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Association: Name: North American Chapter of the International Group for the Psychology of Mathematics Education URL: http://www.pmena.org
Citation: URL: http://www.allacademic.com/meta/p117562_index.html Direct Link: HTML Code:

Bruce, Cathy,. "Building Confidence in Teaching Mathematics: Experiences of Pre-service Teachers that Hinder and Enable Confidence" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117562_index.html>

Bruce, C. D. , 2004-10-21 "Building Confidence in Teaching Mathematics: Experiences of Pre-service Teachers that Hinder and Enable Confidence" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117562_index.html

Publication Type: Conference Paper/Unpublished Manuscript Review Method: Peer Reviewed Abstract: a) Objectives: In a study of preservice teachers at a University in Ontario, those teacher candidates who were preparing to teach Grades K-6 were not confident in their abilities to teach mathematics. This study attempted to identify what was most challenging for these preservice teachers and what factors hindered or enhanced their confidence as mathematics teachers. b) Research Perspectives: If we want teachers to provide powerful mathematics learning opportunities for students, we must provide teachers with these same opportunities (Feiman-Nemser, 2001). Mathematics education has been an area of concern across North America for two decades since the critical American publication of A Nation at Risk (National Commission on Excellence in Education, 1983). Professional development and reform in the area of mathematics teaching has been well represented in the literature (Simon Tzur, Heinz, Kinzel, 2000; Ross, 1999; Spugun, 1996; NCTM Yearbook 1994; Borko, Davinroy, Bliem and Cumbo, 2000). The related topic of preservice teacher confidence in mathematics teaching is building its own small body of recent literature that focuses on the mathematics methods courses associated with preservice programs. (Fieman-Nemser, 2001; Freeman & Smith D.L., 1997; Spungin, 1996). How do preservice teachers build the confidence to teach using a standards-based mathematics approach? Specifically, what do preservice teachers think contributes to or hinders their professional confidence? c) Methods of Inquiry & d) Data Sources The site for the study was a newly established Canadian school of professional learning with a commitment to social constructivist interpretations of teaching and learning. Students (N=50) engaged in a mathematics methods course participated in (N=18) focus groups about their experiences in learning to teach mathematics Open ended survey (n=50) Participants completed a survey with eight questions. They responded in writing at the beginning of the methods course. Data was collated and summarized to assist with selection of focus group participants. Focus group interviews (18 study participants in 3 groups of 6) Each member of the focus group was asked to draw an image with key words that represented how they saw themselves as math teachers. The images encouraged interaction amongst group members that was experience based. Focus group interview transcripts were analysed for reoccurring themes and consistent patterns using a grounded theory approach (Creswell, 1998; Strauss and Corbin, 1990). Participant Observer A participant observer was included during the focus group interviews to provide an additional perspective beyond those of participants and the instructor of the mathematics methods course. Data analysis of focus group interviews: The researcher and participant observer analysed the transcripts independently to ensure consideration of all possible categories and themes as well as to look for consistent interpretation of the transcripts. Themes repeatedly identified by both analysts in independent open coding (Strauss & Corbin, 1990) were deemed of greater reliability. Processes of axial and selective coding were then applied to determine commonalities, contradictions and groupings of themes. e) Results Four overlapping themes emerged from the data. 1. Preservice Teachers’ Inner Tensions What do preservice teachers think challenges their professional confidence? 1a. Healing old wounds: In knowing that they would be taking a mathematics course, the preservice teachers indicated that they revisited their prior experiences as students learning mathematics. The stories they told in the focus group illustrated a series of predominantly negative experiences. These memories, although recalled from the distant past, were vivid for the participants. They left lasting impressions that affected preservice teacher abilities to enter the course with confidence. 1b. Transmission style learning as prior experience: The use of manipulatives, math discourse and meaning making as central to the methods course attempted to model approaches that would be most effective for student learning. Throughout the focus group interviews, preservice teachers emphasized the value of making meaning for themselves as mathematicians so that they could facilitate student construction of meaning in their own classrooms. The methods course allowed these preservice candidates to build some beginning confidence as effective mathematics teachers. 1c. Tension of high stakes, layered learning: As the preservice teachers were learning to teach math, they were developing new conceptual understandings of math for themselves. Sandy said “It has to make sense to me first. I have to get over myself.” The sense of fragility and redefining of self through powerful mathematical understandings were deep and affected the preservice teachers’ sense of self as people and as teachers. 2. The Importance of Building a Math Community What do preservice teachers think enables their professional confidence? 2a. The importance of a positive and safe learning environment: Preservice teachers voiced their beliefs that they would only take risks in math learning within a safe, positive environment. Danny described the environment as “something organic and something that evolves and it starts with trust and respect and openness.” The preservice program offered a safe learning environment through explicit development of a community of learners that encouraged risk taking, asking questions and investigating theories. 2b. Components of a math community: The group discussed their understanding of the notion of ‘mathematics community’ throughout the interviews. The preservice teachers saw a need to build math community in their own classrooms as we were attempting to build community in our methods course. The key elements were math discourse, multiple solutions and math terminology, and the use of manipulatives in small groups 3. Understanding the Meaning of ‘Engagement’ with Mathematics What other elements of the methods course enabled preservice teachers to build their professional confidence? 3a. Fun versus engagement: Particular focus group discussions highlighted how the preservice teachers had arrived at a point where they recognized that struggling with mathematical problems could be challenging and engaging. This was significantly different from their earlier impressions that mathematics was not ‘fun’ or engaging. 3b. Use of manipulatives for meaning making: The use of manipulatives throughout the mathematics methods course served as a key vehicle to allow for exploration of mathematical ideas. It is important here to distinguish between the use of manipulatives that merely represent existing concepts (such as plastic coins to represent money) and the use of manipulatives to explore concepts in mathematics (such as the use of objects and blocks to create pattern or the use of a circle of string and grid paper to explore fixed perimeter and changing area). For those preservice teachers who struggled with nebulous mathematical ideas (such as infinity, zero, and, capacity) the manipulatives became an anchor for meaning-making. 3c. Real life applications of math: Two preservice teachers independently drew images of spider webs during the focus group interviews. For Sandy and Andi, making real world connections was a critical feature of building their confidence in understanding and teaching mathematics and their webs were symbols of that real world connection. 4. Developing Personal Professional Identity: How did growing confidence affect preservice teachers’ sense of self? 4a. Learning by teaching: Opportunities to teach mathematics while on placement proved to be an enormous confidence builder for preservice teachers. Although some were originally reluctant to try, they did, and were rewarded with new learning and increased confidence in their abilities to teach mathematics. This enhanced the preservice teachers’ sense of identity as capable mathematics teachers. 4b. Changing view of self: The theme of teacher candidates redefining themselves as people, and as teachers of mathematics was an intriguing issue that was difficult to for individuals to describe. Although this state of ‘reconstructing’ identity challenged preservice teacher confidence, it paradoxically, also led to new found confidence as mathematicians. Conclusion Primary junior preservice teachers struggled with a host of experiences that challenged their confidence teaching mathematics. Earlier experiences as students of mathematics seemed to have significant impact on levels of confidence of teacher candidates. This is in agreement with previous research in the area of learning mathematics in preservice constructivist classrooms (Anderson & Piazza, 1996; Ross, McDougall, & Hogaboam-Grey, 2002). As preservice teachers were exposed to constructivist teaching methods, they entered a layered learning process which involved participants in ‘doing and learning’ mathematics by making meaning while learning how to ‘teach’ mathematics. Issues of teaching in ways they had not experienced surfaced as challenges to confidence. This was further complicated by their desire to effectively use tools such as manipulatives, computers and calculators to facilitate student understanding. Simultaneously, in experiencing a safe, active, community based mathematics classroom, confidence of preservice teachers increased. This combination of challenges coupled with an enabling environment made for a charged learning environment that questioned self, other, methodology, and mathematics as preservice teachers gained confidence in their mathematics teaching. References Anderson, D.S. & Piazza, J.A. (1996). Changing beliefs: Teaching and learning mathematics in constructivist preservice classrooms. Action in Teacher Education, 17(2), 51-62. Beck, C. & Kosnik, C. (2003). Social Constructivism in Preservice Education. OISE/UT Preliminary Draft, July 31, 2003. Beck, C. & Kosnik, C. (2001). From Cohort to Community in a Preservice Teacher Education Program. Teaching and Teacher Education, 17, 925-948. Berg, B.L. (2001). Qualitative Research Methods for the Social Sciences. Allyn and Bacon of Pearson Education Co., Needham Heights, MA. Brewer, J. & Daane, C.J., Translating Constructivist Theory into Practice in Primary-Grade Mathematics. Education, Vol. 123, Issue 2, 416-423. Creswell, J.W., (1998). Qualitative Inquiry and Research Design; Choosing Among Five Traditions. Sage Publications, Thousand Oaks, CA. Edmunds, H. (1999). The Focus Group Research Handbook, Thousand Oaks, CA: Sage. Eisenhart, M., Borko, H., Underhill, R., Brown, C., Agard, P., (1993). Conceptual Knowledge Falls Through the Cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, Vol. 24, No1, 8-40. Feiman-Nemser, S. (2001). From Preparation to Practice: Designing a Continuum to Strengthen and Sustain Teaching. Teachers College Record, Vol. 103, NO.6, December. Freeman Cook, C., Smith, D. L.. (1997). Active and Engaged? Lessons from an Interdisciplinary and Collaborative College Mathematics and Science Course for Preservice Teachers. Meeting Paper, AERA, Chicago, IL. March, 24-28. Kosnik, C. & Beck, C. (2003). The Contributions of Faculty to Community Building in a Teacher Education Program: A Student Teacher Perspective. Teacher Education Quarterly. Summer 2003. Kvale, Steinar. (1996). Interviews: An Introduction to Qualitative Research Interviewing. Sage Publications, Thousand Oaks, CAL. Morgan, D. (1988). Focus groups as qualitative research, Newbury, CA: Sage Publications. Munby, H. Lock, D. Hutchinson, N., Whitehead, L., & Martin, A. (1999). Evaluation by teaching candidates of a field-based teacher education program using focus groups. Teacher Education Quarterly, Spring, 35-51. National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics, 2000. Reston, Va. Panyan, M., Hillman, S., & Liggett, A. (1997). The role of focus groups in evaluating and revising teacher education programs. Teacher Education and Special Education, 20(1), 37-46. Ringstaff, C. & JH Sandholtz. (2002). Out-of-Field Assignments: Case Studies of Two Beginning Teachers, Teachers College Record, Vol. 104, No.4, June. Ross, J. A.(1999). Implementing Mathematics Education Reform: What the Research Says. Paper prepared for the Impact Math Project, Ontario Ministry of Education, Sept. Ross, J. A., McDougall, D. and Hogaboam-Gray, A. (2002). Research on Reform in Mathematics Education, 1993-2000. The Alberta Journal of Educational Research. Vol. XLVIII, No. 2, Summer 2002, 122-138. Simon, M.A., Tzur, R. Heinz, K, & Kinzel, M. (2000). Characterizing a Perspective Underlying the Practice of Mathematics Teachers in Transition. Journal for Research in Mathematics Education, Vol.31, No.5, 579-601. Spugin, R. (1996). Teaching Teachers to Teach Mathematics. Journal of Education, Vol.178 No.1. Strauss, A. & J. Corbin (1990). Basics of Qualitative Research: Grounded theory procedures and techniques. Sage, Newbury Park, CA. Wenger, E. (1998). Communities of Practice: Learning, Meaning, and Identity. Cambridge University Press, UK. Woolfolk, A. E., & Hoy, W. K. (1990). Prospective teachers' sense of efficacy and beliefs about control. Journal of Educational Psychology, 82(1), 81-91. Woolfolk, A. E., Rosoff, B., & Hoy, W. K. (1990). Teachers' sense of efficacy and their beliefs about managing students. Teaching and Teacher Education, 6(2), 137-148.

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