An analysis of pre-service mathematics teachers’ performance in modelling tasks in terms of spatial visualisation ability

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  An analysis of pre-service mathematics teachers’ performance in modelling tasks in terms of spatial visualisation ability
  CURRENT REPORTAn analysis of pre-service mathematics teachers’ performance inmodelling tasks in terms of spatial visualisation ability Halil Ibrahim Tasova* and Ali Delice Department of Mathematics Education, University of Marmara, Istanbul, Turkey Mathematical modelling involves mathematical constructions chosen to representsome real world situations and the relationships among them; it is the process of expressing a real world situation mathematically (Kertil 2008). Visualisation can playa significant role in the development of thinking or understanding mathematicalconcepts, and also make abstract material more concrete. Earlier research has shownthat students’ visualisation abilities may affect their chosen representations (Sevimliand Delice 2011). Meanwhile, researchers have wondered how students’ spatialabilities affect the process of modelling. This study aims to investigate learners’ levelof visualisation abilities when they begin the mathematical modelling process, andthe visual process they go through. The purpose is to find out how pre-serviceteachers’ spatial abilities affect the visualisation process in modelling tasks and, as aresult, how much their abilities affect performance.The participants were 75 pre-service mathematics teachers pursuing a post-graduate degree (MA without dissertation) at the Secondary School MathematicsEducation Department of a state university in Turkey. In order to identify pre-serviceteachers’ spatial abilities, the multiple choice Spatial Abilities Tests (SAT) developedby Ekstrom, French, Harman and Derman (1976) were administered. Following theidentification of their spatial visualisation skills, the teachers were given problemsolving tasks in line with the modelling approach. The tasks required skills such asidentifying the variables of real life situations and events and stating the relationshipsbetween these variables, using mathematical expressions. The tasks were prepared byKertil (2008) to take 30 minutes. A sample task is: In windy weather the height of a straw above the water is measured at an initial position.Then wind drags the straw to a terminal position and the distance between the initial andterminal position is measured as well as the height of the straw above the water at theterminalposition.Whatcanbesaidaboutthedepthofthelakeusingthesemeasurements? Data were analysed using categorisation and descriptive statistics. First, SAT testresponses were categorised into correct, incorrect and no answer groups. Secondly,each answer for the modelling tasks was grouped and evaluated into categories of correct (CA), partially correct (PA), incorrect (IA) and no answer (NA). The pre-service teachers were compared in terms of their performance in modelling tasksaccording to their spatial abilities, as in Table 1. *Corresponding author. Email: Research in Mathematics Education Vol. 14, No. 3, December 2012, 297    298 ISSN 1479-4802 print/ISSN 1754-0178 online # 2012 British Society for Research into Learning Mathematics  It is worth noting that more than half of the participants who could not answerthe modelling tasks were the pre-service teachers who had low spatial ability, whereasalmost half of those with average and high spatial ability gave correct answers to themodelling tasks.Figure 1 shows that one teacher, who had low spatial ability, could not visualise theverbal expression in the question, or could not correctly create a mental picture. Thedrawingdepictsanincorrectrealisticfigure;therootofthestrawisattachedtothegroundunderthewater,andthusitmakesitdifficulttodrawthemotionofthestrawinthewind.Modelling tasks, which are contextually related to real life, and which require anintegrated use of various skills such as visualisation and algebraic operations in thesolution process, can be perceived as an area in which pre-service teachers havedifficulties in applying their knowledge. Lower success with modelling activities byteachers who had low spatial ability could be due to their inability to link visualcomponents with abstract/mathematical concepts, by approaching the solvingprocess from different perspectives. Sevimli and Delice (2011) also stated thatstudents who have low spatial visualisation abilities are less capable with translationbetween representations. Here, insufficient use of visual representations may haveinfluenced modelling behaviour. The research also suggests that mathematicalmodelling tasks could be incorporated in lessons to improve modelling performance. Acknowledgement This study is part of a project (project number EGT-C-YLP-040310-0058) funded by theMarmara University Scientific Research Projects Board. References Ekstrom, R., J. French, H. Harmon, and D. Derman. 1976.  Manual for kit of factor-referenced cognitive tests . Princeton, NJ: Educational Testing Service.Kertil, M. 2008.  Matematik O¨  g ˘ retmen Adaylarının Problem C  ¸o¨ zme Becerilerinin Matematiksel Modelleme Su¨ recinde I ˙ncelenmesi  . MA diss., University of Marmara, Turkey.Sevimli, E., and A. Delice. 2011. The influence of teacher candidates’ spatial visualizationability on the use of multiple representations in problem solving of definite integrals:A qualitative analysis.  Research in Mathematics Education  13, no. 1: 93    4.Table 1. Performance in modelling tasks according to spatial ability.Answer Types% CA IA PA NASpatialAbilityLevelLow 41 41 14 3Average 55 28 17 0High 52 23 24 0Figure 1. Solution to modelling task by a pre-service teacher who had low spatial ability. 298  H.I. Tasova and A. Delice  Copyright of Research in Mathematics Education is the property of Routledge and its content may not be copiedor emailed to multiple sites or posted to a listserv without the copyright holder's express written permission.However, users may print, download, or email articles for individual use.
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