Mathematical Association Of America Research Articles

A Preliminary Report on Students’ Reflections about Their Learning in an Active Learning Classroom

In the past decades, College Algebra has become a big hurdle for students to graduate or further pursue STEM or related careers. For most of the student population, College Algebra is a terminal course and only a small portion of students take it for further mathematics courses. The traditional content of College Algebra does not serve either group of students well (Mathematical Association of America, 2004; Mathematical Association of America & National Council of Teachers of Mathematics, 2012). In recent years, at a large Hispanic-serving university, the course design for liberal arts students has been changed. An active-learning curriculum has been implemented, namely Quantitative Reasoning. This curriculum engages students with opportunities to learn math concepts from relevant everyday sources and even their own personally collected data. Students build their own understanding of mathematics by relevant data-based situations experienced through preview activities designed to prepare students for class, collaboration in class discussion and discovery through relevant problem situations, and practice activities extending learning after each lesson. The purpose of this study was to investigate student perceptions of their learning outcomes from an active-learning structured course. That is, what impact does a course design with pre-assignment tasks, authentic problem solving through collaboration in class, and practice assignments after lessons have on diverse student populations in a quantitative reasoning course?

In the Shadow of the Palms: The Selected Works of David Eugene Smith

In the Shadow of the Palms: The Selected Works of David Eugene Smith

Report on the 49th Annual USA Mathematical Olympiad

The American Mathematics Competitions (AMC) program of the Mathematical Association of America consists of a series of examinations for middle school, high school, and college students, designed to...

Yeuh-Gin Gung and Dr. Charles Y. Hu Award for 2021 to Deanna Haunsperger for Distinguished Service

The 2021 Gung and Hu Award is enthusiastically bestowed upon Deanna Haunsperger for her prolific service to mathematics including with the Mathematical Association of America, for her influential l...

Quarantine Cartoon Contest

In March 14, 2020, the Southeastern Section of the Mathematical Association of America was scheduled to hold its annual section meeting at High Point University in North Carolina. The meeting typic...

Paying Our Dues: The Role of Professional Societies in the Evolution of Mathematical Biology Education.

Mathematical biology education provides key foundational underpinnings for the scholarly work of mathematical biology. Professional societies support such education efforts via funding, public speaking opportunities, Web presence, publishing, workshops, prizes, opportunities to discuss curriculum design, and support of mentorship and other means of sustained communication among communities of scholars. Such programs have been critical to the broad expansion of the range and visibility of research and educational activities in mathematical biology. We review these efforts, past and present, across multiple societies-the Society for Mathematical Biology (SMB), the Symposium on Biomathematics and Ecology Education and Research (BEER), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM). We then proceed to suggest ways that professional societies can serve as advocates and community builders for mathematical biologists at all levels, noting that education continues throughout a career and also emphasizing the value of educating new generations of students. Our suggestions include collecting and disseminating data related to biomath education; developing and maintaining mentoring systems and research communities; and providing incentives and visibility for educational efforts within mathematical biology.

Mathematics Graduate Student Instructor Observation Protocol (GSIOP): Development and Validation Study

This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions particularly relevant for students’ development of conceptual understanding, called the Mathematical Classroom Observation Protocol for Practices (MCOP2). Instrument validation involved content input from mathematics education researchers and upper-level mathematics graduate student instructors at two universities, internal consistency analysis, interrater reliability analysis, and structure analyses via scree plot analysis and exploratory factor analysis. A Cronbach-Alpha level of 0.868 illustrated a viable level for internal consistency. Crosstabulation and correlations illustrate high level of interrater reliability for all but one item, and high levels across all subsections. Collaborating a scree plot with the exploratory factor analysis illustrated three critical groupings aligning with the factors from the MCOP2 (student engagement and teacher facilitation) while adding a third factor, lesson design practices. Taken collectively, these results indicate that the GSIOP measures the degree to which instructors’ and students’ actions in undergraduate mathematics classrooms align with practices recommended by the Mathematical Association of America (MAA) using a three-factor structure of teacher facilitation, student engagement, and design practices.

Research Trends on Proof Without Words : Focused on the Journals of the Mathematical Association of America

Research Trends on Proof Without Words : Focused on the Journals of the Mathematical Association of America

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.

Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America by Janet L. Beery, Sarah J. Greenwald, Jacqueline A. Jensen-Vallin, and Maura B. Mast (eds.)

Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America by Janet L. Beery, Sarah J. Greenwald, Jacqueline A. Jensen-Vallin, and Maura B. Mast (eds.)

The effects of different versions of a gateway STEM course on student attitudes and beliefs

BackgroundSubstantial research has been conducted focusing on student outcomes in mathematics courses in order to better understand the ways in which these outcomes depend on the underlying instructional methodologies found in the courses. From 2009 to 2014, the Mathematical Association of America (MAA) studied Calculus I instruction in United States (US) colleges and universities in the Characteristics of Successful Programs of College Calculus (CSPCC). One aspect of this study attempted to understand the impact of these courses on student experience.ResultsIn this paper, we describe results from an examination of the effect of course structure on students’ attitudes and beliefs across different versions of Calculus I at a large research university in the USA. To do this, we implemented a follow-up study of the national MAA study of calculus programs in part to identify potential relationships between various course structures and changes in attitudes and beliefs during the course. We compare our results both internally across these course structures and to the national data set.ConclusionsWe find that the statistically significant changes measured in confidence and enjoyment exhibit differences across the different calculus implementations and that these changes are statistically independent of the underlying student academic backgrounds as shown by standardized test scores and high school GPA. This suggests that these observed changes in attitudes and beliefs relate to the experience in our varied course structures and not to the academic characteristics of students as they enter the course. In addition to our findings, we show how this national study can be used locally to study effects of courses on student affective traits.

Marjorie Rice and the MAA tiling

ABSTRACTThe tiling in the lobby of the headquarters building of the Mathematical Association of America (MAA) in Washington, DC, is unusual. Congruent pentagonal tiles fit together to fill the space, with no readily discernable pattern. Also unusual is the history of how the tiling came to be, and who discovered it. Not a mathematician, Marjorie Rice discovered this tiling while pursuing for years her self-assigned task of finding all types of convex pentagons that can tile the plane.

A Cross-Discipline Modeling Capstone Experience

The Mathematical Association of America (MAA) and the American Statistical Association (ASA) have both updated and revised their curriculum guidelines. The guidelines of both associations recommend that students engage in a “capstone” experience, be exposed to applications, and have opportunities to communicate mathematical and statistical analysis, among other recommendations. In this article, we describe a mathematics and statistics capstone course, implemented at a small liberal arts college. We provide evidence that this course accomplishes the goals set forth by the MAA and ASA. We include guidance for other institutions on implementing a similar course.

Experience sharing: Mathematical Contest in Modelling (MCM)

In January 2016, Coventry University’s sigma Mathematics Support Centre (MSC) funded three students for MCM, a multi-day mathematics competition held annually in the USA. This is organised by the Consortium for Mathematics and Its Applications (COMAP) and sponsored by the Mathematical Association of America (MAA), the Society of Industrial and Applied Mathematics (SIAM) and the Institute for Operations Research and the Management Sciences (INFORMS). In this article the team leader and advisor reflect on their experience.

My introduction to copulas

Roger Nelsen is Professor Emeritus of Mathematics at Lewis & Clark College in Portland, Oregon, USA. He studied mathematics at DePauw University (BA, 1964) and Duke University (PhD, 1969). Roger joined the faculty at Lewis & Clark in the fall of 1969, and retired in 2009. Prior to Lewis & Clark, Roger spent a year with the Biostatistics Unit of the Centre International de Recherche sur le Cancer in Lyon, France. He has had visiting appointments at the University of Massachusetts in Amherst and Mount Holyoke College in South Hadley, Massachusetts. In addition to his monograph An Introduction to Copulas, Roger has authored or co-authored eleven books published by the Mathematical Association of America. He has served on the editorial boards of two MAA journals and several of their book series. The fifth interview of this series features a conversation with Roger Nelsen. His Springer book An Introduction to Copulas is eponymous for a mathematical precise and well written entrance into the fascinating field of copulas. Moreover, it serves as a classical reference book, a large number of citations bear witness to this. He collaborated with seminal researchers in our field, and kindly shares his view and memories with us. Roger’s second strand of research – a combination of mathematical puzzles, art, and visualization – are “Proofs Without Words.” He published several books, containing elegant visual justifications of mathematical statements. In the following, our questions to Roger Nelsen are typeset in bold-face.

Students’ Reactions to Reform Mathematics Pedagogy in a Postsecondary Remedial Mathematics Course

IntroductionMany students in the United States who have desired to earn a postsecondary degree have found themselves underprepared for postsecondary mathematics and were required to take remedial mathematics courses (Fike & Fike, 2007; Alliance for Excellent Education [AEE], 2011; Radford et al., 2012). Unfortunately, mathematics has become a gatekeeper for college success (Massachusetts Community College Executive Office, 2006; Fike & Fike, 2007; Epper & Baker, 2009) since attrition rates for postsecondary remedial mathematics courses have often been reported around 50% (Phoenix, 1990; Ellington, 2005; Attewell et al., 2006; Fike & Fike, 2007; Bahr, 2008; Virginia College Community System [VCCS], 2011). Even though traditional lecture techniques provide little benefit to students in remedial mathematics courses (Boylan & Saxon, 1999, Trenholm, 2006), many instructors continue to present their material to passive, uninvolved students (Fry, Ketteridge, & Marshall, 2003; White-Clark, DiCarlo, & Gilchriest, 2008). In order to improve student success in mathematics courses, several mathematics education organizations including The National Council of Teacher of Mathematics (NCTM), The American Mathematical Association of Two-Year Colleges (AMATYC), and the Mathematical Association of America (MAA) have recommended specific practices for mathematics teachers to use in their classrooms. For the purposes of this paper, the recommendations made by these organizations will be referred to as practices and include a shift toward active student learning through group work and exploration of mathematical phenomena before formal presentation of mathematical theorems.A quasi-experimental study was conducted at a small four-year southeast university in Spring 2012 through Spring 2013 that examined the effectiveness of using reform-oriented techniques in a remedial mathematics course (Intermediate Algebra). In Spring 2012, one course was taught in a reform-oriented manner; in Fall 2012 and Spring 2013, one course was taught each semester in a traditional didactic manner. At the end of each of the three courses, an anonymous free-response survey was issued to the students to gauge their reactions to the type of instruction they received in their respective courses. This article will present the findings of those surveys with a focus on the feedback given by students in the reform-oriented course; the feedback from students in the traditional lecture courses will serve as a backdrop by which to interpret the feedback obtained from the reform-oriented course.Review of LiteratureResearchers in the reform mathematics movement emphasize the importance of balancing conceptual understanding with procedural fluency. This balance can be maintained when students actively participate in the learning process by exploring mathematical concepts in groups with the help of technology and by discussing and justifying their findings with their classmates. As a result, students may develop problem solving abilities and also understand the reasoning behind the mathematical principles they are taught. Because of the countercultural recommendations made by reformists (Smith & Star, 2007), researchers have examined the effectiveness of reform pedagogical practices at various grade levels and through a variety of metrics.Research at the middle and secondary school level is worth considering since much of the content taught at this level is also included in postsecondary remedial mathematics courses (Bahr, 2008). Two relevant studies at the middle school level examined students' mathematical success in terms of statewide exams. Reys et al. (2003) found that middle school students who had used reform-based curricula for at least two years performed as well or better than matched comparison students on the Missouri Assessment Program mathematics exam. Thompson (2009) examined the instructional techniques used by middle school mathematics teachers and found that students whose teachers who used multiple reform techniques (including manipulatives and group-based projects) scored higher on the Iowa Test of Basic Skills than did students whose teachers used primarily traditional lecture techniques. …

Interview With Robert W. Hayden

Robert Hayden is retired from Plymouth State University and now teaches online for Statistics.com. He has been active in the Mathematical Association of America and the American Statistical Associa...

Journal Problems Sections: Modern Challenges and Teaching Tools

SummaryAs the Mathematical Association of America enters its second century, this article cites some historical mathematical challenges, relating this unique disciplinary practice to the problems sections in today's journals. It presents some results of a survey conducted with the editors of problems sections in various journals and with several mathematicians active throughout their careers as posers and solvers of problems. For example, it includes their views on the general role of problem solving in the mathematical enterprise, their experience with specific applications in both teaching and research, and a sample of their all-time favorite problems.

A brief history of partitions of numbers, partition functions and their modern applications

‘Number rules the universe.’The Pythagoras‘If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.’Henri Poincaré‘The primary source (Urqell) of all mathematics are integers.’Hermann MinkowskiThis paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers’ graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss’ triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose– Einstein, Fermi– Dirac, Gentile, and Maxwell– Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2015 to W. James Lewis for Distinguished Service to Mathematics

The Mathematical Association of America presented the 2015 Gung and Hu Award for Distinguished Service to Mathematics to W. James Lewis for his outstanding contributions to the mathematics education of teachers, for his leadership in the mathematics profession and in academia at all levels, for his work increasing the visibility and participation of women in mathematics, for his exemplary work serving the state of Nebraska, and especially for his vision and ability to bring together diverse stakeholders in support of positive change in mathematics.