2013 Conference Proceedings - University of Nevada, Las Vegas

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summer professional development activities. We believe this to be a direct result of our effortsat introducing problems that could be solved using both conventional and non-conventionaltechniques and having to argue to justify whether something worked always, sometimes, ornever.In the analysis of the observation notes and videos of the teachers doing rich problems it wasnoted that in the early stages of the grant most of the teachers worked the problems alone at first.They only shared out when the faculty asked them to do so. This sharing initially consisted ofthem showing each other how they did the problems. The more confident the teacher the morethey wanted to share. As the grant progressed and teachers had multiple opportunities to solveproblems and experience non-conventional approaches, all teachers were more likely to sharetheir methods of solving the problem. We also observed that the teachers began to engage inboth presenting their reasoning and listening to and critiquing the reasoning of others. So bothour notes and analysis of videos (of teachers engaged in doing rich tasks in the PD) supportedthat teachers did learn mathematics that would help to support their teaching of high schoolmathematics.Table 1 below contains the results of a survey of the teacher’s view of the nature ofmathematics. They completed this survey after two years of professional development had beencompleted.Table 1MT = Mathematics teacher. Int. Sp. = Intervention SpecialistSubgroupPart I(Absolutist-Fallibilist)Part II(Authoritarian-Social Constructivist)AC – Int. Sp. 3 3.4JE –MT 3.88 4.4AB – MT 3.11 3.8DM – MT 3.66 3KT - MT 3.33 4.8MN - MT 3 3.2TB - MT 3.44 3.4TR - MT 3.22 4CW – Int. Sp. 3.22 3.8SS – Int. Sp. 3.33 4.2JF - MT 3.33 3Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 121
DiscussionOn part I of the survey the teacher’s chose their view of the nature of mathematics. If theaverage score was 4 – 5, then the person had a more applied (fallibilist) view of the nature ofmathematics. If the average score was 3, then the person had a mixed view of the nature ofmathematics. If the average score was 1 – 2, then the person had a more pure (absolutist) viewof the nature of mathematics. From the teacher’s view of mathematics we see two of them areclassified as having a mixed view, while all of the others scored between 3 and 4. While not“clearly” in the Fallibilist camp these teachers did appear to be more open toward the belief thatthe nature of mathematics may not be fixed and that what is important regarding mathematics isevolving. It is also fair to say that their original belief about mathematics is still nearly asinfluential despite hundreds of hours of professional development working to open up theirviews and beliefs.In part two of the survey the teachers indicated their view of mathematics teaching andlearning. If the average score was 4 – 5, then the person had a more social constructivist view ofthe nature of mathematics education. If the average score was 3, then the person had a mixedview of the nature of mathematics education. If the average score was 1 – 2, then the person hada more authoritarian view of the nature of mathematics education. Four of the teachers scored asbeing social constructivist, two averaged 3, which means they have a mixed view, and theremaining five teachers scored between 3 and 4. So nine of the teachers seem to believe that thenature of teaching and learning of mathematics is aligned more closely to a social constructivistpoint of view. We believe that these scores should be interpreted as steps toward changes inteaching. When we reviewed the RTOP scores the teachers were still predominately teaching bytelling as opposed to helping students to make sense of the mathematics on their own. Thispassage from the final report about the RTOP results clarifies how teachers are talking abouttransforming their classes but they haven’t yet made these changes in their own teaching.The teaching style is almost exclusively teacher-focused where the teachermaintains the role of the mathematical authority. Teachers have voiced their lackconfidence in the students’ ability to be challenged either believing the students lackpre-requisite knowledge or/and a disposition toward mathematical thinking andperseverance. This belief plays out in many of the observed lessons. In grantProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 122
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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
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their ability to teach the mathemat
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SPATIAL REASONING IN UNDERGRADUATE
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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 and 124: THE PATH OF REFORM IN SECONDARY MAT
Page 125 and 126: Our collaboration model was formed
Page 127: internal evaluator) were analyzed.
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
Page 175 and 176: curriculum. The nature of the onlin
Page 177 and 178: 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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