2013 Conference Proceedings - University of Nevada, Las Vegas

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During the academic year teachers were grouped with common courses and togetherprepared a common lesson. A mathematics topic was discussed, lesson goals were developed, atask was identified and each teacher in the group taught the common lesson to one of theirclasses while the others in the group observed both teacher and students. The teachers in thisgroup met prior to school starting to coordinate the day, and immediately after each teacher inthe group taught the lesson to debrief about what we observed. The final debriefing involvedsome analysis and recommendations for future teaching. These common lessons yielded onecommon comment by all these teachers; “…we need to have the students do more of the work”.This common finding is in agreement with what Hiebert and Stigler (2004) found in their videoanalysis. Because of these experiences the teachers recognized and vocalized the need to gettheir students more involved in the lessons and have them take more responsibility for their ownlearning of mathematics.Teachers and university partners also met regularly to work with the group on commonassessments (a school-wide initiative) and adjustments to their curriculum. There were alsomany small group-based requests for non-regular meetings. An example of these non-regularmeetings was the planning of a family mathematics night where teachers took charge ofpreparing demonstrations for students and parents of the changes to the curriculum and teaching.In addition, some teachers wanted to know more about differences in learning of students fromurban areas and low socio-economic backgrounds. We formed a reading group for the bookTeaching with Poverty in Mind: What Being Poor Does to Kids’ Brains and What Schools CanDo about it by Eric Jensen. (2009, ASCD, Alexandria, VA). Additional activities with smallgroups of teachers (never single teachers working) were supported though out the three years.Each of the professional development activities helped to form stronger knowledge of thecontent, how students learned the content, or to build a professional learning community amongall the partners involved in the grant.Instruments and measuresA mixed methods design for this research was implemented to measure a complex set ofvariables that may affect the teaching and learning of mathematics. Data of the contentknowledge of the teachers was gathered using an adaptation (for high school teachers) of theLMT (Learning of Mathematics for Teaching) assessment and a collection of artifacts (solutionsto the rich problem tasks, observations of teachers using the RTOP, and interviews by theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 119
internal evaluator) were analyzed. We also administered a survey of the nature of mathematicsand mathematics teaching and learning to the teachers. The adaptation of the LMT consisted ofchoosing only those items that pertained to upper elementary mathematics topics. Topics of ratioand proportion, geometry and reasoning, and fundamental concepts of algebra were included.The test had 11 separate items, a few with 3 or 4 parts, and all items were multiple choice. Themodified LMT given toward the beginning of the PD work and at the end of year one had similaritems, however, because of these modifications the scores were used to identify where at leasthalf of the faculty involved had misconceptions. The analysis of the rich problems also helped tocharacterize the knowledge that these mathematics teachers displayed in PD activities.ResultsOne of the problems, as is a trait of the LMT, had teachers analyze an alternate method fordividing two fractions. The student said that he divided the two numerators and the twodenominators in68 ¸ 12=64. The teachers were asked to choose one of the following about whatthis student’s teacher was thinking about the students method (number of teachers selecting ananswer): a) He knew that the method was wrong, even though he happened to get the rightanswer for this problem (3); b) He knew that the student’s answer was actually wrong (0); c) Heknew that the student’s answer was right, but that for many numbers this would produce a messyanswer (4); d) He knew that the student’s method only works for some fractions (6). The correctanswer was selected by only 4 of the 13 teachers. Answers a and d were selected by 9 of thesehigh school mathematics teachers. These two selections imply that the teachers themselves knewthat the student had gotten the right answer and that either they didn’t or couldn’t determine ifthe work presented was equivalent to the standard algorithm for dividing two fractions. Basedon other mathematics problems similar to this question it was clear that these teachers were notused to thinking about alternative methods for solving problems and why various algorithms thatthey used regularly worked or how they were derived. On an exit interview with the internalevaluator near the end of year 2 all of the teachers except one indicated that they believed theirknowledge of mathematics and of the common core state standards had increased. When askedwhy they believe this to be true they referred to the rich mathematical tasks that they solved andhad to demonstrate their reasoning for their solutions. They also indicated that they were moreconfident in being able to implement the common core state standards as a result of theirparticipation in the grant activities as was also supported by our observations and analysis of theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 120
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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
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 and 124: THE PATH OF REFORM IN SECONDARY MAT
Page 125: Our collaboration model was formed
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
Page 175 and 176: 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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