2013 Conference Proceedings - University of Nevada, Las Vegas

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The analysis of the four AB factors from time-points 1 to 5 using repeated measuresANOVA suggested that over the nine month study, participants believed more strongly that therewas a single way to solve problems (p < 0.001) despite the learning experiences provided by theMethods instructors to demonstrate multiple ways of solving problems. In addition, participantsfound mathematics more enjoyable (p < 0.001) over nine months. The regression in participantmathematical reasoning and the greater focus on finding the right answer may have limitedparticipants’ ability to think out of the box and to think about higher mathematics effectively.Overall, the participants’ lack of growth may have been due to incorrect assumptions aboutincoming pre-service teachers core mathematical skills. Participants had a weaker mathematicalbackground entering Methods relative to other studies of pre-service teachers using the MKTmeasures. These previous studies either used the measures as published (mean = 0), or createdforms using MKT items with mean = -0.25 (ME.ET, 2009; Welder, 2007). The initial MKTscores for the study participants were: (a) mean = -0.55 for number sense, and (b) mean =-0.47algebraic thinking. The Methods course was designed based on prerequisites that may have beeninconsistent with the actual pre-service teachers’ mathematics aptitude. Thus, participants mayhave been incapable of leveraging the full opportunity of Methods.The results of the study were discussed with a panel of three university Methods instructors(all full-time faculty). The instructors believed that the attitudes and beliefs of the participantstowards mathematics may have contributed to their low performance. Elementary pre-serviceteachers are characteristically fearful of mathematics due to lack of success as a student ofmathematics themselves. In addition, the high cognitive demand of the MKT measurescombined with a low level of mathematics understanding may have resulted in frequentguessing. Participants may have also lacked motivation when completing the measures as theywere not tied to their course grade. Suggestions for further study included: (a) administer theMKT measures to pre-service teachers as they enter the first mathematics content course, thenincrease the time between time-points ending with Student Teaching, (b) provide a greaterincentive to motivate participants, and (c) conduct personal interviews with participants to gainfurther insight as to how participants perceived the measures and how they selected theiranswers.Although the participants’ demographics were typical of students enrolled in a traditionalelementary teacher preparation program, the initial low-level of mathematics knowledge andProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 39
deep rooted belief in a single way of solving mathematics problems may have limited the impactof the Methods course. In order to successfully match learning strategies and activities withstudents, situations, and opportunities, teachers must have a deep understanding of mathematicscontent, a large repertoire of pedagogical strategies, and the ability to make decisions aboutwhich tool will be the most effective in a given situation.In practice, the three periods of a teachers’ development of mathematics knowledge isgreatly influenced by the pre-service teachers’ own schooling. The relatively short period oftime spent in the teacher preparation program may only be able to begin reshaping their priorexperiences. Based on the findings of this study, recommendations include (a) the re-evaluationof minimum teacher preparation program entry requirements for mathematics contentknowledge, and (b) review the current Methods curriculum, and (c) for new teachers alreadyentering the field, participation in continued professional development focused on bothmathematics content knowledge and reform-based pedagogy in order to strengthen teachersconceptual knowledge of mathematics and to continue to peel away deep-rooted beliefs towardsmathematics.ReferencesBall, D.L., (2003, February 6). What mathematical knowledge is needed for teachingmathematics? Remarks prepared for the Secretary’s Summit on Mathematics, U.S.Department of Education, Washington DC.Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: Whatmakes it special? Journal of Teacher Education, 59(5), 389-407.Byrne, B. M. (2012). Structural equation modeling with Mplus: Basic concepts,applications, and programming. New York: Routledge.Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30.Johnson, B. (2001). Toward a new classification of nonexperimental quantitative research.Educational Researcher, 30(2), 3-13.Kajander, A. (2010). Elementary mathematics teacher preparation in an era of reform: Thedevelopment and assessment of mathematics for teaching. Canadian Journal of Education,33(1), 228-255.Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding offundamental mathematics in China and the United States. New York: Routledge.The Mathematical Education of Elementary Teachers (ME.ET) Project (2009, January 4).Advisory board progress report.Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights.Boston, MA: Beacon Press.Muthén, L. K., & Muthén, B. O. (1998-2010). Mplus statistical analysis with latentvariables user’s guide (6 th ed.). Los Angeles, CA:Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 40
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: MKT Measures ScoresMathematics in G
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
Page 93 and 94: isolated and often occur in tandem
Page 95 and 96: 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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