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«PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION EDITORS STACY BROWN SEAN LARSEN KAREN MARRONGELLE ...»

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Part 3. Now think about helping teachers in a PD workshop to build skills in writing story problems.

What challenges might you expect 6th to 8th grade teachers to encounter in creating such a story problem?

Part 4. [Give examples of two different teachers problem posing efforts] How would you respond to each of the teachers?

Conclusion Intercultural orientation is embedded in each component of the TL-PCK model in Figure 3. How and what a teacher leader notices, how and what a teacher notices, and what a teacher leader does with the noticed things in working with teachers are all connected to self-awareness and other-awareness, (i.e., to the intercultural orientations of all in the professional development classroom – teacher leaders and teachers). Though beyond the scope of this proposal, we are also aware of yet another layer that can be added to Figure 3, of university teacher-leader educators, whose students are teacher leaders and for whom the “content” is the entirety of Figure 3.

References Aud, S., Fox, M., & KewalRamani, A. (2010). Status and Trends in the Education of Racial and Ethnic Groups (Tech. Report; NCES 2010-015). U.S. Department of Education, National Center for Education Statistics. Washington, DC: U.S. Government Printing Office.

Bennett, M. J. (2004). Becoming interculturally competent. In J. Wurzel (Ed.), Towards

multiculturalism: A reader in multicultural education (2nd ed., pp. 62–77). Newton, MA:

Intercultural Resource Corporation.

Bennett, M. J. (1993). Towards ethnorelativism: A developmental model of intercultural sensitivity. In R. M. Paige (Ed.), Education for the intercultural experience (2nd ed., pp. 21Yarmouth ME: Intercultural Press.

Bennett, J. M. & Bennett, M. J. (2004). Developing intercultural sensitivity: An integrative approach to global and domestic diversity. In D. Landis, J. M. Bennett, & M. J. Bennett (Eds.), Handbook of intercultural training (pp. 147–165). Thousand Oaks, CA: Sage.

Borko, H. (2004). Professional development and teacher learning: Mapping the terrain.

Educational Researcher, 33(8).

DeJaeghere, J. G., & Cao, Y. (2009). Developing U.S. teachers’ intercultural competence: Does professional development matter? International Journal of Intercultural Relations, 33, 437Dozier, T. K. (2007). Turning good teachers into great leaders. Educational Leadership, 65(1), 54-58.

Hammer, M. R. (2009). Solving problems and resolving conflict using the intercultural conflict style model and inventory. In M. A. Moodian (Ed.), Contemporary leadership and intercultural competence: Exploring the cross-cultural dynamics within organizations (pp.

219-232). Thousand Oaks, CA: Sage.

Hill, H.C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge:

Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.

Jackson, B., Rice, L., Noblet., K. (2011). What do we see? Real time assessment of middle and secondary teachers’ pedagogical content knowledge. In S. Brown (Ed.) Proceedings of the 14th annual conference on Research in Undergraduate Mathematics Education.

454 15TH Annual Conference on Research in Undergraduate Mathematics Education!

Lieberman, A., & Miller, L. (2007). What research says about teacher leadership. In R. H.

Ackerman, & S. V. Mackenzie (Eds.), Uncovering teacher leadership: Essays and voices from the field (pp. 37-50). Thousand Oaks, CA: Corwin Press.

York-Barr, J., & Duke, K. (2004). What do we know about teacher leadership? Findings from two decades of scholarship. Review of Educational Research, 74(3), 255-316.

Yow, J. (2007). A mathematics teacher leader profile: Attributes and actions to improve mathematics teaching & learning. Journal of Mathematics Education Leadership, 9(2), 45TH Annual Conference on Research in Undergraduate Mathematics Education 455 !

Figure 1. Working definition of “culture.

” Short definition of culture: A dynamic social system of values, beliefs, behaviors, and norms for a specific group, organization, or other collectivity; the shared values, beliefs, behaviors, and norms are learned, internalized, and changeable by members of the society (Hammer, 2009).

Figure 2. The intercultural competence developmental continuum.

Figure 3. Layered model for intercultural teacher leader pedagogical content knowledge.

Figure 4. Goals of the Teacher Leadership Program

• Develop a shared vision of mathematics teacher leadership

• Enhance mathematics content knowledge

• Expand understanding of how teachers build knowledge for teaching mathematics

• Increase pedagogical content knowledge for teaching teachers

• Develop understanding of equity and culture in mathematics in schools and districts

• Build self-efficacy as teacher-leaders of mathematics !

456 15TH Annual Conference on Research in Undergraduate Mathematics Education !

Figure 5. Teacher professional learning goals

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Abstract

Although some research indicates that the number of women in science, technology, engineering, and mathematics disciplines have been growing (Astin et al., 1983), women and other minorities in mathematics classrooms that serve these disciplines are still largely absent (Pattatucci, 1998).

Given the lack of women and minorities in the classroom, how can instructors develop equity and quality in mathematics programs and fields where mathematics acts as a gatekeeper? By utilizing data collected in a differential equations course, we engage in a discussion that explores what leads to students’ success in mathematics. We were interested in the interrelationship between students’ demographic backgrounds and classroom dynamics to see how we can better serve women, minorities, and those from rural and first generation university backgrounds

Keywords: Gender, student success, equity, differential equations

Purpose Although some research indicates that the number of women in science, technology, engineering, and mathematics (STEM) disciplines have been growing (Astin et al., 1983;

Eisenhart & Holland, 2001), women and other minorities are still largely absent in mathematics classrooms that serve STEM disciplines (Pattatucci, 1998; Wyer et al., 2001). This is particularly the case at the Midwestern land grant institution that was the focal point of our research, where the ratio of men to women enrolled in differential equations at the time of the study was 9:1. Since this course is required of mathematics majors and many other STEM fields, it prompted us to investigate this issue.

Given the lack of women and minorities in the classroom, how can instructors at a rural land grant university develop equity and quality in mathematics programs and fields where mathematics acts as a gatekeeper? By utilizing data collected during a spring semester differential equations course, we engage in a discussion that explores what leads to students’ success in mathematics. In particular, we were interested in the interrelationship between students’ demographic backgrounds and classroom dynamics to see how we can better serve women, minorities, and those from rural and first generation university backgrounds.

Perspectives Previous research provides insight into understanding the lack of women’s presence and success in the STEM fields (Correll, 2001; Eisenhart & Holland 2001; Keller, 1985 & 2001;

Zuckerman, 2001). Much of the research emphasizes the ways in which young women are discouraged, through gender socialization, to take seriously a career in the sciences (Correll, 2001; Eisenhart & Holland, 2001; Keller, 1985, 2001; Muller & Pavone, 1998; Zuckerman, 2001). Correll discusses the importance of gender in men and women’s choices to step into careers in STEM. In particular, cultural beliefs about men and women’s ability to do 458 15TH Annual Conference on Research in Undergraduate Mathematics Education mathematics impact women’s self perception of competency in this field, which ultimately impacts the career paths that women take. In addition, Muller and Pavone discuss how young women are more likely to “internalize failure, and are thus less apt to persist in an area in which they have not been particularly encouraged” (p. 250). Research also emphasizes that the first year of college is essential to tracking majors in the sciences, and if young women are lacking self-confidence and encouragement from their experiences in middle- and high school, they will be less likely to move into those major areas of study.

Although there are studies that provide personal narratives about women’s success in STEM fields (Keller, 2001; Pattatucci, 1998; Sands, 2001), there is little research that examines women and other underrepresented groups’ success in mathematics classrooms. From the personal narratives and interviews of successful women and minority students in the sciences, their success is largely a product of a variety of factors, ranging from parental support to personal tenacity. It is our goal to broaden this understanding and provide a working model that can encourage systemic support for women and other underrepresented students in the mathematics classroom. In turn, we explore the following research questions: (a) Who is succeeding in mathematics courses?, (b) When are students choosing their mathematics-based majors?, and (c) What do students feel has contributed most to their success in mathematics coursework?

Methods To examine the success of women and other underrepresented groups, students who had almost completed a differential equations in mathematics were purposively selected as participants in the study. By reaching this level of mathematics, they have proven to be successful in mathematics. We define success by the fact that students in a differential equations class have passed the calculus series in mathematics, which are often used at universities as “weed out” courses for the STEM fields. At this point, they are in their last required mathematics course for engineering, and the students who are not engineers are likely to be continuing on to another STEM field. At the end of the spring semester, five sections of students (n = 150) enrolled in a differential equations course were surveyed. One hundred and one surveys were completed for a response rate of 70%.

Survey Instrument The survey instrument, which was created by the authors, was used to examine students’ perceptions of their success in mathematics courses, both in high school and at the university level. A mixed-method (Johnson & Christensen, 2004) approach was used when creating the survey. Specifically, the survey contained 10 open-response items and 23 closed-response items.

The formation of these questions was informed by the background literature as well as by questions we had about student success in mathematics. In the surveys, we collected information on each student’s academic background, university classroom experiences, demographic background, and parent’s educational and economic background. We were particularly interested in what students attributed to their success in their major and how they dealt with challenges Data Analysis The researchers worked as a team to enter all of the closed-ended survey responses into EXCEL spreadsheets and the open-ended responses were entered into the HyperRESEARCH software program. From here, the researchers compiled the data both section-by-section and as a whole. Demographic information was compiled first to allow data from females, first generation college students, and non-traditional students to be recorded separately, as well as with each larger group. Thus far, the researchers have only examined the quantitative data by using simple 15TH Annual Conference on Research in Undergraduate Mathematics Education 459 descriptive statistics. In the final paper, the researchers will include results that compare responses to closed-response items that have been analyzed using statistics that allow for group comparisons. Open-ended response items will be used for triangluation purposes to help ensure reliability of the results. These results and the coding scheme will be discussed further in the final paper.

Results In our analysis of the data thus far, we have focused on who is succeeding in mathematics courses, as well as to what they attribute that success. We also wanted to look at when students are choosing their mathematics-based majors and how students “feel” about being in these classes. Results pertaining to students’ feeling about their coursework will be included in the final paper. Here we provide a brief overview of the preliminary findings.

Who is succeeding in mathematics courses?

We began our data analysis by determining the demographic nature of the students who had made it to the level of differential equations. It was important to know who was succeeding in the mathematics before we were to examine why they thought they were successful in mathematics. The gender gap was quite pronounced, as only 15.84% (n = 15) of the respondents were female and 84.16% (n = 85) participants were male. It should be noted that the university is made up of 57% males and 43% females. In addition, only 1.9% (n = 2) of the respondents were non-white. There were no African-American respondents. These descriptive statistics, in and of themselves, tell us that some groups are underrepresented in the final mathematics course required from most STEM majors (in particular for the field of engineering) at this institution.

With an expectation that these discrepancies may arise after obtaining information from the registrar on the demographics of the students enrolled in differential equations in the previous year, we were interested in finding out when these students selected their majors.

When are students choosing their mathematics-based majors?



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