2013 Conference Proceedings - University of Nevada, Las Vegas

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FOSTERING PRE-SERVICE TEACHERS’ MATHEMATICAL EMPOWERMENT:EXAMINING MATHEMATICAL BELIEFS IN A MATHEMATICS CONTENTCOURSEMary HarperEast Central Universitymharper@ecok.eduStacy ReederUniversity of Oklahomareeder@ou.eduThis study explored the influence of curriculum and experiences in a mathematics content coursehad on pre-service teachers’ mathematical empowerment as reflected in their beliefs aboutmathematics and mathematics teaching and learning. The results indicate that the pre-serviceteachers increased their feeling of mathematical power and their beliefs about mathematicsteaching and learning were impacted by a college-level mathematics course taught in a nontraditionalmanner.Empowerment denotes “the gaining of power in particular domains of activity by individualsor groups and the processes of giving power to them, or processes that foster and facilitate theirtaking of power” (Ernest, 2002). The National Council of Teachers of Mathematics (1989)introduced the idea of empowerment related to mathematics teaching and learning to a muchbroader audience of mathematics educators with the publication of the Curriculum andEvaluation Standards for School Mathematics. NCTM stated the following:Mathematical power denotes an individual’s capabilities necessary to explore, conjecture,and reason logically as well as the ability to use a variety of mathematical methodseffectively to solve non-routine problems. This notion is based on the fact thatmathematics is more than a collection of concepts and skills to be mastered. It includesmethods of investigating and reasoning, means of communication, and notions of context.In addition, for each individual it involves the development of personal self-confidence(NCTM, 1989, p. 5).Developing the mathematical power of students is a noteworthy goal but unfortunately it ispredicated on the notion that teachers of mathematics themselves are mathematicallyempowered; that their beliefs about the nature of mathematics, how mathematics should betaught, and their own mathematics abilities allow them to be confident and flexible. They mustbe able to solve non-routine problems and hold a view of mathematics that it is more than acollection of concepts and sills to be mastered. In this way, there is an inextricable connectionbetween one’s beliefs about mathematics teaching and learning and one’s mathematicalempowerment.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 59
The research presented in this paper encompassed challenging pre-service teachers’ beliefsabout mathematics and mathematics teaching and learning while asking them to reflect upontheir beliefs. The study took place with students in a university level mathematics content coursefocused on number theory, sets, and functions that integrated content and pedagogy as Cooney(1999) suggested. The structure of the course was consistent with reform teaching practices asopposed to a traditional university mathematics classroom structure. The following researchquestion guided the study:What influence, if any, do pre-service teachers believe the curriculum and experiences inthis mathematics course have on their mathematical empowerment as reflected in theirbeliefs about mathematics and mathematics teaching and learning?Related LiteratureThe notion of empowerment, in mathematics education literature, is often used to mean thesame as autonomy or efficacy. In order to avoid confusion, the word empowerment will be usedsolely in place of the other two throughout this paper.Mathematical, Social, and Epistemological EmpowermentMathematical empowerment involves gaining power over the domain of schoolmathematics which entails using and applying the language, practices, and skills of mathematics;likewise, it has cognitive and semiotic perspectives which are complementary (Ernest, 2002).The cognitive psychological perspective of mathematical empowerment involves theprocurement of concepts, skills, facts, and general problem solving strategies whereas thesemiotic perspective demands the development of power over the ‘texts’ of mathematics. Thesepowers over the ‘texts’ of mathematics include the abilities to read and make sense ofmathematical tasks, transform text into smaller tasks, pose problems and write questions, andmake sense of text in computational form (Ernest, 2002).Social empowerment encompasses the use of mathematics to increase a person’s life chancesand critical participation in work, study, and society (Ernest, 2002). In a utilitarian way,throughout history success in mathematics (often judged by performance on examinations)serves as a ‘gatekeeper’ or ‘critical filter’ controlling access into further education as well asoccupations with greater pay (Ernest, 2002; Lemann, 1999; Oakes, 1985; Oakes, Ormseth, Bell,& Camp, 1990; Stanic, 1986; Standards, 1989). Moreover, researchers have long noted theperceived inequity in mathematics education for women and other minorities (Fennema &Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 60
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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., &
Page 15 and 16: 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: Slovin, H., Venenciano, L., Ishihar
Page 69 and 70: students’ confidence. Because bel
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
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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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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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