RME (Realistic Mathematics Education) is a constructional approach which connect Mathematics with the human truth or reality. One way to apply this constructional approach is giving contextual problems to the students. The fact that most of nowadays students are lazy to read and they don’t like Mathematics problems in the form of text. And of course their ability of understanding a text may inﬂuence the result they get in doing van Hiele Test (VHT) because VHT needs good reading comprehension to be able to do it well. RME should be a fun constructional approach to connect Mathematics with reality of life. Contextual problems in the form of text should be a fun Mathematics problem for student who understand it.

The idea to ﬁnd correlation of students’ reading ability and geometrical thinking level came when the VHT was given to students as pretest of an experiment. Some of students directly asked what the number eleven means. For the teacher, the question is easy enough to understand but not for the students. This caused the teacher thought that their reading comprehension ability was not good enough, and this could make the students got low level of van Hiele geometrical thinking. On the other hand, the higher level of van Hiele test, the more words and sentences in the questions. So, it is no wonder why the students who had low ability of reading comprehension would get low level of van Hiele geometrical thinking. This became the reason for the researcher to proof the correlation of students’ reading comprehension ability and their geometrical thinking levels. Therefore, the aim of this research is to describe the relation between reading comprehension ability and geometrical thinking.

In his journal, Vellem

For senior high school students in SMA or MA as the native speaker of Bahasa Indonesia, they should reach the highest level of reading comprehension. They should be able to understand and interpret a text. In mathematics, this ability can be tested by asking the students change the contextual mathematics problems into mathematics models.

While in van Hiele Theory, there are 5 levels of geometrical understanding. The higher the level is, the many more words or sentence in the geometry problem given. These van Hiele levels are described by van Hiele in many places. The geometrical thinking levels given by van Hiele are: Level 1 Recognition or visualization, Level 2 analysis, Level 3 order or abstraction, Level 4 deduction and Level 5 rigor. At level 1 or Recognition, students are able to recognize the name of shapes, but they think that square and rectangle are so different, they think that nothing of them are same. At level 2 or analysis, students are able to identify the characteristics of shapes, and they would say that a rectangle has four right angles. At level 3 or order, students can logically construct the shapes and construct the relation of the shapes, but they cannot operate them in Mathematics system. In this third level, a simple deduction can be followed by them, but they do not understand the prooﬁng. At level 4 or deduction, students understand the importance of deduction, the role of postulates, theorems and proofs. In this forth level, they can write the proof by their own understanding. At level 5 which is called Rigor, students are very careful and thoroughly strict using the rules of geometry. In this highest level of geometrical thinking, the students do understand the importance of carefully works and they can make abstract deductions

The van Hiele test in Usiskin modified by Rofii

A student is considered to be in a level when he completed the previous levels. Student who completed a level without completing the previous level considered to get correct answer by guessing, so he is not considered to be in that level. Students who are not able to complete the ﬁrst level is considered to be in zero level.

Blankenship

Magi

Vista

Isphording

Mohd Salleh Abu

Jiri

Bulut

Although in the above studies using van Hiele questions at level 1, 2 and 3 for students at those schools, researchers tried to give questions at level 4 and 5 on this research because researchers were optimistic that there would be level 4 in the research subject and it is possible that there would be students who reach the rigor level considering that one of their senior was a champion of the provincial level mathematics olympiade.

This is a correlational designed research. The research was done in Madrasah Aliyah Negeri 2 Jember, Jawa Timur, Indonesia. It is a state islamic Senior High School under the religion ministry. The research started at the beginning of November 2018 and ﬁnished at the end of December 2018. The population of this research was 31 students of a natural science class. The aim of this research is to know the correlation of students’ reading comprehension and geometrical thinking levels.

The subjects of this research were students of X.IPA.5, a superior natural science class at Madrasah Aliyah Negeri 2 Jember. Their age range from 15 to 17 years old. We chose this class because after doing van Hiele Test in all ten grade classes at Madrasah Aliyah 2 Jember, the results of the test indicate that class X.IPA.5 gives the most varied results in grouping the level of students’ geometric thinking. In other classes, students reached the maximum level was at level 2. But in this superior class, there was a student who reached level 3 and 2 students who reached level 4. The results of the Van Hiele test on this class of achievement can be seen in table 1.

vHT resut of X.IPA.5 students

van Hiele Level | Students | Percentage |

0 | 6 | 19% |

1 | 12 | 39% |

2 | 10 | 32% |

3 | 1 | 3% |

4 | 2 | 6% |

5 | 0 | 0% |

Total | 31 | 100% |

The ﬁrst collected data was the geometrical thinking levels and the reading comprehension scores of 31 students in class X.IPA.5. The level of students ’geometry thinking was measured using van Hiele Test (VHT) and the students’ ability to understand the text was done by giving contextual problems as a Reading Comprehension Test (RCT). The type of data collected is quantitative data.

The instrument used to collect data in this study is the van Hiele test (VHT) which consists of 25 multiple choice questions and Reading Comprehension Test (RCT). There are 5 questions for each van Hiele level. For students at level one, he really understands the names of shapes and will not be confused even though the shape is tilted. The following is an example of the level one van Hiele question in number 4.

Figure for van Hiele Question Number 4.

"Which of these are squares?

Students who are at level 2 already understand the characteristics of shapes. Students get questions related to the characteristics of shapes like the questions in number 6 below

Figure for van Hiele Question Number 6

“PQRS is a square.

Which relationship is true in all squares?

To measure students' ability in understanding questions, tests in the form of eight contextual problems are given and students are asked to make mathematical models for these problems. Because their current subject matter is a three-variable system of linear equations, the questions given were related to that subject matter. The question bellow is a question of number 3 to test the ability of students in understanding Mathematics problem in the text form.

“A glass factory has 3 machines, they are machine A, machine B and machine C. If three of them are used, then 5,700 glasses will be produced in a week. If only machine A and machine B are used, then 3,400 glasses will be produced in a week. If only machine A and machine C are used, then 4,200 glasses will be produced in a week. So, how many glasses are produced by each machine every week?”

Problem number 3 above is the most correctly answered question by students, where there are 28 students who answered correctly on this number. The following is question number 6 where only 3 students correctly answer this number.

"There are two numbers where the second number is equal to six times the first number after minus one. If the first number is squared then added by three, the result is also the same as the second number. Each of the two numbers are ..."

Because students and teachers discussed about three variables linear equation system for several days before the research, of course for question number 3 there were many students who answered correctly because the problem model had been recognized by the students. Problem number 6 is deliberately given to test students' understanding of what they read. Students might suspect that the mathematical model for question number 6 is also a system of three-variable linear equations, but for students who really understand what they are reading, he will write a mathematical model for number 6 in the form of a two-variable system of linear quadratic equations.

Because the test of problem solving ability given to students is to change the story problem into a mathematical model with the theme of a three variables linear equation system, then each question students are challenged to make three equations combined into a system of equations. Every time student gives a right mathematical equation for the Mathematics model, the value given is one. Because each number of the equations formed is three, the score of each number range from 0 to 3. Correlation of data consisting students’ geometry level and score of Reading Comprehension Ability were evaluated using SPSS.

percentage of students’ right answer on van Hiele

From table 2, it can be seen that the least correctly answered question by students is van Hiele question number 14. The given problem is as follows:

“Which is true?

Things that might cause only one student who correctly answer question number 4 is the level of students difficulty in understand the text. The students may not understand the characteristics of shapes and they are confuse to catch what the question means.

Next, the least correctly answered question by the students is question number 18. If we look at the question, we will understand that students who answer incorrectly for question number 18 have difficulty in understanding the series of words or the combination of words in the question. Here is the question of van Hiele number 18.

“Here are two statements.

I : If a figure is a rectangle, then its diagonals bisect each other.

II: If the diagonals of a figure bisect each other, the figure is a rectangle.

Which is correct?

The series of words in van Hiele number 19 is also more than the questions at other levels have. This could be the cause of the low level of student reading comprehension towards the van Hiele level. Next, we test the correlation of the relationship between the two types of student abilities using SPSS.

Before determining that the VHT and RCT results were tested by Pearson Correlation, the normality of the data was checked using SPSS. Asymp Value. Sig. (2-tailed) for VHT is 0.666 and for RCT is 0.089 which means that both data from the test results are normally distributed.

Result of VHT and RCT

Student | VHT | RCT | Student | VHT | RCT |

1 | 2 | 54,2 | 17 | 2 | 50 |

2 | 0 | 33,3 | 18 | 1 | 41,7 |

3 | 1 | 54,2 | 19 | 4 | 45,8 |

4 | 2 | 50 | 20 | 0 | 25 |

5 | 1 | 37,5 | 21 | 1 | 58,3 |

6 | 2 | 41,7 | 22 | 0 | 50 |

7 | 1 | 41,7 | 23 | 2 | 54,2 |

8 | 2 | 62,5 | 24 | 1 | 41,7 |

9 | 0 | 29,2 | 25 | 2 | 45,8 |

10 | 1 | 37,5 | 26 | 3 | 29,2 |

11 | 4 | 54,2 | 27 | 1 | 41,7 |

12 | 2 | 33,3 | 28 | 2 | 50 |

13 | 1 | 16,7 | 29 | 1 | 33,3 |

14 | 0 | 0 | 30 | 2 | 37,5 |

15 | 0 | 37,5 | 31 | 1 | 45,8 |

16 | 1 | 41,7 |

The results of the correlation test using SPSS showed the significance value between the Geometry Thinking Level (VanHieleTest) and the Reading Comprehension Ability (ReadingComprehension) was 0.004 < 0.05. This means that there is a significant correlation between the level of students' geometric thinking and their ability to understand the text. Correlation coefficient r = 0.466 is positive, which means that the higher the ability of students to understand the text, the higher the level of geometry thinking will be. However, the correlation of both students' abilities is low or not too strong because the number of correlation coefficient r is not greater than 0.5.

From the results of the study, it can be said that students who did not complete at level 1 felt confused when a shape was tilted. They thought that a tilted square is not a square, so is a tilted parallelogram. This can be seen from the research data that students who did not complete at level one answered the least correctly in numbers 4 and 5. They even had difficulty distinguishing between square and rectangle. At number 1, many of them chose D as an answer, which means they think that a rectangle (persegi panjang) is a long square (persegi yang panjang). This is a risk when two different shapes have similar names in Indonesian. This wrong thought are caused by their tending to see the meaning of the name, not the characteristics of the shapes. In addition, the questions on level one contain fewer words than the questions at the next levels. Questions at level 1 test whether students really know the names of the shapes they see. If it is associated with the reading comprehension level, the questions at level 1 are at level A1 of reading comprehension level.

Students who are unable to solve questions at level 2 are at most wrong in answering question number 6. This means that they do not understand the characteristics of a square. Words that they might not understand at number 6 are square, perpendicular and angle. They might also not understand that the square diagonal is longer than the square side. The second smallest percentage after number 6 is numbers 8, 9 and 10 where there are only 25% of students or 3 of 12 students who answer correctly. For number 8, it is possible for students to think if it is a parallelogram or a kite even though it had already been written that it is a rhombus. Students believe more in what they see than what he reads. When working on number 9, students may think that the triangle is an equilateral triangle even though what is written on the question is an isosceles triangle. The incomprehension of the shapes’ names in detail can lead to students misunderstand in imagining the shapes and the shapes’ characteristics. Likewise in question number 10, when students do not understand that all the radius of a circle have the same length, he cannot guess that PSQR is a kite shape. Students who cannot distinguish rhombus, kite and parallelogram will be wrong in giving answers.

Students who could not complete level 3 answer the most incorrectly at number 12 and 14. Students who do not know the full characteristics of shapes would answer these questions incorrectly, especially if students only imagine the shapes’ properties and relate them to the problem. If the student who understands the characteristics of shapes writes the characteristics on the paper then compares them, he will be correct in answering. So the difficulty of the question in this number is to imagine what they read and associate it with the answer choices. Questions like this are at the highest level of reading comprehension ability, namely level C2.

From Blankenship

Magi

Contrary, Isphording

Geometry contains terms that are not usually used by students. Students may have gotten geometric terms at the previous level of learning but they may have forgotten or indeed they did not understand it from the beginning. Students studying in high school use their own language to study with their friends and their teacher because they are not immigrant students, of course, they should master the language used in school. If we include their level of ability to understand the text, they are naturally at level C1 or C2 where students are able to interpret the text he reads into mathematical models. However, the lack of mastery of geometric terms may resist their geometric abilities to a higher level of geometrical thinking.