2013 Conference Proceedings - University of Nevada, Las Vegas

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esulting in a statistically significant difference across emotions for the before, during and aftermeasurements (F = 11.13, p < 0.0001). Results also showed a statistically significant quadraticbehavior using an appropriate contrast (F = 14.87, p = 0.0001). Additionally, using a HSDTukey’s analysis procedure, emotion score means after treatment were found significantly higherfrom means during (p < 0.0001) and before (p = 0.0185) treatment.Quadratic behavior over time was also indicated in student journals. A student wrote, “TheTower of Hanoi was very challenging and frustrating at first. Then in the middle of trying tofigure out the puzzle I had a breakthrough and everything started to come together and I wasn’tso frustrated. When I was able to solve the puzzle and figure out the pattern to solve it I feltrelaxed and very pleased that I was able to come up with the answer to the puzzle.”Figure 3. Distribution of emotions before, during and after the task (Bins signify scoredquestionnaires before, during and after engaging with the task).Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 21
ConclusionsStruggle and frustration during the task were balanced mostly by positive emotions at theoutcome, such as accomplishment and satisfaction. A student wrote, “I was definitely frustratedagain…. I was so excited, way too excited for just having completed a math problem but I surefelt like I accomplished something.” Another explained, “Even though it took a while for us tosolve it I felt really proud of myself afterwards. I felt like I had accomplished something that notmost people could.” Results from this study were similar to those found in the literature, thatchallenge and struggle can be paired with satisfaction and accomplishment. When preserviceteachers are engaged with such tasks and find the value of working through frustration to elation,it may help change their beliefs and attitudes toward mathematics.ReferencesAllen, B. D., & Carifio, J. (1995, May). Methodology for the analysis of emotion experiencesduring mathematical problem solving. Paper presented at the Annual Conference of the NewEngland Educational Research Organization, Portsmouth, NH. Retrieved from ERICdatabase. (392606)Allen, B. D., & Carifio, J. (1999). The development and validation of an emotion questionnairefor the investigation of affect during mathematical problem solving. Retrieved from ERICdatabase. (434037)Allen, B. D., & Carifio, J. (2007). Mathematical sophistication and differentiated emotionsduring mathematical problem solving. Journal of Mathematics and Statistics, 3(4), 163-167.Anderson, J. R., Albert, M. V., & Fincham, J. M. (2005, August). Tracing problem solving inreal time: fMRI analysis of the subject-paced Tower of Hanoi. Journal of CognitiveNeuroscience, 17(8), 1261-1274.Belavkin, R. V. (2001). The role of emotion in problem solving. In the AISB'01 Symposium onEmotion, Cognition and Affective Computing Proceedings (pp. 49-57), March 21-24,Heslington, England.Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.Carifio, J. (2004). Mathematical discovery: A covariance analysis. The Free Library. Retrievedfrom http://www.thefreelibrary.com/Mathematical+discovery%3a+a+covariance+analysis.-a0121714100Danesi, M. (2004). The liar’s paradox and the towers of Hanoi: The ten greatest puzzles of alltime. New Jersey: John Wiley.Dolcos, F., LaBar, K. S., & Cabeza, R. (2004). Interaction between the amygdala and the medialtemporal lobe memory system predicts better memory for emotional events. Neuron, 42, 855-863.Duvallet, D., & Clement, E. (2005). Identification of emotional manifestations during problemsolving activities. Invited speakers for the Comprehension, Raisonnement et Acquisition deConnaissances conference, February 17, 2005, University of Rouen, France.Friesen, N., & Francis-Poscente, K. (2008). The Tower of Hanoi and the experience of livednumber. Proceedings from the Media – Knowledge – Education Conference (pp. 171-183).Münster, Germany: Waxmann.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 22
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 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: Number of journals containingEmotio
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
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
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given to the 33 students on the MPI
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to advance our way of life, then sp
Page 83 and 84:
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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