2013 Conference Proceedings - University of Nevada, Las Vegas

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PREPARING K-10 TEACHERS THROUGH COMMON CORE FOR REASONING ANDSENSE MAKING 1Jonathan BosticBowling Green State UniversityBosticj@bgsu.eduGabriel MatneyBowling Green State UniversityGmatney@bgsu.eduThere looms an uncertainty about the Common Core State Standards for mathematics for manyteachers. Teachers have indicated that they want professional development (PD) focused onlearning about the new standards (Bostic & Matney, in press). This manuscript describes PDprograms for K-10 mathematics teachers and offers results from one activity aimed to helpteachers unpack the Standards for Mathematical Practice (SFMP). Four major themes arosefrom interpretive analysis of teachers’ perceptions of the SFMP. These findings suggest (1) thePD supported teachers to make sense of the SFMP and (2) teachers may have misperceptionsabout the SFMP that require further PD.Standards for Mathematical PracticeMathematics instruction in the era of Common Core State Standards for mathematics(CCSSM; Council of Chief State School Officers [CCSSO], 2010) will require teachers toreevaluate their current instruction (National Council of Teachers of Mathematics [NCTM],2010). The CCSSM built upon decades of work “to define the mathematics that students need toknow and be able to do” (NCTM, 2010, p. ix). A critical element of the CCSSM is theoverarching emphasis given to the Standards for Mathematical Practice (SFMP). The SFMPoffer descriptions of behaviors that students should demonstrate while learning mathematics. TheSFMP were created from two foundational texts: Principles and Standards for SchoolMathematics (NCTM, 2000) and Adding it Up (Kilpatrick, Swafford, & Findell, 2001). NCTM’s(2000) process standards are problem solving, reasoning and proof, communication, connections,and representation. The notion of mathematical proficiency includes conceptual understanding,procedural fluency, adaptive reasoning, strategic competence, and productive disposition(Kilpatrick et al, 2001). Elements from the process standards and the mathematical proficiencyare evident in the SFMP. Unfortunately, these ideas are not evident in every classroom. Thus,professional development must be designed to enhance teachers’ understanding of the SFMP andways to encourage these behaviors in their mathematics classrooms. These behaviors are not1 This manuscript is supported by two Ohio Board of Regents Improving Teacher Quality grants. Any opinionsexpressed herein are those of the authors and do not necessarily represent the views of the Ohio Board of Regents.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 85
isolated and often occur in tandem with one another because they are interrelated behaviors(CCSSO, 2010). For example, making sense of problems and looking for mathematical structureare likely to occur during a problem-solving session. In order for students to elicit behaviorsindicative of the SFMP, teachers must design and enact instruction that allow students to wrestlewith mathematics content and its applications in an environment that supports and sustainsmeaningful engagement with mathematics.There is no prescribed set curriculum or pathway for teachers to encourage these behaviors intheir students; however, worthwhile tasks and mathematical discourse provide a vehicle forsupporting students’ mathematical thinking (NCTM, 2007). Video analyses of USA teachers’instruction indicates that generally speaking, teachers are not promoting the process standards ormathematical proficiency (Hiebert et al., 2005), much less the SFMP. Hence, mathematicsteacher educators should provide professional development that assists K-12 mathematicsteachers’ understandings of the student behaviors found in the SFMP and how those behaviorscan be promoted through their instruction. The purpose of this paper is to discuss K-10mathematics teachers’ perceptions about the SFMP.Professional DevelopmentTeachers need professional development during the transition to the CCSSM. This PD “willrequire practical, intensive, and ongoing professional learning - no one-off ‘spray and pray’training” (Hirsh, 2012). An underlying goal of most professional development is to enhanceteachers’ understanding of content, pedagogy, or content-focused pedagogy. Results from anational sample of more than 1,000 mathematics and science teachers indicated that three factorsare most likely to influence teachers’ practices: (1) connection to teachers’ prior experiences, (2)alignment with standards, and (3) opportunities to share ideas with other teachers (Garet, Porter,Desimoney, Birman, & Yoon, 2001). Engaging teachers with mathematics content in a way thatfosters hands-on learning and finding ways to integrate PD activities into a teachers’ daily lifeled to longer lasting positive instructional outcomes (Garet et al., 2001). Thus, mathematicsteacher educators ought to focus on these factors to promote coherent PD.A metaanalyis of PD suggests that there are some key features to designing effectiveinservice teacher education (Guskey & Yoon, 2009). First, workshops and summer institutesthat focus on implementing research-based instructional practices, active learning, andopportunities to adapt these practices in the classroom were highly correlated with positiveProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 86
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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
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 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: APPENDIXTo use two decks of cards t
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
Page 119 and 120: classroom. “I would like to know
Page 121 and 122: I had never been brave enough to tr
Page 123 and 124: THE PATH OF REFORM IN SECONDARY MAT
Page 125 and 126: Our collaboration model was formed
Page 127 and 128: internal evaluator) were analyzed.
Page 129 and 130: DiscussionOn part I of the survey t
Page 131 and 132: whole department of secondary mathe
Page 133 and 134: discussion. Many texts include wild
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
Page 141 and 142: 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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