2013 Conference Proceedings - University of Nevada, Las Vegas

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ReferencesBatanero, C., Navarro-Pelayo, V., & Godino, J. (1997). Effect of the implicit combinatorialmodel on combinatorial reasoning in secondary school pupils. Educational Studies inMathematics, 32, pp. 181–199.Benjamin, A.T. (2009). Discrete mathematics: The Great Course Guidebook. Chantilly, VA:The Teaching Company.Berg, B., & Lune, H. (2012). Qualitative research methods for the social sciences (8 th ed.).Boston, MA: Pearson.English, L. D. (1991). Young children's combinatorics strategies. Educational Studies inMathematics, 22, pp. 451–474.Kapur, J.N. (1970). Combinatorial analysis and school mathematics. Educational Studies inMathematics, 3, pp. 111-127.Lobato, J. (2003). How design experiments can inform a rethinking of transfer and vice versa.Educational Researcher, 32(1), pp. 17–20.Lockwood, E. (2011). Student connections among counting problems: An exploration usingactor-oriented transfer. Educational Studies in Mathematics, 78(3), pp. 307-322.Schoenfeld, A.H., & Herrmann, D.J. (1982). Problem perception and knowledge structure inexpert and novice mathematical problem solvers. Journal of Experimental Psychology:Learning, Memory, and Cognition, 8(5), pp. 484-494.Tucker, A. (2006). Applied Combinatorics (5 th ed.). New York: Wiley.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 153
APPENDIXTable 5Description of Combinatorics Problems in Focus Group for participants to solveName Description Type & SolutionSequenceAn exam contains 15 multiple-choice questions, each with 4 choices. HowMC Exams1many possible ways of answering these 15 questions are there?Plane RoutesSupremeCourtDecisionsSummedDigitsGift CardsSkittlesThe M/FCommitteesProblemNetflixMC Exams24-letter wordsMarblesPizzaToppingsA plane starts in New York City and will travel to 7 different cities before itreturns. How many different ways can the plane do this?In how many different ways can the nine members of the Supreme Courtreach a six-to-three decision?How many numbers between 1 and 10,000 have the sum of their digitsequal to 9?How many ways can you distribute a $1, $2, $5, $10, and $20 gift card to 8friends?16 skittles go into the small Halloween skittle bags. There are 5 colors tochoose from in each bag – Red, Green, Yellow, Orange, and Purple. Howmany different possible bags of skittle are there?There are 7 women and 4 men in a club. How many different 4-personcommittees have at least two women?You have 24 different movies on your Netflix account. In how manydifferent ways could you order them?An exam contains 15 multiple-choice questions, each with 4 choices. Inhow many of the possible ways to answer the exam are at least 10 correct?Suppose you make a 4-letter “word” (nonsense words count) from theletters A, B, C, D, and E, where you can repeat letters. How many different“words” are possible?How many ways are there to distribute 25 indistinguishable marbles into 7different containers?How many ways are there to make a pizza with 2 toppings, if the choicesare pepperoni, olives, sausage, ham, mushrooms, and anchovies (doubletoppings allowed)?4 15Arrangement7!Subsetæ 9öçè 6 ÷ ø= æ 9 öçè 3 ÷øMultisubsetææ4ööçèçè 9÷ø÷ ø= æ 9 + 3 öçè 3 ÷øSequence8 5Multisubsetææ5 ööçèçè16÷ø÷ ø= æ 16 + 4 öçè 4 ÷øSubsetæ 7öæ 4öçè 2÷øçè 2 ÷ ø+ æ 7 ö æ 4öçè 3 ÷øçè1÷ ø+ æ 7 öçè 4 ÷øArrangement24!Subset15åk=10æ15öçè k ÷øSequence5 4Multisubsetææ7 ö öçèçè 25÷ø ÷ø= æ 25 + 6 öçè 6 ÷øMultisubsetææ6ööçèçè 2÷ø ÷ø= æ 2 + 5 öçè 5 ÷øProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 154
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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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Page 123 and 124: THE PATH OF REFORM IN SECONDARY MAT
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Page 129 and 130: DiscussionOn part I of the survey t
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Page 157 and 158: Table 4The group’s categories and
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Page 169 and 170: Performance, 33, 1410-1419.Cohen Ka
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Page 177 and 178: Cox, G., Carr, T., & Hall, M. (2004
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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 193 and 194: Figure 2. A Display of Student Stra
Page 195 and 196: ReferencesAnderson, J. R., Greeno,
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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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