2013 Conference Proceedings - University of Nevada, Las Vegas

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Sherman, 1977; Oakes, 1985; Oakes, Ormseth, Bell, & Camp, 1990; Sells, 1976; Walkerdine,1997).Epistemological empowerment concerns both one’s confidence in the use of mathematicsand a “personal sense of power over the creation and validation of knowledge” (Ernest, 2002, p.8). It is in this category that the professional empowerment (or pedagogical empowerment) of themathematics teacher falls. For many teachers and students, past experiences supports andsustains their belief that knowledge is created, legitimized, and exists outside of themselves. It iswith this conception of empowering the learner that teacher mathematical empowerment can beseen as equally vital.Pedagogical EmpowermentPedagogical empowerment (or professional empowerment) refers to teachers developinginto autonomous and reflective participants in education. Empowered teachers contain theconfidence to critically assess and construct mathematics teaching and learning experiences withand for their students (Ernest, 2002). Szydlik, Szydlik, and Benson (2003) found that the cultureand socio-mathematical norms of the classroom affected a change in pre-service teachers’mathematical beliefs as well as served to further their autonomy. Socio-mathematical normsestablished in the classroom are distinct from social norms in that they are unique to mathematicsclassrooms (Yackel & Cobb, 1996). For example, adequate justification is a social norm in manysubject areas but what constitutes as relevant and elegant for proof of a claim remains exclusivefor mathematics. Additionally,what becomes mathematically normative in a classroom is constrained by the currentgoals, beliefs, suppositions, and assumptions of the classroom participants. At the sametime these goals and largely implicit understandings are themselves influenced by what islegitimized as acceptable mathematical activity. (Yackel & Cobb, 1996, p. 460)The socio-mathematical norms established in the classroom studied by Szydlik et al. (2003)were shown to affect their participants’ autonomy. These participants indicated that they were“now aware that mathematics is a human creation and they can be a part of making mathematicsthemselves” (p. 272) in a culture that views mathematics as making sense. Additionally,Anderson and Piazza (1996) found that a classroom practice that eliminated lecture as the mainform of instruction together with the use of physical models (manipulatives, pictures, diagrams)served to reduce students’ anxiety about learning and teaching mathematics and increaseProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 61
students’ confidence. Because beliefs are socially and contextually constructed, many preserviceteachers’ views of teaching mathematics are consistent with the ways in which they experiencedmathematics learning (Ball, 1990; Cooney, 1999). For many preservice teachers, the beliefs theybring with them are created from an “apprenticeship of observation” (Anderson & Piazza, 1996)during their many years of schooling (Ball, 1988; Ball, 1996; Calderhead & Robson, 1991;Philipp, 2000). Consequently, it is possible that the culture of the classroom can contribute to theempowerment of pre-service teachers mathematically and pedagogically. This study sought toexplore the relationship between beliefs about mathematics and mathematics pedagogy and theimpact on preservice teacher empowerment as told from their perspective. This study sought tointentionally explain the participants’ experiences from their perspective as much as possible inthe vein of their own words.MethodologyThe Setting for the Study and the ParticipantsThe design of the course in which the study was conducted incorporated a view of preserviceteachers as social constructors of knowledge—as entering the teacher education programwith preconceived beliefs (and knowledge) about mathematics and mathematics teaching andlearning formed through an apprenticeship of observation during their formal education(Anderson & Piazz, 1996; Ball, 1988; Calderhead & Robson, 1991; Philipp, 2000). Instructionwas situated in a university level mathematics content course focused on number theory, sets,and functions among a reform model based upon conceptual rather than a procedural orientationwith a focus on meaning making, connections, patterns, justification, and dialogue. Because therelationship between reflection and perturbations are vital to change in teacher beliefs,perplexing classroom experiences were developed which evolved throughout the course of thestudy. The goal throughout this course was to provide an opportunity for a new kind of“apprenticeship of observation”, to develop “teachers’ ability and their desire to think seriously,deeply, and continuously about the purposes and consequences of what they do—about the waysin which their curriculum and teaching methods, classroom and school organization, testing andgrading procedures, affect purpose and are affected by it” (Silberman, 1970, pg. 472) as well asreflect on their own belief systems. The classroom did not follow a “traditional” format in thatlecture was eliminated as the primary form of instruction during classroom learning experiences.Instead, group work and active learning using manipulatives, pictures, and diagrams were theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 62
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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
Page 17 and 18: Table 1Identified Mathematical Prac
Page 19 and 20: justify their statements, included
Page 21 and 22: Finally, engagement in MP.6 was ass
Page 23 and 24: PRESERVICE TEACHERS’ EMOTIONAL EN
Page 25 and 26: “experiences that are charged wit
Page 27 and 28: Number of journals containingEmotio
Page 29 and 30: ConclusionsStruggle and frustration
Page 31 and 32: Mathematics Teacher Candidates’ U
Page 33 and 34: function and applied the vertical l
Page 35 and 36: semester, about half of the course
Page 37 and 38: They further state that “the impo
Page 39 and 40: C. Laborde (Eds.) International Han
Page 41 and 42: (SCK), or knowledge of mathematics
Page 43 and 44: level of difficulty for each partic
Page 45 and 46: MKT Measures ScoresMathematics in G
Page 47 and 48: deep rooted belief in a single way
Page 49 and 50: THE INTERVIEW PROJECTAngel Rowe Abn
Page 51 and 52: involving addition and subtraction:
Page 53 and 54: 6+7 4+9=6+(6+1) Substitution =4+(10
Page 55 and 56: We strongly believe that this inter
Page 57 and 58: AN INNOVATIVE APPROACH FOR SUPPORTI
Page 59 and 60: Practice throughout the investigati
Page 61 and 62: are expected to pursue. Teacher not
Page 63 and 64: students to organize their reports
Page 65 and 66: Slovin, H., Venenciano, L., Ishihar
Page 67: The research presented in this pape
Page 71 and 72: triangulation necessitated examinat
Page 73 and 74: their ability to teach the mathemat
Page 75 and 76: SPATIAL REASONING IN UNDERGRADUATE
Page 77 and 78: journal prompt would be given as a
Page 79 and 80: given to the 33 students on the MPI
Page 81 and 82: to advance our way of life, then sp
Page 83 and 84: STUDENT CONCEPTIONS OF “BEST” S
Page 85 and 86: students are likely to interact wit
Page 87 and 88: opinion of the student body. This q
Page 89 and 90: At the highest level of reasoning a
Page 91 and 92: APPENDIXTo use two decks of cards t
Page 93 and 94: isolated and often occur in tandem
Page 95 and 96: with the CCSSM. Teachers read and d
Page 97 and 98: teachers’ role-play of SFMP #4. A
Page 99 and 100: Durkin, D. (1978-1979). What classr
Page 101 and 102: as well as the alignment between th
Page 103 and 104: Table 2Number of teachers per grade
Page 105 and 106: Table 4Classification Categories fo
Page 107 and 108: field so that research on the initi
Page 109 and 110: dynamic approach to learning conten
Page 111 and 112: Kindergarten Lesson FormatHow May W
Page 113 and 114: team’s goals? As much as possible
Page 115 and 116: 6. While preparing the lesson, teac
Page 117 and 118: 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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discussion. Many texts include wild
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Data collection consisted of tests,
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I've not used children's literature
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could extend this inquiry to high s
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course titled Calculus with Busines
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no mathematical sense and should no
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Adopts the “111” (a term coined
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Specifically, clicking the “Click
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algebraic expression is carried out
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Retrieved from http://secc.sedl.org
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furthermore, each model may result
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After instruction in the course, th
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Table 4The group’s categories and
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you choose three place values, æ 4
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APPENDIXTable 5Description of Combi
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of the presented number. Later, the
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Figure 1: Mean trajectories and MD
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Figure 2: Mean trajectories and MD
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Performance, 33, 1410-1419.Cohen Ka
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Moyer, 2007). At his or her own pac
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logged by the system and then retri
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curriculum. The nature of the onlin
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Cox, G., Carr, T., & Hall, M. (2004
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curriculum locally, within individu
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Popularity tallied whether or not a
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Amazingly, despite there being a fe
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ReferencesBlack, M. (1962). Models
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connections are connections or rela
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Table 1Instructional TasksSquareTab
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t-charts made it easier for student
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Figure 2. A Display of Student Stra
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ReferencesAnderson, J. R., Greeno,
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their parents in phenotype (observa
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student learning calls for differen
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Figure 2. (A) P3. (B). Extension of
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the usual phenotypic assessments an
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teachers is the discrepancy between
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expected to learn and the inquiry a
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his partner about his observations,
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hard for some children? The nature
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Lakoff and Nunez: specifically, tha
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Figure 5: Average hand trajectories
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Figure 6: Distributions of maximum
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ReferencesAnderson, J. R. (2005). H
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Social system perspectives view the
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urged students to think of some way
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Figure 1: The Discourse Patterns Du
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Figure 3 blow illustrates the devel
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