Women in the 1950s vs 2000s free essay sample

Mike Rose is a widely praised essayist and teacher in the School of Education at UCLA and has won numerous honors for his work. In this choice called â€Å"I Just Wanna Be Average† taken from his book Lives on the Boundary, Rose offers his experience walking through the normalized professional training track. Through his own record, the creator brings up that society and even workforce inside these schools name the understudies as â€Å"slow† leaving the understudies with a goal of needing to turn out to be simply normal so as to compensate for their assumed feeling of deficiency given by their purported teachers. In this choice, Rose uses a great deal of easygoing language and stories of encounters in secondary school so as to connect with understudies of any age who may be battling to discover the estimation of their own scholarly limit covered inside the measures of what educational systems thinks about scholarly. We will compose a custom exposition test on Ladies during the 1950s versus 2000s or then again any comparable theme explicitly for you Don't WasteYour Time Recruit WRITER Just 13.90/page Through the style of his narrating, he passes on his message to his crowd without fundamentally constraining the thought on Throughout the section, Rose portrays his secondary school involvement with sequential request. He initially portrays the transport outing to class and a large number of the characters that he went over in thisâ environment like Christy Biggars, the multi year old seller or Bill Cobb, â€Å"the oil pencil craftsman extraordinaire†. The creator additionally gives definite depictions of what the educators, for example, the â€Å"troubled and unstable† Brother Dill or Mr. Mitropetros who Mike Rose professed to have small preparing in English yet still figured out how to get a new line of work as an English educator. Before portraying what the training framework in a professional school, the creator gives us some foundation data on a portion of the understudy segment and a portion of the instructors that were accountable for these wild understudies. Giving a point by point portrayal of these individuals gives perusers a more critical look in the general condition before investigating the framework. The peruser would already be able to see that these understudies, under initial introduction, are unmotivated to learn and that the educators have issues of their own and makes the peruser question the fitness of a portion of these employees. As Rose keeps on portraying what his classes resemble, he gives progressively definite portrayals of some more colleagues and classmates. From his depictions, the peruser can get to truly observe the lost potential in a portion of these understudies. Ted Richard, a realized road battle inâ school, was very the philosophical character who appreciated perusing anything he could and chatted with anybody from a vagrant to a representative. Rose depicted him as forming into â€Å"one of those harsh slashed educated people whose sources a blend of the scholarly and the apocryphal† (161). With these instances of the kinds of understudies that go back and forth through professional school, Rose unpretentiously uncovers how these normalized schools have neglected to cause understudies to understand their maximum capacity. All through this entire choice Rose makes references to numerous circumstances that most any understudy, current or past, may identify with. He utilizes language, for example, â€Å"You’ll see a bunch of understudies far exceed expectations you in courses that sound exotic† (162). By utilizing this sort of language the writer makes an exceptional space where he can speak with the peruser on a progressively close to home level. There is a feeling that the writer is conversing with the peruser rather than talking at them or just clearly recounting to a story. He effectively attempts to pull the crowd in to all the more likely comprehend his story by empowering the perusers to think once again into their own encounters also. With the utilization of his own secondary school understanding, the crowd can stroll along withâ the creator as he defeats snags and restrictions. He doesn't give an unremarkable clarification of how he battled in school, however he portrays the sentiments of insufficiency when the very framework that is assumed cultivate learning and the procurement of information is the one that is smothering its understudies and defining their limits. Despite the fact that Rose never legitimately guarantees this is what's going on, however we the crowd can see this event in his story as well as encountering this in our own undertakings in the quest for information.

Deaf Culture Paper Free Essays

To all the more likely acknowledge what Deaf culture is, let’s go to a restricting perspective and investigate what Deaf culture isn't. There are the individuals who demand there is nothing of the sort as Deaf culture. A few people will contend that deafness is just a handicap, an incapacity that must be fixed. We will compose a custom article test on Hard of hearing Culture Paper or on the other hand any comparable point just for you Request Now Getting this inability â€Å"fixed† may include rehashed visits to an audiologist, getting fitted for portable amplifiers, going to various language training meetings, or in any event, experiencing medical procedure to get a cochlear embed. This is what’s called the neurotic way to deal with deafness. It centers around what’s wrongâ€the failure to hearâ€and uses various innovative and restorative methodologies to take care of the issue. The achievement of this methodology shifts from individual to person. For some in need of a hearing aide or late-stunned individuals, innovation might be an invited expansion that permits them to keep working in their preferred realm. â€Å"Deafness is an inability that is so one of a kind, its very nature makes a culture rise up out of it. Cooperation in this culture is intentional. † There have been various Deaf distributions throughout the years, for example, Silent News, DeafNation, SIGNews, Deaf Life, and that's just the beginning. There are additionally lists stuffed with books composed by Deaf writers covering a wide scope of subjects. A portion of these books incorporate interesting records of Deaf history and fables. We’ve been honored with various Deaf performing specialists, for example, Clayton Valli, Patrick Graybill, Bernard Bragg, Mary Beth Miller, Freda Norman, Gil Eastman, Peter Cook, C. J. Jones, Nathie Marbury, Evelyn Zola, The Wild Zappers, Rathskellar, and some more. In hearing society, it is discourteous to gaze. In any case, in Deaf culture, gazing is important. On the off chance that you look away while an individual is marking to you, you are amazingly discourteous. That’s like stopping your ears when somebody is addressing you. In hearing society, outward appearance is exceptionally restricted. On the off chance that you move your face or body a great deal while you are talking, you can be viewed as â€Å"weird† (and no one needs to be abnormal). Nonetheless, in Deaf culture, outward appearance and body development is required for ASL. It’s part of ASL language. It’s OK to be â€Å"weird† in Deaf culture†¦ it’s typical! What's more, completely vital. In hearing society, you regularly present yourself by your first name as it were. Hard of hearing individuals, be that as it may, present themselves by their complete names, and here and there even what city they’re from or what school they went to. By city, I mean the city you experienced childhood in, not what city you are right now dwelling in. Also, by school I typically mean a private school you joined in. The Deaf people group is extremely little, and Deaf individuals like to locate those particular shared characteristics with one another. Men are bound to create hearing misfortune or complete deafness than ladies. About 20% of Americans have detailed some level of hearing misfortune. 2-3 kids out of 1,000 are brought into the world hard of hearing each year. 9/10 kids with a level of hearing misfortune are conceived from hearing guardians. 1 out of 5 individuals who’d advantage from portable amplifiers; really wear them. Around 4,000 instances of unexpected deafness happen every year. 10-15 percent of unexpected deafness patients know how they lost their hearing. Step by step instructions to refer to Deaf Culture Paper, Essay models

Catholics and Evolution :: essays research papers

Catholics and Evolution      One of the most significant inquiries for each informed Catholic of today is: What is to be thought of the hypothesis of development? Is it to be dismissed as unwarranted and antagonistic to Christianity, or is it to be acknowledged as a set up hypothesis inside and out perfect with the standards of a Christian origination of the universe?      We should cautiously recognize the various implications of the words hypothesis of advancement so as to offer an unmistakable and right response to this inquiry. We should recognize (1) between the hypothesis of advancement as a logical theory and as a philosophical hypothesis; (2) between the hypothesis of development as dependent on mystical standards and as dependent on a materialistic and agnostic establishment; (3) between the hypothesis of advancement and Darwinism; (4) between the hypothesis of development as applied to the vegetable and creature realms and as applied to man. (1) Scientific Hypothesis versus Philosophical Speculation      As a logical speculation, the hypothesis of advancement looks to decide the verifiable progression of the different types of plants and of creatures on our earth, and, with the guide of palã ¦ontology and different sciences, for example, relative morphology, embryology, and bionomy, to show how over the span of the diverse geographical ages they slowly advance from their beginnings by absolutely characteristic reasons for explicit turn of events. The hypothesis of advancement, at that point, as a logical theory, doesn't think about the current types of plants and of creatures as structures straightforwardly made by God, yet as the conclusive outcome of a development from different species existing in previous geographical periods. Consequently it is called "the hypothesis of evolution", or "the hypothesis of descent", since it suggests the plummet of the present from terminated species. This hypoth esis is against the hypothesis of consistency, which accept the unchanging nature of natural species. The logical hypothesis of advancement, in this way, doesn't fret about the source of life. It only asks into the hereditary relations of efficient species, genera, and families, and tries to orchestrate them as indicated by common arrangement of plunge (hereditary trees).      How far is the hypothesis of advancement dependent on watched realities? It is comprehended to be still just a theory. The development of new species is straightforwardly seen in however a couple of cases, and just concerning such structures as are firmly identified with one another; for example, the methodical types of the plant-variety Ã…'nothera, and of the bug family Dimarda.

Effects of School Feeding Programme on Education

Impacts of School Feeding Program on Education The administration of Ghana has perceived essential training as a principal building square of the economy. This progression is in accordance with objective two of the Millennium Development Goals (MDGs) which tries to accomplishing an all inclusive essential training constantly 2015 (Ghana MDG Report, 2009). Likewise, in compatibility with GPRS II (GPRS, 2006), Article 38 of the 1992 constitution urges government to give access to Free Compulsory Universal Basic Education (fCUBE) to all offspring of school going age (Constitution of Ghana, 1992). In compatibility of this necessity, various plans and projects have been propelled with the legislature setting out upon a few instructive changes and organizing new arrangement measures toward making training increasingly open to all. These incorporate the fCUBE program, training vital arrangement, the capitation award; which makes essential school liberated from any type of school expenses and the NEPAD School Feeding Program (SFP) (ESP, 2003). Note that entrance to training isn't an end in itself, however an unfortunate chore. The final products of the training procedure is that it ought to convert into quality human capital/asset for the state as the GPRSII imagines, henceforth, the energy of governments to put resources into the instruction of their kin. The capitation award for the most part should bring about higher enrolment and maintenance in schools. The school taking care of program supplements this by accommodating the understudies wholesome needs and upgrading their learning capacities. All these ought to convert into better by understudies and so far as that is concerned, the creation of value human asset required for state improvement. It ought to be noticed that, before the presentation of the legislatures school taking care of program, the Catholic Relief Service (CRS,) had just founded the strategy of taking care of younger students in the area. This aside, the establishment of the Northern Scholarship Scheme had likewise been set up in the locale since the late 1950s, dealing with the taking care of cost of understudies in Senior High Schools in the region. These had noteworthy effect on training of the zone. Truth be told, numerous educators and taught elites in the area owe their present status to these plans (Nadowli District, 2008) THE PROBLEM STATEMENT The presentation of the administration school taking care of program was to enhance different mediations, for example, free school uniform and capitation awards. It has since assumed an essential job nearby different intercessions in improving both Gross Enrolment Ratio (GER) and Net Enrolment Ratio (NER) in schools in Ghana. The Upper West Region when all is said in done, recorded GER increment of 74.1% from 1991/199 2002/2003, 77.3% from 2002/2003 2004/2005 and 81.1% 2004/2005/2006 (RSER-UWR, 2006). In spite of the increments in the enrolment figures, denied regions in Ghana keep on experiencing genuine troubles in pulling in prepared educators; homeroom settlement keeps on being an issue with access to instructing and learning materials staying a migraine to partners. These contrarily influence the nature of instruction in these regions including the Nadowli District. The ascent in enrolment figures with no comparing increment in the quantity of instructors as a rule lead to lopsided Pupils-Teacher Ratio (PTR). Congestion in study halls additionally gets sensational of such circumstances with expanded enrolment with little consideration regarding the development homerooms in light of the expanding numbers which doesn't just now and again lead to the episode of maladies yet in addition influences nature of instructing antagonistically. The examination thusly looks to research how the expanding enrolment figures influence the nature of essential instruction in the Nadowli District. RESEARCH QUESTIONS Primary Question How has the school taking care of program influenced elementary school instruction in the Nadowli District? Sub-questions How has the SFP impacted elementary school enrolment in the region? How has the SFP impacted student maintenance in schools in the region? What are the ramifications of the SFP on PTR? How has SFP influenced study halls action and TLM? Are there exercises for arrangement plans? Principle objective To look at the impacts of the school taking care of program on elementary school instruction in Nadowli District Sub-destinations To decide how the SFP has impacted elementary school enrolment in the region To evaluate the impact of SFP on understudies maintenance in school To inspect the ramifications of the SFP on PTR To inspect the impacts of SFP on homerooms action and TLMs To draw exercises from the examination for strategy plan RESEARCH METHODOLOGY Information assortment instruments Both likelihood and non likelihood information assortment devices will be utilized in the assortment of essential information in the investigation. In particular, I will utilize studies, semi-organized meetings and perceptions. The overviews will be utilized to request general data from the respondents on their perspectives on the theme, for example, on the impacts of the SFP on the pace of enrolment. The studies will likewise yield quantitative information. The meetings will be utilized to create subjective, explicit and inside and out realities about the examination. The perception will be utilized addition direct data on the examination. Wellsprings of information The investigation will gather information from educators, guardians, students, cooks of the program, and staff from the locale directorate of instruction and providers of food these schools. Optional wellsprings of information, for example, papers, article and web sources will be utilized. Records of enrolment previously and during the SFP will likewise be utilized for examinations. Examining strategies and inspecting units I will utilize purposive examining to gather information from authorities of the area training directorate (the region executive, the official accountable for measurements, the arranging official, chief of human asset and a circuit manager), cooks, head instructors, school consuls, PTA chairpersons, and providers of food to the schools. Examining size An example size of 38 will be reviewed. This will be made of: 8 head instructors, 8 school regents, 8 PTA chairpersons, 8 cooks, 5 authorities of the area training directorate and 1 provider of food to the schools in the region. Information investigation and introduction Subjective information gathered will be summed up into topics, dissected and deciphered by the utilization of enlightening procedures. Quantitative information investigation will be finished utilizing PC programs like the SPSS. Tables, diagrams and charts would be utilized to outline and present discoveries for simpler comprehension and understanding. Importance OF THE STUDY Through discoveries of the investigation, partners will be all around educated regarding the importance or in any case of the SFP on essential instruction in the area. Positive result will get them focused on progress and sustainace of the program. Additionally, negative impacts of the program whenever found will likewise be tended to. Aside filling in as base information for additional exploration deal with the subject, discoveries of the investigation will help in arrangement plan on the program. Association OF THE RESEARCH REPORT The examination report will be composed into six parts as follows for clear introduction. The general presentation of the examination just as the difficult proclamation and the exploration addresses will go into section one. This part will likewise contain the examination goals, defense of the investigation and a concise profile of the investigation region. Section two is the audit of writing on the theme. It will have a go at conceptualizing and characterizing issues that identify with the investigation and put them in context. It will attempt to investigate and fill holes in existing writing accessible on the examination. Part three will look at the procedure utilized in the examination for the assortment of information. How information gathered is broke down and introduced will likewise be clarified in this part. Discoveries of the investigation and the conversations on it will be introduced in part four of the report. This will likewise deal with auxiliary information examination on the investigation. Representations with tables, figures outlines and charts will be made for simpler comprehension and understanding of discoveries. Outlines of discoveries, end and proposals will be introduced in the fifth and last section of the report. Writing REVIEW The writing survey targets investigating for zones of understandings and differences on the point. From this, leaving holes will be recognized and endeavors made to fill them. The survey will cover regions like: effect of training related mediations in Ghana, the historical backdrop of school taking care of in Ghana, Ghana instruction arrangement structure, ongoing training related intercessions in Ghana and the SFP (contentions and against). See an example audit underneath. Effect of instruction related intercessions in Ghana Nations in Sub-Saharan Africa have been investigating methods of improving their instruction frameworks so as to accomplish their promise to training for all. Guaranteeing that youngsters approach free, obligatory and great quality essential training is getting significant consideration from governments and help offices the same as is given a thought in the (GPRS II, 2006). Two fundamental frameworks through which certain administrations are utilizing to accomplish this point are the cancelation of school expenses and the School Feeding Program. Studies have demonstrated that these intercessions are having noteworthy effect in the zone of training in the nation (ISSER, 2009). The historical backdrop of school taking care of in Ghana The issue of school taking care of goes back to the 1950s when the CPP government founded the Northern Scholarship Scheme to provide food for the taking care of cost of understudies in the northern piece of the nation. The Catholic Relief Services likewise presented a taking care of plan in fundamental schools in the north. The two plans were intended to spur understudies to get instructed. The latest of these plans is the SFP which is being guided in all locale in the nation. Instruction Policy F

Devastation of War Research Paper Example | Topics and Well Written Essays - 1000 words

Pulverization of War - Research Paper Example The sonnet â€Å"refugee ship† is increasingly unequivocal around one being an alien to her own ethnicity. A mother who didn't care for the possibility of her little girl being a captive to the Spanish culture and as such attempted to keep the girl in the dimness about her ethnicity raised the young lady. The mother didn't show the young lady the way of life neither did she show her the language. The grandma of the young lady attempts to do what the mother didn't do by making a decent attempt to instruct her the way of life and the language so she can be familiar with the Spanish way of life. In spite of the fact that she attempts to learn, she battles to articulate the words however that was normal, as she had no up welcoming on that issue. The young lady feels so befuddled and consequently feels caught between the sort of character her mom raised her to be and what her identity is relied upon to be by the general public. She is clashed on the grounds that is an evacuee from two unique societies and the ship...will never dock... in light of the fact that the boat speaks to her life and she should carry on with that life to become what she is to be. In the sonnet the â€Å"refugee ship†, an image is painted of one who is befuddled as a result of the two societies she needs to manage. Actually, she doesn't have the foggiest idea what the importance of the things mean and abuses a few words improperly. She voices her disappointments while discussing the boat never docking. Indeed, it very well may be reasoned that she is socially destitute. This sonnet gives an away from of what could have occurred because of movement. Learning another culture would be troublesome as one would not know about what the person in question becomes because of the disarray that radiates from not having the option to appreciate the other culture and ace it for endurance. The sonnet â€Å"refugee ship† is an old style picture that attempts to illustrate the experience of the Vietnamese while utilizing the vessel as a transportation mode (Chmidt and Crockett, 5). A top to bottom examination of the sonnet would portray what occurred from an alternate point of view. In the sonnet, there is a granddaughter and the grandma attempting to get along, however one significant test is that they are not in understanding as they can't comprehend each other due to the language obstruction. It appears to be however that the two are in an alternate world. This illustrates the Vietnamese during the hour of escaping the obliterations of war. As an outsider the principal challenge one would confront is the issue of correspondence as one isn't a situation to argue since they can't comprehend. During the war that turned the Vietnamese as evacuees and settlers, greater parts were outstandingly influenced. The way of life stun was one of to such an extent that was a major test. Around then, bigotry was likewise a significant issue and along these lines, they had no way out, however to confront the difficulties that accompanied their new status are migrants. Canada was one of those nations that facilitated various outsiders from Vietnam. For example, if any of the displaced people or workers took a gander at the sonnet outcast boat, at that point it would remind them who they were before and how they gained their status. As displaced people, the Vietnamese lost a great deal as far as social safeguarding and improvement throughout everyday life. For instance, numerous youngsters missed some significant phases of youth at the hour of war, as some couldn't appreciate or have the benefit of growing up with their companions a factor that is significant for youth improvement. Some couldn't likewise go to class and it along these lines implied they falled behind as their capacity to peruse and compose were not upgraded. A significant obliteration of wa s the horrendous encounters of war. War has the amazing ability to destabilize a general public in a brief timeframe. Numerous people who knew and ignorant of the war have felt the obliteration of that battle. Many individuals had to escape from their local home in light of the fact that the war had become a major issue and lose of life had gotten famous. Practically 2.5 million individuals were said to have

2016 Early Action Decision Timeline - UGA Undergraduate Admissions

2016 Early Action Decision Timeline - UGA Undergraduate Admissions 2016 Early Action Decision Timeline For all of you who are waiting anxiously by your computer/mailbox, nervous about your Early Action decision, here is some good news. UGA is planning on releasing the EA decisions on the myStatus page on Friday, November 20 in the late afternoon, unless some serious problem arises, which I do not expect. If this changes, we will let you know, but this is the plan at this time. If there are issues, the release date and time would then be a little later, either over the weekend or the early part of the next week. Do not call/email/text/message/tweet asking for the exact time of late afternoon, as I cannot give an exact time. We will post a message here when it opens up. We are excited about this, and I am guessing you are as well, and hopefully it will allow for a little less nerve-wracking Thanksgiving break for some of you. In addition to the decisions being available on the myStatus page, letters will go out in the mail for Accepted, Deferred and Incomplete students. Freshman denial letters will not be mailed out, as almost all applicants see their decisions online, and we, along with a number of colleges, did not want to have a letter that only served to reinforce the negative feelings they might already have. Here are a few suggestions on how to react to the four different decisions: Admit: Celebrate with family, buy a lot of UGA gear to wear for the Thanksgiving break, but remember that not everyone has received a decision of admission, and so be a little more low key with friends and classmates. In other words, do not run up to you best friend during English class and scream I got into Georgia while 10-15 of your classmates are mentally creating new and painful ways for you to meet your doom. In addition, be patient with the other parts of campus (commitment deposit, housing, the UGA myID system, etc.), as they might need a few days to take in your information. Remember, it takes a little while for information to flow to other offices. Read the materials we give you online and in an acceptance packet as it will instruct you on what to do next. Defer: This is the most challenging one, as these are applicants who are truly strong students, but we want to see more about them, as well as the rest of the applicant pool, before making a final decision. Please remember, this is not a denial at all, but instead a way for us to be able to review you in full, from your co-curricular activities, your essays, and your recommendations. As I usually state, defer is not a four letter word (even though you might feel this way), only a delay in an admission decision. This is your chance to let us know what you are like as an overall applicant. While this is probably not the answer you would like, I would suggest you treat it as a call-back for a second audition. Some roles have already been cast (or admitted), and we now want to look at you in more detail to see how you compare to the rest of the people auditioning (or applying). One of the worst things you can do is give up and not do the essays. The second worst thing is to call us up and berate us for not admitting you. We will be happy to talk to people, but make sure to communicate in a positive tone, understand that we cannot talk about other applicants, and please remember that defer does not mean denial. In past years, just under half of the deferred applicants who completed part II were later admitted. Each year, about 1,400 deferred students do not complete part II, so we never even have a chance to even review them! If you are serious about UGA, take the time to complete your application, and then be patient as we review all of these files throughout Jan., Feb. and March. When completing part II/the essays, you do NOT need to do an entirely new application, and there is no new/additional application fee. You just need to go to your myStatus page after decisions are out, complete part II/the essays, and hit submit. As well, get a teacher from an academic area to write your teacher recommendation. Remember, UGA is in no way done with the overall freshman admission process. We still have a long way to go, with a great deal of files to read and admission offers to make, so make sure you do your best to show UGA what you are like as an overall student/citizen. Deny: While this is not a fun situation at all, the reality is that if you have been denied Early Action, you are truly not competitive for admission at UGA as compared to the rest of the applicant pool. It is not easy to write that, and it is very difficult to tell this to a student or parent, but when we look at this students application in comparison with the other 14,515 EA applicants (and remember, we expect to get over 9,000 RD applicants as well), they do not match up academically with the others. It is better to tell you now instead of waiting until late March, as this gives you time to make other plans. Unless there seems to be a serious error (you are in the top of your class, take a very challenging course load, and have a strong test score), my suggestion is to not contact us about the decision, but instead move forward with plan B. While we do not mind talking with you at all, the reality is that an Early Action denial means that the admission to UGA is not possible as a freshman. Incomplete: For the small number of students who did not complete your EA file, you are now automatically deferred to the next step, and so you will need to get in the missing materials from EA, and also submit part II of the application and a teacher recommendation. We went three plus weeks beyond the deadline allowing you to get in the missing documents, sending reminder emails, indicating what was missing through the myStatus page, and it was your responsibility to get in the required materials. So I do not suggest contacting us to see if we can take items late, as that time has passed. Focus instead on sending in what is needed to be reviewed in the next round. When completing part II/the essays, you do NOT need/want to do an entirely new application, and there is no new/additional application fee. You just need to go to your myStatus page after decisions are out, complete part II/the essays, and hit submit. Go Dawgs!

Geometric Thinking - Free Essay Example

Students Geometric Thinking 8 CHAPTER 1 Introduction In the last 20 years, the perception of learning as internalization of knowledge is criticized and problemized in mathematics education society (Lave Wenger, 1991; Sfard, 2000; Forman Ansell, 2001). Lave and Wenger (1991) describe learning as a process of increasing participation in communities of practices (p.49). Sfard (2000) also emphasized the new understanding of learning as Today, rather than speaking about acquisition of knowledge, many people prefer to view learning as becoming a participant in a certain discourse (p.160). This new perspective in the understanding of learning brings different views to mathematics teaching practice. While the structure of mathematics lessons is organized in the sequence of Initiation- Response-Evaluation (IRE) in the traditional mathematics classrooms, with the reform movement, participation of the students become the centre of the mathematics classrooms (O Connor, 1993; Steele, 2001). Initiating topic or problems, starting or enhancing discussions, providing explanations are the role of the teacher in the traditional classrooms but these roles become a part of students responsibilities in the reform mathematics classrooms (Forman, 1996). Turkey also tries to organize their mathematics curriculum according to these reform movements. With the new elementary mathematics curriculum, in addition to developing mathematical concepts, the goal of mathematics education is defined as enhancing students problem solving, communication and reasoning abilities. Doing mathematics is no more defined only as remembering basic mathematical facts and rules and following procedures, it also described as solving problems, discussing the ideas and solution strategies, explaining and defending own views, and relating mathematical concepts with other mathematical concepts and disciplines (MEB, 2006). Parallel to new understanding of learning, reform movements in mathematics education, and new Turkish elementary mathematics curriculum, students roles such as developing alternative solution strategies and sharing and discussing these strategies gain great importance in mathematics education. Mathematics teachers are advised to create classroom discourse in which students will be encouraged to use different approaches for solving problems and to justify their thinking. This means that some researches and new mathematics curriculum give so much importance to encourage students to develop alternative problem solving strategies and share them with others. (MEB, 2006; Carpenter, Fennema, Franke, Levi Empson, 1999; Reid, 1995). One of the aims of the new mathematics curriculum is that the students stated their mathematical thinking and their implications during the mathematical problem solving process (MEB, 2006). According to new curriculum, the students should have opportunity to solve the problems using different strategies and to explain their thinking related to problem solving to their friends and teacher. Moreover, the students should state their own mathematical thinking and implications during the problem solving process and they should develop problem solving strategies in mathematics classrooms (MEB, 2006). Fraivillig, Murphy and Fuson (1999) reported that creating this kind of classrooms requires that teacher has knowledge about students mathematical thinking. One of the most important studies related to childrens mathematical thinking is Cognitively Guided Instruction (CGI). The aim of this study is to help the teachers organize and expand their understanding of childrens thinking and to explore how to use this knowledge to make instructional decisions such as choice of problems, questions to ask children to acquire their understanding. The study was conducted from kindergarten through 3rd grade students. At the beginning of the study, researchers tried to explore students problem solving strategies related to content domains addition, subtraction, multiplication and division. The findings from this investigation is that students solve the problems by using direct modeling strategies, counting strategies derived facts strategy and invented algorithms. In order to share their findings with teachers, they conducted workshops. With these workshops, the teachers realized that the students are able to solve the problems using a variety of stra tegies. After this realization, they started to listen to their students mathematical explanations, tried to elicit those strategies by asking questions, tried to understand childrens thinking and encouraged the use of multiple strategies to solve the problems in their classrooms (Franke, Kazemi, 2001, Fennema, Carpenter, Franke, 1992). At the end of the study, the students whose teachers encourage them to solve the questions with different strategies and spend more time for discussing these solutions showed higher performance (Fennema, Carpenter, Franke, Levi, Jacobs, Empson, 1996). Similar finding is also observed the study of Hiebert and Wearne (1993). They concluded that when the students solve few problems, spend more time for each problem and explain their alternative solution strategies, they get higher performance. As indicated the new curriculum in Turkey (MEB,2006), the teacher should create a classroom in which students develop different problem solving strategies, share these with their classmates and their teacher and set a high value on different problem solving strategies during the problem solving process. Encouraging the students to solve the problems is important since while they are solving the problems, they have a chance to overview their own understanding and they take notice of their lack of understandings or misunderstandings (Chi Bassock, 1989, as cited in Webb, Nemer Ing, 2006). Moreover, Forman and Ansell (2001) stated that if the students develop their own problem solving strategies, their self confidence will be increase and they ca n build their mathematical informal knowledge. Not only mathematical thinking, but also geometrical thinking has very crucial role for developing mathematical thinking since National Council of Teachers of Mathematics in USA (2000) stated that geometry offers an aspect of mathematical thinking that is different from, but connected to, the world of numbers (p.97). While students are engaging in shapes, structures and transformations, they understand geometry and also mathematics since these concepts also help them improve their number skills. There are some studies which dealt with childrens thinking but a few of them examine childrens geometrical thinking especially two dimensional and three dimensional geometry. One of the most important studies related to geometrical thinking is van Hiele Theory. The theory categorizes childrens geometrical thinking in a hierarchical structure and there are five hierarchical levels (van Hiele, 1986). According to these levels, initially students recognize the shapes as a whole (Level 0), then they discover the properties of figures and recognize the relationship between the figures and their properties (level 1 and 2). Lastly the students differentiate axioms, definitions and theorems and they prove the theorems (level 3 and 4) (Fuys, Geddes, Tischler, 1988). Besides, there are some other studies which examined geometrical thinking in different point of view. For example, the study of Ng (1998) is related to students understanding in area and volume at grade 4 and 5. But, Battista and Clements (1996) and Ben-Chaim (1985) investigated students geometric thinking by describing students solution strategies and errors in 3-D cube arrays at grades 3, 4 and 5. On the other hand, Chang (1992) carried out a study to understand spatial and geometric reasoning abilities of college students. Besides of these studies, Seil (2000), Olkun (2001), Olkun, Toluk (2004), zbellek (2003) and Okur (2006) have been conducted studies in Turkey. Generally, the studies are about students geometric problem solving strategies (Seil, 2000), the reason of failure in geometry and ways of solution (Okur, 2006), the misconceptions and missing understandings of the students related to the subject angles at grade 6 and 7 (zbellek, 2003). In addition to these, studies has been done to investigate the difficulties of students related to calculating the volume of solids which are formed by the unit cubes (Olkun, 2001), number and geometry concepts and the effects of using materials on students geometric thinking (Olkun Toluk, 2004). When the studies are examined which has been done in Turkey, the number of studies related to spatial ability is limited. Spatial ability is described as the ability to perceive the essential relationships among the elements of a given visual situation and the ability to mentally manipulate one or two elements and is logically related to learning geometry (as cited in Moses, 1977, p.18). Some researchers claimed that it has an important role for mathematics education since spatial skills contribute an important way to the learning of mathematics (Fennema Sherman,1978; Smith, 1964) and Anderson (2000) claimed that mathematical thinking or mathematical ability is strongly related with spatial ability. On the other hand, Moses (1977) and Battista (1990) found that geometric problem solving and achievement are positively correlated with spatial ability. So, developing students spatial ability will have benefit to improve students geometrical and also mathematical thinking and it may fost er students interest in mathematics. Problem Statement Since spatial ability and geometric thinking are basis of mathematics achievement, then one of the problems for researchers may be to investigate students geometric thinking (NCTM, 2000; Anderson, 2000; Fennema Sherman, 1978; Smith, 1964). For this reason, generally this study will focus on students geometrical thinking. Particularly, it deals with how students think in three-dimensional and two-dimensional geometry, their solution strategies in order to solve three-dimensional and two-dimensional geometry problems, the difficulties which they confront with while they are solving them and the misconceptions related to geometry. Also, whether or not the students use their mathematics knowledge or daily life experiences while solving geometry questions are the main questions for this study. Purpose Statement The purpose of this study is to assess and describe students geometric thinking. Particularly, its purpose is to explain how the students approach to three-dimensional geometry, how they solve the questions related to three-dimensional geometry, what kind of solution strategies they develop, and what kind of difficulties they are confronted with when they are solving three-dimensional geometry problems. Also, the other purpose is to analyze how students associate their mathematics knowledge and daily life experience with geometry. The study attempt to answer the following questions: 1. How do 4th, 5th, 6th, 7th and 8th grade elementary students solve the questions related to three-dimensional geometry problems? 2. What kind of solution strategies do 4th, 5th, 6th, 7th and 8th elementary students develop in order to solve three-dimensional geometry problems? 3. What kind of difficulties do 4th, 5th, 6th, 7th and 8th elementary students face with while they are solving three-dimensional geometry problems? 4. How do 4th, 5th, 6th, 7th and 8th elementary students associate their mathematics knowledge and daily life experience with geometry problems? Rationale Most of the countries have changed their educational program in order to make learning be more meaningful (NCTM, 2000; MEB, 2006). The development of Turkish curriculum from 2003 to up till now can be assessed the part of the international educational reform. Particularly, the aim of the changes in elementary mathematics education is to make the students give meaning to learning by concretizing in their mind and to make the learning be more meaningful (MEB, 2006). In order to make learning more meaningful, knowing how the students think is critically important. For this reason, this study will investigate students mathematical thinking especially geometrical thinking since geometry provides opportunity to encourage students mathematical thinking (NCTM,2006). The result of the international exams such as Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) and national exams Secondary School Entrance Exam Ortaretim Kurumlar renci Seme Snav (OKS) show that the success of Turkish students in mathematics and especially in geometry is too low. Ministry of National Education in Turkey stated that although international average is 487 at TIMSS-1999, Turkish students mathematics average is 429. Moreover, they are 31st country among 38 countries. When the sub topics are analyzed, geometry has least average (EARGED, 2003). The similar result can be seen the Programme for International Student Assessment (PISA). According to result of PISA-2003, Turkish students are 28th county among 40 countries and Turkish students mathematics average is 423 but the international average is 489. When geometry average is considered, it is not different from the result of TIMSS-1999 since intern ational geometry average is 486 but the average of Turkey is 417 ((EARGED, 2005). As it can be realized from result of both TIMSS-1999 and PISA-2003, Turkish students average is significantly lower than the international average. Since in order to get higher mathematical performance, being aware of childrens mathematical thinking has crucial role (Fennema, Carpenter, Franke, Levi, Jacobs, Empson, 1996). For this reason, knowing students geometric thinking, their solution strategies and their difficulties related to geometry problems will help to explore some of the reasons of Turkish students low geometry performance in international assessment, Trends in International Mathematics and Science Study (TIMSS) and Program for International Student Assessment (PISA), and in national assessment, Secondary School Entrance Exam Ortaretim Kurumlar renci Seme Snav (OKS). As a result, when geometry and being aware of students problems solving strategies and their difficulties when they are solving geometry problems has important roles on mathematics achievement are taken into consideration, studies related to geometry and students geometric thinking are needed. Besides, Turkish students performance in international assessments is considered; it is not difficult to realize that there should be more studies related to geometry. For these reasons, the study will assist in Turkish education literature. Significance of the Study Teachers knowledge about childrens mathematical thinking effect their instructional method. They teach the subjects in the way of childrens thinking and they encourage students to think over the problems and to develop solution strategies. With such instructional method, classes are more successful (Fennema, Carpenter, Franke, 1992). Geometry is one of the sub topic of mathematics (MEB,2006) and it has crucial role in representing and solving problems in other sub topics of mathematics. Besides, geometry has important contribution to develop childrens mathematical thinking. On the other hand, in order to understand geometry, spatial ability is useful tool (NCTM, 2000). Battista et al.(1998), Fennema and Tartre (1985) and Moses (1977) emphasized that there is a relationship between spatial ability and achievement in geometry. Moreover, mathematical thinking and mathematical ability is positively correlated with spatial thinking (Anderson 2000). Since geometry, spatial ability and mathematical thinking are positively correlated, being successful in geometry will get higher mathematics achievement. To increase geometry achievement, the teachers should know students geometric thinking. Particularly, how students solve problems, what kind of strategies they develop, and what kind of difficulties they face with while t hey are solving the problems are important concepts in order to get idea about students thinking (Fennema, Carpenter, Franke, 1992). With this study, the teachers will be informed how children think while they are solving geometry problems especially three-dimensional geometry problems, what kind of strategies they develop to solve them, what kind of difficulties they face with related to geometry problems. Furthermore, university instructors will benefit from this study to have knowledge about childrens geometric thinking and this knowledge may be valuable for them. Since they may inform pre-service teachers about childrens thinking and the importance of knowing childrens thinking while making instructional decisions. As a result, knowing students geometric thinking will benefit to increase their geometry achievement and also mathematical achievement, and consequently, this will help to raise the Turkish students success of the international exams CHAPTER 2 Literature Review Geometry can be considered as the part of mathematics and it provides opportunities to encourage students mathematical thinking. Also, geometry offers students an aspect of mathematical thinking since when students engage in geometry, they become familiar with shape, location and transformation, and they also understand other mathematics topics (NCTM, 2000). Therefore, understanding of students geometrical thinking, their geometry problem solving strategies and their difficulties in geometry become the base for their mathematical thinking. Also, since geometry is a science of space as well as logical structure, to understand students geometrical thinking requires knowledge of spatial ability and cognitive ability (NCTM, 1989, p.48). This chapter deals with some of the literature in four areas related to the problem of this study. The first section of this chapter is related to the van Hiele theory since van Hiele theory explains the level of childrens geometrical thinking (van Hiele, 1986). The second section of this chapter deals with the research studies related to students mathematical and geometrical thinking. The third section is devoted to research studies related to spatial ability. And the last section of this chapter reviews the research related to relationship between spatial ability and mathematics achievement. Section 1: The van Hiele Theory The van Hiele theory is related to childrens thinking especially their geometrical thinking since the theory categorizes childrens geometrical thinking in a hierarchical structure (van Hiele, 1986). According to theory of Pierre and Diana van Hiele, students learn the geometry subjects through levels of thought and they stated that the van Hiele Theory provided instructional direction to the learning and teaching of geometry. The van Hiele model has five hierarchical sequences. Van Hiele stated that each level has its own language because in each level, the connection of the terms, definitions, logic and symbol are different. The first level is visual level (level 0) (van Hiele, 1986). In this level, children recognize the figures according to their appearance. They might distinguish one figure to another but they do not consider the geometric properties of the figures. For instance, they do not consider the rectangle as a type of a parallelogram. The second level is descriptive leve l (level 1). In this level, students recognize the shapes by their properties. For instance, a student might think of a square which has four equal sides, four equal angles and equal diagonals. But they can not make relationships between these properties. For example, they can not grasp that equal diagonal can be deduced from equal sides and equal angles. The third level is theoretical level (level 3). The students can recognize the relationship between the figures and the properties. They discover properties of various shapes. For instance, some of the properties of the square satisfy the definition of the rectangle and they conclude that every square is a rectangle. The fourth level is formal logic level (level 4). The students realize the differences between axioms, definitions and theorems. Also, they prove the theorems and make relationships between the theorems. The fifth level is rigor level (level 4). In this level, students establish the theorems in different postulation sy stems (Fuys, Geddes, Tischler, 1988). As a result, the levels give information about students geometric thinking to the researchers and mathematics teachers. Mathematics teachers may guess whether the geometry problem will be solved by students or not and at which grade they will solve them. Section 2: Children thinking The van Hiele theory explains the students thinking level in geometry. The levels are important but how students think is as important as their thinking level. To ascertain how students think related to mathematics and especially geometry, a number of studies have been conducted (Carpenter, Fennema, Franke, 1996; Chang, 1992; Battista, Clements, 1995; zbellek, 2003; Olkun, 2005; Ng, 1998; Okur, 2006). Some of these studies are related to mathematical thinking and some of them geometrical thinking. Carpenter et al. (1999) and Olkun (2005) studied 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 related to childrens geometrical thinking. An important study related to mathematical thinking has been conduct by Carpenter, Fennema and Franke initiated over 15 years ago in USA and the name of this study is Cognitively Guided Instruction (CGI) which is described as the teacher development program. Cognitively Guided Instruction sought to bring together research on the development of childrens mathematical thinking and research on teaching (Franke, Kazemi, 2001). Carpenter, Fennema and Franke (1996) stated that Cognitively Guided Instruction (CGI) focuses on childrens understanding of specific mathematical concepts which provide a basis for teachers to develop their knowledge more broadly. The Cognitively Guided Instruction (CGI) Professional Development Program engages teachers in learning about the development of childrens mathematical thinking within particular content domains. (Carpenter, Fennema, Franke, Levi, Empson, 1999). These content domains include investigation of childrens thinking at different problem situat ions that characterize addition, subtraction, multiplication and division (Fennema, Carpenter, Franke, 1992). In order to understand how the children categorize the problems, Carpenter et al. (1992) conducted a study. According to this study, Fennema, Carpenter, and Franke (1996) portrayed how basic concepts of addition, subtraction, multiplication, and division develop in children and how they can construct concepts of place value and multidigit computational procedures based on their intuitive mathematical knowledge. At the end of this study, with the help of childrens actions and relations in the problem, for addition and subtraction, four basic classes of problems can be identified: Join Separate, Part-Part-Whole, and Compare and Carpenter et all. (1999) reported that according to these problem types, children develop different strategies to solve them. The similar study has been carried out by Olkun et al (2005) in Turkey. The purpose of these two studies is the same but the s ubjects and the grade level are different. Olkun et al (2005) studied with the students from kindergarten to 5th grade but the students who participated in Carpenters study is from kindergarten through 3rd grade (Fennema, Carpenter, Franke, 1992). Furthermore, CGI is related to concepts addition, subtraction, multiplication and division but the content of the study done in Turkey is addition, multiplication, number and geometrical concepts (Olkun et al, 2005). Although the grade level and the subjects were different, for the same subjects, addition and multiplication, the solution strategies of the students in Olkuns study are almost the same as the students in CGI. But the students in the study of Carpenter used wider variety of strategies than the students in Turkey even if they are smaller than the students who participated in Olkuns study. This means that grade level or age is not important for developing problem solving strategies. On the other hand, there are some studies related to childrens geometrical thinking which are interested in different side of geometrical thinking. Ng (1998) had conducted a study related to students understanding in area and volume. There were seven participants at grade 4 and 5. For the study, she interviewed with all participants one by one and she presented her dialogues with students while they are solving the questions. She reported that students who participated in the study voluntarily have different understanding level for the concepts of area, and volume. She explained that when students pass from one level to another, 4th grade to 5th grade, their thinking becomes more integrated. With regard 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 three-dimensional geometry. These levels were determined by the Spatial Geometry test. According to this study, students at lower levels of thinking use more manipulative and less definitions and theorems to solve the problems than high level of thinking. On the other hand, the levels of two-dimensional geometry identified by the van Hiele theory. The results were the same as the three-dimensional geometry. In this case, Chang (1992) stated that the students at the lower levels of thinking request more apparatus and less definitions and theorems to solve the problems. Moreover, for both cases, the students at the higher levels of thinking want manipulative at the later times in the problem-solving process than the students at the lower level of students. The result of this study indicated that using manipulative require higher level of thinking. By providing necessary manipulative, I hope th e students use higher level of thinking and solve the problems with different strategy. Besides of these studies, Ben-Chaim et all. (1985) carried out the study to investigate errors in the three-dimensional geometry. They reported four types of errors on the problem related to determining the volume of the three-dimensional objects which are composed of the cubes. Particularly, they categorize these errors two major types which students made. These major types of errors defined as dealing with two dimensional rather than three and not counting hidden cubes (Ben-Chaim, 1985). The similar study was conducted by Olkun (2001). The aim of this study is to explain students difficulties which they faced with calculating the volume of the solids. He concluded that while students were finding the volume of the rectangular solids with the help of the unit cubes, most of the students were forced open to find the number of the unit cubes in the rectangular solids. Also, the students found the big prism complicated and they were forced open to give life to the organization of the p rism which was formed by the unit cubes based on the column, line and layers in their mind, i.e. they got stuck on to imagine the prism readily. (Olkun, 2001). The categorization of students difficulties will 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 respect such as Battista and Clements categorized problem solving strategies but Ben-Chaim and Olkun defined students difficulties while reaching correct answer. Categorization of the students problem solving strategies in the study of Battista and Clements (1996) is like the following: Category A: The students conceptualized the set of cubes as a 3-D rectangular array organized into layers. Category B: The students conceptualized the set of cubes as space filling, attempting to count all cubes in the interior and exterior. Category C: The students conceptualized the set of cubes in terms of its faces; he or she counted all or a subset of the visible faces of cubes. Category D: The students explicitly used the formula L x W x H, but with no indication that he or she understood the formula in terms of layers. Category E: Other. This category includes strategies such as multiplying the number of squares on one face times the number on other face. (Battista Clements ,1996). At another study of Battista and Clements (1998), their categorization was nearly the same but their names were different than the study which has done in 1996. In this study, they categorized the strategies as seeing buildings as unstructured sets of cubes, seeing buildings as unstructured sets of cubes, seeing buildings as space filling, seeing buildings in terms of layer and use of formula. Battista and Clements (1996, 1998) concluded that spatial structuring is basic concept to understand students strategies for calculating the volume of the objects which are formed by the cubes. Students should establish the units, establish relationships between units and comprehend 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 categorization of students geometry problems strategies will 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) have been conducted studies in Turkey. Seil (2000) has investigated students problem solving strategies in geometry and Okur (2006) have studied the reason of failure in geometry and ways of solution. In the study of zbellek, the misconceptions and missing understandings of the students related to the subject angles at grade 6 and 7. Also, studies has been done to investigate the difficulties of students related to calculating the volume of solids which are formed 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. Some of them were related to children mathematical thinking and some of them were interested 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 common idea is that spatial ability and geometrical thinking are correlated positively. Since spatial reasoning is intellectual operation to construct an organization or form for objects and it has important role to for constructing students geometric knowledge (Battista, 1998). Section 3: Spatial Ability The USA National Council of Teachers of Mathematics (2000)explained that the spatial ability is useful tool to interpret, understand and appreciate 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 invert a pictorially presented stimulus object. Since spatial ability is important for childrens geometric thinking, the development of it has been investigated by several studies. First and foremost study has been carried by Piaget and Inhelder (1967). Piaget et al. (1967) defined the development of spatial ability in young children and the properties of the task they accomplish as they grow up. Piaget divides the development of children into four stages (Malerstein Ahern, 1979). According to the Childs Conception of Space (1967), in the first stage, sensorimotor stage, the children recognize only the shapes, not recognizes differences between the shapes. In the second stage, preoperational stage, children recognize figures different shapes, differentiate lines from curve. In the third stage, operational stage, children understand the X-Y axis. This means that they coordinate the point according to the reference point. And finally, in the fourth stage, formal operational stage, children reach the concept of proportionality for all dimensional relations. In the Childs Conception of Geometry (1960), Piaget and Inhelder connect the spatial ability and geometric understanding. They describe the childrens understanding of conservation, measurement of length, area, and volume. When the children reach stage three, they comprehend the measurement, conversation, area and volume. According to Piaget, understanding of children changes when they grow up, from stage to stage. On the other hand, some researchers claimed that spatial ability does not depend on the age. It depends on learning.) have demonstrated that ability to represent three-dimensional objects with two-dimensional drawings can be learned at any age. As a result, spatial ability is positively correlated with geometry learning. Piaget and Inhelder (1967) claimed that spatial ability develops with increasing age but other researchers do not agree the claim of Piaget (Bishop, 1979; and Presmag, 1989). They demonstrated that spatial ability is not related to age, it is related to function of learning. Section 4: The Relationship between Spatial Ability and Mathematics Achievement Large number of researchers thought that spatial ability has an important role in mathematics learning. Battista (1980), Fennema and Sherman (1977), Fennema and Tartre (1985), Ferrini-Mundy (1987), and Moses (1977) have been carried out studies to explore the relationship between spatial ability, mathematical problem-solving and mathematics achievement. The results of these studies are inconsistent and unclear. The relationship between spatial ability and mathematical achievement are different from one study to another. In the field of mathematics, some mathematicians have claimed that all mathematical tasks require spatial thinking (as cited in Lean Clements, 1981, p.267). Moses (1977) reported that in order to improve students mathematical performance, they should be trained on spatial tasks. The results of several studies supported this claim and they showed that spatial ability and mathematical achievement are positively correlated (Aiken, 1971; Battista, 1980; Fennema Sherman ,1977) and Battista (1990) explained this correlation in the range of .30 to .60. The study of Fennema and Sherman (1977) verified this result and they specified that spatial ability and mathematical achievement are positively related. This means that there is direct proportion between spatial ability and mathematical problem-solving and Smith (1964) confirmed that if a person solve high-level mathematical problem, s/he generally have greater spatial ability than person who cannot solve high-level mathematical problem. N evertheless, Battista (1990) investigated the role of spatial thinking and logical reasoning in high school geometry. According to the results of the study showed that spatial thinking and logical reasoning are significantly related to geometry achievement and problem-solving. Particularly, geometric problem-solving correlated higher with spatial thinking than logical reasoning. But on the other hand, Fennema and Tartre (1985) reported that spatial ability does not guarantee success in problem-solving in their later study. Battista et al. (1982) agreed their findings since after investigating the relationship between spatial ability and mathematics performance, the role of spatial thinking in mathematical performance did not described adequately. It is not known that how important spatial ability is to learn several topics in mathematics. Lean and Clementss studies (1981) supported the findings of Battista et al. Lean and Clements (1981) claimed that there is not any correlation between them. Moreover, Chase (1960) agrees the findings of Lean and Clements and Battista et all. Since Chase found that spatial ability did not have any contribution to the problem-solving ability. As a result, there has been several research related to spatial ability and mathematics achievement. Although some researches claimed that there is positive correlation between spatial ability and mathematics achievement, some of them reported that the relationship between them have not described adequately yet. Summary The aim of this literature review to present the result of earlier studies related to van Hiele theory, childrens thinking, spatial ability and lastly the relationship between spatial ability and mathematics performance. According to van Hiele, there is a hierarchical structure of the levels of childrens thinking and the progress of thinking depends on instruction. On the other hand, Piaget claimed that the progress of thinking develops when the child grows up. Several studies have been conducted to understand children thinking and most of the studies found that geometrical thinking is positively correlated with spatial thinking and spatial thinking is related to mathematical achievement. Since the purpose of study is to explore and assess the students geometrical thinking, these studies are related to my study and I get related information from them in terms of level of geometric thinking of van Hiele Theory, difficulties of students while solving geometry problems and categorization of the strategies to solve geometry problems. CHAPTER 3 Methodology This study is designed to explore and assess elementary students geometrical thinking. Particularly, it is concerned with how students solve the questions related to three-dimensional and two-dimensional geometry, what kind of strategies they develop, and what kind of difficulties they are confronted with when they are solving these kinds of problems. Sampling This study will be conducted in a private elementary school in Istanbul during the fall semester of 2007 and approximately 25 students from this school will be selected. In order to select the school and the students, convenience sampling method will be used. Since I plan to find out students different solution strategies, the criterion of the selection of the students will be mathematics and geometry achievement of the students. To increase variety of students solution strategies, the grade level of the students will be different and the students will be 5th, 6th, 7th and 8th grade students. Instrumentation In order to collect data, approximately 10 questions related to three-dimensional geometry will be asked. These questions have been taken from the articles ( Haws, 2002; Ben-Haim, 1985; Battista, Clements, 1996) and the dissertation (Ng, 1998). The questions were translated from English to Turkish using back translation method. In line with this method, I translated the questions from English to Turkish and one of my friends who is an English teacher translated Turkish version to English. Then I compared the original version of the questions with the translation of my friend. Also, I asked for advice to my advisor and other instructors. In order to select the questions, the important factor is that the students can solve the questions by using more than one solution method. The following questions are examples. In both questions, the possible solution method can be the followings. 1. Counting the cubes by using materials 2. Counting from the figure 3. Counting the layers of the cubes 4. Using the formula of volume of cube Moreover, to realize how students solve the questions, there will be some materials such as base-ten blocks and unit cubes. I provide these materials to make the students solve the problems with different methods. Consequently, while I was selecting the questions, I take care of having more than one solution strategies. Data Collection The data will be collected from approximately 25 students in an elementary school in stanbul in October and November of 2007. . During the data collection period, firstly I will interview with the students teacher. I will want them predict whether their students solve the questions or not, what strategies the students will be use, what kind of difficulties they may confront while they are solving them, and so on. The aim of this interview is to learn how much teachers know students geometric knowledge and thinking. Secondly, I will interview with students one by one. At the beginning of the interview, I will not tell anything to them. I want them think and solve the questions. While they are solving the questions, I will use the think aloud method to clarify students thoughts. Particularly, with think aloud method, I will make the students tell what they think while they are solving a problem. During problem solving process, I will encourage them tell how they find the solution of th e problem and I will ask some prompting questions to get more information about what they think while they are solving the problems. During the interview, if possible, I will videotape or audiotape. If it is not possible, I will take detailed notes. After I analysis the data, if there is some missing part or unclear part, I will interview with the same students again. When I finish the interviews with the students and analyze the data, I will share this information with the teacher and I try to state how much they know their students thinking or geometry achievement expressly. Data Analysis The data analysis mainly based on the study of Battista and Clements (1996) for some questions. In this study, they categorized students strategies for finding the number of cubes in a rectangular prism. In this categorization, there are 5 basic groups and each group has some sub groups. After I get the data, I will match students strategies with these strategies and the problem solving strategies which is presented by Ministry of National Education in Turkey. These strategies are listed below (MEB, 2006): Trial and error Using shapes, tables, etc. Using materials Searching pattern Working backwards Guess Using assumptions Expressing the problem differently Implication Using equations Animation and imagine Also, I will categorize the solution strategies by taking care of whether they use materials or formulas to solve them or not. On the other hand, I will explain the difficulties which the students confronted with while they are solving the questions. At the end of the study, I hope to get different solution strategies of students to categorize them. Since this study is qualitative study, while I am collecting and analyzing the data, I should establish the trustworthiness of the procedures such as voluntary participation and guarantee of anonymity, purposeful sampling, triangulation, prolonged engagement, natural situation, peer debriefing and member checks. The students who will participate in the study will be volunteers. If they did not want to participate in the study, I will not force them even if their geometry achievement is higher. The students will be selected from the elementary school which is convenience for me and they will be selected according to their mathematics and geometry achievement. Most probably, the students will be my students so there will be no problem related to mutual comfort. Also, the identity of the students will be secret. On the other hand, I will get data from different sources by interviewing the teachers and I will share my results with them. So they may control my results. Furthermore, in ter ms of member checking, I will share my interpretations with the students whether I comprehend and interpret their problem strategies or not. The data collection and data analysis part will take approximately 4 months. Limitations The aim of the study is to define students solution strategies and their difficulties. I will plan to categorize students strategies. If students do not solve problems by using different strategies, than I may not get sufficient information. To overcome his limitation, I will choose the participants according to their mathematics achievement and I may make them think over the problems to solve the problems in different way. The other limitation is that if I could not audiotape or videotape the interviews, I may be forced to collect data and analyze the data. Also, in order to provide mutual comfort, I plan to choose participants from the school which I will work. 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