2013 Conference Proceedings - University of Nevada, Las Vegas

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Partnership for Assessment of Readiness for College and Careers (PARCC). (August, 2012).PARCC model content frameworks for mathematics: Grades 3-11. PARCC.Riordan, J. E., & Noyce, P. E. (2001). The impact of two standards-based mathematics curriculaon student achievement in Massachusetts. Journal for Research in Mathematics Education,32(4), 368-398.Senk, S., & Thompson, D. (Eds.). (2003). Standards-oriented school mathematics curricula:What does the research say about student outcomes? Mahwah, NJ: Erlbaum.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 15
PRESERVICE TEACHERS’ EMOTIONAL ENGAGEMENTWITH THE TOWER OF HANOIElaine YoungTexas A&M University-Corpus ChristiElaine.Young@Tamucc.EduSarah IvesTexas A&M University-Corpus ChristiSarah.Ives@Tamucc.EduJose GuardiolaTexas A&M University-Corpus ChristiJose.Guardiola@Tamucc.EduThe Tower of Hanoi is a traditional problem solving task for several fields of discipline.Preservice teachers engaged with this task and provided reflective journals and questionnaireswhich were used to answer two research questions: “What emotions do preservice teachersexperience before, during, and after the task?” and “How do emotions change across time?”Journals were mined for emotional words/phrases; questionnaires were scored on a Likert scaleand then analyzed. Results indicated significant quadratic behavior in emotions over time.Student voices in journals supported outcomes of qualitative and quantitative analyses.If the student had no opportunity in school to familiarize himself with the varyingemotions of the struggle for the solution, his mathematical education failed in themost vital point (Polya, 1957, p. 94).The Tower of Hanoi puzzle has its roots in Cardano’s description of the Far East (Danesi,2004). In 1883, Edouard Lucas, a French number theorist, marketed the puzzle as a brain teaser(Poole, 1994). The puzzle is a popular task in mathematics and a traditional programmingproblem in computer science. Kopecky, Chang, Klorman, Thatcher and Borgstedt (2005)described its use in psychology and psychiatry to test for mental disorders, attention measuresand problem-solving efficacy.The Tower of Hanoi task was used in the first of three mathematics content courses forpreservice elementary and middle school teachers. The task paired accessibility with highcognitive demand, as well as a blend of challenge and intrigue. It encouraged students tocollaborate, communicate mathematically, and develop mathematical reasoning. The task modelsBruner’s (1966) successive modes of intelligence: enactive, iconic, and symbolic representations,as students worked with concrete models, then recorded data, and finally identified recursive andexplicit formulas. Students wrote reflective journals; instructors noticed that there wereProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 16
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 and 18: Table 1Identified Mathematical Prac
Page 19 and 20: justify their statements, included
Page 21: Finally, engagement in MP.6 was ass
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
Page 71 and 72: 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
Page 225 and 226:
Figure 1: The Discourse Patterns Du
Page 227 and 228:
Figure 3 blow illustrates the devel
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