Problem Solving Geometry of Visualization, Analysis, and Informal Deduction Subject Based on SOLO Taxonomy

Problem solving is a way which will be conducted someone by employing acquired skills, knowledge, and understanding in order to solve certain problem. Problem solving stages which attained in this research is according to Polya which encompasses comprehending problem, arranging plan completion, and rechecking the result. Mathematics concept understanding is required in order to solve the problem. SOLO Taxonomy classifies the subject’s ability of solving problem into five different level, prestructural, unistructural, multistructural, relational, and extended abstract. The aim of this research is to describe geometry problem solving of visualization, analysis and informal deduction according to SOLO Taxonomy. Additionally, qualitative descriptive method is used to analyze the data. Subjects of this research are subjects who possess high mathematics thinking ability of visualization geometry, analysis and informal deduction. Besides, the type of data collection technique uses problem solving geometry test and interview. According to the result of research, subjects who possess in visualization geometry thinking level to solve the problem tend to use the aspect of unistructural level of SOLO Taxonomy. Then, subjects with analysis geometry thinking level to solve the problem mostly use multistructural level of SOLO Taxonomy. Lastly, subjects who own informal deduction geometry thinking level to solve the problem apparently use relational level of SOLO Taxonomy.


INTRODUCTION
Mathematics is one of the important lessons and always taught in various ladder of education starting from the very basic school.It is based on content standard for elementary school and junior high school in mathematics (Regulation Minister National Education No.22 of 2006 content on standard).Geometry is one of the important materials in mathematics according to Usiskin [1] and Van de Walle [2].The aim of learning geometry is that subjects are expected to analyze problem, solve problems, and build a relation between mathematics and real life.(Yildiz et al., [3]; Aydogdu [4].According to the NCTM [5], "The Geometry Standard takes a broader view of the power of geometry by calling on subjects to analyze characteristics of geometric shapes and the make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems ".However, the results from some research shows that there are some learners that still have difficulties in solving issues related to geometry as on the research of Clement and Sarama [6]. Problem solving is a way to overcome issues that someone can do by using skills, knowledge, and understanding for each problem.(Krulik and Rudnick [7]; Aydogdu [4]).Polya [8] defines 4 stages in solving problem, they are: (1) understanding the problem; (2) devising a plan; (3) carrying out the plan (4) looking back.To solve mathematic problem especially geometry, subjects are required to be able to understand the concepts of mathematics and could apply it in solving a problem.To use the right concept for solving problems, subjects must have a good thinking skill.Furthermore, thinking skill could be classified in SOLO Taxonomy.SOLO Taxonomy classifies subject's understanding ability in solving a problem into five different levels, namely: prestructural, unistructural, multistructural, relational and extended abstract.Levels on SOLO Taxonomy describe subject's ability in stirring concept for solving problems.Jurdak [9] in his study made a comparison between Van Hiele geometrical thinking skills and SOLO model used in this study.SOLO levels created for determining the levels of responses provided by subjects not for determining the levels of subjects.Therefore, in this comparison the aim was generally to determine at which Van Hiele level the students were according to their own responses.

METHODS
The purpose of this study is to describe the geometry problem solving of student's visualization, analysis and informal deduction according to SOLO Taxonomy.This study used descriptive qualitative approach that produced descriptive data.The subject of this study is a student of ninth grade who has studied the geometric concept.Technique of data collecting were conducted with task of concept understanding and task-based interviews

RESULTS AND DISCUSSION
Based on the result analysis from the three subjects having different thinking skill in geometry, researcher obtains the problem solving in geometry problem.For the geometry achievement test solving are as following:  In the step of devising a plan, subject of visualization is able to determine concepts, principles, procedures or the relevant methods with accomplishing problem.He can indeed mention these two concepts, namely the volume of the tube and the volume of the beam, but in fact, when he was asked about the formula of tube volume, he could not explain it.Furthermore, he was reasoning that he has forgotten about the formula of the tube volume.In the step of carrying out the plan, subject visualization uses the concept, principle, procedures or the relevant methods to settle the problem but the conclusions obtained are irrelevant.He can only understand and complete the course of the procedure, namely the volume of the beam, he did not know the relationship between the concepts A full of water tubular can with a diameter base of 14 cm and 10 cm height.When the water is poured entirely into an empty shaped-beam canister with a rectangular base that has a length and a width of 10 cm and 7 cm respectively, and the height of the Problem 2: A full of water beam can with a rectangular base that has a length and a width of 12 cm and 11 cm respectively, and the height the can is 28 cm.When the water is poured entirely into an empty shape-tubular canister with a diameter base of 14 cm and 20 cm that exist on the matter.He reasoned that he did not like about the geometry or materials of space.Therefore, he did not pay attention when the teacher explains the material geometry.For the step of looking back, SV is to recheck the process or procedures.He did re-examine the process and results by means of double-checking the formula back and recalculate the results.This could be seen from the following interview transcription.However, he added a picture as an illustration or modeling so that he can easily do the given test.In the step of devising a plan, subject analysis is aimed to determine some concepts, principles, procedures or the relevant methods with solving any problem.He can mention two concepts, namely the volume of the tube and the volume of beams and also the formula of both.Furthermore, he gives the reason why he was choosing a formula which is because of a known volume of the matter is the content block and the contents of the tube.In the step of carrying out a plan subject analysis uses some concepts, principles, procedures or the relevant methods for solving problem but the conclusions obtained are irrelevant.He may complete the analysis of several procedures that solve the beam and cube volume and subtracting both.But he did not know the relationship between concepts.Therefore, the questions asked in the question is unanswered.In the step of looking back, subject analysis can recheck process or procedures.He did reexamine the analysis of the process and results by means of double-checking the formula back and recalculate the results.This could be seen from the following interview transcription.problem and said the reason that what is known and what is being asked that is already listed in the matter.In the step of devising a plan, informal subject deduction determines some of the concepts, principles, procedures or methods that are relevant to solving problem.He can mention two concepts, namely the volume of the tube and the volume of beams and also mention the formula of both.Furthermore, he gives the reason why choosing a formula for a known volume of the matter which are the content beam and the contents of the tube.In the step of carrying out a plan, informal subject deduction was able to find the relationship of concepts, principles, procedures, or methods that are relevant and also able to apply it, then linking with other data and processes so as to draw the relevant conclusions.He can complete the test from the mentioned formulas to be used, give reasons why he is using these formulas, to tell his own process of work on the problems that he was working on.Furthermore, he is also capable of connecting concepts, principle, and procedures that he already knew that the answers he got was relevant to what was requested.In the step of looking back, informal subject deduction is to check back processes or procedures.He did re-examine the process and results by means of double-checking the formula back and recalculate the results.But he could not solve the problem using another way.This could be seen from the following interview.

CONCLUSION
In this step of understanding the problem, the subject visualization, analysis and informal deduction can identify what is known and what is being asked.However, subject analysis also added a picture as an illustration or modeling so that he can easily solve a given problem.In the step of devising a plan, the subject visualization can only mention a concept or a formula related to the matter.But subject analysis and informal deduction are able to mention a few concepts or formulas relating to the matter.In the step of carrying out a plan, only informal subject deduction can solve problems to obtain the relevant answers.This is because the informal subject deduction can connect multiple concepts or formulas that he had known.It is in contrast with the subject analysis that know some concept or formula but he cannot connect between the concept or formula.Moreover, subject analysis only knows one concept or formula.However, he cannot resolve the matter to obtain relevant answers.Finally, In the step of looking back, subject visualization, analysis and informal deduction are alike which is to re-examine the process or procedure that has been done.All in all, subjects who possess in visualization geometry thinking level tend to use the aspect of unistructural.Then, subjects who possess in visualization geometry thinking level to solve the problem tend to use the aspect of unistructural level of SOLO Taxonomy.Then, subjects with analysis geometry thinking level to solve the problem mostly use multistructural level of SOLO Taxonomy.Lastly, subjects who own informal deduction geometry thinking level to solve the problem apparently uses relational level of SOLO Taxonomy.It's corresponds to Jurdak [9], "There seems to be theoretical as well as empirical support for the possibility of matching the SOLO and Van Hiele levels".

Figure 3 .Figure 4 .
Figure 3.The answer given by visualization subject's to GAT 1

Figure 7 . 1 Figure 8 .
Figure 7.The answer given by analysis subject to GAT 1

P:
Are you sure about your answer?S: Yes, I am P: How many times did you check your answer?S: 3 -4 times approximately P: How did you check that?S: I rechecked my answers by matching it P: Are you sure about your answer?S: Yes sir.P: How many times did you check your answer?S: 3 -4 times approximately P: How did you check that?S: I rechecked my answers by matching it with

Figure 11 .Figure 12 .
Figure 11.The answer given by informal deduction subject's to GAT 1

Figure 13 .Figure 14 .
Figure 13.The interview transcription on GAT 1 Figure 14.The interview transcription on GAT 2 P: Then, are you sure about your answer?S: Yes, I am P: How many times did you check your answer?S: I did check the answers several times P: How did you check that?S: I rechecked my answers by matching it with P: Then, are you sure about your answer?S: Yes, I am P: How many times did you check your answer?S: I did check the answers several times P: How did you check that?S: I rechecked my answers by matching it with