Building Learning Path of Mathematical Creative Thinking of Junior Students on Geometry Topics by Implementing Metacognitive Approach

Mathematical creative ability is one of the most important skills students must have to process the information provided in resolving the problem. Before using mathematical creative skills, prior knowledge becomes the most crucial thing that allows students to connect all existing information so that they can construct new knowledge through assimilation or accommodation processes. The process of forming mathematical concepts with metacognitive questions that might be carried out by students causes a metacognitive process in students that will affect their mathematical behavior. The purpose of this study is to (1) analyze prior knowledge of what students miss or forget so that they have difficulty to answer the given geometry problem, (2) how the learning path of creative thinking of students with the application of metacognitive approach. This type of research is Design Research to improve the quality of learning. This type of research is research design, data collection techniques .The researcher gave 2 geometry questions to 38 8th graders selected randomly in SMP Medan city. Questions given are tailored to Cognitive level 4 (C4) for questions 1 and C5 for question 2 based on Bloom's taxonomy. Data analysis techniques are descriptive qualitative.This study shows that prior knowledge becomes important to build students' mathematical creative ability to gain new knowledge, especially in the field of geometry. The most problematic topics that make it difficult for them to understand geometry are the area of the rectangle and the cube webs. In dividing the rectangle into two equal parts, students still have not created another form of flat build or have not been able to get out of the rectangular pattern or exactly the same as the available problem. There are five phases of learning trajectory of hierarchically creative mathematical thinking, which is orientation to problem, problem solving plan, plan realization, previous knowledge mastery / concept of mathematical creativity and evaluation of result obtained. Students do metacognition on the learning path of creative thinking in a comprehensive way from evaluation to planning, action to the formation of prior knowledge and selection of creative ideas. From these explanations, it is important that teachers need to ensure students have enough prior knowledge to make it easier to construct new knowledge, as well as to make learning fun and meaningful so that students will remember knowledge in long-term memory.


Introduction
Thinking is a necessary thing in a process that involves manipulating and transforming information in memory.The ability to create new and original ideas in manipulating and transforming information is called creative thinking.Gardner (2004) views creativity as one of the 'multiple intelligences' that encompass a wide range of brain functions of constructing cognitive schemes.A student's cognitive level will work broadly when using creativity.The creative aspects of the brain can help explain and interpret abstract concepts, allowing children to attain greater mastery, on subjects such as mathematics, especially geometry that are often difficult to understand with regards to spatial abilities.In the process of solving mathematical problems students need to come up with creative ideas.The process of creative thinking can be seen from the perspective of Wallas' (1926) theory.Wallas in his book The Art of Thought states that the creative process includes four stages: preparation (gathering relevant information), incubation (received inspiration), and verification (testing and evaluating ideas acquired).From Figure 4, it can be seen that there is an increase in the average of mathematical creative ability in fluency indicator of 0.10, on flexibility indicator is 0.26, at elaboration indicator is 0,06, and at indicator of originality equal to 0,16.This shows the students' mathematical creative thinking ability using learning tools developed based on metacognitive approach has increased from trial I to trial II.Here is an example of the problem and completion of the students in Table 1 below.This study consists of three stages with two repetitions that can be done repeatedly until found a new theory which is the result of a revision of the experimental learning theory.Here are the steps in research design.

Phase I: Preliminary Design
At this stage a literature study of square materials and cube webs and metacognitive approaches can be established in a strategy conjecture and the path of students' mathematical creative learning.Then proceed with a discussion between the researcher and teacher about the condition of the class, the needs of research, schedule and how the implementation of research with the teacher concerned.At this stage also designed learning trajectory and hypothetical learning trajectory.Then from local instructional theory is formulated which consists of learning objectives.This conjecture aims as a guide (guide) to anticipate the strategies and thoughts of students who appear and develop in learning activities.Conjectures are dynamic and can be organized and revised during the teaching experiment.

Stage II: Teaching Experiment
In this second phase is to pilot teaching activities that have been designed in the first phase of the class.This trial aims to explore and hypothesize students' strategies and thoughts during the learning process.During the process, conjecture can be modified as a revision of local instructional theory for subsequent activities.Teachers act as teachers and researchers as the focus of observing each activity and key moments during the testing process.At this stage a series of learning activities conducted then researchers observe and analyze what happened during the learning process that took place in the classroom.

Stage III: Retrospective Analysis
After testing the data obtained from the learning activities in the class were analyzed and the results of this analysis were used to plan the activities as well as to develop the design on the next learning activity.The purpose of retrospective analysis in general is to develop local level instructional theory.At this stage the HLT is compared to the students' creative learning path points as the findings of this research are 5 points of the path, i.e. problem orientation, problem solving plan, plan realization, previous knowledge mastery / mathematical creativity concept and evaluation of the results obtained.Students do metacognition on the learning path of creative thinking in a comprehensive way from evaluation to planning, action to the formation of prior knowledge and selection of creative ideas.
This finding is in line with Osbon (1953) developing seven stages of the creative thinking process: orientation, preparation, analysis, ideas, incubation, synthesis, and evaluation.This means that the orientation to the problem as the starting point of the learning path of students' creative mathematics on the findings of this research is in line with Osbon's (1953) opinion that someone doing problem orientation at the stage of the creative thinking process is the first step in the introduction of the problem.In addition, the researchers found that students metacognition activities in line with the opinion Schoenfeld (1992) states that there are 3 ways to do metacognition in learning mathematics, namely belief or intuition, knowledge of thought processes, and self-awareness in the independence of learning.One's beliefs influence the problem solving of mathematics in building a way / strategy to solve the problem.Knowledge of the thinking process refers to how effectively one uses his thinking process, while consciousness itself refers to the accuracy of a person in preparing what to do in solving math problems.
When students are able to design, monitor, and reflect their learning process consciously, in essence they will become more confident and more independent in learning.Learning independence is a private possession for students to continue their long journey in meeting intellectual needs.The teacher's job is to develop the metacognitive ability of all students as a learner, without exception.
The concept of metacognition is the idea of thinking about the mind to oneself.Gravemeijer and van Eerde (2009) argue that students should provide opportunities to build and develop their ideas and thoughts when constructing mathematics.Educators can choose appropriate learning activities as a basis to stimulate students to think and act when constructing mathematics.In the process of the activity, the educator must anticipate any mental activity that arises from the student by still paying attention to the purpose of learning, imagery and anticipation is called Hypothetical Learning Trojectory (HLT).
Actually the whole concept of mathematics has been learned since they sat in elementary school and the characteristics of mathematics are continuous learning.So actually in some concepts, reviews remember waking flat square, constructing six square pieces into a wake-up space, and mentioning objects that resemble cubes in everyday life.
But in reality they also do not really understand this math concept.The researcher then conducted an interview with a mathematics teacher at the school and found that he thought geometry was the most difficult material to understand.For the topic of geometry itself, students find it hard to imagine the position of points, lines and spaces in space and to relate the information provided and understand the problem itself.According to the researcher, this can actually happen because they do not have enough prior knowledge to be able to connect information, process it, and represent the given problem so that it can be reflected in their mind until finally students can understand the purpose of the given problem.Also have a shadow of how to do the problem.
Before students recognize the difference between cube nets and non-cube nets students are trained to make cube nets.The preceding knowledge that the student must possess is square and its properties by giving examples and non-square instances, then cubes and their properties after the students understand continued with the introduction of cube nets and so on.The full path can be seen in Table 2 below:  Before the students assigned to solve the problems associated with the properties of rectangles, students should understand it in advance with real objects or drawing a rectangle with the mention of anything that is in the rectangle so that it is students understand the sense of the rectangle.Any point in the creative learning path should be passed students to solve the problem by finding creative solutions to mathematics.To know every path of creative thinking can be viewed from the characteristics/behaviors of students when learning activities taking place, for example, students always want to get solutions to problems encountered, like to get ideas of mathematics and would like to browse what information know and asked the question.The points of the trajectory of the complete creative learning in Learning Trajectory serve at Table 3 here.

Conclusion
In answering the question of dividing rectangles into two equal parts, all students can provide answers to fluency, flexibility, elaboration and originality.But the ability of students to provide many answers to each indicator of creative thinking varies.The ability of mathematical creative thinking that students have is not a single ability to solve the problem of dividing a rectangle into 2 equal parts and drawing cube nets.Other capabilities such as the ability to draw a flat building connect the concept of flat building with other sciences, aesthetic values of flat-build images; suspect the broad similarity of two flat wakes and the ability to intuit mathematical concepts.There are five phases of learning trajectory of hierarchically creative mathematical thinking, which is orientation to problem, problem solving plan, plan realization, previous knowledge mastery/concept of mathematical creativity, and evaluation of result obtained.Students do metacognition on the learning path of creative thinking in a comprehensive way from evaluation to planning, action to the formation of prior knowledge and selection of creative ideas.
From these explanations, teachers should also help ensure students have enough prior knowledge to make it easier to build new knowledge, as well as to make learning fun and meaningful so that students will remember knowledge in long-term memory.For the next researcher is how to build their previous knowledge that can support the learning of geometry in accordance with the time given in the learning process.

Table 2 .
Hypothetical learning of cube net

Table 3 .
Learning trajectory the rectangle topic for grade viii at junior high school