2013 Conference Proceedings - University of Nevada, Las Vegas

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PERCEPTIONS OF THE STANDARDS OF MATHEMATICAL PRACTICES ANDPLANS FOR IMPLEMENTATIONTravis A. OlsonUniversity of Nevada, Las Vegastravis.olson@unlv.eduStephanie CapenUniversity of Hawaiistephaniecapen@gmail.comMelfried OlsonUniversity of Hawaiimelfried@hawaii.eduWe solicited feedback from over 20 teachers on two questions related to each Standard forMathematical Practice. Specifically, after reading each standard, we asked the teachers: 1)Name one or two things that caught your eye as you read the standard, and 2) What is one wayyou are, or plan on being, more intentional about this standard in your teaching? In our paperwe discuss the responses regarding ideas that stand out for teachers per standard and classifytheir plans for being more intentional about the standards in their teaching.The Common Core State Standards of Mathematics (CCSSM) (National GovernorsAssociation Center for Best Practices, Council of Chief State School Officers [CCSSI], 2010)essentially are now established as the mathematics curriculum framework for the United States.This framework describes well-articulated standards of mathematical content delineated forstudents at each grade level in grades K – 8 (K – 12 in the Integrated Pathway) as well as bysubjects (e.g. Algebra I, Geometry) in the Traditional Pathway. This framework also articulateseight Standards for Mathematical Practice (SMP) described as behaviors, attitudes, skills, orattributions that students should possess. In introducing the SMP, the authors of the CCSSMstate, “The Standards for Mathematical Practice describe varieties of expertise that mathematicseducators at all levels should develop in their students” (CCSSI, 2010, p.6). Each SMP beginswith the words “Mathematically proficient students” and goes on to articulate what studentsshould be doing to develop the necessary proficiency related to that SMP. Both the standards formathematical content and standards for mathematical practice are being implemented in moststates with high expectations for student achievement and teacher implementation.While the SMP describe proficiencies students should develop, little is said how teachersshould to develop these proficiencies with their students. The standards documents published bythe National Council of Teachers of Mathematics (NCTM) (1989, 1991, 2000) address teachingof mathematics and serve as one basis for the CCSSM SMP (CCSSI, 2010). Researchers haveinvestigated the degree to which teachers are aware of the various NCTM standards documents,Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 93
as well as the alignment between the standards and teachers’ beliefs (LaBerge, Sons, & Zollman,1999; Markward, 1996; Mudge 1993; Perrin, 2012; Zollman & Mason, 1992). These studiesindicate a range of teachers’ familiarity and awareness of the NCTM standards documents. Theyalso highlight varying degrees of alignment between teachers’ beliefs and the philosophiesimplied by the standards. As highlighted by Heck, et al. (2011), however, given the recentpublication of the CCSSM, similar studies are likely only emerging with regard to the CCSSM.Consequently, questions arise as to what mathematics teachers obtain from initial readings of theSMP regarding how they believe they can implement, or are implementing the ideas therein.Specifically, the research reported in this paper addresses the following two research questions:1) When teachers initially read the SMP, what do they report as noteworthy?2) When teachers initially read the SMP, what aspects of each standard do teachers identifyas influencing their intentions to address the SMP in their instruction?Framework and Related LiteratureOur formulation of the research questions and associated analysis of teacher’s responses wereframed primarily by timely policy oriented discussions regarding research on the CCSSM. Inparticular, a recent report of a national meeting to examine the impact of the CCSSM, and tooutline a priority research agenda for understanding their influence identified five research areaswas published (Heck et al., 2011). The Priority Case Study Focus #5 of the document, Teacherresponses to the CCSSM, is stated as follows:Since teachers’ knowledge, interpretations, self-efficacy, beliefs, dispositions, and skill,as well as their specific intentions and plans, affect what transpires in classrooms, it iscritical to understand how teachers respond to the CCSSM, and what kinds of classroomlearning opportunities for their students result. (Heck et al., p. 13)Within this priority case study focus, Heck et al. (2011) articulate four broad areas ofquestions that should provide a focus for studies undertaken to investigate teacher responses tothe CCSSM. Our paper focuses on the questions used to describe and explain studies that addressthe second set of such questions, “What implications do teachers see for their mathematicsinstruction? What aspects of their mathematics instruction do they see as validated by theCCSSM, and what aspects do they consider in need of change based on the CCSSM?” (p.13).Additionally, the research reported in this paper addresses the call by Heck et al. (2011) forresearch “status studies” that report the current status of CCSSM adoption and implementation.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 94
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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
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 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
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Page 89 and 90: At the highest level of reasoning a
Page 91 and 92: APPENDIXTo use two decks of cards t
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Page 95 and 96: with the CCSSM. Teachers read and d
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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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Page 119 and 120: classroom. “I would like to know
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Page 123 and 124: THE PATH OF REFORM IN SECONDARY MAT
Page 125 and 126: Our collaboration model was formed
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Page 129 and 130: DiscussionOn part I of the survey t
Page 131 and 132: whole department of secondary mathe
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Page 135 and 136: Data collection consisted of tests,
Page 137 and 138: I've not used children's literature
Page 139 and 140: could extend this inquiry to high s
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Page 145 and 146: Adopts the “111” (a term coined
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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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