2013 Conference Proceedings - University of Nevada, Las Vegas

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automatic activation of numerical size that was carried out in participants hand movements (seeFigure 2). This directly supports the hypothesis of embodied cognition. However, this patterncould have also resulted from an “averaging” across trials; on inconsistent trials, the mousemovement could have initially been in the wrong direction, then immediately corrected midflightto the correct response alternative. However, an trial-by-trial analysis rules this possibility out(see Figure 3).Together, these results comprise an important first step in establishing the embodiment ofnumerical cognition. From the work of Lakoff and Nunez (2000), an important philosophicalclaim was made: mathematics is entirely the creation of humans using entirely human qualities.In other words, mathematics as we know it could not have been “invented” without the bodilyaffordances that make us human. While this claim may seem more the realm of philosophersand science fiction writers, the present results provide some evidence that even numericaldecisions are intimately tied to our bodily states.General DiscussionThe results of the present study indicate that numerical processing does not take placeindependently from our bodily states. Specifically, we found that when tracking handmovements in even the most simple task (a parity judgment task), the hand movements reflecteda continuous, dynamic system of partially activated cognitive states that would not be possible inthe traditional, computer-based metaphor of mind.At first, it may be difficult to see how these results relate to discussions in mathematicseducation. Indeed, the results from such research are valuable to mathematics educators because,together, they lend theoretical support to the idea of embodied mathematics. Embodiedmathematics is the view that mathematics is not completely an abstract, or “pure,” discipline, butrather is the product of a conceptual system that is ultimately grounded in bodily states. In asense, this “humanizes” mathematics. This kind of evidence also tells us that since mathematicsis tied to our body-grounded conceptual systems, it should be taught from that point of view.That is, as Nunez and colleagues put it:“Students (and teachers) should know that mathematical theorems, proofs, and objectsare about ideas, and that these ideas are situated and meaningful because they aregrounded in our bodily experience as social animals.” (Nunez, Edwards, & Matos, 1999,p. 62).Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 211
ReferencesAnderson, J. R. (2005). Human symbol manipulation within an integrated cognitive architecture.Cognitive Science, 29, 313-341.Ashcraft MH, Battaglia J (1978) Cognitive arithmetic: evidence for retrieval and decisionprocesses in mental addition. Journal of Experimental Psychology: Human Learning andMemory, 4, 527-538.Dehaene S., Bossini S., Giraux P. (1993). The mental representation of parity and numericalmagnitude. Journal of Experimental Psychology: General, 122, 371–396.Freeman, J., & Ambady, N. (2010). MouseTracker: Software for studying real-time mentalprocessing using a computer mouse-tracking method. Behavior Research Methods, 42, 226-241.Lakoff, G., & Nunez, R. E. (2000). Where Mathematics Comes From: How the Embodied MindBrings Mathematics into Being. New York, NY: Basic Books.Nunez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding forsituatedness and context in mathematics education. Educational Studies in Mathematics, 39,45-65.Spivey, M. (2007). The Continuity of Mind. New York, NY: Oxford University Press.Spivey, M., Grosjean, M., & Knoblich, G. (2005). Continuous attraction toward phonologicalcompetitors. Proceedings of the National Academy of Sciences, 102, 10393-10398.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 212
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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
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own problem solving, which is criti
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to get started and persistence. Tea
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Posamentier, A. S., Smith, B. S., &
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conceptual understanding, applicati
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Table 1Identified Mathematical Prac
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justify their statements, included
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Finally, engagement in MP.6 was ass
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PRESERVICE TEACHERS’ EMOTIONAL EN
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“experiences that are charged wit
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Number of journals containingEmotio
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ConclusionsStruggle and frustration
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Mathematics Teacher Candidates’ U
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function and applied the vertical l
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semester, about half of the course
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They further state that “the impo
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C. Laborde (Eds.) International Han
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(SCK), or knowledge of mathematics
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level of difficulty for each partic
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MKT Measures ScoresMathematics in G
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deep rooted belief in a single way
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THE INTERVIEW PROJECTAngel Rowe Abn
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involving addition and subtraction:
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6+7 4+9=6+(6+1) Substitution =4+(10
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We strongly believe that this inter
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AN INNOVATIVE APPROACH FOR SUPPORTI
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Practice throughout the investigati
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are expected to pursue. Teacher not
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students to organize their reports
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Slovin, H., Venenciano, L., Ishihar
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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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Page 179 and 180: curriculum locally, within individu
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Page 183 and 184: Amazingly, despite there being a fe
Page 185 and 186: ReferencesBlack, M. (1962). Models
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Page 189 and 190: Table 1Instructional TasksSquareTab
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Page 211 and 212: hard for some children? The nature
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Page 215 and 216: Figure 5: Average hand trajectories
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Page 221 and 222: Social system perspectives view the
Page 223 and 224: urged students to think of some way
Page 225 and 226: Figure 1: The Discourse Patterns Du
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