2013 Conference Proceedings - University of Nevada, Las Vegas

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Vinner (1986)). Thus, it is important that MML addresses the “right” answer with a wrongprocess issue in order to not foster mishandlings within the study of limits.Note that tree diagrams have been used by several mathematics education researchers (e.g.,Ernest (1987), Kirshner and Awtry (2004), Sleeman (1984), and Thompson and Thompson(1987)) to illustrate the idea of operation precedence within algebraic expressions (the lower anoperation appears in a tree, the higher its precedence is), and that the computation of the(a)(b)(c)(d)(e)(f)(g)(h)Figure 3: An Example of Limit Computation Tree.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 141
algebraic expression is carried out from the bottom of the tree toward the top of the tree (bottomup).In this sense, the limit computation tree has an “opposite” meaning to that of the algebraicexpression trees as the first limit property to be chosen to apply to the expression is determinedby the operation with the least precedence in that expression. That is, the computation of thelimit of an expression starts from the top of the tree and moves downwards (top-down).We believe that the students’ trouble in understanding the structure of math expressions isrelated to their reading habit. There is an obvious disparity in the reading of symbols/mathexpressions and prose. Students are accustomed to reading prose from left to right and top tobottom. Quinnell and Carter (2012, p.36) stated, “…. students must use judgment or experiencein deciding how to read a symbol. This could be why some students manage to grasp thesubtleties of decoding symbols, while others remain perplexed.”Regarding the popularity and claimed success of MML (see resources mentioned at thebeginning of the paper), we do note that in most of those cases, students’ success is defined bytheir completing a course with a grade of A, B, or C, and most of the results were reported viavenue associated with Pearson Education. Southeast Comprehensive Center (SECC) of SEDL(2011) conducted a search to collect studies related to the effectiveness of mathematics softwareproducts; no MML research studies were located. Nevertheless, a study by Kodippili andSenaratne (2008) does indicate a strong MML-related student success rate, although the authorsadmit some methodological shortcomings.Concluding RemarksMathematics learning, especially problem solving, is not just about finding the (correct)answers. Rather, gaining a substantial understanding for relevant concepts and subsequentlyapplying this understanding logically in problem solving is more important than the answeritself. MML, as the leading computer software for mathematics education on the market,unfortunately takes an unsound approach in that all it requires from the student for problemsolving is a correct answer. In order to address this issue, we have proposed two specificsolutions in this paper toward improving MML. We believe that the paper makes the followingcontributions: The “111” style for limit computation, which can be easily implemented on MML,rectifies MML’s “answers only” problem.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 142
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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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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
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 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: Specifically, clicking the “Click
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
Page 179 and 180: curriculum locally, within individu
Page 181 and 182: Popularity tallied whether or not a
Page 183 and 184: Amazingly, despite there being a fe
Page 185 and 186: ReferencesBlack, M. (1962). Models
Page 187 and 188: connections are connections or rela
Page 189 and 190: Table 1Instructional TasksSquareTab
Page 191 and 192: t-charts made it easier for student
Page 193 and 194: Figure 2. A Display of Student Stra
Page 195 and 196: ReferencesAnderson, J. R., Greeno,
Page 197 and 198: 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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