2013 Conference Proceedings - University of Nevada, Las Vegas

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KINDERGARTEN STUDENTS EXPLORING BIG IDEAS:AN EVOLUTION FOR TEACHERSMelfried OlsonUniversity of Hawai‘imelfried@hawaii.eduFay ZenigamiUniversity of Hawai‘izenigami@hawaii.eduThis paper describes the experiences of a team of kindergarten teachers as they came to gripswith what ideas students could meaningfully explore, represent, and communicate. We sharehow teachers collaboratively planned a problem-solving lesson for their students and in theprocess explored the mathematics for themselves as well. We discuss students’ workdemonstrating their engagement in the mathematics of the lesson and teachers’ reflections on thelesson, thoughts about the significance of students’ thinking, and efforts to orchestratecommunication.Often kindergarten teachers think they have little influence on the mathematics learning oftheir children because they do not see the significance of ideas with which children can work.This paper describes a three-year effort made by all kindergarten teachers in one school tounderstand and influence their students’ thinking about mathematical ideas. We discuss aprofessional development program that had a major influence on how teachers felt they impactedthe mathematical development of their students. We explain how a Lesson Study process helpedfacilitate growth in teacher knowledge as they sought appropriate tasks in which to engagestudents, expand teachers’ efforts to orchestrate opportunities for students to model and representmathematical ideas, and make visible decisions teachers made to foster discourse to benefit thelearning of all students by choosing the order in which students shared their work.Theoretical FrameworkThe goal of the three-year project (KARES) funded through a Mathematics and SciencePartnerships grant from the Hawai‘i Department of Education was to promote deeper studentunderstanding of mathematics through professional development designed to improve teachers’mathematics content understanding and instructional strategies. The authors were the KARESProject Director and Project Manager, respectively, and were involved in conducting all aspectsof the professional development. Carpenter, Blanton, Cobb, Franke, Kaput & McCain (2004)state that the two most critical things teachers need to learn are content knowledge and studentlearning trajectories specific to that knowledge. Ball (2003) and her colleagues found that whenprofessional development for teachers focused on the mathematical content knowledge they needfor teaching, the effects are maximized. Such professional development situated in context is aProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 101
dynamic approach to learning content that incorporates the idea that content cannot be presentedin a way that is divorced from what goes on in the classroom. The objectives of the projectincluded developing deep mathematics content knowledge for teachers; increasing teachers’ useof instructional strategies that include problem solving, reasoning, and communication; createand evaluate Educative Curriculum Materials (Davis and Krajcik, 2005) that strengthen teacherand student mathematics content knowledge; and develop a professional teaching communitythrough the use of Lesson Study (Lewis, Perry, & Murata, 2006).MethodologyKARES was conceptualized in three phases: Phase 1 involved an in-depth look at content ofelementary school mathematics. Phase 2 involved researching and investigating selected contentat each grade level, with a focus on developing related curriculum materials. Phase 3 involvedplanning and conducting research lessons to investigate the interaction between teaching andlearning at each grade level. The phases were not necessarily disjoint. Because they moredirectly relate to this paper, Phases 2 and 3 are described relative to the effort of the kindergartenteachers.Phase 2 - Researching the content at the kindergarten levelThe kindergarten teachers began Phase 2 by investigating the Hawai‘i Content andPerformance Standards, National Council of Teachers of Mathematics (NCTM) focal points forkindergarten (NCTM, 2008), and initial drafts of the Common Core State Standards forMathematics (CCSSM) (National Governors Association Center for Best Practices, Council ofChief State School Officers [CCSSI], 2010). They discussed what it meant for kindergartenstudents to understand the NCTM focal points and how the ideas compared and contrasted withthe kindergarten standards in the CCSSM. As they were researching the CCSSM kindergartenstandards the teachers engaged in lengthy discussions as to the meaning of some standards anddevelopmentally appropriate instructional sequences needed to implement the intent of thestandards. They eventually focused on operations and numbers for their research, materialsdevelopment, and lesson development. These discussions helped them in their planning for Phase3. When documenting their planning, Higa-Funada (2011) wrote, “When planning for the firstlesson in 2011 – 2012 we examined the CCSD (her acronym for CCSSM). As it was early in theyear, we wanted to focus on multiple ways to know a number. Even though the CCSD standardfor this was more limiting than we thought, we decided to delve into...ways of knowing 10.”Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 102
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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
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THE INTERVIEW PROJECTAngel Rowe Abn
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involving addition and subtraction:
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6+7 4+9=6+(6+1) Substitution =4+(10
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We strongly believe that this inter
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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
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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
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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: field so that research on the initi
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
Page 143 and 144: no mathematical sense and should no
Page 145 and 146: Adopts the “111” (a term coined
Page 147 and 148: Specifically, clicking the “Click
Page 149 and 150: algebraic expression is carried out
Page 151 and 152: Retrieved from http://secc.sedl.org
Page 153 and 154: furthermore, each model may result
Page 155 and 156: After instruction in the course, th
Page 157 and 158: 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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