2013 Conference Proceedings - University of Nevada, Las Vegas

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MethodologyThe methodology of this study involved quantitative and qualitative methods. The sampleconsisted of 34 new teachers in the New York City Teaching Fellows alternative certificationprogram enrolled in a graduate algebra content mathematics course for teachers that involvedrigorous derivations and proofs. Teachers were given a problem-solving examination at thebeginning and end of the semester. The problem solving examinations were different on thepretest and posttest instruments and the problems presented were unfamiliar to the teachers. Theproblems were selected from the literature. However, while the instruments were developed byan experienced mathematics educator with background in mathematics problem solving, alimitation is that the problem solving examinations were not analyzed for construct and contentvalidity and reliability. Finally, teachers were also required to reflect upon both their students’and their own problem solving at the beginning and end of the semester.ResultsThe first research question was answered using scores from the problem-solvingexamination, and data were analyzed using paired samples t-test (see Table 1), which revealed astatistically significant difference between pretest scores and posttest scores for the problemsolvingexamination, and there was a very large effect size. Caution should be taken ininterpreting these results since it may be expected that teacher test scores would rise from pretestto posttest. However, the problems on the posttest were different problems from the pretest andwere unfamiliar to the teachers taking the examination.Table 1Paired Samples t-Test Results for Problem Solving AbilityProblem Solving Examination Mean SD t-value d-valuePretest4.91 1.654 -8.679** 2.08Posttest8.35 1.649N = 34, df = 33, two-tailed** p < 0.01The second research question was answered using teacher reflections analyzed to determineteacher perceptions of student problem solving as well as their perceptions of their own problemsolving. At the beginning of the semester teachers categorized their students as having weakproblem-solving abilities and skills. The most commonly reported problems were knowing howProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 3
to get started and persistence. Teachers said many students did not understand the problems theyhad to solve. At the end of the semester teachers found many of the problems they encounteredwith their students in the beginning of the semester still persisted. Teachers felt there wereseveral things they could do to help improve their students’ problem-solving abilities and skills.Most commonly mentioned were the steps to problem solving as outlined by Polya (1945).Teachers commonly said that scaffolding and differentiated instruction could be used to helpimprove problem solving in their students.At the beginning of the semester teachers reported that they shared many of the issues thattheir students have such as knowing how to start, persistence, understanding what the problem isasking. At the end of the semester, most teachers said that having the algebra content class thatfocused on derivations and proofs had improved their problem-solving abilities greatly. Severalused the phase, “I have come a long way,” referring to their problem-solving abilities. Many saidthat it was the analytic nature of derivations and developing proofs that helped improve theirproblem-solving abilities. Additionally, many found understanding how mathematics “works” inthe class furthered their analytic skills.Conclusions and Educational ImplicationsSince there was an increase in problem-solving scores over the course of the semester it canbe argued that the a strong mathematics requirement for alternative certification mathematicsteachers, combined with their own teaching experiences, can lead to stronger problem-solvingachievement, which is important given the emphasis of teaching mathematics from a problemsolvingperspective (Clark, 1997; NCSM, 1978; NCTM, 2000; Posamentier et al., 2008). Futureresearch should examine how much of this is due to the effects of content classes for teachers orhow much is due to the effects of their teaching experience, particularly in alternativecertification programs.Teachers perceived that students did not persevere in their problem solving because theywere reliant on the teacher giving them the solutions in previous years. While this reliance onteachers providing solutions may be partially due to negative attitudes toward problem solvingheld by the students (Arslan & Altun, 2007), it also could be a problem with teachers not givingenough time for students to engage in problem solving. Perhaps there is a need to give studentsmore time in their problem solving, and to resist the temptation to simply “give” the solutions tothe students. This should be further investigated.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 4
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: own problem solving, which is criti
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 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
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are expected to pursue. Teacher not
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students to organize their reports
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Slovin, H., Venenciano, L., Ishihar
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The research presented in this pape
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students’ confidence. Because bel
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triangulation necessitated examinat
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their ability to teach the mathemat
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SPATIAL REASONING IN UNDERGRADUATE
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journal prompt would be given as a
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given to the 33 students on the MPI
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to advance our way of life, then sp
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STUDENT CONCEPTIONS OF “BEST” S
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students are likely to interact wit
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opinion of the student body. This q
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At the highest level of reasoning a
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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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