2013 Conference Proceedings - University of Nevada, Las Vegas

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the Inside Mathematics website. Furthermore, due to the timing of PSTs’ field experience (acourse component), there were no in-class discussions of either problem set.Analysis was both quantitative and qualitative. Quantitative analysis consisted of summarystatistics and focused on the frequencies with which specific practices or practice combinationswere chosen by PSTs amongst a problem, a domain, particular problem characteristics, or by aparticular PST. Qualitative analysis involved the examination of PSTs’ written descriptions forwhat they took as evidence that any given practice had been engaged in. Such analysisattempted to identify and characterize those mathematical practice aspects that appeared to bemost influential in PSTs’ identification of any given practice.FindingsFor Problem Set #4, only 12 PSTs completed the part of the assignment requesting they solvethe problem and identify the mathematical practices (MPs) they believed students would engagein and potentially exhibit in their written work. One additional PST completed this part of theassignment for Problem Set #5. Furthermore, PSTs were asked to solve the problem and to thinkabout how students might engage in the problem, prior to or in concert with making theirpractice selection(s).Tables 1 and 2 display those practices PSTs identified for each of the seven problems ofProblem Set #4 and #5, respectively. Specifically, the tables indicate PST by name, problemnumber (e.g., P1 is the first problem), and the mathematical practice(s) chosen (e.g., Amieindicated problem #1 of Problem Set #4 involved MP.1 and MP.6). “None” indicates nopractices were identified for that problem.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 9
Table 1Identified Mathematical Practices by PST and by Problem (Problem Set #4)PST P1 P2 P3 P4 P5 P6 P7Alejandra 7 1 8 3 1 1, 3 1, 3, 4, 5Amie 1, 6 7 2 2 none 1, 2 4Blondell 4, 8 2, 6 1, 6 7 1 2 8Bulah 2, 4, 5, 6 1, 5, 8 1, 5, 6 3, 5 1, 3, 4, 6, 2, 3, 4, 7 47, 8Jamie 1, 8 1, 5 6, 8 1, 8 1, 5 none 1, 4, 5, 6Kelly 1, 3, 6 1, 4, 5 1, 3, 4, 5 1, 4, 5, 6 1, 6 1, 3, 4, 6 1, 8Kurt 2, 4, 7 5, 6 2, 3 1, 4, 7 2, 4, 5, 7, 8 1, 8 1, 4, 6Loraine 2 1 7 6 1 3 1, 4, 6, 8Myra 1, 3, 4, 5 1, 2, 3, 5 1, 2, 3, 5 1, 2, 3, 5 1, 3, 4, 5 1, 3, 4, 5 4Neil 1, 3, 4, 8 1, 4, 5 1, 4, 6, 8 1, 5, 6 1, 5, 6 1, 6 1, 4, 5, 6Stella 1, 2, 5, 6 1, 3, 4, 5, 1, 3, 7 1, 2, 4, 5 1, 2, 5, 7 none noneValene 1, 4, 5, 6,7, 8Table 26, 71, 4, 5, 6,7, 81, 4, 5, 7 1, 4, 5, 7 1, 4, 5, 7 1, 4, 5, 7 1, 5, 7, 8Identified Mathematical Practices by PST and by Problem (Problem Set #5)PST P1 P2 P3 P4 P5 P6 P7Alejandra 1, 4 4 3, 7 3, 7 8 1, 3 3Amie none 1 2 6 3 4 noneBlondell 3, 7 4 4 4 2 4 4Bulah 1, 4, 5 2, 4, 5, 8 1, 2, 5, 7 2, 3, 5, 7 1, 3, 8 1, 4, 5, 6 1, 4, 5, 6Carlene 1, 4, 7 1, 4, 6 2, 4 1, 3 3 2, 4 2, 4, 7Jamie 2, 4 1 6, 8 1, 7 1, 7 1, 4, 5 1, 4, 5Kelly 1, 2, 3, 4, 6 1, 3, 5, 6 1, 2, 3, 6 2, 3 1, 2, 3 1, 2, 3, 4, 1, 4, 5, 65, 6Kurt 1, 4, 6 7 1, 4, 7 6, 7 4, 6, 7, 8 6, 7 1, 2, 7 1, 3Loraine 1, 2 4 3 1, 3 3, 8 1, 2 1, 4Myra 1, 3, 4, 5, 6 1, 3, 4, 5 1, 2, 3 1, 3, 4, 5, 6 1, 2, 3, 6 1, 3, 4, 5, 6 1, 3, 4, 5Neil 1, 4, 6 1, 4, 5, 6 1, 4, 5, 6 1, 3, 4, 5 1, 3, 5, 6, 8 1, 3, 6 1, 5, 6Stella 1, 2, 3 1, 2, 5, 6 1, 3, 7 1, 2, 3, 6, 7 1, 2, 7 1, 4 1, 2, 3Valene 1, 4, 5, 6 1, 4, 5, 6, 7 1, 4, 5, 6 1, 4, 5, 6, 7 1, 5, 6, 8 1, 4, 5, 6 1, 2, 4, 5As illustrated in the tables above, there was a reasonable degree of variability in themathematical practices (MPs) chosen amongst and within problems, and amongst and withinPSTs for each problem set. In addition, there was a reasonable degree of variability amongst thecombinations and number of practices chosen. For example, for problem #2 of Problem Set #4(Table 1), the number of practices chosen by any one PST ranged from one (Amie) to six(Stella). Furthermore, although Bulah and Blondell each solved problem #1 of Problem Set #5showing very similar written work, Bulah identified the problem as involving MP.3 and MP.7,whereas Blondell identified MP.1, MP.4, and MP.5.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 10
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: conceptual understanding, applicati
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 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
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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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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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