2013 Conference Proceedings - University of Nevada, Las Vegas

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teachers to continue to develop an understanding of the conceptual metaphors used by teachers.The claim is that identifying teacher metaphors directly aids in teacher meaningful listening.These results will be discussed at the conference.If the vehicle for this methodology is conceptual metaphors, teacher listening fuels thisvehicle. In Michael Gilbert’s (2005) article, An examination of listening effectiveness ofeducators: Performance and preference, he identifies how different personalities in educationhave different indicators of effective listening. Gilbert identifies that teachers expect students tolisten 65-90% in the traditional classroom, but how do mathematics teachers listen? Thepersonality type for most mathematics teachers is the persistor; conscientious, dedicated, andobservant believers in their craft. According to Gilbert, these personalities scored very low oneffective listening. This is no surprise as Gilbert recognizes the limited training we give toeducators on how to listen.The significance to teacher listening can be perceived from the pervasive need for allteachers to see metaphors as an intimate form of communication at all levels of education (Petrie& Oshlag, 1993), to the specific understanding that metaphors directly imply an embodiedmathematics that is not mind-free (Lakoff & Nunez, 2000). Davis (1997) discovered through aseries of vignettes that mathematics teachers listen through “concept study” with three levels oflistening: evaluative listening (assessment-based paradigm), interpretive listening (constructivistparadigm), and hermeneutic listening (conceptual participation paradigm). The third form oflistening Davis suggests is what teachers should strive to develop, an immersed perspective ofgenuinely participating and sharing in the cognitive experiential development of the meaningbehind the mathematical topic. In no way is this restricted to problem solving. Problem solvingwas my means to discovering this methodology, but not its only use.What my research proposes is that CMT analysis allows for this participatoryconceptualization by analyzing and interpreting the shared experiences of the students throughtheir conceptual metaphors. This is not to suggest that teachers must follow my methodology inthe classroom as this is ridiculously time and energy consuming. Instead, I suggest throughpractice and professional development with conceptual metaphor theory, teacher’s ability tolisten her will advance from interpretive listening to hermeneutic listening so that mathematics iscontextualized for the student in terms of their experiences and not the teachers.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 177
ReferencesBlack, M. (1962). Models and metaphors: Studies in language and philosophy. Ithaca, N.Y.:Cornell University Press.Cobb, P. (2007). Putting philosophy to work: Coping with multiple theoretical perspectives. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: Aproject of the National Council of Teachers of Mathematics (pp. 3-38). Charlotte, NC:Information Age Pub.Danesi, M. (2003). Conceptual metaphor theory and the teaching of mathematics: Findings of apilot project. Semiotica, 145, 71-83.Danesi, M. (2007). A conceptual metaphor framework for the teaching of mathematics. Studiesof Philosophy and Education, 26, 225-236. doi: DOI 10.1007/s11217-007-9035-5Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching.Journal for Research in Mathematics Education, 28(3), 355.Eatough, V., & Smith, J. A. (2008). Interpretative phenomenological analysis. In C. Willig & W.Stainton Rogers (Eds.), Qualitative research in psychology (pp. 179-194). Los Angeles:Sage Publications.Gilbert, M. B. (2005). An Examination of Listening Effectiveness of Educators: Performanceand Preference. Professional Educator, 27(1-2), 1-16.Glasersfeld, E. v. (1991). Radical constructivism in mathematics education. Dordrecht, TheNetherlands ; Boston: Kluwer Academic.Kövecses, Z., & Benczes, R. (2010). Metaphor: A practical introduction (2nd ed.). New York:Oxford University Press.Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge;New York: Cambridge University Press.Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor andthought (Vol. 2, pp. 202-251). Cambridge England; New York, NY, USA: CambridgeUniversity Press.Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from: How the embodied mindbrings mathematics into being. New York, NY: Basic Books.Merriam-Webster, I. (2011). Merriam-Webster's dictionary and thesaurus. Springfield, Mass.:Merriam-Webster.Ortony, A. (1993). Metaphor and thought. Cambridge England; New York, NY, USA:Cambridge University Press.Pólya, G. (1954). Induction and analogy in mathematics. Princeton, N.J.: Princeton UniversityPress.Presmeg, N. C. (1997). Reasoning with metaphors,and metonymies in mathematics learning. InL. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp.267-280). Mahwah, N.J.: L. Erlbaum.Sfard, A. (1997). Commentary: On metaphorical roots of conceptual growth. In L. D. English(Ed.), Mathematical reasoning :analogies, metaphors, and images (pp. 339-372).Mahwah, N.J.: L. Erlbaum.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 178
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….where the Mathematicscomes swee
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THANK YOU TO OUR REVIEWERSKeith Ado
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Table of ContentsPreservice Teacher
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Support for Students Learning Mathe
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own problem solving, which is criti
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to get started and persistence. Tea
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Posamentier, A. S., Smith, B. S., &
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conceptual understanding, applicati
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Table 1Identified Mathematical Prac
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justify their statements, included
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Finally, engagement in MP.6 was ass
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PRESERVICE TEACHERS’ EMOTIONAL EN
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“experiences that are charged wit
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Number of journals containingEmotio
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ConclusionsStruggle and frustration
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Mathematics Teacher Candidates’ U
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function and applied the vertical l
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semester, about half of the course
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They further state that “the impo
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C. Laborde (Eds.) International Han
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(SCK), or knowledge of mathematics
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level of difficulty for each partic
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MKT Measures ScoresMathematics in G
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deep rooted belief in a single way
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THE INTERVIEW PROJECTAngel Rowe Abn
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involving addition and subtraction:
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6+7 4+9=6+(6+1) Substitution =4+(10
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We strongly believe that this inter
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AN INNOVATIVE APPROACH FOR SUPPORTI
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Practice throughout the investigati
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are expected to pursue. Teacher not
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students to organize their reports
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Slovin, H., Venenciano, L., Ishihar
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The research presented in this pape
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students’ confidence. Because bel
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triangulation necessitated examinat
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their ability to teach the mathemat
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SPATIAL REASONING IN UNDERGRADUATE
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journal prompt would be given as a
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given to the 33 students on the MPI
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to advance our way of life, then sp
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STUDENT CONCEPTIONS OF “BEST” S
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students are likely to interact wit
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opinion of the student body. This q
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At the highest level of reasoning a
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APPENDIXTo use two decks of cards t
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isolated and often occur in tandem
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with the CCSSM. Teachers read and d
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teachers’ role-play of SFMP #4. A
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Durkin, D. (1978-1979). What classr
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as well as the alignment between th
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Table 2Number of teachers per grade
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Table 4Classification Categories fo
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field so that research on the initi
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dynamic approach to learning conten
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Kindergarten Lesson FormatHow May W
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team’s goals? As much as possible
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6. While preparing the lesson, teac
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active learning and collective part
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classroom. “I would like to know
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I had never been brave enough to tr
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THE PATH OF REFORM IN SECONDARY MAT
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Our collaboration model was formed
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internal evaluator) were analyzed.
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DiscussionOn part I of the survey t
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whole department of secondary mathe
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