2013 Conference Proceedings - University of Nevada, Las Vegas

More documents

Recommendations

Info

Overview of the StudyThe purpose of this embedded case study was to understand how the inclusion of spatialtasks influenced undergraduate students’ spatial visualization ability, problem-solving strategies,and beliefs about spatial thinking. Despite decades of reform, the U.S. still trails economiccompetitors like Japan (National Center for Education Statistics, 2003). One explanation couldbe the lackluster ability of U.S. students to think spatially and problem solve with regard tomathematics. As a result, this study examined undergraduate students’ abilities and beliefsregarding spatial thinking by addressing the following research questions:1. How does the integration of spatial activities in an undergraduate mathematics contentcourse impact student spatial ability?2. In what ways does the integration of spatial reasoning tasks into an undergraduatemathematics content course influence problem-solving strategies?3. How does the integration of spatial reasoning tasks influence the beliefs on spatialthinking of pre-service elementary teachers?The participants were 33 undergraduate students enrolled in the researcher’s Fall 2011Survey of Mathematics course. Quantitative data were collected through the Purdue SpatialVisualization Test (PSVT), the Mathematical Processing Instrument (MPI), and the SpatialThinking Attitude Survey (STAS). Qualitative data were garnered through student-writtenjournal responses, focus group interviews, and observations. A focus group was formed and wascomprised of 17 participants who were pre-service elementary education majors. This group meton three separate occasions throughout the study to discuss topics related to the study. Thepurpose of the focus group was to give deeper insight into the participants’ experiences with thestudy as well as beliefs about spatial thinking.Implementation began with a description of the study followed by the pre-measures of thePSVT, the MPI and the STAS. During the following eight weeks, a range of daily spatialthinking activities as well as reflective journal prompts were incorporated into classroompractices. For example, one in-class activity asked students to draw the net of a threedimensional figure that they were not allowed to touch. Once the student had completed theirdrawings, they were asked to share results with the entire class. Activities such as this sparkedclass discussions, allowing for insightful student observations. These activities would take upapproximately 10 minutes of class each day. Then, if further discussion was appropriate, aProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 69
journal prompt would be given as a follow up. During the final two weeks of the study, the finalfocus group discussion was held, and post-measures of the PSVT, the MPI, and the STAS wereexecuted and scored. These data were collected and fully analyzed.Results from the quantitative data were used to determine if the integration of eight weeks ofspatial activities resulted in significant differences in scores on the PSVT, the MPI, andindividual statements on the STAS. Analysis of the qualitative data—responses to journalprompts, focus group interviews, and observations—was used to examine the influence of thespatial tasks on the perceptions and beliefs about spatial thinking on students and pre-serviceelementary teachers. Moreover, the same data were used to evaluate how pre-service teachersviewed their own understanding of spatial thinking and its relevance in their daily lives andfuture classrooms. After the quantitative data had been scored and tested and the qualitative datahad been coded and themed, the data were analyzed in its entirety and conclusions were drawn.Summary of the FindingsSpatial Tasks and Spatial AbilityThe first research question investigated the influence of spatial tasks on students’ spatialvisualization abilities. Bruner (1973) believed children explore new things first through actionthen through imagery before, finally, using language to describe and comprehend the worldaround them. Through this reasoning, spatial thinking is a necessary step to learning.To help investigate the first research question, both qualitative and quantitative data werecollected and analyzed. Qualitative analysis on student-written responses and focus groupdiscussions revealed that students believed their spatial thinking abilities could improve withpractice. This was encouraging given the fact that 60.6% of the class described themselves aspossessing average or below-average ability at best in response to a journal prompt which askedstudents to describe their ability to think spatially. Using quantitative analysis, the PSVT servedas a pre- and post-measure to assess student spatial visualization ability. The PSVT, developedby Guay (1980), was comprised of three parts: Developments, Rotations, and Views. TheDevelopments section (PSVT/DEV) measured spatial structuring; the Rotations section(PSVT/ROT) measured mental rotation ability; while the Views section (PSVT/VIEW)measured spatial perception. Initial assessment of the data revealed an increase in test scores anda decrease in the number of incomplete responses. The DEV, ROT and VIEW sections of thePSVT showed a 27.9%, 33.3% and 60% increase in correct responses from the pre- to post-Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 70
Page 1 and 2:
….where the Mathematicscomes swee
Page 3 and 4:
THANK YOU TO OUR REVIEWERSKeith Ado
Page 5 and 6:
Table of ContentsPreservice Teacher
Page 7 and 8:
Support for Students Learning Mathe
Page 9 and 10:
own problem solving, which is criti
Page 11 and 12:
to get started and persistence. Tea
Page 13 and 14:
Posamentier, A. S., Smith, B. S., &
Page 15 and 16:
conceptual understanding, applicati
Page 17 and 18:
Table 1Identified Mathematical Prac
Page 19 and 20:
justify their statements, included
Page 21 and 22:
Finally, engagement in MP.6 was ass
Page 23 and 24:
PRESERVICE TEACHERS’ EMOTIONAL EN
Page 25 and 26: “experiences that are charged wit
Page 27 and 28: Number of journals containingEmotio
Page 29 and 30: ConclusionsStruggle and frustration
Page 31 and 32: Mathematics Teacher Candidates’ U
Page 33 and 34: function and applied the vertical l
Page 35 and 36: semester, about half of the course
Page 37 and 38: They further state that “the impo
Page 39 and 40: C. Laborde (Eds.) International Han
Page 41 and 42: (SCK), or knowledge of mathematics
Page 43 and 44: level of difficulty for each partic
Page 45 and 46: MKT Measures ScoresMathematics in G
Page 47 and 48: deep rooted belief in a single way
Page 49 and 50: THE INTERVIEW PROJECTAngel Rowe Abn
Page 51 and 52: involving addition and subtraction:
Page 53 and 54: 6+7 4+9=6+(6+1) Substitution =4+(10
Page 55 and 56: We strongly believe that this inter
Page 57 and 58: AN INNOVATIVE APPROACH FOR SUPPORTI
Page 59 and 60: Practice throughout the investigati
Page 61 and 62: 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: SPATIAL REASONING IN UNDERGRADUATE
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 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 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
Page 199 and 200:
student learning calls for differen
Page 201 and 202:
Figure 2. (A) P3. (B). Extension of
Page 203 and 204:
the usual phenotypic assessments an
Page 205 and 206:
teachers is the discrepancy between
Page 207 and 208:
expected to learn and the inquiry a
Page 209 and 210:
his partner about his observations,
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
Page 221 and 222:
Social system perspectives view the
Page 223 and 224:
urged students to think of some way
Page 225 and 226:
Figure 1: The Discourse Patterns Du
Page 227 and 228:
Figure 3 blow illustrates the devel
show all

2013 Conference Proceedings - University of Nevada, Las Vegas

Create successful ePaper yourself

Delete template?

Save as template?