis of the interaction revealed an asymmetrical structure: one student led the mathematizing, while his partner followed and invested considerable efforts to avoid making a mathematical contribution. The leader’s attempts to switch positions and inquiry into the follower’s recurrent refusals to mathematize entailed loaded exchanges that took a toll on both students in terms of identity and affect. I compare these findings to previous studies with school students to discuss possible sources of ineffective communication in situations where students are expected to learn through collaborations.

Student Engagement with Technology-Enhanced Resources in Mathematics in Higher Education: A Review

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics.

Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes

Humanistic geographers distinguish between space and place: “What begins as undifferentiated space becomes place as we get to know it better and endow it with value” (Tuan, 1977, page 6). In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place illuminating for understanding important aspects of students’ learning experiences during the coronavirus pandemic—and possibly beyond. Specifically, after introducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online education. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education.

Undergraduate Mathematics Education Students’ Visual Representations of Multivariable Functions

Undergraduate Mathematics Education Students’ Visual Representations of Multivariable Functions

Co-operative Learning in Undergraduate Mathematics and Science Education: A Scoping Review

To cope with an unpredictable future, higher education in mathematics and science (MS) needs to educate a knowledgeable and skilled workforce. Co-operative learning (CL) is a teaching method associated with increased academic achievement and development of generic skills. Thus, the purposes of this scoping review are to assess the evidence base of CL in undergraduate MS education to inform teaching practices and to identify potential knowledge gaps to inform future research. The review covers 24 empirical studies conducted from 2010 to 2020 on the prevalence, uses, and outcomes of CL elements in undergraduate MS education. The results show that there are few such studies, and these are rarely conducted outside the US or in disciplines other than chemistry. The most frequently implemented CL elements in the included studies are heterogeneous group formation, the use of roles, and different CL structures. The most prevalent student outcome of implemented CL elements in the reviewed studies is enhanced academic success, followed by student attitudes, generic skills, and psychological health. The results have implications for future implementation of and research on CL in international MS higher education.

The role of affective learner characteristics for learning about abstract algebra: A multiple linear regression analysis

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students’ abstract thinking. However, in addition to research on cognitive processes, learners’ affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students’ affective characteristics within a two-weeks course program–the Hildesheim teaching concept. In our study, this concept was used to introduce pre-service primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.

Evaluation of Bilingual Mathematics Learning Program at Al-Azhar Islamic Middle School, South Tangerang

This study evaluates the bilingual mathematics learning program at SMP Islam Al-Azhar 25, South Tangerang. The evaluation model used is CIPP (Context, Input, Process, Product). Data collection techniques using interviews, observation, and document analysis. The evaluation results show that the bilingual mathematics learning program at SMP Islam Al-Azhar 25 South Tangerang has been running well. The program aims to follow the school's "globally competitive" vision. Facilities and infrastructure are categorized as very good, teachers have met the academic qualifications of undergraduate Mathematics Education, students have met the qualifications with tested students through the stages of entering the bilingual class, and the readiness of teachers and students of class VII is categorized as good, and the readiness of teachers and students of class VIII categorized as very good. The mathematics learning process uses the Bilingual Immersion type of learning, with a translation and transcription approach. The average score for daily assignments and tests is above the KKM (Minimum Completeness Criteria). The evaluation component has met the criteria for success, but some need to be improved and developed, such as the availability of a language laboratory and the development of bilingual classes from two classes to all classes so that there are no social gaps.

Exploring Calculus I students’ performance between varying course times among other predictive variables

This study focuses on the analysis of certain performance predictors for calculus I. We collected data from 717 students from 2013 through 2018 at a southeastern university in the United States to explore any correlation between course times (particularly very early versus the rest) and student performance in this specific course, along with a handful of other variables. This represented all calculus I students over this time period. A two-proportion test confirmed that time was a significant variable in performance. We then used regression to determine similar impacts of gender, major, instructor, and term on student performance. Initial findings portrayed statistical differences between terms and course times; other findings included the significance of major and instructor in different contexts. Interaction effects were used with time to complete our analysis of its impact, and controls were later used accordingly. We also display appropriate models for comparing categories. We conclude with some basic assertions and argue some departmental recommendations on how to use these findings in undergraduate mathematics education.

Assessing Learners’ Conceptual Understanding of Introductory Group Theory Using the CI2GT: Development and Analysis of a Concept Inventory

Prior research has shown how incorporating group theory into upper secondary school or undergraduate mathematics education may positively impact learners’ conceptual understanding of mathematics in general and algebraic concepts in particular. Despite a recently increasing number of empirical research into student learning of introductory group theory, the development of a concept inventory that allows for the valid assessment of a respective conceptual understanding constitutes a desideratum to date. In this article, we contribute to closing this gap: We present the development and evaluation of the Concept Inventory of Introductory Group Theory—the CI2GT. Its development is based on a modern mathematics education research perspective regarding students‘ conceptual mathematics understanding. For the evaluation of the CI2GT, we follow a contemporary conception of validity: We report on results from two consecutive studies to empirically justify that our concept inventory allows for a valid test score interpretation. On the one hand, we present N=9 experts‘ opinions on various aspects of our concept inventory. On the other hand, we administered the CI2GT to N=143 pre-service primary school teachers as a post-test after a two weeks course into introductory group theory. The data allow for a psychometric characterization of the instrument, both from classical and probabilistic test theory perspectives. It is shown that the CI2GT has good to excellent psychometric properties, and the data show a good fit to the Rasch model. This establishes a valuable new concept inventory for assessing students’ conceptual understanding of introductory group theory and, thus, may serve as a fruitful starting point for future research into student learning of abstract algebra.

Institutionalizing evidence-based STEM reform through faculty professional development and support structures

BackgroundEven though student-centered instruction leads to positive student outcomes, direct instruction methods are still prevalent. Multiple barriers prevent faculty from further adopting evidence-based student-centered practices and holistic approaches to faculty support are necessary to promote faculty change. The Collaborative for Institutionalizing Scientific Learning (CISL) is an HHMI-funded program to reform undergraduate science and mathematics education at a large Hispanic-Serving public research university. The program has established a Faculty Scholar support model to impact the number of science and mathematics faculty using evidence-based practices in their classrooms. Through this program, Scholars are selected to undertake a transformation of a course of their choice and conduct an assessment of the impact of the reform on students—while receiving multiple supports including summer salary, undergraduate Learning Assistants, professional development, course assessment and education research support, and opportunities to develop manuscripts on their course transformations.ResultsCISL has supported over 40 Faculty Scholars in the transformation of both introductory and upper division biology, chemistry, physics and mathematics courses. Faculty are motivated to transform a course due to factors related to their own experiences and beliefs, their students’ needs, the course structure, and/or departmental elements. Quantitative analysis of the impact of the project on student success show that, overall, students in CISL-supported courses have higher passing rates compared to students in traditional classrooms. Survey and interviews of Faculty Scholars identified that the most valuable elements of the program were the personnel support from undergraduate Learning Assistants during reform implementation and guidance from the program’s Assistant Director during design, implementation and evaluation.ConclusionsThe CISL program provides an example of significant effort sustained over several years to systematically improve the quality and culture of undergraduate education in a large research-intensive Hispanic Serving Institution. The program has had an overall positive impact on the professional development of Faculty Scholars and led to an increase in the number of STEM courses implementing evidence-based teaching practices, thus, taking a step towards solidifying a culture of evidence-based instructional strategies in STEM departments.

Mentoring Female Undergraduates in Research-Centered Outreach

Math Girls ock! is a year-long, two-tiered mathematics mentoring program that prepares female undergraduate mentors to facilitate high school girls engagement in challenging mathematics concepts through a dynamic after-school program. In this article, we describe the distinct educational component of this program in which female faculty members mentor female undergraduate mathematics and mathematics education students in researching and developing the content to be presented at the high schools. In addition, we discuss some of the feedback collected from program participants about various aspects of this program relating to the involvement of the undergraduate students. In conclusion, we share advice for those interested in starting and running similar outreach programs.