2013 Conference Proceedings - University of Nevada, Las Vegas

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etween mathematicians and mathematics educators with close connections to classroompractice. The MET document further suggests that professional development should be aimedat: deepening the understanding of the fundamental mathematics beyond what is usually reachedwith an integration of content knowledge, cognitive science, and teaching experience; to developeffective “habits of mind” for thinking mathematically; to develop realistic strategies for in-depthimplementation of the NCTM Process Standards; to analyze teaching practices in light of deepcontent and mathematical pedagogical knowledge; to reflect upon personal beliefs aboutmathematics content and pedagogy over time; to develop a high level of confidence and apositive disposition for mathematics in order to provide appropriate instruction for all childrenand gain parental support and understanding (CBMS, 2001). In order for the practice ofsecondary teachers to change with the recommendations in the MET document teachers mustthemselves engage in looking at the mathematics they are teaching from different points of view.They need to develop a more comprehensive understanding of the connections of themathematical ideas being taught and develop a collaborative network of support for their workon the content and on implementing various changes within their classrooms. Improvingachievement in mathematics education involves many components. Current research focuses onstrengthening content knowledge of teachers that will enable them to understand mathematicalconnections among ideas and the sequence of ideas that make sense both mathematically anddevelopmentally (Ferrini-Mundy, & Schmidt, 2007, Ball, Thames, & Phelps, 2008).This paper reports the results of a study of the effects of a professional developmentpartnership with an entire mathematics department and 4 intervention specialists in an urbanschool district in NE Ohio, three mathematics educators and three mathematicians from a localuniversity. The goals of the professional development were to: 1) Deepen teacher mathematicalcontent knowledge and knowledge for teaching; 2) Create and maintain a professional learningcommunity; 3) Transform teachers’ ways of thinking to incorporate dispositions that holdstudents accountable for engaging in the common core standards for mathematical practice; and4) Project sustainability through the creation of a community of vested partners, where partnersinterpret, enact, and sustain the Common Core Standards vision of developing mathematicallycompetent students. Ultimately, the aim was to improve the teaching and learning ofmathematics at the high school level.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 117
Our collaboration model was formed using a combination of existing models: the Yale/NewHaven National Teacher Institute Model and the Focus on Mathematics (BostonUniversity/Educational Development Center’s National Science Foundation’s MSP). Twopremises were followed from these models: all partners involved had equal say in the directionof the professional development and that there would be core involvement of mathematicians inthe partnership. The high school teachers and university faculty used the hybrid model to designthe professional development opportunities that were cogenerated. This co-planning of thedirection of the professional development was enacted in face-to-face meetings each week of theschool year as well as 2 weeks in late summer and 2 days after each school year was completed.Ideas from the project staff were presented and specific teacher problems and issues werepresented by the participants. Discussions took place to determine the most needed professionaldevelopment.MethodologyParticipantsAll eleven mathematics faculty and 4 intervention specialists were part of this study. All ofthe teachers have the appropriate license for their teaching assignments. The teachers ranged inexperience from 2 years to 25 years. All signed an agreement to participate in the grant and inreturn the grant provide the professional development, $500 in teaching materials for theirclassrooms, and stipends when PD occurred outside their regular teaching contracts.The treatment/professional developmentEach year the teachers had approximately 100 hours of professional development focused atthe goals mentioned above. This occurred during summers (60 hours), each week prior toclasses starting (20 hours), and once a month (20 hours) during an early release time.During the summers teachers were engaged in doing mathematics problems. This is whereour mathematicians helped to lead these discussions about the problems, various methods ofthinking about the problems, reasoning for solutions, and connections to other areas ofmathematics and the common core state standards. During this time, one goal was to buildconfidence and community among all participants. We collected samples of the rich problemsteachers worked and videotaped these experiences. We also surveyed the teachers on theirbeliefs about the nature of mathematics and the teaching and learning of mathematics.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 118
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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
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justify their statements, included
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Finally, engagement in MP.6 was ass
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PRESERVICE TEACHERS’ EMOTIONAL EN
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“experiences that are charged wit
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Number of journals containingEmotio
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ConclusionsStruggle and frustration
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Mathematics Teacher Candidates’ U
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function and applied the vertical l
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semester, about half of the course
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They further state that “the impo
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C. Laborde (Eds.) International Han
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(SCK), or knowledge of mathematics
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level of difficulty for each partic
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MKT Measures ScoresMathematics in G
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deep rooted belief in a single way
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THE INTERVIEW PROJECTAngel Rowe Abn
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involving addition and subtraction:
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6+7 4+9=6+(6+1) Substitution =4+(10
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We strongly believe that this inter
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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
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
Page 121 and 122: I had never been brave enough to tr
Page 123: THE PATH OF REFORM IN SECONDARY MAT
Page 127 and 128: internal evaluator) were analyzed.
Page 129 and 130: DiscussionOn part I of the survey t
Page 131 and 132: whole department of secondary mathe
Page 133 and 134: discussion. Many texts include wild
Page 135 and 136: Data collection consisted of tests,
Page 137 and 138: I've not used children's literature
Page 139 and 140: could extend this inquiry to high s
Page 141 and 142: course titled Calculus with Busines
Page 143 and 144: no mathematical sense and should no
Page 145 and 146: Adopts the “111” (a term coined
Page 147 and 148: Specifically, clicking the “Click
Page 149 and 150: algebraic expression is carried out
Page 151 and 152: Retrieved from http://secc.sedl.org
Page 153 and 154: furthermore, each model may result
Page 155 and 156: After instruction in the course, th
Page 157 and 158: Table 4The group’s categories and
Page 159 and 160: you choose three place values, æ 4
Page 161 and 162: APPENDIXTable 5Description of Combi
Page 163 and 164: of the presented number. Later, the
Page 165 and 166: Figure 1: Mean trajectories and MD
Page 167 and 168: Figure 2: Mean trajectories and MD
Page 169 and 170: Performance, 33, 1410-1419.Cohen Ka
Page 171 and 172: Moyer, 2007). At his or her own pac
Page 173 and 174: 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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