Undergraduate Mathematics Education Research Articles

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.

Transformative Pedagogy via Digital Technology in Undergraduate Mathematics Education

The main purpose of this paper is to review the different papers and theories regarding transformative pedagogy used in mathematics education at the undergraduate level and draw transformative praxis used and unfold the gaps for further research betterment. Also, this paper explores the philosophical theory/idea that guides the transformative pedagogical practices via Digital Technology in education over the globe and analyzes digital boundaries in higher education in Nepal.

We need to make up for the gap: University student teachers’ difficulties associated with basic algebraic manipulations

With the increasing number of students enrolling in South African Higher Education institutions, it is essential to determine what level of mathematical knowledge gaps and understanding they bring from secondary school level. This was the context for a study of first year undergraduate mathematics education students at the University of Limpopo. In this paper, we present our autoethnographical experiences of lecturing calculus courses for a teacher preparation programme. The patterns that emerged from our interactions with students revealed that they experienced difficulties in understanding basic algebraic procedures and recognising structure to solve algebraic problems in the context of differentiation. This made us aware that we needed to configure effective strategies to make up for the identified elementary mathematics knowledge gaps, which we assumed students brought with from Grade 12. Our quest to make up for the algebraic knowledge gaps does not only serve the purpose of enabling our student teachers’ mathematical knowledge, but to ensure that they develop good knowledge base needed to teach the subject during their training as well as once they qualify as teachers.

The Changing Scenario of Mathematics Formative Assessment in the Era of Globalization

Researches on formative assessment have mentioned its importance in the teaching and learning method. However, there are little to no known researches on formative assessment centered in Mathematics and higher education. This research intends to investigate the awareness and development of formative assessment in undergraduate Mathematics education in a top university in the Philippines, Saint Louis University, currently having more than 30,000 students. Specifically, this research determines the current scenario of formative assessment as it seeks to recognize the adaptation and usage of formative assessment, identify the challenges and opportunities that Mathematics educators face in formative assessment with regards to globalization, and describe the characteristics of the Mathematics educators based on their extent of use of 21st century formative assessment strategies and tools. Furthermore, this descriptive qualitative research attempts to identify the challenges needed to be overcome by the Mathematics sector to satisfy the globalized skills students needed to attain.

How an inquiry-oriented textbook shaped a calculus instructor’s planning

We investigate how an inquiry-oriented, dynamic, open-source calculus textbook shaped one college instructor’s planning. We rely on Dietiker et al.’s [(2018). Research commentary: Curricular noticing: A framework to describe teachers’ interactions with curriculum materials. Journal for Research in Mathematics Education, 49(5), 521–532. https://doi.org/10.5951/jresematheduc.49.5.0521] curriculum noticing framework to situate the instructor’s actions during lesson planning using data from surveys, logs and interviews. The instructor’s planning practices are characterized by intense use of the textbook, including creating additional curricular material related to its content. Our observations suggest that the textbook supported and influenced the instructor in implementing his inquiry-oriented visions and goals while planning his lessons. We conclude by suggesting further investigation of how textbooks shape undergraduate mathematics education and the textbooks’ role in shaping undergraduate mathematics planning practices.

Authentic Engineering Problems in Service Mathematics Assignments: Principles, Processes and Products from Twenty Years of Task Design

A central problem in undergraduate mathematics education for future engineers consists in the perceived and actual relevance of the mathematical content. One strategy to strengthen both is to let students experience how that content appears in posing and solving authentic problems from the field of engineering which the students have signed up to study. This paper proposes a way to develop such a strategy, both in terms of theoretical precision (e.g. to clarify what “authentic” could mean in this context), and in terms of the institutional and epistemological conditions and constraints for realizing the strategy. The paper is based on cases and formats developed over twenty years at the Technical University of Denmark.

“He was poking holes …” A case study on figuring out metadiscursive rules through primary sources

An important aspect of participation in a new academic discourse pertains to the metadiscursive rules which govern that discourse. Researchers have documented the viability of using primary sources in undergraduate mathematics education for scaffolding students’ recognition of those rules. Our research explores the related question of whether the use of primary sources can support students’ learning of metadiscursive rules in a way that goes beyond mere recognition. We present a case study of one student’s “figuring out” of metadiscursive rules in a university Analysis course as a result of her experience with a Primary Source Project, illustrate evidence for three dimensions of “figuring out” (adoption, acceptance, awareness) that emerged from that case study, and discuss the implications of our findings for classroom instruction and future research.

Detailing Racialized and Gendered Mechanisms of Undergraduate Precalculus and Calculus Classroom Instruction

Undergraduate mathematics education can be experienced in discouraging and marginalizing ways among Black students, Latin* students, and white women. Precalculus and calculus courses, in particular, operate as gatekeepers that contribute to racialized and gendered attrition in persistence with mathematics coursework and pursuits in STEM (science, technology, engineering, and mathematics). However, student perceptions of instruction in these introductory mathematics courses have yet to be systematically examined as a contributor to such attrition. This paper presents findings from a study of 20 historically marginalized students’ perceptions of precalculus and calculus instruction to document features that they found discouraging and marginalizing. Our analysis revealed how students across different race-gender identities reported stereotyping as well as issues of representation in introductory mathematics classrooms and STEM fields as shaping their perceptions of instruction. These perceptions pointed to the operation of three racialized and gendered mechanisms in instruction: (i) creating differential opportunities for participation and support, (ii) limiting support from same-race, same-gender peers to manage negativity in instruction, and (iii) activating exclusionary ideas about who belongs in STEM fields. We draw on our findings to raise implications for research and practice in undergraduate mathematics education.

The Qualms and Quarrels with Online Undergraduate Mathematics: The Experiences of African American Male STEM Majors

ABSTRACT Equity-related issues are a critical contemporary concern in mathematics education, and one specific area that has been taken up deals with equitable instructional modalities. However, the focus of many of these discussions, meetings, and publications is on K–12 mathematics education. This study reports on one aspect of an ongoing, equity issue in undergraduate mathematics education – face-to-face versus online mathematics instruction. In so doing, it investigates this issue surrounding online mathematics learning with African American (Both African American and Black are used interchangeably throughout this article, and these terms refer to students who were born and completed their schooling in the United States.) male Science, Technology, Engineering, and Mathematics (STEM) majors who have successfully completed the Calculus sequence using a critical race perspective. Findings show that these Black men did not prefer online mathematics instruction. Recommendations are shared to deal with the qualms and quarrels of online mathematics and ultimately better prepare African American male students for STEM majors.

Students’ activeness in jigsaw type cooperative learning and rank 1 games on sets topic

Student activity in learning is essential so that learning objectives can be achieved. This study aims to describe the activeness of students in the application of Jigsaw cooperative learning and Rank 1 games on the topic of sets. This research was conducted at Universitas Negeri Malang school year of 2019/2020. The method used is quantitative descriptive. In this study applied Jigsaw type cooperative learning and Rank 1 games. At the same time, the research subjects were the 5th-semester students who were taking the Social Mathematics course, in the topic of mathematical sets, Undergraduate Mathematics Education Program of Universitas Negeri Malang year 2017 with a total of 30 students. Based on the analysis results of students’ activeness observation, an average percentage of 91.83% was obtained. It shows that the students’ activeness in the Social Mathematics course, especially on the topic of sets, was categorized as excellent.

An Analysis of Knowledge in STEM: Solving Algebraic Problems

This study was conducted to assess the students’ level of abilities in solving algebraic word problems which is a main component in Science, Technology, Engineering and Mathematics (STEM). It also aims to determine the students’ difficulties in solving these problems by using Newman’s Model of Error Analysis (NMEA). Furthermore, this study was conducted to investigate the attitudes of undergraduate students towards STEM and its relationship to the achievement of the test. The instruments are a test on algebraic problems and a set of questionnaire on attitudes towards STEM. The test which was validated by an expert from a university was adopted and adapted from a problem solving source. The test contained questions from one of the main areas of algebra which focused on two parts namely algebraic knowledge (AK) and algebraic knowledge in the context of science (AKCS). There were a total of 63 undergraduate mathematics education students who took part in this study. This study was carried out using the mixed-methods qualitative approach. The result showed that the majority of the students have a low level of algebraic knowledge as well as algebraic knowledge in the context of science. For the attitude towards STEM, findings displayed that the majority of the students were interested and gave positive attitude towards STEM.
 Keywords: algebraic knowledge (AK), algebraic knowledge in the context of science (AKCS), Newman’s Model of Error Analysis (NMEA), attitudes towards STEM

Towards Anti-Deficit Education in Undergraduate Mathematics Education: How Deficit Perspectives Work to Structure Inequality and What Can Be Done About It

A deficit perspective is a propensity to locate the source of academic problems in deficiencies within students, their families, their communities, or their membership in social categories (such as race and gender). While the deficit perspective is a common topic of discussion in K–12 mathematics education, it is a much rarer topic of discussion in undergraduate mathematics education. I argue that undergraduate mathematics instructors should take the deficit perspective seriously, because it structures educational experiences for students and instructors. In this survey article, I provide a brief review of the literature on deficit perspectives in mathematics education, and I offer practical suggestions for education from an anti-deficit perspective.

WeBWorK log files as a rich source of data on student homework behaviours

ABSTRACT The online homework system WeBWorK has been successfully used at several hundred colleges and universities. Despite its popularity, the WeBWorK system does not provide detailed metrics of student performance to instructors. In this article, we illustrate how an analysis of the log files of the WeBWorK system can provide information such as the amount of time students spend on WeBWorK assignments and how long they persist on problems. We estimate the time spent on an assignment by combining log file events into sessions of student activity. The validity of this method is confirmed by cross referencing with another time estimate obtained from a learning management system. As an application of these performance metrics, we contrast the behaviour of students with WeBWorK scores less than 50% with the remainder of the class in a first year Calculus course. This reveals that on average, the students who perform poorly on their homework start later, have shorter activity sessions, and are less persistent when solving problems. We conclude by discussing the implications of WeBWorK analytics for instructional practices and for the future of learning analytics in undergraduate mathematics education.

Active learning strategies with positive effects on students’ achievements in undergraduate mathematics education

The paper describes active learning strategies used in undergraduate college algebra and business calculus courses. There are a variety of active learning strategies described in the literature. We wanted to implement a few that together, satisfy the key characteristics of active learning strategies. The active learning strategies described in this paper are, interactive presentation style, group-work with discussion and feedback, volunteer presentations of solutions by groups, raise students’ learning interest towards specific topics, involve students in mathematical explorations, experiments, and projects, and last but not least, continuous motivation and engagement of students. We analyse the relationship between the average results of 27 college algebra and business calculus sections and the effects of the level of use of these active learning strategies. We demonstrate that the application of these strategies has a positive effect on the average results of the sections and the passing rates of the students.

The Role of Epistemology and Epistemic Games in Mediating the Use of Mathematics in Chemistry: Implications for Mathematics Instruction and Research on Undergraduate Mathematics Education

Mathematics is used in the physical sciences to describe and model phenomena, resulting in a unique interface between mathematics and disciplines such as chemistry and physics. This paper focuses on themes emerging from a larger project that investigated how students understand and use mathematics in chemical kinetics, a field of study concerned with monitoring the rate of chemical reactions. The primary data source for this study involved a subset of the data from the larger project, focusing on semi-structured interviews with 40 students sampled from a second-semester general chemistry course. During the interviews students were asked to work through chemical kinetics problems that could be solved without calculations (using relationships between quantities and chemistry principles) or they could be solved algorithmically (using equations and the provided data). The interviews were analyzed using the construct of epistemic games, which describe a collection of resources and an associated structure that define and guide problem-solving and reflect epistemological commitments. Findings indicate students have productive resources and approaches for engaging in problem-solving, reflected by the observed shared set of epistemic games. Implications emphasize the role of scaffolding and explicit questioning to prevent compartmentalization of chemistry and mathematics, suggesting the need for more support to help students productively apply the knowledge and skills learned in mathematics courses to contexts such as chemistry.