2013 Conference Proceedings - University of Nevada, Las Vegas

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easoning, number sense, and algebraic thinking (Schoenfeld, 2008; Welder & Simonsen, 2011),reflects the importance of mathematics literacy, especially in algebra, for students’ futureeconomic independence (Moses & Cobb, 2011).MethodsThe following research questions were developed to guide the study: (RQ1) What is theimpact of a mathematics methods course followed by a student teaching assignment on thedevelopment of MKT in (a) number sense, and (b) algebraic thinking among undergraduateelementary pre-service teachers, and (RQ2) what are the relationships between changes in MKTin number sense and algebraic thinking and (a) participant demographics, (b) prior knowledge ofmathematics, and (c) attitudes and beliefs towards mathematics? Evidence for causality wassupported by the collection of longitudinal data from the same panel of participants, data ondependent variables at the beginning of the study, and the use of confirmatory structural equationanalysis (Byrne, 2012; Johnson, 2001).Participants (n = 176) were recruited during fall 2011 semester of their final year of a fouryearuniversity teacher preparation program at a large public university in north Texas. Prior toentering the fourth and final year of the preparation program, pre-service teachers are required totake two mathematics content courses (for elementary teachers) in the mathematics department.During fall 2011, participants were enrolled in an elementary mathematics methods course(henceforth called Methods) taught by the College of Education. During spring 2012,participants completed a full-time student teaching assignment (henceforth called StudentTeaching) over 15 weeks. The demographics of the study participants (e.g. 79% between 21-25years in age, 13.1% Hispanic) were representative of the pre-service teachers enrolled in atraditional university teacher preparation program in the United States (USDE, 2011). Although Itaught several sections of Methods in prior semesters, I was not teaching any of the Methodssections during the time of the study.In order to measure each participants’ mathematical content knowledge, a computer adaptivetest version of the MKT measures developed by the Learning Mathematics for Teaching project(Hill, Schilling, & Ball, 2004) was administered to the participants at five time-points (every sixweeks) over nine months. The MKT measures were designed to measure both CCK and SCK,addressed in the Methods course. The multiple time-points were essential to the growth modelanalysis. The computer adaptive test version allowed for the (a) selection and adjustment of theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 35
level of difficulty for each participant, (b) efficient use of time, and (c) reduction in test fatigue.Scores for number sense (elementary number concepts and operations) and algebraic thinking(elementary patterns, functions, and algebra) were reported in standard deviation units based onthe expected performance of the average K-8 inservice teacher, mean = 0, SD = 1. The MKTmeasures have enabled the documentation of growth in mathematical knowledge amongelementary teachers participating in professional development and among elementary pre-serviceteachers following the completion of mathematics content courses designed for teachers. Whenthe MKT measures were used with pre-service teachers, the level of difficulty was adjusted aslow as -0.25 since pre-service teachers have had less time in the classroom working withmathematics curriculum (Welder, 2007).In order to evaluate the influence of participant’s prior knowledge of mathematics, andattitudes and beliefs towards mathematics, a background survey and an Attitudes and Beliefssurvey (henceforth known as AB survey) was adapted from the Student Assessment, Parts 1 & 3from the ME.ET project. The background survey gathered information on participantdemographics and prior knowledge of mathematics (e.g. mathematics courses taken, examscores, high school GPA). The background survey was administered once at the beginning ofthe study. Items on the AB survey were grouped into four factors: (a) usefulness of mathematics,(b) multiple ways of doing mathematics, (c) nature of mathematics (rigor and precision), and (d)processes of doing mathematics (enjoyment). The AB survey was administered to allparticipants at each of the five time-points along with the MKT measures.To evaluate the performance of the participants on the MKT measures and AB survey, as afunction of their progression through Methods and Student Teaching, the data was analyzedusing a piecewise growth model. MPlus statistical software (Muthén & Muthén, 1998-2010)was used to model the longitudinal developmental trajectories of MKT (number sense andalgebraic thinking) and to identify possible influencing factors related to (a) demographics, and(b) prior knowledge of mathematics from the background survey, and (c) attitudes and beliefstowards mathematics from the AB survey. This confirmatory approach founded in structuralequation modeling, allowed for the analysis of data for inferential purposes, using longitudinaldata over multiple phases (Byrne, 2012; Johnson, 2001). A repeated measures ANOVA wasused to analyze changes in the AB factors over the nine months.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 36
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: (SCK), or knowledge of mathematics
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 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
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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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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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