2013 Conference Proceedings - University of Nevada, Las Vegas

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Steffe, L. P., von Glasersfeld, E., Richards, J. & Cobb, P. (1983). Children’s counting types:Philosophy, theory, and application. New York: Praeger.Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, part I: ateacher’s struggle, Journal for Research in Mathematics Education, 25(3), 279-303.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 49
AN INNOVATIVE APPROACH FOR SUPPORTINGAT-RISK STUDENTS IN ALGEBRA IJudith OlsonUniversity of Hawai‘ijkolson@hawaii.eduLinda VenencianoUniversity of Hawai‘ilhirashi@hawaii.eduMelfried OlsonUniversity of Hawai‘imelfried@hawaii.eduHannah SlovinUniversity of Hawai‘ihslovin@hawaii.eduFay ZenigamiUniversity of Hawai‘izenigami@hawaii.eduThe Curriculum Research & Development Group has developed A Modeling Approach toAlgebra, a curriculum created to support ninth-grade students’ effort to learn Algebra I. Fundedby a contract with the Hawai‘i State Department of Education, materials were developed tosupport struggling learners by emphasizing modeling mathematical content and practice asdescribed in the Common Core Curriculum Standards for Mathematics. In this paper we discussthe curriculum research and development from a design research perspective.To successfully complete the mathematics requirements created by adopting the CommonCore State Standards in Mathematics (CCSSM) (National Governors Association Center for BestPractices, Council of Chief State School Officers, 2010) raises the bar for students. This is ofparticular concern for Algebra I, the traditional entry point to high school mathematics. Such isthe case in Hawai’i where pre-algebra is no longer a high school course. Partially as a result ofthese policies, approximately one in three students do not succeed in high school Algebra I(Gottlieb, personal communication, Spring 2011). To address the Algebra I failure rate, a course,Modeling our World (MOW), focusing on modeling and opportunities to learn mathematics in amore investigative manner was established. Although designed for struggling learners, MOW isnot remedial and is intended to be taken concurrently with Algebra I.The Curriculum Research & Development Group (CRDG) at the University of Hawai’i wascontracted to design and develop the curriculum materials for the MOW course. The CCSSMtogether with CRDG’s previous curriculum research and development projects, e.g. Algebra I: AProcess Approach (Rachlin, Matsumoto, Wada, & Dougherty, 2001), Reshaping Mathematicsfor Understanding (Slovin, Venenciano, Ishihara, & Beppu, 2003), provided a research basefrom which to begin the development for MOW. The modeling standards embedded in theCCSSM were established as the framework around which to build the materials. This paperProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 50
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….where the Mathematicscomes swee
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THANK YOU TO OUR REVIEWERSKeith Ado
Page 5 and 6: Table of ContentsPreservice Teacher
Page 7 and 8: Support for Students Learning Mathe
Page 9 and 10: own problem solving, which is criti
Page 11 and 12: to get started and persistence. Tea
Page 13 and 14: 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: We strongly believe that this inter
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 and 68: The research presented in this pape
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
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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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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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