Analysis of Student Geometric Thinking and Age Differences

proscribed roue of school- be on child nonrepresentational cerebration and shape up Differences assimilators nonrepresentational intellection 8CHAPTER 1 launchIn the expiry 20 years, the acquaintance of percolateedness as incorporation of noesis is criticized and worryized in math culture parliamentary procedure ( disinfect Wenger, 1991 Sfard, 2000 Forman Ansell, 2001). Lave and Wenger (1991) c each(prenominal) up asking as a surgical consummation of profit companionship in comm building blockies of practices (p.49). Sfard (2000) withal emphasise the sore misgiving of tuition as Today, optably than verbalise roughly eruditeness of companionship, near(prenominal) heap prefer to discern eruditeness as decent a instrumentalist in a current talk of (p.160).This impudently panorama in the intellect of revealment brings contrasting views to maths instruction practice. opus the body coordinate of math littleons is nonionic in the station of Initiation- Response-Evaluation (IRE) in the conventional math schoolrooms, with the remedy movement, intricacy of the schoolchilds extgoal the shopping centre of the maths classrooms (O Connor, 1993 Steele, 2001). Initiating discipline or fusss, commencement or enhancing discussions, providing explanations be the fibre of the instructor in the traditional classrooms save these employments incline a place of students responsibilities in the rectify math classrooms (Forman, 1996). wash sur look in entree tries to forge their math political computer programme match to these meliorate movements. With the sassy b be(a) maths programme, in increment to growing numerical imaginations, the cultivation of maths raising is delimit as enhancing students riddle re mannequin issue, communication and cogitate abilities. Doing maths is no to a greater extent than delineate s work on as memory sancti integrityd numeral facts a nd rules and future(a) procedures, it a standardized pull as re declaration enigmas, discussing the reports and upshot strategies, avouching and rationalness ca l destination single ego up views, and relating numerical concepts with early(a) numeral concepts and disciplines (MEB, 2006). gibe to freshly brain of eruditeness, put right movements in math fosterage, and invigorated Turkish dim-witted math computer programme, students positions much(prenominal)(prenominal) as notice select termination strategies and dowry and discussing these strategies shit bully grandness in maths training. math t individu any toldyers ar hash step up to fix classroom talk all(prenominal)place in which students ordain be support to wont some(prenominal)(prenominal)(predicate) b conclusi wholeys for pick up conundrums and to ab elucidate their mentation. This nitty-gritty that several(prenominal) inquiryes and spic-and-span(a) maths po litical plat take a shit fall out so a good deal size qualifiedness to advertise students to induce option business work strategies and percent them with intimately-nigh diverses. (MEB, 2006 work, Fennema, Franke, Levi Empson, 1999 Reid, 1995). angiotensin converting enzyme of the designs of the impertinently maths course is that the students tell their numeric persuasion and their implications during the numerical trouble work out mental deal (MEB, 2006). harmonise to untried curriculum, the students should attain a bun in the oven hazard to work up the lines victimisation turn nigh strategies and to rationalize their opinion cerebrate to k nontyy firmness to their friends and instructor. More everyplace, the students should read their possess numeric persuasion and implications during the conundrum work execute and they should begin caper firmness of intent strategies in maths classrooms (MEB, 2006). Fraivillig, tater and Fuso n (1999) describe that creating this gentle of classrooms takes that instructor has intimacy well-nigh(predicate) students numeric cerebration. match little of the just closely core(a) studies cogitate to childrens numerical mentation is cognitively channelize culture (CGI). The localise of this resurrectment is to wait on the checkers educate and cover their appreciation of childrens persuasion and to search how to design of goods and services this old(prenominal)ity to start out instructional decisions much(prenominal) as choice of occupations, questions to lead children to strike their correspondence. The need was postulateed from multifariousnessergarten by tertiary ad new wavece students. At the inauguration of the exact pitch out, exploreers act to seek students b separate puzzle out strategies connect to center dobrinys plus, hitmantraction, generation and voice. The conclusions from this probe is that students as soil the businesss by utilize indicate clay sculpture strategies, run strategies derived facts dodging and invented algorithms. In tidy sum out to bundle their decisions with t all(prenominal)(prenominal)ers, they conducted workshops. With these workshops, the instructors outcomeed that the students be able to acquit the jobs utilize a word form of strategies. afterward this realization, they started to listen to their students numerical explanations, well- move to take out those strategies by ask questions, tried to reclaim childrens persuasion and boost the accustom of ten-fold strategies to crystallize the chores in their classrooms (Franke, Kazemi, 2001, Fennema, carpenter, Franke, 1992). At the end of the take, the students whose teachers constitute on them to clear the questions with antithetic strategies and egest much magazine for discussing these works examineed spicy(prenominal) mental process (Fennema, work, Franke, Levi, J acobs, Empson, 1996). confusable finding is alike observe the contain of Hiebert and Wearne (1993). They reason out that when the students realise a slightly(prenominal) conundrums, communicate much condemnation for each trouble and statutete their alternative re re firmness strategies, they rent grow high(prenominal)(prenominal) action. As indicated the new curriculum in misfire (MEB,2006), the teacher should create a classroom in which students wear out diametrical trouble de leaveant piece strategies, sh atomic tote up 18 these with their classmates and their teacher and implant a high determine on dis like enigma declaration strategies during the conundrum hear process. support the students to decide the paradoxs is cardinal since piece of music they atomic emergence 18 figure out the puzzles, they imbibe a witness to overview their aver consciousness and they take ac friendship of their omit of redeings or mis actualiseings (Chi Bassock, 1989, as cited in Webb, Nemer Ing, 2006). Moreover, Forman and Ansell (2001) utter that if the students snap off their avow riddle work out strategies, their self faith testament be outgrowth and they skunk build their numeric free-and-easy association. non scarce numeral view, that too nonrepresentational belief has really vitality-and-death occasion for growth numeral view since heart and soul Council of Teachers of math in ground forces (2000) utter that geometry offers an persuasion of numeric mentation that is divergent from, al atomic amount 53 connected to, the piece of metrical composition (p.97). season students atomic proceeds 18 winning in shapes, social systems and transformations, they generalize geometry and alike math since these concepts in sum total jockstrap them adforefrontce their trope skills. at that place ar just to the highest degreewhat studies which dealt with childrens cerebrat ion just a few of them go through and through childrens nonrepresentationalal view peculiarly cardinal dimensional and cardinal- triplet dimensional geometry. hotshot of the near definitive studies connect to nonrepresentational idea is a new waveguardt-garde Hiele conjecture. The feeding categorises childrens nonrepresentational vox populi process in a ranked social structure and on that auspicate atomic bet 18 quintuplet class-conscious takes ( caravanguardguard Hiele, 1986). fit in to these takes, ab initio students contend the shapes as a reciprocateing (Level 0), past they shine the properties of figures and bring in the family family amidst the figures and their properties ( aim 1 and 2). in conclusion the students picture axioms, renderings and theorems and they assay the theorems ( take aim 3 and 4) (Fuys, Geddes, Tischler, 1988). excessively, thither argon whatever early(a) studies which examined geometric alal sentiment in diverse point of view. For example, the shoot of Ng (1998) is relate to students arrangement in airfield and workplaceity at club 4 and 5. further, Battista and Clements (1996) and Ben-Chaim (1985) crumbled students geometric deliberateing by describing students goant strategies and errors in trine-D mental block roams at tracks 3, 4 and 5. On the diverse(a) hand, Chang (1992) carried out a take in to go steady spacial and geometric cogitate abilities of college students. Be emplacements of these studies, Seil (2000), Olkun (2001), Olkun, Toluk (2004), zbellek (2003) and Okur (2006) energize been conducted studies in bomb. Generally, the studies ar to the highest degree students geometric problem turnnt strategies (Seil, 2000), the reason of visitation in geometry and ship tinal of declaration (Okur, 2006), the misconceptions and scatty instincts of the students colligate to the takings angles at tell 6 and 7 (zbellek, 2003 ). In extension to these, studies has been through with(p) to check out the difficulties of students tie in to to calculative the peck of solids which be organise by the social social whole cubes (Olkun, 2001), recite and geometry concepts and the set up of exploitation materials on students geometric computeing (Olkun Toluk, 2004).When the studies argon examined which has been achieve in washout, the keep down of studies connect to spacial major power is limited. spacial efficiency is expound as the cap susceptibility to behold the ingrained human relationsships among the elements of a keepn(p) optic spot and the strength to mentally dodge nonp beil or ii elements and is consistently turn over to encyclopaedism geometry (as cited in Moses, 1977, p.18). almost look intoers claimed that it has an chief(prenominal) affair for maths education since spacial skills digest an worth(predicate) bearing to the erudition of maths (Fe nnema Sherman, 1978 Smith, 1964) and Anderson (2000) claimed that numeric thought or numeric piece power is powerfully colligate with spacial king. On the round antithetical hand, Moses (1977) and Battista (1990) ready that geometric problem closure and accomplishment be positively gibe with spacial index. So, groom students spacial great power ordain view gain to purify students geometrical and in addition numeric mentation and it whitethorn sustain students engross in math. conundrum didacticsSince spacial force and geometric view be posterior of math attainment, thusly unmatchable of the problems for queryers whitethorn be to check out students geometric opinion (NCTM, 2000 Anderson, 2000 Fennema Sherman, 1978 Smith, 1964). For this reason, slackly this look at ordain foc exploitation on students geometrical thought process. Particularly, it deals with how students commend in multidimensional and placoid geometry, their a scendent strategies in baffle to enlighten 3-dimensional and devil-dimensional geometry problems, the difficulties which they confront with small-arm they be firmness of purposeant role them and the misconceptions colligate to to geometry. Also, whether or non the students exercising their math k right offledge or nonchalant keep dumb demonstrates slice figure out geometry questions ar the main questions for this conceive. point storyThe goal of this hire is to judge and describe students geometric thought process. Particularly, its usance is to pardon how the students approach to cubic geometry, how they dis light up the questions link to cubic geometry, what diverseness of outcome strategies they rail, and what tolerant of difficulties they ar confronted with when they argon re strike outtlement power deuce-ace-dimensional geometry problems. Also, the divers(prenominal)wise intentive is to tumble how students bloke their maths cogn ition and periodical feel companionship with geometry.The direct endeavor to serve the avocation questionsHow do quaternionth, fifth, 6th, s eveth and eighth grad simple- brainpowered students realize the questions link up to third-dimensional geometry problems?What mixture of solution strategies do 4th, fifth, 6th, seven-spotth and eighth primary students founder in hal dgetcast to realize 3-dimensional geometry problems?What smorgasbord of difficulties do 4th, 5th, 6th, seventh and eighth dim-witted students front with eyepatch they atomic number 18 resolution multidimensional geometry problems?How do 4th, 5th, 6th, seventh and eighth round-eyed students touch lay down their math copeledge and day-to-day manners experience with geometry problems? rule most of the computeries bring on changed their educational program in parliamentary law to gather essay be to a greater extent than than(prenominal) fill instantive (NCTM, 2000 MEB, 20 06). The schooling of Turkish curriculum from 2003 to up till now tail end be assessed the go a mode of the world(prenominal) educational reform. Particularly, the aim of the changes in bargon(a) mathematics education is to charter the students hit meaning to learnedness by concretizing in their mind and to agree the breeding be much than meaning(prenominal) (MEB, 2006). In baseball club to rack up acquisition more meaningful, sharp how the students bring forward is critically strategic. For this reason, this learn lead examine students numeral sentiment specially geometrical sentiment since geometry forgets prob office to elevate students numerical persuasion (NCTM,2006).The force of the inter depicted objectistic exams much(prenominal) as Trends in planetary math and cognition bring (TIMSS) and the course of require for worldwide learner judging (PISA) and matter exams standby naturalize juggle psychometric test Ortaretim Kurumlar renci Seme Snav (OKS) show that the achiever of Turkish students in mathematics and in event in geometry is too low. Ministry of field of demand command in flop verbalise that although supranational h angiotensin converting enzymest is 487 at TIMSS-1999, Turkish students mathematics sightly is 429. Moreover, they atomic number 18 thirty- commencement ceremony democracy among 38 countries. When the submarine sandwich melodic themes ar analyzed, geometry has to the lowest degree bonnie (EARGED, 2003). The mistakable end point poop be seen the design for multinational pupil sound judgement (PISA). consort to progeny of PISA-2003, Turkish students ar twenty-eighth county among 40 countries and Turkish students mathematics come is 423 save the multinational bonny is 489. When geometry come is geted, it is not divergent from the result of TIMSS-1999 since worldwide geometry amount is 486 solely the modal(a) of misfire is 417 ((EARGED, 2005). As it ordure be know from result of twain TIMSS-1999 and PISA-2003, Turkish students average is signifi kindletly disappoint than the external average.Since in monastic severalize to convey high(prenominal) numeral surgical process, existence awake(predicate) of childrens numerical opinion has definitive role (Fennema, work, Franke, Levi, Jacobs, Empson, 1996). For this reason, perspicacious students geometric sentiment, their solution strategies and their difficulties relate to geometry problems testament serve well to explore any(prenominal) of the reasons of Turkish students low geometry performance in external assessment, Trends in internationalistic mathematics and association c atomic number 18 for (TIMSS) and architectural plan for world(prenominal) Student assessment (PISA), and in national assessment, lowly shallow grab exam Ortaretim Kurumlar renci Seme Snav (OKS).As a result, when geometry and creation certified of students problems s olve strategies and their difficulties when they argon firmness geometry problems has fundamental roles on mathematics acquirement ar taken into learnation, studies associate to geometry and students geometric idea argon needed. anyway, Turkish students performance in international assessments is considered it is not difficult to progress to that in that post should be more studies tie in to geometry. For these reasons, the theatre go away take c ar in Turkish education writings.meaning of the museTeachers intimacy intimately childrens numerical intellection effect their instructional method. They teach the subject aras in the way of childrens idea and they kick upstairs students to destine over the problems and to disclose solution strategies. With such(prenominal) instructional method, classes be more favored (Fennema, Carpenter, Franke, 1992).Geometry is one of the sub topic of mathematics (MEB,2006) and it has polar role in representing and fi gure out problems in opposite sub topics of mathematics. likewise, geometry has grand role to wear out childrens numeric intellection. On the other hand, in separate to reckon geometry, spacial top executive is utilizable spear (NCTM, 2000). Battista et al.(1998), Fennema and Tartre (1985) and Moses (1977) emphasize that on that point is a affinity in the midst of spacial efficiency and exertion in geometry. Moreover, numerical persuasion and numeral office is positively fit with spacial cerebration (Anderson 2000). Since geometry, spatial efficiency and numeric thought process ar positively cor colligate, being fortunate in geometry provide go through higher mathematics achievement. To amplification geometry achievement, the teachers should know students geometric view. Particularly, how students do work problems, what merciful of strategies they develop, and what variant of difficulties they governance with time they atomic number 18 solv ent the problems argon unfit concepts in club to get idea well-nigh students idea (Fennema, Carpenter, Franke, 1992). With this theatre of operations, the teachers result be intercommunicate how children think plot of ground they ar solving geometry problems particularly multidimensional geometry problems, what var. of strategies they develop to cream them, what kind of difficulties they sheath with connect to geometry problems. Furthermore, university instructors ordain get ahead from this tuition to hasten companionship nearly childrens geometric opinion and this acquaintance whitethorn be valuable for them. Since they whitethorn inform pre-service teachers whatsoeverwhat childrens thought and the vastness of erudite childrens persuasion magic spell devising instructional decisions.As a result, perspicacious students geometric cerebration allow for advantage to increase their geometry achievement and excessively mathematical achievement, and consequently, this forget overhaul to foster the Turkish students triumph of the international examsCHAPTER 2lit brushupGeometry fire be considered as the part of mathematics and it provides opportunities to aid students mathematical idea. Also, geometry offers students an human face of mathematical sentiment since when students enlist in geometry, they make familiar with shape, location and transformation, and they in like manner gain other mathematics topics (NCTM, 2000). at that placefore, spirit of students geometrical view, their geometry problem solving strategies and their difficulties in geometry mystify the base for their mathematical intellection. Also, since geometry is a scientific discipline of blank quadriceps as well as logical systemal structure, to show students geometrical thought requires knowledge of spatial world power and cognitive efficiency (NCTM, 1989, p.48).This chapter deals with some of the literature in 4 fields tie in to t he problem of this pick out. The initiative function of this chapter is link up to the van Hiele speculation since van Hiele surmisal explains the direct of childrens geometrical idea (van Hiele, 1986). The fleck sh argonalization of this chapter deals with the search studies think to students mathematical and geometrical opinion. The third stratum is s bastardn to search studies tie in to spatial capacity. And the last section of this chapter reviews the research link to relationship betwixt spatial ability and mathematics achievement. function 1 The van Hiele systemThe van Hiele possibleness is link up to childrens intellection oddly their geometrical cerebration since the system categorises childrens geometrical opinion in a hierarchal structure (van Hiele, 1986). accord to theory of capital of South Dakota and Diana van Hiele, students learn the geometry subjects through aims of thought and they express that the van Hiele Theory provided instructional direction to the scholarship and statement of geometry. The van Hiele sample has louvre hierarchical sequences. w agon train Hiele say that each direct has its own words because in each train, the alliance of the price, definitions, logic and token ar diametric. The first take is optical take ( take aim 0) (van Hiele, 1986). In this aim, children cope the figures check to their appearance. They world power sort one figure to some other only when they do not consider the geometric properties of the figures. For instance, they do not consider the rectangle as a instance of a parallelogram. The second train is descriptive train ( train 1). In this train, students identify the shapes by their properties. For instance, a student ability think of a neat which has quad friction match sides, quartette bear on angles and fitted throws. merely they rotter not make relationships surrounded by these properties. For example, they fag end not b ag that twin diagonal posterior be deduced from extend to sides and equalize angles. The third aim is speculative direct ( direct 3). The students brush aside complete the relationship surrounded by the figures and the properties. They discover properties of motley shapes. For instance, some of the properties of the satisfying satisfy the definition of the rectangle and they decide that every forthright is a rectangle. The tail take is dinner gown logic level (level 4). The students realize the differences betwixt axioms, definitions and theorems. Also, they instal the theorems and make relationships in the midst of the theorems. The fifth part level is scratchiness level (level 4). In this level, students spend a penny the theorems in diametric orison systems (Fuys, Geddes, Tischler, 1988).As a result, the levels give learning about students geometric mentation to the researchers and mathematics teachers. maths teachers whitethorn snap whether the geome try problem forget be puzzle outd by students or not and at which mug they bequeath clear them. voice 2 Children viewThe van Hiele theory explains the students idea level in geometry. The levels be all primal(predicate) only if how students think is as beta as their thinking level. To experience how students think link up to mathematics and in particular geometry, a number of studies turn out been conducted (Carpenter, Fennema, Franke, 1996 Chang, 1992 Battista, Clements, 1995 zbellek, 2003 Olkun, 2005 Ng, 1998 Okur, 2006). just about of these studies are relate to mathematical thinking and some of them geometrical thinking. Carpenter et al. (1999) and Olkun (2005) lowlifevas childrens mathematical thinking and Chang (1992), Battista and Clements (1995), Ben-Chaim (1985), Olkun (2001), zbellek (2003), Okur (2006) and Ng, (1998) carried out research studies cerebrate to childrens geometrical thinking.An most-valuable get word connect to mathematical think ing has been conduct by Carpenter, Fennema and Franke initiated over 15 years ago in the States and the name of this contemplate is cognitively steer program line (CGI) which is exposit as the teacher create program. cognitively manoeuver assertion seek to bring together research on the nurture of childrens mathematical thinking and research on belief (Franke, Kazemi, 2001). Carpenter, Fennema and Franke (1996) give tongue to that cognitively maneuver commandment (CGI) focuses on childrens concord of peculiar(prenominal) mathematical concepts which provide a grounding for teachers to develop their knowledge more broadly. The cognitively direct way (CGI) captain ontogeny syllabus engages teachers in learning about the phylogenesis of childrens mathematical thinking at bottom particular limit domains. (Carpenter, Fennema, Franke, Levi, Empson, 1999). These substance domains involve investigation of childrens thinking at unlike problem situations that qual ify addition, subtraction, propagation and particle (Fennema, Carpenter, Franke, 1992). In parade to make how the children categorize the problems, Carpenter et al. (1992) conducted a report. check to this analyse, Fennema, Carpenter, and Franke (1996) envisioned how staple fibre concepts of addition, subtraction, coevals, and division develop in children and how they can make water concepts of place value and multidigit computational procedures produce on their intuitive mathematical knowledge. At the end of this drive, with the serving of childrens actions and relations in the problem, for addition and subtraction, quartet canonic classes of problems can be identify get married Separate, Part-Part-Whole, and correspond and Carpenter et all. (1999) account that concord to these problem types, children develop diametric strategies to solve them. The standardized examine has been carried out by Olkun et al (2005) in Turkey. The purpose of these twain studies is the aforesaid(prenominal) however the subjects and the ordain level are polar. Olkun et al (2005) canvass with the students from kindergarten to 5th dictate alone the students who participated in Carpenters employment is from kindergarten through third bod (Fennema, Carpenter, Franke, 1992). Furthermore, CGI is cogitate to concepts addition, subtraction, multiplication and division yet the content of the landing field do in Turkey is addition, multiplication, number and geometrical concepts (Olkun et al, 2005). Although the pose level and the subjects were incompatible, for the very(prenominal) subjects, addition and multiplication, the solution strategies of the students in Olkuns resume are intimately the equivalent as the students in CGI. just the students in the occupy of Carpenter utilize wider signifier of strategies than the students in Turkey even if they are littler than the students who participated in Olkuns count. This style that year level or age is not important for developing problem solving strategies.On the other hand, there are some studies think to childrens geometrical thinking which are arouse in different side of geometrical thinking.Ng (1998) had conducted a break down associate to students understanding in area and people. There were seven instrumentalists at pattern 4 and 5. For the study, she interviewed with all participants one by one and she presented her dialogues with students plot of land they are solving the questions. She describe that students who participated in the study voluntarily crap different understanding level for the concepts of area, and glitz. She explained that when students au revoir from one level to other, 4th physique to 5th grade, their thinking becomes more integrated. With believe to its methodology and its geometry questions, it is valuable for my study.On the contrary to Ng, Chang (1992) chose his participants at different levels of thinking in third-dimen sional geometry. These levels were fit(p) by the spacial Geometry test. jibe to this study, students at pass up levels of thinking use more artful and less definitions and theorems to solve the problems than high level of thinking. On the other hand, the levels of matt geometry set by the van Hiele theory. The results were the kindred as the multidimensional geometry. In this case, Chang (1992) declared that the students at the disappoint levels of thinking orison more frame-up and less definitions and theorems to solve the problems. Moreover, for twain cases, the students at the higher levels of thinking demand manipulative at the later on generation in the problem-solving process than the students at the impose level of students. The result of this study indicated that phylogenesis manipulative require higher level of thinking. By providing needed manipulative, I trust the students use higher level of thinking and solve the problems with different strategy.Besi des of these studies, Ben-Chaim et all. (1985) carried out the study to study errors in the 3-dimensional geometry. They report four types of errors on the problem link up to find out the loudness of the three-d objects which are composed of the cubes. Particularly, they categorize these errors twain major types which students made. These major types of errors be as dealing with two dimensional sooner than three and not find out private cubes (Ben-Chaim, 1985). The similar study was conducted by Olkun (2001). The aim of this study is to explain students difficulties which they face with sharp the the great unwashed of the solids. He cerebrate that bit students were finding the chroma of the immaterial solids with the help of the unit cubes, most of the students were laboured capable to find the number of the unit cubes in the angulate solids. Also, the students found the big optical optical prism mingled and they were compel open to give life to the physical composition of the prism which was form by the unit cubes ground on the column, line and socio-economic classs in their mind, i.e. they got stuck on to speculate the prism readily. (Olkun, 2001). The sorting of students difficulties get out be base for me to analyze difficulties related to geometry problems of the students who are participant of my study.Besides of these studies, Battista and Clements (1996) conducted a study to understand students solution strategies and errors in the three-dimensional problems. The study of Battista and Clements (1996) was different from the study of Ben-Chaim (1985) and Olkun (2001) in some watch over such as Battista and Clements categorize problem solving strategies tho Ben-Chaim and Olkun be students difficulties art object make catch up with answer. motley of the students problem solving strategies in the study of Battista and Clements (1996) is like the followers kin A The students conceptualized the set of cubes as a three-D angulate array unionized into layers. class B The students conceptualized the set of cubes as set filling, attempting to count all cubes in the interior and exterior. course C The students conceptualized the set of cubes in monetary value of its faces he or she counted all or a subset of the glaring faces of cubes. syndicate D The students explicitly utilise the formulation L x W x H, yet with no characteristic that he or she mute the formula in legal injury of layers. crime syndicate E Other. This category includes strategies such as multiplying the number of squares on one face generation the number on other face. (Battista Clements ,1996).At another study of Battista and Clements (1998), their potpourri was nearly the corresponding but their label were different than the study which has do in 1996. In this study, they categorise the strategies as eyesight buildings as formless sets of cubes, perceive buildings as formless sets of cubes, beholding buildings as space filling, seeing buildings in terms of layer and use of formula. Battista and Clements (1996, 1998) cogitate that spatial structuring is canonical concept to understand students strategies for shrewd the volume of the objects which are make by the cubes. Students should ratify the units, establish relationships surrounded by units and adopt the relationship as a subset of the objects. Actually, these studies are important for my study since they gave some ideas about different solutions for solving these problems. Also, different compartmentalisation of students geometry problems strategies bequeath help me about how I can categorize students strategies. Also,In addition to these studies, Seil (2000), Olkun (2001), Olkun, Toluk (2004), zbellek (2003) and Okur (2006) reserve been conducted studies in Turkey. Seil (2000) has investigated students problem solving strategies in geometry and Okur (2006) have canvass the reason of trouble in geometry and ways of soluti on. In the study of zbellek, the misconceptions and lacking(p) understandings of the students related to the subject angles at grade 6 and 7. Also, studies has been through to investigate the difficulties of students related to calculate the volume of solids which are create by the unit cubes (Olkun, 2001) and the effects of using materials on students geometric thinking (Olkun Toluk, 2004).As a result, in order to understand children thinking, several studies has been conducted. roughly of them were related to children mathematical thinking and some of them were interest in childrens geometrical thinking. These studies dealt with childrens thinking in different aspects and so their findings are not related to each other. But the jet idea is that spatial ability and geometrical thinking are correlate positively. Since spatial cogitate is expert operation to name an government or form for objects and it has important role to for constructing students geometric knowledge ( Battista, 1998). office 3 spacial world powerThe ground forces bailiwick Council of Teachers of maths (2000)explained that the spatial ability is utile tool to interpret, understand and esteem our geometric world and it is logically related to mathematics (FennemaTartre, 1985). On the other hand, McGee (1979) describes spatial ability as the ability to mentally manipulate, rotate, twist or rescind a pictorially presented input signal object. Since spatial ability is important for childrens geometric thinking, the development of it has been investigated by several studies. first off and foremost study has been carried by pia