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Kwon, O., Allen, K., & Rasmussen, C. (2005). Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105 (5), 227–240.

Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modelling perspectives on mathematics problem solving, learning, and teaching? In Modelling and applications in mathematics education (pp. 161–170). Springer.

Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thoughtrevealing activities for students and teachers. In A. E. Kelly & R. Lesh (Eds.), Handbook

of research design in mathematics and science education (pp. 591–645). Mahwah, NJ:

Lawrence Ealbaum Associates.

Lesh, R., Doerr, H. M., Carmona, G., & Hjalmarson, M. (2003, April). Beyond constructivism. Mathematical Thinking and Learning, 5 (2), 211–233.

Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 1–30). New York, NY: Springer.

Rasmussen, C., & Blumenfeld, H. (2007). Reinventing solutions to systems of linear differential equations: a case of emergent models involving analytic expressions. The Journal of Mathematical Behavior, 26 (3), 195–210.

394 15TH Annual Conference on Research in Undergraduate Mathematics Education

Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity:

a practice-oriented view of advanced mathematical thinking. Mathematical Thinking and Learning, 7 (1), 51–73.

Shternberg, B., & Yerushalmy, M. (2003). Models of functions and models of situations:

on the design of modeling-based learning environments. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 479–498). Mahwah, NJ: Lawrence Erlbaum and Associates.

Standler, R. B. (1990). Editorial: mathematics for enigneers. The Journal of Undergraduate Mathematics and Its Applications, 11, 1–6.

Zbiek, R. M., & Conner, A. (2006, May). Beyond motivation: exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics.

Educational Studies in Mathematics, 63 (1), 89–112.

Figure 1. : Schematic of the modeling process (Zbiek & Conner, 2006) 15TH Annual Conference on Research in Undergraduate Mathematics Education 395


Future Teachers’ Views of Mathematics and Intentions for Gender Equity: Are These Carried Forward into Their Own Classrooms?

Author Name and Affiliation:

Jacqueline M. Dewar Loyola Marymount University

Abstract (Preliminary Research Report):

Previous work indicated that an interdisciplinary mathematics and gender course about women mathematicians and their contributions to the field shifts students’ views away from seeing mathematics as the study of numbers and toward a more expert view of what the subject entails.

In addition, at the end of the course in the reflective writing portion of a portfolio, future teachers frequently volunteer their intentions to foster gender equity in their own classrooms. This preliminary research report will explore whether, and how, this enriched view of mathematics and the resolve for equity persist and influence the classroom teaching of four former students.

It will also seek to determine the particular learning experiences that most contributed to any positive findings. Ethnographic methods, including interviews and classroom observations, will be employed.

Keywords: K-12 teacher preparation, gender equity, views of mathematics, case study Students throughout K-12, as well as many in college, even those majoring in STEM (Science, Technology, Engineering and Mathematics) fields consider mathematics to be the study of numbers (Dewar, 2008; Forringer, 2010). In contrast, experts in the field, namely mathematics faculty, describe mathematics as being concerned with patterns, proof, abstraction and generalization (Devlin, 1994; Dewar, 2008). Concern about students’ understanding of their discipline is longstanding. Schwab (1964) argued the importance of undergraduates, and especially future teachers, learning the underlying structures and principles of their majors. Teaching disciplinary specific practice continues to be a matter of concern to this day (Leamnson, 1999; Riordan & Roth, 2005). In mathematics, the phenomenon known as stereotype-threat (Steele, Spencer, & Aronson, 2002), wherein the performance of members of a group about which there is a negative stereotype suffers due to anxiety that that their performance will conform to the stereotype, makes excelling in mathematics even more challenging for female and minority students.

A small study (n = 7) of future teachers enrolled in 2004 in an interdisciplinary mathematics and gender course titled, Women and Mathematics, indicated that this course was successful in moving students toward a more expert view of mathematics, based primarily on a content analysis of their descriptions of mathematics as a field of study at the beginning and the end of the course, whereas traditional courses in the mathematics major curriculum did not. In addition, reflective writing in their end-of-course portfolios revealed that the students were very determined to present mathematics in their future classrooms as a desirable activity for all students. Eighteen months later, three of these seven students were interviewed, two of whom were teaching. These interviews 396 15TH Annual Conference on Research in Undergraduate Mathematics Education suggested that the two who were teaching had maintained their richer views of mathematics. The former student who was not teaching (she was working in student affairs on a local college campus) had shifted back to a description of mathematics being mostly about numbers. These results were intriguing and begged to be explored in greater depth with additional students, especially with those who had actual K-12 classroom teaching experience.

This new study explores whether, and how, the enriched views of mathematics and the resolve for equity persist and influence the classroom teaching of a new cohort of former students. For any positive findings, it seeks to determine the particular learning experiences that most contributed to those. Specifically,

• Do the former students’ enriched views of mathematics persist?

• Is there evidence that the more expert views espoused at the end of the Women and Mathematics course are influencing the instruction of these former students who are now teaching in their own classrooms?

• In what ways have the former students carried out their stated commitment to equitable mathematics instruction?

• What courses, learning experiences or other factors influenced the teachers’ views of mathematics or their approaches to equitable instruction?

• What role, if any, did participation in several pre-professional opportunities (presenting workshops at conferences for future teachers or at a math/science career day for junior high girls) associated with the second cohort, but not experienced by students in the first study, play in developing students’ resolve to provide equitable mathematics instruction and helping them to achieve this goal once they were teaching?

The subjects of the current study, four former students of the Women and Mathematics course in 2008, are now in their third year of teaching. Data similar to that gathered in the first study was collected during the course to determine their views and intentions for gender equity. Ethnographic methods including classroom observations and interviews are being employed to determine whether their views of mathematics persist and are influencing instruction, whether resolve to create an equitable classroom is carried out, and what courses, learning experiences or other factors contributed to any positive findings. The observations and interviews are being conducted in October and November of 2011. The data being gathered relative to gender equity in the observations and interviews includes seating assignments, grouping assignments, classroom displays, differences in classroom discourse, how teachers describe an equitable classroom, how their classroom fits that description, their views of the similarities and differences between the girls and boys in their class relative to cognition, behavior, motivation, beliefs about their ability to do mathematics, and how those views influence the way they design their instruction. Relative to the teachers’ views of mathematics, the evidence being collected is how they currently describe mathematics, what they want their students to think mathematics is all about, how that was reflected in the lesson observed, how it might appear in other lessons, whether student work samples reflect those aspects of mathematics. They are also being asked to identify which courses, learning experiences or other factors influenced their views of mathematics and equity.

The findings of this study have the potential to be useful to undergraduate mathematics major programs as well as mathematics teacher preparation programs. Presumably, college faculty have an intrinsic interest in what views of the discipline their students hold. Program review and assessment 15TH Annual Conference on Research in Undergraduate Mathematics Education 397 requirements certainly invite and encourage departments to investigate student understanding of their discipline. Further, the importance of this question for future K-12 teachers can hardly be exaggerated, since what views they hold will influence their choices about what content they teach and how they approach it, given that precollege-level mathematics teaching is so constrained by the realities of State standards and “No Child Left Behind.” Enlightening future teachers about the facts and fallacies that underlie the widely held idea that boys are better at math than girls is one way to empower them to confront these stereotypes personally and then, in turn, with their students. Providing information about role models and awareness that women have contributed to the development of mathematics is another important strategy.

Convincing students that mathematics is as important for girls to learn as for boys is yet another challenge faced by K-12 teachers (Gilbert & Gilbert, 2002). The Women and Mathematics course addresses all of these topics in addition to displaying mathematics as a study of patterns, emphasizing and contrasting the use of inductive and deductive reasoning, and providing multiple representations for many mathematical concepts. Which of these aspects of the course, if any, has a positive and enduring influence on future teachers is something this study seeks to answer.

For this Preliminary Research Report suggested Discussion Questions are:

• Would undertaking similar observations and interviews with teachers who have not taken the Women and Mathematics courses, as points of comparison, be a worthwhile undertaking? If so, how should this comparison group of teachers be chosen?

• How does one determine how a view of mathematics influences instruction?

• How does one accurately determine what factors influenced a person’s view of mathematics?

• How does one accurately determine what informs a future teacher about the need for equitable instruction?

• How might one determine what is effective in helping them develop the resolve to achieve that and give them useful tools toward that end?

Devlin, K. (1994) Mathematics, the Science of Patterns. New York: Scientific American Library.

Dewar, J. (2008). What is mathematics: Student and faculty views. Electronic Proceedings for the Eleventh Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education Conference on Research in Undergraduate Mathematics Education, San Diego, CA, 2008.

Forringer, R. (2010, August). My favorite lesson: The first day of class. The Mathematics Teacher.

104(1), 80.

Gilbert, M. & Gilbert, L. (2002, May). Challenges in implementing strategies for gender-aware teaching. Mathematics Teaching in Middle School. 7(9). 522.

Leamnson, R. (1999). Thinking About Teaching and Learning: Developing Habits of Learning with First Year College and University Students. Sterling, VA: Stylus.

398 15TH Annual Conference on Research in Undergraduate Mathematics Education

Riordan, T. & Roth, J. (2005). Disciplines as Frameworks for Student Learning. Sterling, VA:


Schwab, J. (1964). Structure of the disciplines. In G. W. Ford and L. Pugno (Eds.), The structure of knowledge and the curriculum. Skokie, IL: Rand McNally.

Steele, C., Spencer, S., & Aronson, J. (2002). Contending with group image: The psychology of stereotype and social identity threat. In M. Zanna (Ed.), Advances in Experimental Social Psychology Vol. 37. San Diego, CA: Academic Press.

–  –  –

Title: Authority dynamics in mathematics discussions Authors: Rebecca-Anne Dibbs, University of Northern Colorado David Glassmeyer, University of Northern Colorado Michael Oehrtman, University of Northern Colorado Craig Swinyard, University of Portland Jason Martin, University of Central Arkansas


We employed grounded theory techniques to examine the evolution and influences of authority relationships in an undergraduate mathematics education research study. Our analysis focused on video data from a five day teaching experiment with two faculty researchers engaging two second-semester calculus students in a guided reinvention of formal limit definitions. We will discuss our model for authority in a mathematical discussion and characterize the patterns, influence and evolution of authority that we identified in the guided reinvention. Finally, we illustrate the need for researchers to be cognizant of authority patterns in group data collection settings, since such patterns can mask individual evidence of knowledge and reasoning.

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