Abstract
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.
Highlights
Mathematical problem solving ability is one of the most important abilities students must have to process the information provided in solving problems
It can be concluded that prior knowledge is important to build new knowledge of learners, and as an important initial capital in solving a problem so that the ability to solve mathematical problems can be created well
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
Summary
Problem is a thing that all individuals will discover, both unconsciously they indicat that is a problem. Vol 12, No 2; 2019 because in the process of solving problems students need to monitor or monitor the thinking process such as how and why he did the solving step, whether the solving step is going well or there are obstacles that can encourage students to think of other alternatives or try to understand the problem again This is in line with Setyadi, Subanji, and Muksar’s (2016) research which states conceptually metacognition as the knowledge or awareness of one’s thinking process, the ability to monitor and manage the thinking process and its thinking, and to evaluate the thinking process and its thought result. Researchers want to know how the trajectory of learning of ability problem solving of mathematical learners on the material tangent circle by using teaching materials that based on approach metacognistion
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