Collegiate Mathematics Education Research Articles

Professional Development in Teaching for Mathematics Graduate Students

The purpose of this article is twofold: to give a sense of the current lay of the land in the preparation of mathematics graduate student teaching assistants (TAs) and to describe the collegiate mathematics education research base informing the next generation of college mathematics instructor preparation. We anchor discussion in three common types of TA preparation programs, each represented in one of the quotes above. Notably, the first quote represents a sink or swim experience that is becoming rare in US PhD-granting mathematics departments. Preparation of TAs for their instructional roles has blossomed in the last twenty years. The second quote is representative of current practices in many departments. The third quote illustrates the activities in innovative departments that are already implementing best practices suggested by research in collegiate mathematics education: sustained professional growth about teaching and learning. To highlight the challenges and benefits of spending time paying attention to teaching, we provide information from postsecondary and related secondary-level educational research of several types. This includes basic and applied educational research that identifies good instructional practices, examines experiences TAs bring with them to teaching, provides frameworks for the structuring of TA preparation, and gives insight into the kinds of mathematics-specific and teaching-specific knowledge that needs to be developed among TAs. And, once a program for supporting TAs to learn and grow as instructors is put in place, evaluation research explores the implementation of efforts to improve TAs’ teaching and the related impacts on undergraduate student learning. We close with promising practices and sketch anticipations for the future of the field of related research. Though not common thirty years ago, today most doctorateand master’s-granting institutions provide some kind of TA preparation for teaching [4a]. The content for this professional development often comes from mathematicians offering their collective wisdom from practical Jessica M. Deshler is assistant professor of mathematics at West Virginia University. Her email address is deshler@ math.wvu.edu.

Making Materials Based on TeX and CAS/DGS — Reports on CADGME 2012 Conference Working Group —

TeX has become one of the most popular tools for editing teaching materials or textbooks in collegiate mathematics education, since it enables usual mathematics teachers to easily produce high-quality mathematical documents. Its capabilities for visualization and computation are fairly limited, so that many teachers simultaneously use various software such as Computer Algebra System (CAS) or Dynamic Geometry Software (DGS) to generate and display high-quality mathematical artworks. In this paper, we discuss the conditions under which the graphics generated by CAS/DGS mostly enhance the educational effect of teaching materials edited by TeX. As a result, the use of a CAS macro package for generating high-quality graphics in TeX documents is proposed.

Alternate Trajectories: Women Moving into Mathematics Education

While only about one-third of each year’s doctoral graduates in mathematics are women, about two-thirds of the doctoral graduates in mathematics education are women. This article reports on the results of a qualitative investigation into the nature of the graduate school-related experiences of women in collegiate mathematics education doctoral programs (Toney, 2008). Eight women with advanced mathematics degrees were interviewed. Each woman chose to move into a collegiate mathematics education doctoral program in a mathematics department. The two-interview protocol explored and extended a framework about women doctoral mathematics students’ experiences suggested by the research of Herzig (2002, 2004a, 2004b), Hollenshead, Younce, and Wenzel (1994), and Stage and Maple (1996). Results support an addition of three new categories to this framework: self as scholar, "my teaching," and future possible self. Concluding remarks include suggestions for future research and new directions for practice, graduate program development, and faculty recruitment.

The Teacher's Discourse Moves: A Framework for Analyzing Discourse in Mathematics Classrooms

In this paper a framework is proposed for analyzing the deliberate actions taken by a teacher to participate in or influence the discourse in mathematics classrooms, and such actions are referred to as the teacher's discourse moves. This work synthesizes elements of several other discourse frameworks, including those of Richards, Sfard, Cobb, and Knuth and Peressini. Expanding on the improvisational dance metaphor of Heaton's, the framework views the teacher in the additional multiple roles as a Choreographer/Stage Manager/Director of classroom discourse. Several research applications of the discourse framework to collegiate mathematics education are discussed, including discourse around collaborative problem solving in Treisman Emerging Scholars workshops, a video‐based study of a college‐level geometry course for teachers, discourse in wireless networked classrooms, and the asynchronous discourse in an online statistics course.

Mathematical Literacy and Abstraction in the 21st Century

Ed Dubinsky received his Ph.D. in mathematics from the University of Michigan in 1962 and for the next 25 years engaged in research in theoretical mathematics. In the mid‐80′s he became interested in mathematics education and has worked exclusively in the area since then. In his research, he tries to understand how a person's mind might be working when he or she tries to understand mathematical concepts at the postsecondary level. Based on this research, he has conducted large‐scale curriculum development projects in calculus, discrete mathematics, abstract algebra and cooperative learning. He has been editor or co‐editor of UME Trends, Research in Collegiate Mathematics Education, and the Journal of Computers in Mathematics and Science Teaching. He has held faculty positions at 8 universities in 5 countries on 3 continents: Fourah Bey College (Sierra Leone), University of Ghana, Tulane University, McMaster University, Polish Academy of Sciences, Clarkson University, Purdue University, and Georgia State University. Dr. Dubinsky is presently retired and consults with several universities on education matters.

Research in Collegiate Mathematics Education II

Research in Collegiate Mathematics Education II

Instructional qualities of a successful mathematical problem‐solving class*

* A short version of this article will appear in a special issue of Research in Collegiate Mathematics Education. American Mathematical Society. Problem solving has been an important issue in mathematics education during the last 25 years. Research studies in this area have documented extensively what students show while working with mathematical problems (resources, beliefs, and cognitive and metacognitive strategies). However, there is little information about how mathematical problem‐solving activities should be implemented in regular classrooms. This paper shows what activities have been successful implemented by an expert during a mathematical problem‐solving course. It focuses on the identification of qualities of the problems used to promote the development of students strategies and values that reflect mathematical practice in the classroom. Specia’ attention is paid to the type of question that help students evaluate their own problem‐solving processes and the importance of allowing the students to work in small group activities. Although the course itself does not address a particular sequence of content (algebra, geometry or calculus), there is indication that it could be used as a model to be adjusted to a regular mathematical course.

Lecturing at the "Bored"

Even a superficial review of the literature on collegiate mathematics education reform reveals a common thread: the imperative nature of the college mathematics student's active participation in the learning of mathematics. Active participation in the classroom may take the form of working cooperatively with classmates in small groups, spending time in the computer lab using class-related software, presenting problems or concepts on the board to classmates, or other activities germane to the subject bestdes passively listening to a lecture presented by the instructor. There is a wide range of lectures styles, but the stle to which I refer is one characterized by little expectation of student engagement besides perhaps following the logic of the lesson. Because active learning in the mathematics classroom is advocated by several professional groups ([1], [4], [5], [6], [8]), it is certainly reasonable for mathematics instructors to reflect on their rationale for maintaining a lecture style of teaching, even part of the time. During the 1995-1996 academic year, that is exactly what I did. I was teaching a section of reformed calculus, with a class size of forty. I had planned on extensive use of cooperative groupwork, and had accordingly divided the class into ten groups of four people each. I attempted to make the groups heterogeneous (in gender and ability) by collecting quantitative measures of the students' previous mathematical performance. Several times during the first two sveeks of class, I set aside time for group work. However, due to the physical layout of the classroom (five rows of auditorium seating with twelve seats per row and an aisle up the middle) my students were having a difficult time actually communicating in their groups. Classtime initially devoted to guided discovery in the groups degenerated into work time for forty individuals, certainly not the vision I had foreseen when planning earlier that summer. To restructure this time, I tried to view my entire class as a large cooperative group, with me as the group leader. Instead of breaking the class into four-person groups as before, I would present examples of concepts we were currently studying, and pose open-ended questions to the class. For example, while developing a geometrical approach to Newton's method for finding the roots of an equation, I asked my students which solution they thought the graphical process would yield when the initial guess for the x-value was directly between two of the roots. Was there a pattern that allowed us to predict the general result? Another time wheh discussing inverse functions, we did an impromptu in-class exploration of which Itnear functions, and later, which general functions, are their own inverses. Such discussions involved much conjecturing, arglling, and scratchpaper seatwork, individually and in pairs, among the students, and were opportunities for algebraic, geometric, and numerical exploration. l Because of my class's general enthusiasm and willingness to participate, If felt we had developed a classroom atmosphere free of criticism, and open to conjecturing. The students often presented problems for each other, furthering their own mathematical communication. Although I was somewhat disappointed not to be able to watch my students develop cooperative skills, I felt that we had made the

Review: A New Era in Collegiate Mathematics Education Research: Good Learning of College Mathematics: Can We Recognize, Understand, Foster, and Document It?

Research in college mathematics education is neither new (Suydam, 1975) nor unusual (Becker & Pence, 1994). However, the literature of this field is still very scattered, with many of the articles published in journals that mathematicians do not usually read. Although in recent years a few books have appeared that deal with college mathematics, books that collect papers devoted to research in the field are certainly needed.

Review: A New Era in Collegiate Mathematics Education Research: A Mathematician's View of RCME

For the mathematician interested in issues of learning and teaching, these are, ostensibly, the best of times. The American Mathematical Society has joined the Mathematical Association of America in making choice time slots available at national and regional meetings for discussions of educational issues. These sessions have been well attended, not only by young Ph.D.'s, but also by senior mathematicians, full professors with the protection of tenure, who have the potential to substantially modify the way in which college mathematics teaching is done.

Collegiate Mathematics Education Research: What Would That Be Like?

Collegiate Mathematics Education Research: What Would That Be Like?

Collegiate Mathematics Education Research: What Would That Be Like?

(1993). Collegiate Mathematics Education Research: What Would That Be Like? The College Mathematics Journal: Vol. 24, No. 5, pp. 431-445.

Alternatives to Research

A Formidable challenge to excellence is posed by two trends in collegiate mathematics education: one is the admirable flow of numerous students into fields requiring mathematics, with a consequent demand for good college teachers; the other is the lamentable tendency for undergraduate mathematics faculties to be understaffed and overworked. The two trends together generate a challenge which the CUPM Panel on College Teacher Preparation now confronts: How can undergraduate faculty members achieve and maintain high quality in mathematics teaching?

Alternatives to Research

A FORMIDABLE challenge to excel lence is posed by two trends in collegiate mathematics education: one is the admir able flow of numerous students into fields requiring mathematics, with a consequent demand for good college teachers; the other is the lamentable tendency for undergraduate mathematics faculties to be understaffed and overworked. The two trends together generate a challenge which the CUPM Panel on College Teacher Preparation now confronts: How can undergraduate faculty members achieve and maintain high quality in mathe matics teaching? Let us assume that active enthusiasm for mathematics is one prerequisite for excellent teaching. At universities, we expect research-oriented professors to impart a sense of mathematics as a grow

Notes on the Status and Future of Films and TV in Collegiate Mathematics Education

Notes on the Status and Future of Films and TV in Collegiate Mathematics Education

Notes on the Status and Future of Films and tv in Collegiate Mathematics Education

Notes on the Status and Future of Films and tv in Collegiate Mathematics Education