2013 Conference Proceedings - University of Nevada, Las Vegas

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Although such results might be expected, considering the potential for idiosyncraticinterpretations of the mathematical practices, the interaction and overlap amongst practices(PARCC, 2012, p.13), and the limited opportunities PSTs had to discuss and operationalize thepractices, my intent was to gather data with which to develop a baseline for PSTs’ conceptions ofthe mathematical practices. Such a baseline would then serve to guide future engagements withthese and other teachers.A particular interesting result involved the frequency with which certain pairs ofmathematical practices were identified. Figure 1 illustrates the frequency with which pairs ofpractices were chosen by PSTs (weight of pair connection) for the two problem sets combined.For example, MP.4 and MP.5 occur together in each of the combinations 1, 4, 5 and 4, 5, 7, 8.Figure 1. Strength of mathematical practice pairs. This network graph displays the strength ofpairs of mathematical practices for Problems Sets #4 and #5 combined (generated with Gephi,www.gephi.org).As Figure 1 indicates, other than pairs that included MP.1 (e.g., MP.1 and MP.5), the pairsMP.4 and MP.5, MP.4 and MP.6, and MP.5 and MP.6 occurred with the greatest frequency.This result also held true when each problem set was examined individually. The frequency withwhich the pair MP.4 and MP.5 occurred might be accounted for in light of their relationship(modeling and using tools) in McCallum’s (2011) higher order structure to the practicestandards.In order to attempt to explain the frequencies with which individual, pairs, or combinationsof practices were chosen by PSTs, I looked for potential relationships between the problems’features and the practices selected. Particular features included: whether the problem asked foran explanation, involved a realistic context, asked students to critique another’s reasoning orProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 11
justify their statements, included a mathematical representation or object (e.g., diagram, table,graph, formula, triangle), or requested a mathematical representation be constructed. The mainreason for focusing on the problems’ features was due to PSTs’ limited experiences with thepractices. As such, I anticipated much of PSTs’ decision making would be based on what theydeemed as relevant between the problems’ features and the practice descriptions provided in theCommon Core documents. Table 3 displays the problem features, the problems associated witheach feature (PS4: P6 indicates problem #6 from Problem Set #4), and the standard score foreach mathematical practice (MP).Table 3Mathematical Practice Standard Score by Problem FeatureExplainPS4: P1, P3, P4PS5: P1, P2, P3,P4, P6Standard Score (z)Context Critique/JustifyPS4: P1, P2, P4, PS4: P6P6, P7PS5: P4, P5PS5: P1, P6, P7Includes RepPS4: P1, P2, P3,P4, P5PS5: P3, P4, P5,P7Requests RepPS4: P7PS5: P1, P2MP.1 1.78 1.80 1.89 2.12 1.50MP.2 -0.44 -0.56 -0.13 -0.57 -0.79MP.3 -0.13 -0.39 0.88 0.03 -0.67MP.4 0.89 1.04 0.38 0.03 1.50MP.5 0 0.27 -0.63 0.37 0.01MP.6 0.13 -0.12 -0.63 -0.10 0.13MP.7 -0.70 -0.88 -0.63 -0.57 -0.79MP.8 -1.52 -1.16 -1.14 -1.31 -0.90As Table 3 illustrates, problems involving a realistic context were associated with MP.4being selected (z = 1.04). This was anticipated considering MP.4’s description, “Mathematicallyproficient students can apply the mathematics they know to solve problems arising in everydaylife, society, and the workplace” (CCSSI, 2010, p. 7). For Problem Set #4, MP.5 was alsofrequently chosen (z = 0.51) for “Context” problems, but not for Problem Set #5 (z = 0.03).Problems explicitly requiring students to critique or justify were associated with MP.3 beingselected (z = 0.88). This result was also expected due to the nature of MP.3—“Construct viablearguments and critique the reasoning of other” (CCSSI, 2010, p. 6). Problems requiring studentsto explain their work, their thinking, or their reasoning were associated with MP.4 being selected(z = 0.89). This result was surprising, since I anticipated such problems would motivate PSTs tochoose MP.3, “construct viable arguments” (CCSSI, 2010, p.6) and/or MP.6, “communicateProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 12
Page 1 and 2: ….where the Mathematicscomes swee
Page 3 and 4: THANK YOU TO OUR REVIEWERSKeith Ado
Page 5 and 6: Table of ContentsPreservice Teacher
Page 7 and 8: 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: Table 1Identified Mathematical Prac
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 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
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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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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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