2013 Conference Proceedings - University of Nevada, Las Vegas

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LEARNING MATHEMATICS IN THE 21 ST CENTURY: HIGH SCHOOL STUDENTS’INTERACTIONS WHILE LEARNING MATHEMATICS ONLINECherie IchinoseCalifornia State University Fullertoncichinose@fullerton.eduWhen choosing online learning, educators and administrators are no longer limited in providingthe most effective learning environment for their students. This study provides evidence of thepower of online interactions when learning mathematics. This study showed algebra and prealgebrastudents benefited most from the synchronous, live interactions through webconferencing.Students were able to ask their questions in real-time, thereby fostering deeperrelationships with their teacher. More advanced students preferred the asynchronous (any-time)environment for learning mathematics as shown through the increased collaborativeparticipation through the online discussion boards.In the new age of education, parents are able to explore different learning environments fortheir children. The North American Council for Online Learning (NOCAL) reported that, as ofthe end of 2006, there were 38 state-led online learning programs educating approximately65,000 children (Watson, 2007). A more recent report published by the Sloan Consortiumestimated the number of K-12 students engaged in some kind of online course in 2007-2008 atover one million (Picciano & Seaman, 2009).NOCAL reports one of the top ten myths with online learning is the perceived lack ofinteraction that occurs (2007). Students and teachers typically report an increased level ofinteraction with the content and rich one-on-one interactions with each other (Learning, 2007). InLearning in the 21 st Century: 2010 Trends update, students reported they received more attentionfrom their teachers and were more comfortable asking questions online than in the traditionalsetting (Tomorrow, 2010). These separate physical interactions take on different modalities,however, and can be divided into two categories: synchronous and asynchronous.Theoretical FrameworkWith most online courses, students can log into their courses at any time (asynchronously)and engage with the content through a learning management system. Asynchronous interactionsinclude engaging with online learning modules and working with flash or multi-media activities.Students no longer passively read through mathematical content, but interact with it by linkingvisual and symbolic mathematical representations through guided simulations that lead to stepby-stepsupport of mathematical processes and immediate feedback (Snelson, 2002; Suh &Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 163
Moyer, 2007). At his or her own pace, the student can work though the activity and then receiveimmediate feedback through the computer.A threaded discussion board is also an example of an asynchronous interaction, as is e-mail.Threaded discussion boards are organized systematic learning tools that allow students to postquestions anytime time and receive feedback directly from either the teacher or other students(Holden & Westfal, 2010). When the initial content is delivered by the computer, a teacher isable to spend more time focused on discussion by providing students the opportunity to foster adeeper level of quality mathematical understanding through discourse (Smith et al., 2003;Warschauer, 1997). Collectively, teachers and students have the opportunity to share their ideas,elaborate on their thought process, and compare their ideas with previous statements or work(Simonsen & Banfield, 2006). Smith (et.al.) charges that, in this new milieu, there is a higherexpectation of teachers’ accuracy; specifically, that “their standing may be only as good as theirlast posting” (p.53). The asynchronous nature of the medium allows the teacher the time fornecessary reflection to compose appropriate responses to individual student questions as opposedto traditional settings that require answers on the fly or apparent delayed responses, which canharm teacher credibility (Smith et al., 2003).Unlike the anytime model that asynchronous activities provide, synchronous activities occurin real time and are often described as similar to those in a standard chalk-talk classroom(Wahlstrom et al., 2003). As with a traditional brick-and-mortar setting, a group of students wholog in at a specified time can learn all together, but without a shared physical presence (NationalForum on Educational Statistics, 2006). Studies reported that students felt a strong socialpresence with their teacher, thereby fostering a strong sense of participation in the class(Anderson & Kuskis, 2007; Watson & Ryan, 2006).The balance between such interactions is key. Students can solely interact asynchronouslythrough the online content but as Holden and Westfal suggest, this may be more appropriate foractivities involving drill & practice (2010). However, Anderson suggests synchronousenvironments are “particularly rich and encourage the development of social skills, collaborativelearning, and the development of personal relationships amongst participants as components ofthe learning process” (2003, p. 9). Moore charges that true potential of online stems from the useof each interaction. That is, the program must match the appropriate interactions according tosubject areas as well learning styles and developments (Moore, 1989).Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 164
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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
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teachers’ role-play of SFMP #4. A
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Durkin, D. (1978-1979). What classr
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as well as the alignment between th
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Table 2Number of teachers per grade
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Table 4Classification Categories fo
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field so that research on the initi
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dynamic approach to learning conten
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Kindergarten Lesson FormatHow May W
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team’s goals? As much as possible
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6. While preparing the lesson, teac
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active learning and collective part
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
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: Performance, 33, 1410-1419.Cohen Ka
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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Page 201 and 202: Figure 2. (A) P3. (B). Extension of
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Page 211 and 212: hard for some children? The nature
Page 213 and 214: Lakoff and Nunez: specifically, tha
Page 215 and 216: Figure 5: Average hand trajectories
Page 217 and 218: Figure 6: Distributions of maximum
Page 219 and 220: 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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