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four asked if “spatial thinking skills are useful in other areas besides mathematics.” Seven of the17 students answered “Disagree” or “Strongly Disagree” on the pre-STAS. This numberdropped to only two the post-STAS. A t-test for paired samples was used to measure forsignificant change in responses on all 14 questions of the STAS. A significant change was foundfor the following seven areas of spatial thinking and geometrical drawing: Spatial thinking skillsare important for students to be successful at the elementary school level; I am sure that I canimprove my spatial thinking abilities; Spatial thinking skills are useful in other areas besidesmathematics; Spatial thinking skills can be developed; I will incorporate spatial thinkingactivities into the classroom; I can see spatial thinking in many aspects of my daily life; I amconfident that I can draw geometric shapes accurately.These results indicate that eight weeks of spatial tasks changed the beliefs of pre-serviceelementary teachers. Specifically, after the implementation of spatial activities, the participantswere more likely to believe that spatial skills are malleable, useful outside the mathematicsclassroom, and worthy of inclusion in future curricula. The exercises students experiencedthroughout the eight weeks of implementation promoted understanding of spatial concepts andallowed students the opportunity to identify other areas where spatial skills are useful.Concluding CommentsThe need for practiced spatial thinkers is evident in the growing concern over performance ofU.S. students in mathematics as well as lack of interest in the spatially driven fields of STEM. Inaddition to this need, spatial thinking is a beneficial skill that reaches beyond the STEM fields, asgood problem-solving techniques are valuable for everyday life. Since spatial thinking is relatedto problem solving, and problem solving is important in many facets of life, spatial thinkingshould be a skill that is fostered and encouraged within the classroom.According to NCTM (2000), problem solving is an integral part of all mathematics learning.Therefore, students must be given the opportunity to foster this skill from the beginning to theconclusion of their educational experience. Thankfully, research, including this study, hasshown that this vital skill can be improved as late as post-secondary school. Spatial skills needto be intentionally nurtured if educators desire to give students a global competitive edge andhelp students develop an effective arsenal of strategies to problem solve. While this skill is notexplicitly tested by state exams, the benefits of honing spatial skills will pay off long after thefinal bells of a classroom have rung. If the purpose of education is to create productive citizensProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 73
to advance our way of life, then spatial thinking must be incorporated into the classroom. To dothis, we must first equip our future teachers.The role of research concentrating on pre-service teachers’ spatial thinking and spatial abilityneeds to be a priority if change is desired. The spatial thinking and beliefs surrounding spatialthinking of pre-service educators is a critical component to the likelihood of this skill beingfostered in future mathematics classrooms. The spotlight is now on teacher education programs,because pre-service teachers must first be proficient spatial thinkers before they are able to infusethis skill into their own teaching methods. Mathematics courses—especially those required foreducation majors—should be used as a fundamental piece to this design. In conclusion, forchange to occur, inclusion of spatial thinking and spatial thinking activities must permeate themathematics classrooms and teacher education programs of today and tomorrow.ReferencesBattista, M. (1990). Spatial visualization and gender differences in high school geometry.Journal for Research in Mathematics Education, 21, 47-60.Bruner, J. (1973). The course of cognitive growth. In Beyond the Information Given: Studies inthe Psychology of Knowing (pp. 325-351). New York: W.W. Norton & Co.Edens, K., & Potter, E. (2007). The relationship of drawing and mathematical problem solving:Draw for Math tasks. Studies in Art Education, 48 (3), 282-298.Fisher, R. (2005). Teaching children to think. Trans-Atlantic Publications.Guay, R. (1980). Spatial ability measurement: A critique and an alternative. Paper presented atthe annual meeting of the American Educational Research Association, Boston, MA.Hanlon, A. (2009). The development and validation of a spatial thinking attitude survey: Anexplatory mixed method design. Unpublished manuscript. Oklahoma State University.Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations andmathematical problem solving. Journal of Educational Psychology, 91 (4), 684-689.Moses, B. (1977). The nature of spatial ability and its relationship to mathematical problemsolving. Unpublished doctoral dissertation, Indiana University.National Center for Education Statistics. (2003). Trends in international mathematics andscience study. Retrieved March 23, 2011 from http://nces.ed.gov/pubs/timss03/index.asp.National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards forschool mathematics. Reston, VA: National Council of Teachers of Mathematics.National Research Council. (2006). Learning to think spatially. Washington, DC: The NationalAcademies Press.Presmeg, N. (1986). Visualization in high school mathematics. For the Learning of Mathematics,6 (3), 42-46.Super, D., & Bachrach, P. (1957). Scientific careers and vocational development theory. NewYork: Bureau of Publications, Teachers College, Columbia University.Wheatley, G., & Abshire, G. E. (2002). Developing mathematical fluency: Activities for grades5-8. Bethany Beach, DE: Mathematics Learning.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 74
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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
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 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: given to the 33 students on the MPI
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
Page 125 and 126: Our collaboration model was formed
Page 127 and 128: internal evaluator) were analyzed.
Page 129 and 130: 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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