The Effect Of Dynamic Geometry Software And Physical .

Educational Sciences: Theory & Practicein transformational geometry; displacement androtational transformations are given priority.Table 1 shows how the subject of transformationalgeometry is taught between second and eighthgrades.Transformational Geometry and Primary SchoolTeachersStudents’ geometric mentality and its improvementis closely related to the education received inprimary school. There are many factors involvedin this education, but the most important one isteachers. Teachers play the role of implementer andthey have the greatest responsibility for reachingthe intended goals of education. At this point,a teacher’s knowledge, skills, and abilities cometo the forefront. As is known, teachers who lackknowledge have a negative effect on students (Ball,1990). No matter how well educational goals aredetermined or how functional and organized thetopics are, it is obvious that these goals cannot beachieved unless they are carried out by discerningteachers (Köseoğlu, 1994). For this reason,teachers should first have wide knowledge abouttransformational geometry and know differentmethods of approach in order to teach the topic oftransformational geometry effectively.Primary school mathematics curriculum was renewedin Turkey in 2005, and the topic of transformationalgeometry was added to the curriculum. Naturally,most teachers who are now teaching transformationalgeometry were not trained for the current primaryschool curriculum; they were not educated for teachingtransformational geometry in primary school. Wecan say, namely, that the topic of transformationalgeometry is new to both mathematics classes andclass teachers. It has become important for teachersto reach a sufficient level of experience on this topicduring their undergraduate education. Because of thisimportance, the current study aims to determine whateffect transformational geometry, the DGS Cabri IIPlus program, physical manipulatives, and traditionalmethods have on the success of students studying toteach transformational geometry in primary schools.Dynamic Geometry SoftwareTransformational Geometry(DGS)andNCTM (2000) accepted the use of technology inmathematics education to be one of the principlesand standards of mathematics education, andestablished this by saying “technology affects1420mathematics learning and teaching, andmathematics which is taught with technologyimproves student learning” (p. 11). In Turkey,particular importance is given to the place oftechnology in the renewed primary schoolcurriculum and it is emphasized that technology,especially DGS, should be effectively used at everylevel (MEB, 2005). Using DGS is an especiallypopular technology in geometry educationbecause this kind of software encourages learningby discovery, contributing to the problem-solvingskills of students (Ubuz, Üstün, & Erbaş, 2009).The most important feature of DGS is that it allowsshapes to be dragged while protecting the basicshape’s structure, their points and lines (Hazzan& Goldenberg, 1997). When an original shapeis dragged, the resulting transformations andformations which were implemented on theseshapes can be immediately reviewed on screen. Thus,students have an opportunity to discover practicallyanything by being able to easily plug into the searchenvironment, hypothesizing, testing, formulating,and explaining (Güven & Karataş, 2005).NCTM states the role of DGS in understandingtransformations as follows (Güven, 2012, p. 365):“Dynamic geometry software allows studentsto visualize a transformation by manipulatinga shape and observing the effect of eachmanipulation on its image. By focusing on thepositions, side lengths, and angle measurementsof the original and resulting figures, middlegrades students can gain new insights intocongruence. Transformations can become anobject of study in their own right. Teacherscan ask students to visualize and describe therelationship among lines of reflection, rotationalcenters, and the positions of pre-images andimages. Using the interactive figure, studentsmight see that the result of a reflection is thesame distance from the line of reflection as theoriginal shape (NCTM, 2000).”Cabri II Plus is one of the first dynamic geometrysoftware programs (Gillis, 2005). DGS Cabristrengthens mathematical thought by changingmathematical objects on screen like a tool. Asone can define that some elements of geometryare changeable, some are stable and some can bedefined according to another, this software gives onethe opportunity to examine geometry dynamicallywhen structures are moved accordingly (Baki,2001). As the mobile structure of Cabri II Plusmakes dragging and rotating geometrical shapesavailable, it is thought to be an effective tool for

Kaleli Yılmaz / The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’.teaching transformational geometry, a topic of therenewed primary school curriculum.When research on transformational geometryis investigated, it can be seen that students haveinefficient information on this topic and difficultylearning it (Battista, 1999; Küchemann, 1981;Yavuzsoy-Köse, 2008; Zembat, 2007). In theliterature, DGS has been determined as an effectivetool for overcoming these difficulties (NCTM,2000; Van De Walle, 2004). It is specified that CabriDGS has an effective role among the dynamicgeometry programs for teaching transformationalgeometry (Dixon, 1997; Güven, 2012; Güven &Kaleli-Yılmaz, 2012; Hoyles & Healy, 1997; Kurak,2009; Yavuzsoy-Köse, 2008).DGS software for transformational geometry,especially Cabri II Plus, can be said to increase successand conceptual understanding from this point of view.Teachers should first, however, be informed aboutthis software, and model implementation should bedone in order to see how this holds up in practicalapplications. For that reason, one of the groups in thisstudy participated as a computer group, and Cabri IIPlus was firstly introduced to the teacher candidates;they carried out applications on the software, then thestudy investigated its effects on their transformationalgeometry success.Why Cabri II Plus?In this study, in order to proceed with thecomputer group’s practice, the DGS Cabri II Pluswas used. For all intents and purposes, differentsoftware programs such as GeoGebra or GeometrySketchpad could have been used instead of CabriII Plus. Hence, the many other studies thathave been performed all found an increase ingeometry achievement with software no matterwhich program was used (Dixon, 1997; Harper,2002). In the scope of this study, the reason forselecting Cabri II Plus was because the researcherhas comprehensive experience with the currentsoftware and it has a user-friendly Turkish versionwith easy-to-use menus.Physical Manipulatives and TransformationalGeometryA manipulative is a concrete model that comprisesmathematical concepts with respect to severalaspects that can be touched and moved around bythe learner (Absi & Nofal, 2010). Concrete modelssuch as geometry rods, geo-boards, isometric paper,symmetry mirrors, and so forth, are supposed tohelp students construct geometric ideas (Durmuş& Karakırık, 2006). Teaching activities in whichmanipulatives are used give students the chanceto make observations and apply them to concretemodels of the target and their representations(Heddens, 1997; Suydam & Higgins, 1984).NCTM’s (2000) standards and principles whichwere published on mathematics education showthe importance of using a physical, concretemanipulative, which plays a role in structuring themental process of students in learning mathematics.According to Moyer (2001), a physical manipulativeis designed to represent mathematical terms, and itis a visual and movable object which can move thestudents’ senses. From this point of view, we can saythat physical manipulatives which can be used fortransformational geometry are defined as activitiessuch as symmetry mirrors, using dotted and linedpaper, origami, and drawings on paper.Studies on this TopicWhen reviewing the literature, many studiesperformed on transformational geometry subjectstand out. The important part of these studies isthat they used different dynamic software such asCabri II Plus, Geometry Sketchpad, and GeoGebra;according to the results of these studies, it was seenthat the use of software is effective for increasingtransformational geometry skills (Akgül, 2014;Dixon, 1997; Egelioğlu, 2008; Gürbüz, 2008;Güven, 2012; Güven & Kaleli-Yılmaz, 2012; Harper,2002; Karakuş, 2008; Yavuzsoy-Köse, 2008; Yazlık,2011). These studies also generally preferredto use the experimental method consisting ofunique experiments and a control group. Inthese studies, the experimental group used thedynamic software program and the control groupis learned their lesson using conventional methods.An important part of these studies is that thestudents in experimental groups who were taughtusing dynamic software were more successfulthan students in the control groups who weretaught using conventional methods (Egelioğlu,2008; Güven, 2012; Güven & Kaleli-Yılmaz, 2012;Karakuş, 2008; Yazlık, 2011). For example, Yazlık(2011) performed an experimental study with135 seventh-grade students to find out whetherteaching geometry with Cabri II Plus has any effecton how students learn transformational geometry.The experimental group lesson was taughtwith Cabri II Plus and the control group usedtraditional methods. At the end of this research1421

Educational Sciences: Theory & Practiceboth experimental and control groups’ success wereseen to rise, but the experimental group had highersuccess levels than the control group. Similarly,Güven’s study (2012) searched the effects of DGS(Cabri II Plus) on the success of eighth-gradestudents with transformational geometry. In thatstudy, the experimental method consisted of usingexperiment and control groups. As a consequenceof that study, it was determined that students in theexperimental group who were taught with DGS(Cabri II Plus) were more successful than studentsin the control group who were taught their lessonwith dotted paper and isometric worksheets.should be determined by trying many kinds ofmethods instead of only one. Aside from the manystudies performed that prove DGS is effective inincreasing success in transformational geometry,it was not certain which section this impact wasmore effective on: defining transformations,stating the transformation features, or forming atransformation. This study is important for fillingin the gap in the literature about this topic. Anotherimportant point of this study is to also find an answerto the question of which section of transformationalgeometry success is DGS (Cabri II Plus) and the useof tangible materials more effective.In the body of literature, one frequently onlyencounters unique experiment-control groupexperimental studies; experimental studiesconsisting of two experimental groups arelimited. Furthermore, it was noticed that routineachievement tests were used in those studies, andthe tests did not focus on certain sections such asdefining transformations, stating transformationfeatures, or forming transformations. In this case,this study differs from others because it makes useof two experimental groups and one control group,and the achievement test consists of three separatesections: defining, stating features, and constructing.This study intends to determine how teachingtransformational geometry using different methodsaffects transformational geometry achievement. Inthis scope, the following questions are addressed:The Importance and Aim of the StudyIn Turkey, the mathematics education program forprimary schools was revised in 2005, and the subjectof transformational geometry was convolutedlyadded to the program with this revision. As aresult, the teachers who now teach transformationalgeometry in schools have limited knowledge andexperience with transformational geometry becausethey hadn’t been educated in respect to the revisedmathematics education program while they werestudying to be teachers. When the mathematicseducation program is investigated, the first part ofprimary education (between first and fifth grade)forms the base of transformational geometry andis structured through the concept of symmetry.Recognition of symmetry is known to be a base forthe study of transformational geometry. As such,the teachers who will teach symmetry should haveadequate information and skills in that subject. Forthis reason, important duties fall on the Faculty ofEducation. The Faculty of Education should give thenecessary experience on transformational geometryto teacher candidates through Basic Mathematics,Mathematics Education and other pre-servicescourses (as Teaching Methods, Teaching Practice).How to make this method more successful1422i) Does DGS-based instruction affect the academicachievement of pre-service primary school teachersas far as transformational geometry?ii) Does instruction based on physicalmanipulatives affect the academic achievement ofpre-service primary school teachers with regard totransformational geometry?iii) Is there a significant difference amonggroups related to their academic achievement ontransformational geometry?iv) Are there any significant differences betweenthe different groups’ achievements with respect torecognition, features and construction?MethodModel of the ResearchA quasi-experimental design was used to determinethe effects of DGS-based instruction, physicalmanipulative-based instruction and traditionalbased instruction on the transformationalgeometry academic achievement of freshman preservice primary school teachers.ParticipantsThis study must be performed with teachercandidates who are preparing to teach 1st, 2nd,3rd, or 4th grades due to the aim of studyingthe effect of dynamic geometry software andphysical manipulatives on teacher candidates’transformational geometry success. In this study,freshman teacher candidates were selected to makeup the practice groups via the purposive sampling

Kaleli Yılmaz / The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’.method. Freshman teacher candidates were chosendue to the requirements of this method. In researchusing this method, the experimental and controlgroups need to be selected at random. As a result,one of the other three grades has the probabilityof being selected as the Computer Group. Forthis reason, all participating teacher candidatesin this study should be technologically literateand sufficiently able to use a computer. Freshmanteacher candidates were considered to have moreup-to-date information about computers becausethey had taken Computer I and Computer II classes.On the other hand, thanks to the Basic MathematicsI and Basic Mathematics II classes they had taken,they were seen to have gained the basic skillsfor understanding transformational geometry.As a result, 117 freshman teacher candidatesselected through the purposive sampling methodconstituted the participants of this research.In order to increase both internal and externalvalidity in the scope of this study, groups wereselected at random and any biased behaviors werenot considered. After the random selection ofteacher candidates, the Primary School TeacherDepartment Formal Training Class A was chosenas the Computer Group, the Night Training ClassA was chosen as the Manipulatives Group, andFormal Training Class B was chosen as the controlgroup. A total of 43 students comprised the DGSbased instruction group (Computer Group), 36students comprised the physical manipulativesbased instruction group (Manipulatives Group),and 38 students were in the traditional instructionbased group (Traditional Group).developed by eliminating questions that had similarfeatures or that were abstruse. The developed TGATwas controlled in terms of comprehensibleness andreadability by an academician who is a Turkishlanguage specialist. After incoherent and incorrectpoints were corrected, the TGAT was put into a finalform. An explanation of each section of the TGAT ispresented below.Recognition: In this part, a total of ten shapes weregiven in mixed order. These shapes were aboutsymmetry according to point, symmetry accordingto line, displacement, rotation, and symmetryaxis; two shapes were given for each aspect thattakes place in transformational geometry. Studentswere asked to write which transformation is beingapplied in the blanks under the shapes. In Figures 1and 2, examples are given of the questions asked inthe recognition section.Figure 1: What is the transformation in figure 1?InstrumentThe transformational geometry achievement testwas used in this study as the data collection tool.While developing the achievement test, the body ofliterature was searched to form ideas for potentialquestions to ask about transformational geometry.Next, by collecting the current questions, anitem pool was formed. Because transformationalgeometry success was requested to be investigatedseparately for the sections of recogniton, features, andconstruction, 15 questions for each dimension wereselected from the item pool. Selected questions wereinvestigated by a specialist academician. Accordingto his opinion, 10 questions were considered foreach dimension. The Transformational GeometryAchievement Test (TGAT) with a total of 30questions (short answer, simple illustrative, elective)over 3 dimensions, 10 questions per dimension, wasFigure 2: What is the transformation in figure 2?Features: In this part, ten mixed features oftransformational geometry are given and studentswere asked to write which feature belongs to whichtransformation in the space provided.1423

Educational Sciences: Theory & PracticeTransformation of. direction is when theform, size, and shape are the same.Transformation of. is the image of theshape in the mirror.Construction: In this part, ten transformationswere given to students and they are asked toperform these transformations on the shapes undereach question. Two examples which belong to thispart are given in Figures 3 and 4.ProcedureTreatment of the Computer Group: Before treatment,students in the Computer Group were given six hoursof training on Cabri II Plus because it was new tothem. In this process, all toolbars in Cabri II Pluswere introduced to the students and they were taughthow to form structures using Cabri II Plus. Duringthe treatment, the students received instruction inthe computer laboratory. They individually studiedtransformational geometry topics by using Cabri IIPlus with worksheets along with guidance from theteacher, who was also the researcher.In the Computer Group, practice was performedby means of some work sheets as shown in Figure5 using Cabri II Plus. The worksheets that wereused in this group included extra directions thatrequired the use of Cabri II Plus. In Appendix 1,there is an example of the worksheet used by theComputer Group.Figure 3: Reflection according to the line.Figure 4: 2 units to the right displacement.Treatment of the Manipulatives Group: Thestudents in the Manipulatives Group did notreceive any special training before the treatmentbecause using manipulatives is straight forward.Students in the Manipulatives Group studiedtransformational geometry in a classroomenvironment enriched with physical manipulativessuch as symmetry mirror, dotted and lined papers,and origami. The students in this group alsostudied using worksheets. However, in contrast tothe worksheets used in the Computer Group, thedirections in these worksheets focused on the use ofmanipulatives. A total of five worksheets were usedfor each of the experimental groups. In Appendix2, there is an example of the worksheet used by theManipulatives Group.Treatment of the Traditional Group: TheTraditional Group (control group) receivedFigure 5: Explaining reflection according to line and displacement transformations on Cabri II Plus.1424

Kaleli Yılmaz / The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers’.traditional-based instruction. Here, the studentsreceived teacher-centered instruction. The teacherdrew and explained transformational geometry onthe blackboard. The students tried to answer theteacher’s questions in some parts of the lessons.As students were individually solving problems,the teacher would solve it on the blackboard. Thecontents of the course are presented in Table 2.Table 2Transformational Geometry Course ContentsWeekCourse Content1st week- Identification of transformational geometry,informing students about its importance, andgiving example from daily life.- Explaining the term symmetry axis and determining the axis of different geometric shapes.2st week- Expressing the topic of reflection according toline, giving examples from nature, and taking thereflections of different geometric shapes according to lines (vertical, horizontal and diagonal).3st week- Explaining reflection according

Symmetry is explained through models. 3. Geometry Symmetry Determining symmetry with respect to a line on a shape’s plane and what constitutes a symmetrical shape. 4. Geometry Symmetry Determining symmetrical lines on planar shapes as well as drawing them. 5. Geometry Symmetry Drawing the