2013 Conference Proceedings - University of Nevada, Las Vegas

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Format of AMAA lessonsThe investigations introduce and develop concepts through carefully constructed problems.These investigations give students the opportunity to use aspects of modeling to interpretproblematic situations; understand the goals of a problem; conjecture, represent, test, and revisevarious approaches to solving the problem; and report on results. Students are encouraged tooffer alternate solutions and solution methods, question others’ methods and results, and reflecton their own understanding. Major student projects are included in Units 3, 4, and 5 and aredesigned to be more open-ended to encourage students to employ problem solving skills whileinvestigating complex problems.Digital filesTechnology that provides students the opportunity to interact with dynamic representationsof concepts for classroom instruction is integrated throughout the curriculum. The use oftechnology focuses on using graphical representations for data, encourages conjecturing andvalidation, and emphasizes relationships between quantities. Prepared documents in TI-NspireTeacher software include lessons with specific TI-Nspire documents (i.e., a .tns document)with suggestions in the teacher materials for how to use them during instruction. Thesedocuments are intended to develop the beginning concepts or enhance and extend algebraic ideasof the lessons.In addition to print materials, student pages, teacher notes, and annotated student pages arealso formatted using the TI-Nspire PublishView feature of TI-Nspire Teacher software forteachers’ instructional purposes. Documents are linked so teachers can use TI-Nspire Teachersoftware to present a problem to students; link to Teacher Notes or Annotated Students Pages forassistance during instruction; link to an interactive TI-Nspire document for whole classdiscussion; or, if available, send to students’ TI-Nspire handhelds. Occasionally, links towebsites are provided to introduce a problem or for background information.The development of the teacher materials reflects our work in numerous professionaldevelopment projects (Olson, Zenigami, Slovin, & Olson, 2011) and feedback from teachersdesignated to implement the AMAA materials. Teacher notes are designed and developed aseducative materials (Davis & Krajcik, 2005) and include annotated student pages for each lesson.As educative materials, the teacher notes clarify the mathematical ideas students are expected tolearn, and when appropriate include explanations of the mathematics beyond what the studentsProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 53
are expected to pursue. Teacher notes are intended to help with lesson planning by providing asummary of the content and objectives for the investigation, highlighting opportunities to modelwith mathematics, and anticipating student thinking and possible responses—including commonmisunderstandings. The notes list materials needed and describe ways that technology canenhance student learning as well as provide an alternative approach to understanding therelationships within the lesson.The annotated student pages expand the material from the student book with notes formanaging the investigation and suggest questions to prompt discussion. Questions are intendedto indicate topics and ideas important to the investigation. As students become familiar with theinstructional approach, they are expected to raise these issues themselves or pose the questionsspontaneously to extend a problem or probe its mathematical content.The investigative, problem-based approach changes the roles of teachers and students. Thesuggested pedagogy is student-centered, with students and teacher sharing ideas in the classroommathematical community. Students should be explaining their thinking, questioning their ownand others’ ideas, and analyzing suggested strategies. The teacher should orchestrate thediscussion with thought-provoking questions, select examples of student work to be shared whendoing so furthers the learning opportunity, and provide suggestions for techniques ofmathematical inquiry and discussion when students need guidance.Implementation of materialsFeedback on teacher implementation of the initial set of materials is used to inform thedevelopment work and to determine if what is taking place in the classroom matches the intent ofthe course. In response to an announcement about the initiation of the MOW courseaccompanied by course materials and teacher training, 17 teachers from high schools throughoutthe state participated in professional development in Summer 2012. Seven of those teachers andfour additional teachers not trained during the summer are implementing AMAA in MOWcourses. Support for these teachers also includes four follow-up sessions during 2012–2013 tolearn more about AMAA curriculum materials and approaches for teaching lessons, modelingand the CCSSM, student expectations, and technology integration. During follow-up sessions,teachers share with and learn from other teachers, ask questions and pose teaching problems, andprovide valuable feedback to CRDG researchers. Data is collected on such matters as theappropriateness of lessons by discussing lessons that worked well and lessons that wereProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 54
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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
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 and 56: We strongly believe that this inter
Page 57 and 58: AN INNOVATIVE APPROACH FOR SUPPORTI
Page 59: Practice throughout the investigati
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
Page 107 and 108: field so that research on the initi
Page 109 and 110: 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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2013 Conference Proceedings - University of Nevada, Las Vegas

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