2013 Conference Proceedings - University of Nevada, Las Vegas

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Gasser, K.W. (2011). Five ideas for 21 st century math classrooms. American SecondaryEducation, 39(3), 108-116.Lemann, N. (1999). The big test: The secret history of the American meritocracy. New York:Farrar Straus and Giroux.National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards forschool mathematics. Reston, VA: National Council of Teachers of Mathematics.Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven: Yale UniversityPress.Oakes, J., Ormseth, T., Bell, R., & Camp, P. (1990). Multiplying inequalities: The effects of race,social class, and tracking on opportunities to learn mathematics and science. SantaMonica, CA: Rand Corporation.Philipp, R.A. (2000). Mathematics teachers’ beliefs and affect. In F. Lester (Eds.), Secondhandbook of research on mathematics teaching and learning. United States: InformationAge Pub Inc.Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’smathematics beliefs and teaching practice. Journal for Research in MathematicsEducation, 28, 550-576.Sells, L. (1976). The mathematics filter and the education of women and minorities. Paperpresented at the Annual Meeting of American Association for the Advancement ofScience, Boston, MA.Silberman, C.E. (1970). Crisis in the Classroom: The Remaking of American Education. NewYork: Random House.Stanic, G.M.A. (1986). The growing crisis in mathematics education in the early twentiethcentury. Journal for Research in Mathematics Education, 17(3), 190-205.Strauss, A. & Corbin, J. (1998). Basics of qualitative research (2 nd ed.). Thousand Oaks, CA:Sage.Szydlik, J.E., Szydlik, S.D., & Benson, S.R. (2003). Exploring changes in pre-service elementaryteachers’ mathematical beliefs. Journal of Mathematics Teacher Education, 6, 253-279.Walkerdine, V. (1997). Counting girls out. London: Falmer Press.Wilson, M.S., & Cooney, T. (2002). Mathematics teacher change and development. In G.C.Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematicseducation (pp. 127-147). Dordrecht, The Netherlands: Kluwer.Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy inmathematics. Journal for Research in Mathematics Education, 27(4), 458-477.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 67
SPATIAL REASONING IN UNDERGRADUATE MATHEMATICS: A CASE STUDYLindsay PrughOklahoma Christian Universitylindsay.prugh@oc.eduThe need for spatial thinkers is evident in the lackluster performance of students in mathematicsand the lack of interest in spatially-driven fields. Research has linked spatial thinking toproblem solving, indicating that spatial thinking skills are necessary for success in mathematics.This embedded case study examined how the inclusion of spatial tasks influenced problemsolvingperformance, spatial thinking ability, and beliefs of undergraduate mathematics students.Data were collected through quantitative and qualitative instruments. Findings suggest theinclusion of spatial thinking tasks has an influence on students’ spatial visualization ability,problem-solving strategies, and beliefs about the relevance of spatial thinking.Spatial thinking is not only necessary for success in many aspects of daily life, but it is alsoan essential skill for the STEM fields of Science, Technology, Engineering, and Mathematics,from which many scientific discoveries and progress are made (NRC, 2006). The importance ofspatial thinking throughout a child’s kindergarten through grade-12 education is emphasized inthe geometric standards set forth by the National Council of Teachers of Mathematics (NCTM,2000). This recommendation is mirrored through the work of the National Research Council(NRC), which asserts that spatial thinking is a learnable skill that should be matriculatedthroughout a student’s educational experience. Spatial activities are a worthwhile investment inthe mathematics classroom, since the skill of spatial thinking has been repeatedly linked toproblem solving (Battista, 1990; Edens & Potter, 2007; Moses, 1977).Meaningful mathematics learning is almost always based in spatial imagery. While someforms of mathematical reasoning do not require imagery, the majority of mathematical activitiesinvolve a spatial component (Wheatley & Abshire, 2002). But what does it mean to thinkspatially? Super and Bachrach (1957) describe the skill as the ability to generate, retain,compare, retrieve, manipulate, and transform well-structured mental images. The inclusion ofthese images through well designed spatial tasks could lead to more effective problem-solvingstrategies and improved instructional strategies in the classroom. For these changes to be made,present and future students must be given the opportunity to engage in spatial thinking wheneverpossible, especially in the mathematics classroom.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 68
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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
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 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: their ability to teach the mathemat
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
Page 107 and 108: field so that research on the initi
Page 109 and 110: dynamic approach to learning conten
Page 111 and 112: Kindergarten Lesson FormatHow May W
Page 113 and 114: team’s goals? As much as possible
Page 115 and 116: 6. While preparing the lesson, teac
Page 117 and 118: active learning and collective part
Page 119 and 120: classroom. “I would like to know
Page 121 and 122: I had never been brave enough to tr
Page 123 and 124: 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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