Exploring Philosophy During a Time of Reform in Mathematics Education Dr. Kimberly White-Fredette Gordon State College Barnesville, GA

Theoretical framework  Mathematics curricular reform rooted in a social constructivist view of mathematics  NCTM’s mathematics standards (1989, 2000)  Georgia’s curriculum reform (2005 to present)  Development of Common Core Standards for Mathematics (2010 to present)  Social constructivist view of mathematics is rooted in a humanist/fallibilist philosophy of mathematics

Mathematics educational reform: How do we teach and learn mathematics?  NCTM’s Process Standard  Common Core’s Standards for Mathematical Practice  Students engaged in reasoning and critical thinking  Use of worthwhile tasks  Exploration of multiple pathways towards the solution of complex, real-world problems  Communicating about mathematics  Using multiple representations

Mathematics education reform: What is mathematics?  Social constructivism as a philosophy of mathematics (Ernest, 1991, 1998, 2004)  Why Not Philosophy? Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform (White- Fredette, 2010)

What is mathematics?  Traditional/absolutist view of mathematics  Mathematics as a fixed subject of absolute truths  Exploring a humanist/fallibilist view of mathematics  Mathematics as constructed knowledge

Exploring philosophy: research questions  How do teachers define their personal philosophies of mathematics teaching and learning?  As teachers explore humanist/fallibilist philosophies of mathematics, how do their perceptions of mathematics and mathematics teaching and learning change?

Exploring philosophy: participants  Four mathematics educators  Classroom teachers and instructional coaches  Elementary, middle, and high school  Graduate students engaged in a reading-intensive course focused on philosophy of mathematics  Involved with implementation of reform curriculum at classroom level, as well as district-wide and statewide levels

Exploring philosophy: readings  Russell (1919) Introduction to Mathematical Philosophy  Lakatos (1976) Proofs and Refutations: The logic of mathematical discovery  Davis & Hersh (1981) The Mathematical Experience  Hersh (1997) What is Mathematics, Really?

Exploring philosophy: methodology  Data included:  Reading journals  Reflective essays  Extensive interviews over 18 months  Narrative analysis  Telling of stories  Examining stories on multiple occasions, through multiple sources  Thematic analysis within each narrative  Riessman (1993, 2002, 2008)

Exploring philosophy: teacher stories  New to idea of philosophy of mathematics  Philosophy of mathematics influenced by personal experiences (as students and teachers)  Initial attraction of right/wrong nature of mathematics  Love of mathematics tied to struggles and successes  Effort and hard work  Beyond rules and procedures – “doing math”  Power and mathematics (learner and teacher)  Need to see math as more than computation, more than algorithms, more than memorizing formulas  Struggles to have others (students, teachers) see math differently

Discussion  How do we define mathematics?  What is the purpose of school mathematics?  How do we impact teachers’ and students’ views of mathematics?  Importance of our personal stories of mathematics  Examine, explore, challenge

Works cited  Davis, P. J., & Hersh, R. (1981). The mathematical experience. Boston: Birkhauser.  Ernest, P. (1991). The philosophy of mathematics education. London: The Falmer Press  Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany, NY: State University of New York Press.  Ernest, P. (2004). What is the philosophy of mathematics education? [Electronic Version]. Philosophy of Mathematics Education Journal, 18.  Hersh, R. (1997). What is mathematics, really? New York: Oxford University Press.  Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.  National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.  National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.  Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press. (Original work published in 1945)  Riessman, C. K. (1993). Narrative analysis. Thousand Oaks, CA: Sage.  Riessman, C. K. (2002). Analysis of personal narratives. In J. F. Gubrium & J. A. Holstein (Eds.), Handbook of interview research: Context & Method (pp. 695–710). Thousand Oaks, CA: Sage.  Riessman, C. (2008). Narrative methods for the human sciences. Thousand Oaks, CA: Sage.  Russell, B. (1993). Introduction to mathematical philosophy. New York: Dover. (Original work published 1919)  White-Fredette, K. (2010). Why not philosophy? Problematizing the philosophy of mathematics in a time of curriculum reform. The Mathematics Educator, 19(2).