2013 Conference Proceedings - University of Nevada, Las Vegas

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TOWARD IMPROVING MYMATHLABCong-Cong XingNicholls State Universitycong-cong.xing@nicholls.eduDesLey PlaisanceNicholls State Universitydesley.plaisance@nicholls.eduWhile MyMathLab (MML) has achieved notable success in general mathematics education, ithas some fundamental and pedagogical issues that need to be addressed. In this paper, we (1)identify some MML-associated problems that commonly exist in lower-level college mathematicsteaching and learning; (2) propose our solution to these problems; (3) demonstrate the solutionby examples; and (4) summarize the contribution of this paper. We hope to see an improvedMML in the near future.MyMathLab (MML) is one of the cutting-edge computer-enhanced teaching and learningtools administrated by Pearson Education (2013) where students can practice their mathematicsproblem solving skills with respect to selected textbooks. It has been widely integrated intolower-level mathematics courses in colleges and universities with some success, as indicated forexample in Dries (2012), Livesay (2011), Spence (2007), Rouse (2011), Instructional Media &Magic (2013), and Anderson (2012). However, like many other technological education tools,MML is still in a young state in terms of maturity and needs to be improved, strengthened, andfurther developed.In this short paper, based on our professional experiences, we point out two problems thatstudents commonly suffer in dealing with lower-level college mathematics materials. One of theproblems is particularly due to MML and is causing MML’s mishandling on checking the logicalcorrectness and validity of student work; the other problem refers to the basic understanding orstructure of algebraic expressions which is fundamental to all kinds of mathematical work. Wepropose MML-based pedagogical solutions to both problems.The rest of the paper is organized as follows: section 2 describes the problematic issues;section 3 provides a proposal for resolving the issues; section 4 gives some illustrating examples;section 5 offers the related literature and theoretical framework; and section 6 concludes thepaper.The IssuesWe address two issues that we have noticed throughout the years of teaching. All examplesshown in this section are samples of authentic student work collected by the authors in teaching aProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 133
course titled Calculus with Business and Economic Applications. (This course was used becauseit is taught by both authors and the use of MML was mandated by their University department.)“Answers Only” Needs to be ChangedFor most lower-level mathematics textbooks/courses (e.g., Sullivan (2010), Lial, Hungerford,and Holcomb (2011), and Pirnot (2009)), Pearson offers a matching MML component whichcontains, among other things, the exercises at the end of textbook chapters/sections allowingstudents to complete their homework and tests on line. Unfortunately, for the majority of theseexercises, MML only requires the submission of answers. That is, as long as the final answersubmitted by a student to a problem is correct, then the student will get full credit for thatproblem regardless of the solution process, and even if the solution process is seriously flawed.We give two examples here to show this point. (Throughout the paper, limit properties refer toConstant Property, Identity Function Property, Sum Property, Difference Property, ProductProperty, Quotient Property, Power Property, and Polynomial Property which can be found inany standard calculus-related textbooks.)Example 1. Use limit properties to find(√ )Student solution:(√ )√Here, although the answer (integer 3) is correct, the solution process is fundamentally wrong:√ is not a polynomial and thus the polynomial property cannot be applied to (√) in the first step. Students who make this kind of mistake clearly do not have conceptualunderstanding of polynomials; MML cannot identify this conceptual misunderstanding in that allMML expects from the student is the integer 3. While there may be more than one way to solvethis problem, the following is an example of a valid solution.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 134
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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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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
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Page 119 and 120: classroom. “I would like to know
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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
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Page 135 and 136: Data collection consisted of tests,
Page 137 and 138: I've not used children's literature
Page 139: could extend this inquiry to high s
Page 143 and 144: no mathematical sense and should no
Page 145 and 146: Adopts the “111” (a term coined
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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
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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
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Page 183 and 184: Amazingly, despite there being a fe
Page 185 and 186: ReferencesBlack, M. (1962). Models
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Page 189 and 190: 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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