2013 Conference Proceedings - University of Nevada, Las Vegas

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SECONDARY MATHEMATICS ALTERNATIVE CERTIFICATION TEACHERPROBLEM SOLVINGBrian R. EvansPace Universitybevans@pace.eduThe purpose of this study was to understand alternative certification middle and high schoolteachers’ mathematical problem-solving skills and perceptions. Participants were given aproblem-solving examination and required to reflect upon their students’ and their own problemsolving. Findings revealed there was a significant improvement in problem-solving scores for theteachers over the course of the semester. Teachers perceived their students’ problem-solvingabilities as generally weak due to not understanding how to start a problem, lack of persistence,and poor literacy skills.Problem solving continues to be of high importance in mathematics education (Posamentier& Krulik, 2008; Posamentier, Smith, & Stepelman, 2008) and is one of the five National Councilof Teachers of Mathematics (NCTM) process standards (NCTM, 2000). National Council ofSupervisors of Mathematics (NCSM) has considered problem solving to be the principal reasonfor studying mathematics (NCSM, 1978), and it has been recommended that mathematicscontent be taught from a problem-solving perspective (NCTM, 2000; Schoenfeld, 1985).Additionally, problem solving continues to be of high importance as an element of the CommonCore Standards in which students must make sense of problems confronting them and perseverein solving the problems.In order to understand what problem solving is, first the definition of a mathematical“problem” must be understood. Charles and Lester (1982) defined a mathematical problem astask in which (a) The person confronting it wants or needs to find a solution; (b) The person hasno readily available procedure for finding the solution; and (c) The person must make an attemptto find a solution. According to Krulik and Rudnick (1989), problem solving is a process inwhich an individual uses previously acquired knowledge, skills, and understanding to satisfy thedemands of an unfamiliar situation. Polya (1945), in his seminal work How to Solve It, outlined ageneral problem-solving strategy that consisted of (a) Understanding the problem; (b) Making aplan; (c) Carrying out the plan; and (d) Looking back.The purpose of this study is to understand alternative certification middle and high schoolmathematics teachers’ problem-solving abilities and perceptions about their students’ and theirProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 1
own problem solving, which is critical in supporting them to teach from a problem-solvingperspective. NCTM (2000) said, “Problem solving is not only a goal of learning mathematics butalso a major means of doing so” (p. 52).Theoretical FrameworkIn mathematics education, problem solving is the manifestation of constructivist learning, thetheory that students learn best through constructing their own knowledge, as promoted bythinkers such as Jean Piaget and John Dewey. Authentic problem solving in mathematics is thebasis of reform- and inquiry-based instruction in mathematics (Clark, 1997).It has been shown that teacher beliefs about student ability greatly influence instructionalpractices (Nathan & Koedinger, 2000). Asman and Markkovits (2009) found teachers who areunable to solve difficult non-routine problems were less likely to include these types of problemson student assessments, even if they were willing to address such problems in their instruction.Rosales, Santiago, Chamoso, Munez, and Orrantia (2012) have noted that in the classroomproblem solving can often take on a mechanized procedure in solving problems that involveslimited situational knowledge. To counter this, Hobbs (2012) promoted situating problems usingculturally relevant pedagogical techniques in order to help teachers better engage students fromdiverse backgrounds. Capraro, An, Ma, Rangel-Chavez, and Harbaugh (2012) advocated supportfor preservice problem solving and mathematics proficiency, particularly in open ended problemsolving situations.Polya (1945) laid the groundwork for systematic approaches to solving mathematicalproblems. Additionally, NCSM (1978) and NCTM (2000) have emphasized problem solving asthe purpose of mathematics instruction and a way of teaching.Research Questions1. What differences were there in problem solving scores between the beginning and end of thesemester in a mathematics content course for alternative certification teachers?2. What were teacher perceptions of their students’ and their own problem-solving abilities?Further, what differences in perceptions of their student and their own problem-solvingabilities existed between the beginning and end of the semester in a mathematics contentcourse for alternative certification teachersProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 2
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: Support for Students Learning Mathe
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 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
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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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