2013 Conference Proceedings - University of Nevada, Las Vegas

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emphasis during class time. A concerted effort was made to establish social norms in theclassroom that supported and encouraged discourse, investigation, and questioning. Thestudents’ beliefs about mathematics and mathematics teaching and learning were deliberatelyperturbed through the structure of the class (learning experiences, social norms, etc.).Additionally, writing assignments were incorporated that addressed beliefs (although not alwaysexplicitly).The participants for this study were students from a small 4-year college located in acommunity comprised of approximately 17,000 people in the southern Midwest region of theUnited States. All participants were preservice teachers enrolled in a mathematics content courseintended for early childhood and elementary majors although there were a few participantstaking the course that had other majors such as special education. The research study includedtwo sections of the same mathematics course focused on number theory, sets, and functionstotaling 47 students of which 37 chose to be participants: 35 females (95%) and 2 males (5%).Research Method, Data Collection and AnalysisTeacher action research was a natural research method for this study because it “developsthrough a self-reflective spiral of planning, acting, observing, reflecting, and then replanning,further implementation, observing, and reflecting” (Burnaford, Fischer, & Hobson, 2001, p.43).It allowed for continual action, analysis of data, reflection on the data and the course andopportunities to make adjustments based on those reflections. Data were collected over a periodof time of about four months. The majority of the data were collected from participants’ writingas part of the course structure via short answer response questions on exams and homeworkassignments, but other sources included a personal journal, student metaphors, and classroomconversations. The variety and amount of data compiled helped to advance a more complete andaccurate sense of the participants’ perspectives, experiences, and beliefs.Despite being personally invested in the research, a teacher researcher can take steps to retainvalidity and be purposeful in the level of rigor involved with the use of systematic analysis of thedata, peer examination and discussion, as well as triangulation (Bartlett & Burton, 2006;Foreman-Peck & Murray, 2008). For this study, a systematic analysis of the data involved aconstant comparison method of coding and theming (Strauss & Corbin, 1998); peer examinationand discussion entailed corroboration and examination of the findings and themes with a peer;Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 63
triangulation necessitated examination of the themes from participants’ responses, my reflectivejournal, and the peer discussions.FindingsAnalysis of the data revealed that participants’ perspectives about the nature of mathematicsas well as their selves in relation to mathematics changed significantly for many students. Itappears that their altered beliefs about mathematics and the culture of the classroom dynamicallyinteracted to affect their mathematical autonomy. Students enjoyed learning mathematics andhad greater confidence in their mathematical capabilities. One participant statedI think, in general, most of the experiences in this course have enhanced my confidenceand enthusiasm for mathematics. Being encouraged to work with out-of-the-boxalgorithms has expanded my perceived horizons and opened up a new field of interest forme.Participants’ perceptions about the way in which mathematics is “done” as well as theirfeelings about mathematics changed over the course of a semester in this non-traditionalmathematics content course. Many felt more comfortable with the mathematics that they wouldeventually teach and found a new appreciation for mathematics in general; a few expressed thatthey even grew to like mathematics. Participants talked about this change in confidence levelsextensively; some excerpts from their writings are as follows:After this class, math is still not my most liked subject, however it isn’t my mostdisliked either. I do feel a lot more confident in teaching math to students now that Ihave had this class.I think that this course has made me more confident in learning math because it mademe realize there was not just one way to find the “answers” to math problems… I amnot sure that I will ever really enjoy math but I am not so afraid to take it on now.This class has changed my thoughts about math in many ways. Before this class Ihated math and I struggled in all my other previous math courses. This class hasshowed me that math can be enjoyable and that I can do well in this course and notjust squeeze by.Furthermore, after taking a course structured in a non-traditional format that focused onconceptual understanding, meaning-making, answering “why,” and working in groups,participants’ reported feeling more confidence in their mathematical ability as well as theirpedagogical skills to teach mathematics. They spoke about their mathematical andepistemological empowerment related to understanding the mathematics. Participants oftenProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 64
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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
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 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: students’ confidence. Because bel
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
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
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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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2013 Conference Proceedings - University of Nevada, Las Vegas

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