2013 Conference Proceedings - University of Nevada, Las Vegas

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During whole class discussion, another student described his explicit rule as 2x + 2 =y (where x is number of tables and y is number of people) and explained that this ruleworks because each square table contributes 2 seats to the train and the train has 2 otherseats on its ends. More than a month later, this student was exploring the pentagon tabletask. As seen from her representation, she used reasoning from previous task (squaretable task) to reason about the pentagon table task that 3x + 2 = y where x is the numberof pentagon tables and y is the number of people that can sit around it.Summary and ConclusionTeachers situated learning for students to make connections of mathematical ideas fromdifferent contexts. These connections were between the tasks and (a) between students’strategies, (b) different representations, (c) different tasks, and (d) different ideas in thecurriculum. Connections within one context (e.g., student strategies) also led to connectingmathematical ideas with other contexts (e.g., curriculum and tasks). The discussed example of astudent’s work in Table 3 illustrates the connections across different tasks and differentstrategies. Teachers positioned students to make these connections by asking them to think abouthow the tasks they were working on were similar to other tasks, asking students to identifyunderlying mathematical ideas of different strategies, and asking students to share their ideasduring whole class discussions. Connecting mathematical ideas afforded students’ algebraicthinking in making generalizations and validating those generalizations. The results show thatthe routines of practice reported in this study support students mathematical practices.This study was conducted in an informal setting. Future research may explore routines ofpractice in both informal and formal settings to investigate how participants in mathematicslearning communities can navigate affordances of each setting to further mathematicalunderstanding. Future research may also focus on preparing mathematics teachers, who are ableand willing to connect classroom mathematics activities with out-of-school activities inmeaningful ways for students with diverse backgrounds.AcknowledgementI acknowledge Dr. Sarah Berenson, Dr. Kerri Richardson, and On Track-Learn Mathteam for their help with this study. This study was funded by US Department of Education grantnumbers U215K0900096 and U215K100223. The views do not necessarily reflect those of theUS Department of Education.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 187
ReferencesAnderson, J. R., Greeno, J. G., Reder, L. M., & Simon, H. A. (2000). Perspectives on learning,thinking, and activity. Educational Researcher, 29, 11–13.Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For theLearning of Mathematics, 14 (3), 24–35.Blanton M. L., & Kaput, J. J. (2011). Functional thinking as a route into algebra in theelementary grades. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialoguefrom multiple perspectives (pp. 5–24). Springer-Verlag: Berlin Heidelberg.Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. E. (2006). Arithmetic andalgebra in early mathematics education. Journal for Research in Mathematics Education,37(2), 87–115.Charmaz, K. (2011). Costructivist theory analysis of losing and regaining a valued self. In F. J.Wertz, K. Charmaz, L. M. McMullen, R. Josselson, R. Anderson & E. McSpadden (Eds.),Five ways of doing qualitative analysis: phenomenological psychology, grounded theory,discourse analysis, narrative research, and intuitive inquiry (pp.165–204). NY: GuilfordPress.Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among fiveapproaches (2 nd ed.). CA: Sage Publications, Inc.Greeno J. G., & The Middle School Mathematics Through Applications Project Group. (1998).The situativity of knowing, learning, and research. American Psychologist, 53, 5–26.Greeno, J. G. (2003). Situative research relevant to standards for school mathematics. In J.Kilpatrick, W.G. Martin & D. Schifter (Eds.), A research companion to principles andstandards for school mathematics (pp.304–332).National Council of Teachers of Mathematics. (2000). Principles and standards for schoolmathematics. Reston, VA: Author.Proulx, J., & Berdnarz, N. (2009). Teachers' immersion in mathematical practices and theirteaching practices. For the Learning of Mathematics, 29(1), 28.Sawyer, R. K., & Greeno, J. G. (2009). Situativity and learning. In P. Robbins & M. Ayedede(Eds.), The Cambridge handbook of situated cognition (pp. 347–367). New York:Cambridge University Press.Stephens, A. C. (2005). Developing students understanding of variable. Mathematics Teachingin the Middle School, 11(2), 96–100.Store, J. C. (2012). Conceptualizing routines of practice that support algebraic reasoning inelementary schools: A constructivist grounded theory (Doctoral dissertation). TheUniversity of North Carolina at Greensboro.Sutherland, S. (1991). Unanswered research questions on the teaching and learning of algebra.For the Learning of Mathematics, 11(3), 40–46.Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A.Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97).New York: Macmillan.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 188
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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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