2013 Conference Proceedings - University of Nevada, Las Vegas

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Figure 2: The Structure of the LessonManifestations of Developing Student UnderstandingIn this lesson, the students collectively conjectured about the congruence of quadrilateralsusing four possibilities:1) Four sides and one angle: Side-Side-Side-Side-Angle (SSSSA)2) Three sides and two angles: Side-Angle-Side-Angle-Side (SASAS) and Side-Side-Side-Angle-Angle (SSSAA)3) Two sides and three angles: Side-Side-Angle-Angle-Angle, (SSAAA) and Side-Angle-Side-Angle-Angle-Angle (SASAA)4) One side and four angles: Side-Angle-Angle-Angle-Angle (SAAAA)Students then agreed that two quadrilaterals are congruent under SASAS, SSAAA, andSSSSA and proved these new theorems using common properties of triangle congruence (SSS,SAS, AAS). They also generated counter-examples to show when congruence of twoquadrilaterals cannot be established (for example, SASAA, or a rectangle and a square with twoequal sides). During the exploration of the criteria for the congruence of quadrilaterals, studentsalso explored possible cases regarding the positions of the angles and sides in quadrilaterals. TheProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 219
Figure 3 blow illustrates the developing of students’ reasoning and proof. It also reveals therichness and depth of mathematical understanding and thinking.Figure 3 The Development of Reasoing and ProofEducational SignificanceRecent mathematics education reform has highlighted the importance of robust classroomdiscourse as critical for advancing reasoning and proof of students. In China, exemplary modellessons are often taught by expert teachers during professional development to illustrate thesereform ideas and to suggest possible implementation approaches (Huang, Zhang & Li, 2011).These model lessons manifest successful classroom discourse as the teacher and students developmathematical content jointly. Examination of this particular lesson by Mr. Wu provides insightsand strategies for teachers to develop rich mathematics discourse that promotes reasoning andproof in US mathematics classrooms.ReferencesDavis. B., & Sumara, D. (2006). Complexity and Education: Inquires into learning, teaching,and research. NJ. Lawrence Erlbaum Associates.Fleener, M. J. (2002). Curriculum dynamics: Recreating heart. New York: Peter Lang.Goldin, G. A. (1997). Observing mathematical problem solving through task-based interviews.In A. R. Teppo (Ed.), Qualitative research methods in mathematics education,[Monograph]Journal for Research in Mathematics Education. (Vol. 9, pp. 40-62, 164-177). Reston, VA:NCTM.Harel, G., & Sowder, L (2007). Toward a comprehensive perspective on proof, In F. Lester(Ed.), Second Handbook of Research on Mathematics Teaching and Learning, NationalProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 220
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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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AN INNOVATIVE APPROACH FOR SUPPORTI
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Practice throughout the investigati
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are expected to pursue. Teacher not
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students to organize their reports
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Slovin, H., Venenciano, L., Ishihar
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The research presented in this pape
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students’ confidence. Because bel
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triangulation necessitated examinat
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their ability to teach the mathemat
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SPATIAL REASONING IN UNDERGRADUATE
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journal prompt would be given as a
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given to the 33 students on the MPI
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to advance our way of life, then sp
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STUDENT CONCEPTIONS OF “BEST” S
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students are likely to interact wit
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opinion of the student body. This q
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At the highest level of reasoning a
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APPENDIXTo use two decks of cards t
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isolated and often occur in tandem
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with the CCSSM. Teachers read and d
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teachers’ role-play of SFMP #4. A
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Durkin, D. (1978-1979). What classr
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as well as the alignment between th
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Table 2Number of teachers per grade
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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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Page 185 and 186: ReferencesBlack, M. (1962). Models
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Page 189 and 190: Table 1Instructional TasksSquareTab
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Page 193 and 194: Figure 2. A Display of Student Stra
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Page 211 and 212: hard for some children? The nature
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Page 215 and 216: Figure 5: Average hand trajectories
Page 217 and 218: Figure 6: Distributions of maximum
Page 219 and 220: ReferencesAnderson, J. R. (2005). H
Page 221 and 222: Social system perspectives view the
Page 223 and 224: urged students to think of some way
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