Given the variability in student math preparation and ability upon entering into college, the field of mathematics education has endeavored to make math more accessible to students. Efforts to enhance student learning focus on alternative teaching approaches, including active learning, flipped classrooms, and problem-solving more complex problems in class.
Publications within the field of mathematics education reflect investigations within these areas, in addition to developing students’ conceptual understanding in specific math topic areas and other research. For more information, instructors can look into the special interest group of the Mathematics Association of America (MAA) on Research in Undergraduate Mathematics Education. The MAA offers a Guide to Evidence-Based Instructional Practices in Undergraduate Mathematics for faculty and departments, in addition to a wide variety of other resources and programs.
Journals
Papers and Articles
Abstract: “Faculty development workshops are one strategy for increasing instructor use of evidence-based teaching practices that are known to improve student outcomes in mathematics and other STEM (science, technology, engineering and mathematics) disciplines. Yet relatively little is known about the impact of professional development on teaching practice in higher education. We report findings on participant outcomes from a series of annual, weeklong professional development workshops for college mathematics instructors about Inquiry-Based Learning (IBL) in undergraduate mathematics. We gathered data from surveys with the 139 workshop participants and interviews with a subset of 16 participants. These workshops were found to be effective in encouraging instructors to try this student-centered approach to teaching mathematics, as 58 % of participants reported implementing IBL strategies in the year following the workshop they attended. Analysis suggested that certain features of the workshops supported participants’ adoption of IBL strategies. The findings pointed to the importance of (1) sharing broad, inclusive definitions of IBL, (2) representing viewpoints and experiences from diverse institutional contexts, (3) allowing sufficient time within the workshop to explore and revisit topics, (4) addressing common concerns such as content coverage, student resistance, and skills to implement IBL, and (5) providing ongoing follow-up support and inclusion in the community of IBL practitioners. We also make connections with studies of the impact of instructional development in other STEM disciplines and share implications for effective professional development in general.”
Abstract: “This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia does not investigate 1) whether the emporium serves certain populations differently than others, 2) the nature of mathematical learning that occurs in the ME, or 3) how the emporium is perceived by the enrolled students. In this paper, we used mixed methods to investigate each of these aspects in the case of a single ME serving nearly 300 intermediate algebra students. We found that the emporium appeared to best serve students with higher math achievement, who enjoyed mathematics, and who spent more time taking their exams. In terms of mathematical learning, the emporium appeared to improve students’ ability to recall and use formulas for familiar problem types, but had limited impact in terms of developing meaning for symbols or flexibility in solving unfamiliar tasks. In addition, students expressed mixed feeling about the autonomy provided by the structure of the emporium.”
Abstract: “To test the hypothesis that lecturing maximizes learning and course performance, we metaanalyzed 225 studies that reported data on examination scores or failure rates when comparing student performance in undergraduate science, technology, engineering, and mathematics (STEM) courses under traditional lecturing versus active learning. The effect sizes indicate that on average, student performance on examinations and concept inventories increased by 0.47 SDs under active learning (n = 158 studies), and that the odds ratio for failing was 1.95 under traditional lecturing (n = 67 studies). These results indicate that average examination scores improved by about 6% in active learning sections, and that students in classes with traditional lecturing were 1.5 times more likely to fail than were students in classes with active learning. Heterogeneity analyses indicated that both results hold across the STEM disciplines, that active learning increases scores on concept inventories more than on course examinations, and that active learning appears effective across all class sizes—although the greatest effects are in small (n ≤ 50) classes. Trim and fill analyses and fail-safe n calculations suggest that the results are not due to publication bias. The results also appear robust to variation in the methodological rigor of the included studies, based on the quality of controls over student quality and instructor identity. This is the largest and most comprehensive metaanalysis of undergraduate STEM education published to date. The results raise questions about the continued use of traditional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teaching practice in regular classrooms.”
Abstract: “Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.”
Bressoud DM, Carlson MP, Mesa V, Rasmussen C. (2013). The calculus student: insights from the Mathematical Association of America national study. International Journal of Mathematical Education in Science and Technology, 44(5), 685-698.
Abstract: “In fall 2010, the Mathematical Association of America undertook the first large-scale study of postsecondary Calculus I instruction in the United States, employing multiple instruments. This report describes this study, the background of the students who take calculus and changes from the start to the end of the course in student attitudes towards mathematics and intention to continue in mathematics.”
Abstract: “The traditional lecture style of teaching has long been the norm in college science, technology, engineering, and mathematics (STEM) courses, but an innovative teaching model, facilitated by recent advances in technology, is gaining popularity across college campuses. This new model inverts or ‘flips’ the usual classroom paradigm, in that students learn initial course concepts outside of the classroom, while class time is reserved for more active problem-based learning and practice activities. While the flipped classroom model shows promise for improving STEM learning and increasing student interest in STEM fields, discussions to date of the model and its impact are more anecdotal than data driven – very little research has been undertaken to rigorously assess the potential effects on student learning that can result from the flipped classroom environment. This study involved 55 students in 2 sections of an applied linear algebra course, using the traditional lecture format in one section and the flipped classroom model in another. In the latter, students were expected to prepare for the class in some way, such as watching screencasts prepared by the instructor, or reading the textbook or the instructor’s notes. Student content understanding and course perceptions were examined. Content understanding was measured by the performance on course exams, and students in the flipped classroom environment had a more significant increase between the sequential exams compared to the students in the traditional lecture section, while performing similarly in the final exam. Course perceptions were represented by an end-of-semester survey that indicated that the flipped classroom students were very positive about their experience in the course, and particularly appreciated the student collaboration and instructional video components.”
Abstract: “As a fundamental resource, textbooks shape the way we teach and learn mathematics. Based on examination of secondary school and university textbooks, we describe to what extent, and how, the presentation of mathematics material–in our case study, the concept of the line tangent to the graph of a function–could contribute to creation and strengthening of students’ misconceptions. Our findings, roughly classified in several categories, raise awareness of non-obvious problems that need to be addressed when teaching calculus.”
Abstract: “In recent years, significant numbers of academics from the science and health disciplines at our institution have found that their students lack the appropriate ‘mathematical’ background to cope with first-year science subjects. Consequently, failure rates are on the increase in these subjects. The mathematical background of students entering university has been found to be a problem in other universities in Australia, as well as in the UK, Ireland and the US. In this report, the authors analyse data on current students’ performance and present suggestions for addressing the problems found. The performance of first-year students in four different mathematics and mathematically related subjects is compared to the level of their secondary school mathematics and performance, and to their tertiary entrance score. We conclude that a student’s secondary school mathematics background, not their tertiary entrance score, has a dramatic effect on pass rates. On the basis of our findings, a way forward is suggested.”
Abstract: “The transition (‘gap’) between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. The aim of this paper is to present the ways in which the issues of mathematics transition have been dealt with at McMaster University. Roughly, the process of transition has been broken into three stages: students’ voluntary preparation for university mathematics courses facilitated by the Mathematics Review Manual; administration of Mathematics Background Survey; and redesign of the first-year Calculus (and, subsequently, other mathematics courses).”
