Building Learning Trajectory Mathematical Problem Solving Ability in Circle Tangent Topic by Applying Metacognition Approach

Mathematical problem solving ability is one of the most important abilities students must have to process the information provided in solving problems. Before using mathematical problem solving skills, prior knowledge becomes the most crucial thing that makes students able to connect all available information so that they can construct new knowledge through the process of assimilation or accommodation.The purpose of this reseach is to:(1) Analyze prior knowledge what student has so the student can solve the problem of tangent circle given; (2) Know how learning trajectory in student’s mathematical problem solving ability by applying metacognition approach. This reaseacrch is a design research to improve the quality of learning. In this reseacrh researchers gave 3 test questions on students’ mathematical problem solving abilities. One trial was conducted in class VIII-B and trial II was conducted in class VIII-A, each consisting of 30 students junior high school. The result of students answer analysis shows the mast problematic topic that makes the studnts are difficult to solve the problem is about the tangent cicrcle that is the elements of the circle and the concept of circle circumtance there are three phased in learning path of students mathematical problem solving skill that are under standing the problem, making the problem solving plan by prrior knowledge and doing problem solving and evaluating it. From this explanation, it is better for teachers to ensure students have sufficient prior knowledge to make it easier to construct new knowledge, as well as make the learning process fun and meaningful so that students will remember knowledge in long-term memory.

Problem is a thing that all individuals will discover, both unconsciously they indicat that is a problem.Problem solving ability is important capital in solving and dealing with a problem.Problem solving should be one of the skills developed and thought in schools to home the thinking and reasoning skill.Hudojo (1988, p. 133) states that problem solving is an essential thing in mathematics because (1) the students become skilled in selecting relevant information, than analyzing it and finally re-exanning; (2) intellectual satisfaction will arise from within which is an intrinsic gift to students; (3) students' intellectual potential is increased and; (4) students learn how to make discoveries through the process of discovery.Charles, Lester, and O'Daffer (in Szetela & Nicol, 1992) focused on solving mathematical problems from three aspects: (1) understanding problem; (2) planing mathematical problems; (3) solving the problem (answer the problem).Based on the research survey, the problem solving skills test on the tangent material of the circle concluded that the students' mathematical problem solving ability is still low.Of the 24 students, only 4 (16.16%)students who achieve the minimum criterion value of mastery (KKM) that is equal to 70.
The result of the problem solving test showed that some students could not write down how to calculate the exact length of the bicycle chain and the students only used the formula to find the outline of the two circle outer circles only and did not understand the problem well that the concept of the circumference of the circle was also needed to determine the length of the chain of the bike because the chain is wrapped around the two bike gear.Overall of the students' answers the most students understand the problem, but the ability of students is still low in indikotor problem-solving abilities that are plan completion and solve the problems given.Schoenfeld (1992, p. 38) states that metacognition includes knowledge of the process of thinking, self-awareness and confidence and intuition.Aspects of metacognition can help students in solving problems.Why is that?

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Phase acher matics doctor at the Medan State University and two other Mathematics teachers from the SMP Imelda Medan.Before being tested the ability to solve mathematical problem solving students are examined by the validator logically with the aim of knowing the logic and ease of language of the problem given.The assessment carried out by the validator on the test instrument of mathematical problem solving abilities includes indicators of content validity, language and problem writing, and recommendations.Validator results are shown in Table 2   research that conclud that the mathematical problem solving ability of grade VI students is more successful than class V, which means that students' mathematical problem-solving ability is influenced from their cognitive level.
Metacognition is an idea of the self-contained mind, which includes one's awareness of what he knows (metacognitive knowledge), about what he can do (metacognitive skills), and what he knows about his own cognitive abilities (metacognitive experience).In the results of the students' answers, students activate their cognitive by relying on their initial abilities in answering the given problems, then they make the formula planning that will be used, and they do calculations based on their numeracy skills.
Hypotetical learning trajectory (HLT) in this study is learning goals by determining the goals to be achieved in the tangent material of the circle, namely students can determine the length of the rope wrapped around two circles, learning activity by designing student activities that can improve students' mathematical problem solving abilities tangent circle, hypotetical learning process by designing materials that can support students' thinking in reaching the tangent circle that is knowing the elements of the circle and the concept of broad and circumferential circles, and teacher support by relying on the teacher's ability to apply learning with a metacognition approachIn this case the researcher adds teacher support (help and direction from teacher) as component of HLT.Because according to the researcher in the process of learning assistance and direction of the teacher is of needed at the learning process especially for students who have low ability.
In mathematics learning, as if are climb up the stairs, if one step is missing it is difficult for us to reach the goal, further more two steps lost so we will be more difficult to climb up.That's the learning of mathematics a concept that one with the other has a relationship, to understand the next concept so we must know the previous concept.Therefore, the role of educators is also needed in activating cognitive of students.Arranging of hypotetical learning trajectory must really be done to anticipate what mental activities should be and what knowledge should be possessed by students in understanding a concept in mathematics.
Prior knowledge that is less good causes students difficult to connect each information, manage it, and present the given problem.Before students understand the lines of a circle the students are trained to paint the tangents of the two-circle fellowship.And the initial knowledge that students must be had to solve the problems about the length of the circle of circle is the circle elements, the wide and circumference of the circle, the position of the line on the circle, the length of the tangent alliance of two circles.The full path can be seen in Table 4 below.

Conclusions
From the student's answer in answering the problem of determining the length of the string that wrapped around several circles using the concepts of a two-circle parallelism circle and the circumference of the circle, some students still have not been able to solve the given problems.Students can not plan for problem solving well, due to lack of prior knowledge of students.Prior knowledge of students that make students difficult to solve the problem of tangent circle is the elements of the circle and the concept of the circumference of the circle.There are 3 phases in the learning path of students' mathematical problem solving skills, that are understanding the problem, making the problem-solving plan by prior knowledge, and doing problem solving and evaluating it.Based on these conclusions, educators should ensure that students understand the concepts of a material before continuiting to the next material that requires the concept of the previous material, so that students have sufficient initial knowledge in solving the given problems.Educators should be able to create a fun and meaningful learning atmosphere and orientate the contextual problem in the students' mind.
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Table 1 .
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Table 2 .
below.The result of validation test of mathematical problem solving skill it shows the students' mathematical problem solving test of the five validators, four validators stated that the students' mathematical problem solving tests that designed can be used without revision.A validator stated that for item 1 is necessary to make a small revision, as well as to item 2 and 3 need to do a little revision.Beside validation by the validotor, test of students' mathematical problem solving abilities also conducted previous trials with validation value of each question shown in Table3below.

Table 3 .
Validity of problem solving problems with mathematical problem solving

Table 3 ,
each value of t observe > t table concluded that the test of mathematical problem solving ability was said to be valid.From the result of the students 'mathematical problem solving test in the first experimental test the average of students' mathematical problem solving ability on the problem understanding indicator is 1.92, the troubleshooting plan indicator is 2.26, and the problem solving indicator is 2.51.While in trial II, the average of students' mathematical problem solving ability on the indicator of understanding the problem is 1.94, the indicator of problem-solving plan is 2.44, and the problem solving indicator is 2.63.Seen in Figure3follow.