THE DEVELOPMENT OF MATHEMATICS MODULE BASED ON RELATIONAL THINGKING

Mathematical thingking and problem solving are important goal of learning mathematics. But in fact, mathematics learning in school was focused to compute the final answer. For example in solving algebraic equations, students have difficulty to solving these problems because students not understand about symbols of equivalencies. It’s shows that student need a media that stimulates their relational thinking. Therefore, this research aims to develop mathematics module for secondary students based on relational thinking to increase ability in solving algebraic equation. This is a development research which refers to 3D model. The technique for data collection was taken from questionnaire and test. The results showed that the module included: validity of the contents 84.21%, validity for language 84.21% and validity of display 86.84%. The results of limited test to thirty students received a positive response 94.73% and score of relational included in good category, so that the module is valid as media for mathematical learning.


INTRODUCTION
Mathematical thingking and solving mathematics problem are important goal of learning mathematics. Because students are expected to have the ability to think logically, analytically, systematically, critically, and creativelly, and also they have division are generally seen as a process of computational thingking only. Therefore the understanding of students was only procedural understanding, students according to the example procedure from their teacher.
Computational thingking is represent by twenty students on seventh grade in Kediri. The reseacher find that sixteen students from twenty students who answered algebra equation correctly, can't explain these reason of the problem solving process choosen. All students answered according to the procedure taught by their teachers. These facts indicate that the thinking of students to understand every step in solving mathematical problems less noticed by the teacher.
In other side, students have difficulty to solving algebraic equations because students are required to understand the symbol as an equal with the equivalence relation. In algebraic equations, students must focus on the concept of relationships. Despite the true solutions as an important part, but completing algebraic equation has a different character than applying the algorithm to get the final answer.
For example when students are given about 42 + x = 48 +71, then the student can do some strategies (1) by computing the sum on the right side next to substract these results by 42 to obtain x = 77 or with strategy (2) transform into a right-hand side (42 + 6) + 71 and use the associative of addition and seen the both sides of the relationship on the number 42, the obtained x = 6 + 71 = 77. The thought process as a strategy (2) is to improve in this research because students thinking process already understood relationally not just procedurally.
According Doumas and Hummel (2005) relational thinking is the ability to understand the analogy between objects or events that seem different and apply abstract rules in new situations. Thus the relational thinking is a mental process that is characterized by building linkages between elements of the information provided by the prior knowledge or the knowledge about the properties or structure of mathematics for solving mathematical problems. Through the empowerment of relational thinking process, is expected to enhance the students' problem solving skills.
Based the importance of relational thinking and the important of algebra for secondary students as a new material for them, reseacher would developed a media that stimulate relational thinking skills in learning algebra. For that initiated a development focused learning modules for teachers of SMP (Junior High School), which contains the solving algebraic equation with thought processes based relational thingking.

LITERATURE REVIEW A. Mathematics Modul
The learning module is the unit of the smallest teaching and learning program learned by the students themselves individually or taught by the students to themselves (Winkel, 2009: 472). Meanwhile, according to Anwar (2010) learning module is a systematic and interesting teaching materials that cover the contents of materials, methods and evaluation that can be used independently to achieve the expected competencies. Based on some understanding of the module it can be concluded that the learning module is one form of teaching materials that are packaged in a systematic and interesting so easy to learn independently. Anwar (2010) states that the characterictic of the learning module as follows: 1. Self instructional, students are able to these matters themselves, not dependent on other person. 2. Self contained, all learning materials from one unit of competency learned in one module intact.
3. Stand alone, develop module are not dependent on other media or should not be used in conjunction with other media. 4. Adaptive, the module should have a high adaptive to developement of science and technology.
5. User friendly, the module should also seen the rules of friendship with the student.
6. Consistency in the use of fonts, spacing, and layout. The module in this research is designing as instrument to improve relational thingking ability student in solving algebraic equation.

B. Relational thingking
Relational thingking is thingking use equivalence in another way. The are able to keep the two numbers either side of the equal sign as uncalculated pairs (Stepens, 2006). Relational thingkers seem to abstain from closing some operations because the see possibilities of the variation depend on the numbers and operations involved. Baiduri (2011) point to the importance of enabling students to discern dimensions of variation in whitch some elements in mathematical sentences change while while other elements remain unchanged.
For example when students are given about 42 + x = 48 +71, then the student can do strategies to transform into a right-hand side (42 + 6) + 71 and use the associative of addition and seen the both sides of the relationship on the number 42, the obtained x = 6 + 71 = 77. It marks relational thingking is the capacity to use possibilities of variation in number sentences.

C. Solving Algebraic Equation Problem
Equality and relational thingking are fundamental of algebraic learning. The meaning atributed the equal signs as deficiency of relational thingking could prevent the development of algebraic thingking and success in algebra (Stephens, 2006). As matter of fact, the studies on this issue in mathematics education literature have indicated that the students perceive "equal sign" as an operator sign rather than a relational sign (Carpenter, 2005) : example of algebraic equation To identify the aspects of weaknesses of students, the researcher prepared the assessment rubric for the mathematical relational thingking in solving algebraic equations. While for the ability of mathematics relational thingking there are this indicator are in table 1 as follows: Relational thingking evident for all algebraic equations, for examples, through evidence of progressive calculations and use of algorithms to obtain relevant totals for addition and substractions to solve the equivalence, even where these approach may have resulted in incorect answers, and no evidence of any relational thingking; also where an answer only has been given without any working shown to indicate what methode has been used. 1 A clear attempt to use relational thingking in at least one questions, but not sucsessfully executed. 2 Relationally thingking clearly shown in one question and successfully executed, even if the other problems are solved 3 Relational thingking clearly shown in at least two questions and executed, but where the remaining question or questions are not solved relationally or solved using incorrect relational thingking. 4 All questions solved clearly and successfully using relational thingking, computational solution of equation may also be provided in parallel.

METHODOLOGY
This study is kind of the development research. The stage of designing module follow the procedure of Thiagarajan model and Semmel & Semmel (1974). Development model that used is refer to 4-D model modified that called 3-D model. Where consist of 3 steps namely define, design and develop. This model without dessiminate stage because limited of time and cost. The research instrument used in quesionnaire validation for expert, observation sheets, algebraic quation testing, assessment rubrics, and the questionnaire responses of students.
The try out subject in this research were: (1) a group experts consisting of expert design development of instructional media, material expert of algebra, expert of linguistic, (2) user group for limited trial consisting the seventh grade students of SMP Ar Risalah Kediri and MTs. Al Ikhlas Kediri, East Java, Indonesia. The data collected was in the for of qualitative and quantitative data. Quantitative data was obtained through questionairs assessment developement products prepared with Likert scale by material expert, expert design, expert linguistic and unlimited users as well as the assessment of students respons, limited test and rubric of relational thingking skill for limited users of module, while qualitative data was obtained through the comment and suggestion, both from expert and limited users. Data collecting instrument used consist of questionaires validation, observation sheet during learning, algebraic quation testing, assessment rubrics, and the questionnaire responses of students.
The data analysis technique used in this research is descriptive analysis tecniques. Descriptive data analysis was used to analyze the data in the form of record suggestions and respons from the validations questionnaire. To analyze validity of module, guidlines for the categorization of validities of module are in table 3.1 as follows Descriptive statistical analysis used to analyze the data in the form of scores relational thingking when student solving algebraic equation problem. To analyze relational thingking score, guidlines for the categorization of relational thingking skill are in table 3.2 as follows Total Score Achieved (X) Category X > Xi + 1.5 Si Very High Xi + 0.5Si < X ≤ Xi + 1.5Si High Xi -0.5Si < X ≤ Xi + 0.5Si Medium Xi -1.5Si < X ≤ Xi -0.5Si Low X ≤ Xi -1.5 Si Very Low Xi = ½ (the possible maximum score from rubric + possible minimum score from rubric) and Si = 1/6 (the possible maximum score from rubric -possible minimum score from rubric) (Source: author) So the diagram that illustrates the developement process of module and achievment targets presented in figure 3.1 as follow:

RESULTS and DISCUSSION
Result of development are described as follows: Stage 1: Define This stage are set and defining relational thingking in learning activity by conducting analysis purpose ang material limitations. In stage of define, five activity that must be done namely: front-end analysis, student analysis, concept and material analysis, assignment and formulation of learning purpose. Stage of define in this research are described as follows: a. Front-End Analysis Equality and relational thingking are fundamental of algebraic learning. The meaning atributed the equal signs as deficiency of relational thingking could prevent the development of algebraic thingking. Relational thingking is think about perceive "equal sign" as relational sign. In curricula 2013, algebra is new material for seventh grade student, so they used media to help them solved algebra problems.
b. Student Analysis Information gathering and analysis from the limited test showed that student still rely solving the problem likes the teacher processed. The limited test result in 7 th students SMP Ar-Risalah Lirboyo Kediri, from 18 students, only 5 students has relational thingking skill, and from 20 students in MTs Al Ikhlas Kediri only 2 students has relational thingking skill. Based this analysis, clearly shows that the students are required relational thingking in solving algebraic equation.
c Based of observation, it is also known that algebraic equation materials that are used is still general and some parts are not accordance with the characteristics of students residence. In this case, it is recognized the need of algebraic equations, so the purpose of this research was explained concept of algebraic equation as an equation obtained by equating to zero a sum of a finite number of term each one of which is a product of positive integral powers.

. Concept and Material Analysis
d. Assignment Analysis To analyze relational thingking skill and problem solving ability used some instrumens likes algebraic quation testing, assessment rubrics and quessionaire. And to analyze validity of module, te module must have good criteria such as: self instructional, self contained, stand alone, adaptive, used friendly and consistent.
e. Formulation of Learning Purpose This analysis intended to convert the purpose of assignment analysis and concept analysis into specific learning objectives that expressed by the behaviour of student in learning. In this study, the purpose of learning module are 1) students can explaine concept of algebraic equation as relational equivalence , 2) students has relational thingking skill in problem solving.

Stage 2: Design
Product is developed in form a module which is based on relational thingking. This module for 7 th grade in Junior High School. The development of this module consist of three criteria: visual design, content component and text or language design. Result of design is called draft-1. The activity of this stage begun from identify indicator of learning objective in algebraic equation, identify basic competence, initial design of mathematics module in 7 th grade in Junior High School, and drafting these module manuscript.
Physical design the module consist of outers cover and the size of the yard. The page size is A4 with a weight of 80 grams as standar ISO (International Organization for Standarization). Text design with Times New Roman type 12pt and the visual design dominate for green colour and equivalance picture.
Therefore, the component of the contents of the module that was developed in modules include an introduction, table of contents, instructions for use, the parts of the module, algebraic equation testing, and self assessment.

Stage 3: Develop
At this stage there are four activities, namely; a. Validation Stage of develop, started with validation by expert then validation are conducted to the mathematics module is designed in the stage 2 (draft-1). Subject matter experts as three person who have competence in the field of mathematics, especially algebra (one lecturer of mathematics education), the person competent in the field of graphics (one lecturer of educational technology) and the person competent in language (one lecturer of English language) . Validation are conducted content material, format and language that is used. Aspect that are observed namely: whether subject matter, whether sentences in module is easy to understand, whether sentences in module is not ambigous, whether display and content module is interesting, whether the questions varied, and whether sentences in questions is not ambigous. Data Revision for module presented in table 4.1 as follow:  After get draft-2, the next activity is doing trials on limited group. The trials as called as limited because of its dependence on the scedule learning materials in school where tested. Trial was conducted in two school in Kediri namely: SMP Ar-Risalah Lirboyo Kediri City with 18 students for a limited trial and MTs Al Ikhlas Kediri Distric with 20 students for a limited trial, because according Sadiman (2012) that the small group trial awarded to 10-20 students who can represent the target population. After students learning mathematics module, they get algebraic test and quotionare. Aspect of observed consist of: whether sentences in module is easy to understand, whether sentences in module is not ambigous, whether display and content module is interesting, whether the questions varied, and whether sentences in questions is not ambigous. d. 2 nd Revise After trials has been done, researcher revise the module (draft-2). The revisons are based on invention of trial result. Data after 2 nd revision for module presented in table 4.2 as follow:

Aspect
Content and Cathegory validity of the contents 84.21% ( valid)  32 respondens (students) from 38 respondens said that the algebraic equation problem in module is vary validity for language 86.84% (valid) 33 respondens (students) from 38 respondens said that the sentence of module is easy to understand, and the sentences does not have double meanings. validity of display 84.21% (valid) 32 respondens (students) from 38 respondens said that display of module is interest. students response 94.73% (positive response)  36 respondens (students) from 38 respondens interesting for applying module in mathematics learning. score of relational rubric Good Average  total score archieve in high category.

CONCLUSION
This module based relational thingking may provide an oppotunity for student to learn and have to skill to observe and understand equivalence concept and they get flexibility in algebraic equation problem. Students also practice solving algebraic equation problem with relational thingking . This module also have advantages it is use as a companion teaching materials that can developed problem solving ability in learning mathematics.
Researcher hope taht next time, this module can develope until disseminate stage.