2013 Conference Proceedings - University of Nevada, Las Vegas

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found multiple correct solutions. This is a tribute to the depth of thinking the teachers did indeciding on the task to investigate, and in knowing the significance of the mathematics involved.2. The effort teachers made to fine tune the task paid off. The task was challenging butaccessible. While the CCSSM only focuses on knowing numbers 1 – 5, each child was able towork successfully on this task. Even those students who basically could only approach theproblem by putting tickets one at a time were able to engage meaningfully with the task.3. The teachers were able to use discourse and communication in a meaningful way. Becauseof the specific structure incorporated into the lesson, with anticipated responses and suggestionsfor handling the responses, communication options occurred they never considered before.Students who struggled to find a solution still were comfortable sharing what they made and whythey thought they made 10. Similarly, when a student had an incorrect solution, he or she couldcount and determine that it was not 10. When either of these things happened, teachers askedother students, “How can we help _____ make 10?” Interestingly, students were able to providemultiple answers to this question. This shows the benefits of effective planning for studentresponses and actions the teacher should be prepared to take.4. The task proved well suited for the English Language Learners students in the class. Theycould do the mathematics expected of them while being coached through the words needed toexplain their work. The decision the teachers made to have students record the value of eachlength of scrip used when making their collections provided a representation that helped preparethe students for the explanations they were to give. As a result of their research, teachers becamemore aware that a focus on communication in mathematics supports other parts of thecurriculum.5. Interesting discussions were forthcoming when the teachers asked, “How are these thesame, and how are they different?” While children realized they were all showing 10, thediscussion of same and different led to excellent comparisons. Some children said a 2, 3, 3, 2 anda 2, 2, 3, 3 were the same because they each used two 2s and two 3s, while others said they weredifferent because the order was different. Some saw that 1, 2, 3, 2, 2 and 2, 2, 3, 2, 1 were‘reversed’. The language used in the discussions exceeded teachers’ expectations, suggesting thatthe preliminary discussions the teachers had about these same questions filtered into their lessonsand instruction.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 107
6. While preparing the lesson, teachers became focused on how to use a context to whichtheir children could relate. This led them to focus on the development of the scrip and the “icepop” story. We all observed that throughout the lesson the students were so engaged in thethinking and reasoning involved that the story had become irrelevant.When reflecting on how focused the student were on this lesson and they forgot the story theteachers used to get started, one teacher summed up the positive aspects of their effort to createthis lesson when she said, “It was not about the ice pops, it was about the learning.” Thisstatement captured the essence of the evolutionary journey to involve kindergarten students inthe exploration of big mathematical ideas.ReferencesBall, D. L. (2003). What mathematical knowledge is needed for teaching mathematics?Prepared for the Secretary’s Summit on Mathematics, US Department of Education, February 6,2003; Washington, DC Available at http://www. ed. gov/inits/mathscience.Carpenter, T. P., Blanton, M. L., Cobb, P., Franke, M. L., Kaput, J., & McCain, K. (2004).Scaling up innovative practices in mathematics and science. Madison: University of Wisconsin-Madison, NCISLA. Retrieved July 15, 2004, fromhttp://www.wcer.wisc.edu/ncisla/publications/reports/NCISLAReport1.pdfDavis, E. A. and Krajcik, J. (2005) Designing educative curriculum materials to promoteteacher learning, Educational Researcher 34 (2005) (3), pp. 3–14.Higa-Funada, H. (2011). Personal communication, November 10, 2011.Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructionalimprovement: The case of lesson study. Educational Researcher, 35(3), 3–14.National Council of Teachers of Mathematics. (2000). Principles and standards for schoolmathematics. Reston, VA: Author.National Council of Teachers of Mathematics. (2006). Curriculum focal points forprekindergarten through grade 8 mathematics. Reston, VA: Author.National Governors Association Center for Best Practices, Council of Chief State SchoolOfficers. (2010). Common core state standards for mathematics. Washington, DC: Author.Sakumoto, A. (2011). Personal communication, November, 2011.AcknowledgementWith their permission, we identify and give special thanks to the following whose work,dedication, and collaboration made this paper possible: kindergarten teachers Mia Grant, HeatherHiga-Funada, Kannette Onaga, Stefanie Won, and Donna Wong; curriculum coordinators,Atsuko Sakumoto and Cheryl Taitague; and Principal, Patricia Dang of Kapālama ElementarySchool, Honolulu, Hawai‘i.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 108
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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
Page 63 and 64: students to organize their reports
Page 65 and 66: Slovin, H., Venenciano, L., Ishihar
Page 67 and 68: The research presented in this pape
Page 69 and 70: students’ confidence. Because bel
Page 71 and 72: 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: team’s goals? As much as possible
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 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
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Page 157 and 158: Table 4The group’s categories and
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Page 161 and 162: APPENDIXTable 5Description of Combi
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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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