2013 Conference Proceedings - University of Nevada, Las Vegas

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question. However, 8 pairs weren’t able to pinpoint any specific concept or relate theirinstructional decision back to the framework. In this excerpt it seems clear that these PSTs aresearching for what might be on the cusp of what is possible for the child.If we could continue working with this child [we would give him] problems or conceptsinvolving subtraction with greater values and more division problems so that hecomprehends he is actually doing division. Other problems that would be applicable tothis student are those involving remainders and fractions. This is where his ZPD islocated. We think this because he can do both multiplication and division sufficiently andaccurately, but we are curious as to whether he fully comprehends these concepts. If wecould see him work with numbers in fractions and as a part of a whole we might get abetter feel for his future potential and understanding of the material.Four pairs of PSTs were able to specifically address the levels in the framework and suggestdirections for the child’s mathematics related to particular types of word problems.If I were to continue to work with Allyson, I would probably encourage her to exploremore strategic ways to solve problems. She depended on the counters for much of theinterview, which suggests she is not entirely comfortable with solving word problems inher head or without some sort of physical visual. Perhaps with more practice and morestrategic reasoning, Allyson could move from the INS+ level to SAR.While this pair of PSTs was able to discuss pushing the child from the INS+ Level to the SARLevel by getting the child to become less reliant on physical materials, they were not able to givespecific problems or tasks that would encourage this next level of reasoning. One such examplemight be using a cup or some cover so that some objects are left unseen.DiscussionThe PSTs in our interview project were able to describe and analyze the children’smathematics using the framework from class. They were also able to make some instructionaldecisions. However, because any future instructional decisions were hypothetical, they lackedfocus and were mostly explorational. This leads us to ask the question, would it be worth thetime and additional efforts from our students’ perspective to have them conduct at least a secondinterview with the same child. We feel that this would give them the opportunity to go beyondthe interview and force them to make the instructional decisions.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 47
We strongly believe that this interview project has a great impact on the PSTs and willchange the way they previously felt about teaching mathematics. Some of the typical reflectionsfrom the PSTs about the overall project highlighted their connection of theory to practice, seeingdifferent ways to do mathematics, and making instructional decisions based on children’smathematics. One pair of PSTs noted:We learned a lot about how to apply different concepts like counting from largest,different kinds of word problems, how to figure out a child’s strategy, and so on. We notonly learned a lot from having to analyze everything Kylie was doing, but Kylie actuallyended up teaching us a lot as well! We learned new strategies and realized how muchchildren can teach you about how they think. They can analyze problems so muchdifferently than adults, and sometimes their way seems to work better. In conclusion, wenot only cannot wait to begin teaching students, but in turn, learn from our students.ReferencesAbney, A. R. (2007). Elementary Preservice Teachers’ Working Models of Children’sMathematics. Unpublished Dissertation, University of Georgia, Athens, GA.Carpenter, T., Fennema, E., Franke, M., Levi, L., Empson, S. (1999). Children’s Mathematics:Cognitively Guided Instruction. National Council of Teachers of Mathematics Inc. Reston,VA.D’Ambrosio, B. (2004). Preparing Teachers to Teach Mathematics within a ConstructivistFramework: The Importance of Listening to Children. AMTE Monograph1: The Work ofMathematics Teacher Educators (pp. 135-150).Davis, B. (1996). Toward a Sound Alternative (Vol. 7). Journal for Research in MathematicsEducation, 29, 355-376.McIntyre, DJ, Byrd, DM, & Foxx, SM (1996). Field and laboratory experiences. In J. Sikula(Ed.), Handbook of Research on Teacher Education (2nd ed., pp. 171-193). New York:Macmillan.Mewborn, D. S. (1999). Reflective thinking among preservice elementary mathematics teachers.Journal for Research in Mathematics Education, 30(3), 316-341.Mewborn, D. S. (2000). Meaningful integration of mathematics methods instruction and fieldexperience. Action in Teacher Education 21(4), 50-59.NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA: NationalCouncil of Teachers of Mathematics.Olive, J. (2001). Children’s Number Sequences: An Explanation of Steffe’s Constructs and anExtrapolation to Rational Numbers of Arithmetic. The Mathematics Educator. University ofGeorgia.Steffe, L. P. & Cobb, P. (1988). Construction of arithmetical meanings and strategies. NewYork: Springer-Verlag.Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlyingprinciples and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design inmathematics and science education (pp. 267- 307). Hillsdale, NJ: Erlbaum.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 48
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 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: 6+7 4+9=6+(6+1) Substitution =4+(10
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
Page 79 and 80: given to the 33 students on the MPI
Page 81 and 82: to advance our way of life, then sp
Page 83 and 84: STUDENT CONCEPTIONS OF “BEST” S
Page 85 and 86: students are likely to interact wit
Page 87 and 88: opinion of the student body. This q
Page 89 and 90: At the highest level of reasoning a
Page 91 and 92: APPENDIXTo use two decks of cards t
Page 93 and 94: isolated and often occur in tandem
Page 95 and 96: with the CCSSM. Teachers read and d
Page 97 and 98: teachers’ role-play of SFMP #4. A
Page 99 and 100: Durkin, D. (1978-1979). What classr
Page 101 and 102: as well as the alignment between th
Page 103 and 104: Table 2Number of teachers per grade
Page 105 and 106:
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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