The Mathematical Problem-Solving In Algorithm
Subject
Anggun Badu Kusuma, Reni Untarti
Abstract: The problem-solving capacity is the ability to provide solutions to the challenges given. Challenges in mathematics can be in the form of problems that are rarely done by students or often called non-routine problems. The purpose of this study is to categorise the mathematical problem-solving abilities experienced by students if based on motivation on them. The subjects of this study were students of mathematics education study programs, academic year 2018/2019, Universitas Muhammadiyah Purwokerto. This case study begins by grouping students based on their motivation in learning. Furthermore, an analysis of mathematical problem-solving abilities is based on high and low motivation. The instruments used were the motivation questionnaire, problem-solving ability test, and documentation. The results of this study indicate that students with high motivation can perform all stages of mathematical problem-solving. Stages that can be mastered by students with high motivation understand the problem, drafting the solution plan, implementing the solution plan, and checking the solution. While low motivation students are only able to finish up to the drafting stage of the solution plan.
Index Terms: Problem-Solving, Motivation, Algorithm
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INTRODUCTION
Problem-SOLVING is an ability that must be mastered and is very important in mathematics [1], [2]. This is because problem-solving is one of the backbones of mathematics [3]. Problems are questions or difficulties that require resolution [4]. Whereas, problem-solving is the process of achieving results when no method is known [5]. In mathematics, problem-solving is the most effective concept for transferring mathematical knowledge that is sustainable and meaningful [4]. Research on problem-solving is often only done on how the cognitive thinking process. Such cognitive-limited processes are not suitable if carried out in a school context, because in the process of solving the problem there is also the role of affective abilities that influence it [6]. The results of other studies also revealed that problem-solving is influenced by attitudes, beliefs, values, and orientation of one's motivation [7]. One of the affective roles that influence problem-solving abilities is motivation [3]. Motivation is one of the drivers of people in doing an activity. The existence of student motivation is influenced by various things, including the teacher doing mentoring learning [8] and family conditions [9]. Motivation skills include interest, self-efficacy, and attribution [10]. Motivation greatly affects learning activities, stronger performance, longer learning time, and enjoying learning activities [11], [12]. With differences in learning activities this can affect work outcomes student. For example, is the completeness of the work. People who have high motivation, the work is more detailed when compared to people with low motivation. Accuracy in reading problems, people with high motivation are more careful in exploring the contents of a problem, not just from what is seen. This happens because motivation can have a great influence on a person's behaviour [13]. Algorithm is a compulsory subject in the 4th semester mathematics education study program.
This course aims to train students' logic abilities in solving problems. One of the material in this lecture is how the presentation of the algorithm to solve a given problem in solving. At this time there are very many studies on the role of affective in problem-solving. There are studies that conclude that metacognitive abilities have a significant influence on students' mathematical problem-solving abilities [14]. In addition, there is also a focus of research on student emotions. The results showed that students' emotions could positively influence the problem-solving process [15]. In this study offered about the effect of differences in student motivation in the problem-solving process. The focus of the problem is on the algorithm course.
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METHOD
The subjects of this study were 39 students who took the algorithm course. The procedures of this research alow 1) giving problem-solving tests to students, 2) distributing motivation questionnaires, 3) categorizing student motivation in the high, medium, and low categories, 4) taking samples of students with high and low motivation categories with purposive sampling, and 5) analyze students' mathematical problem-solving abilities. Analysis of the data used is using descriptive qualitative analysis.
3 RESULT AND DISCUSSION
The ability to solve mathematical problems can be seen from how the process of working on a given problem. The review is based on how students understand the problem, drafting the solution plan, implementation of the solution plan, and check the solution. The results of students' mathematical problem solving abilities are as follows
a. The level of understanding of the problem
Students with low group motivation are able to determine what problems must be solved. Students are also able to determine the variables and symbols that will be used. The problem experienced at the stage of understanding the problem is that students cannot mention the things that are known in the problem. In the matter, it is known about the formula of determining profit, but the students mention what is known is profit, buying price, and selling price (fig. 1). This problem does not only occur in one low student but also occurs in all
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• Anggun Badu Kusuma is lecturer in Mathematics Education Departement in Universitas Muhammadiyah Purwokerto, Indonesia, [email protected]
• Reni Untarti is lecturer in Mathematics Education Departement in
Universitas Muhammadiyah Purwokerto, Indonesia,
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low students.
Students with high motivation are able to complete the stage of understanding the problem well. Students are able to determine what problems must be solved, able to determine what data is known, and able to determine the variables and symbols that will be used. When determining supporting data, students are able to determine correctly that the data that is known is the profit-seeking formula (fig. 2).
b. The level of drafting the solution plan
In the compilation of the solution plan, both low and high-level motivation, students are able to complete well. All students are correct in answering it. However, when viewed from the way to answer, there are differences between students with low and high motivation. At this stage students with low motivation in answering only by writing symbols. (fig. 3).
c. The level of implementation of the solution plan
At this stage, students with low motivation make mistakes in implementing the completion plan. For low student 1 in Fig. 5 shows that students made a mistake in entering the formula to calculate profits. In the picture it is seen that students calculate profits with p * l * t, this is not in accordance with the known profit formula. For low student 2, according to Fig. 5 it appears that students make a mistake in the answer enter the value of z. The z value in the answer should be a process value, not a value that is "input" by the user. In addition, for what is printed as "output" the program should not be the z formula, but the value of the z.
For students with high motivation can pass this stage well. Students are able to write the steps to determine the value of sales profits.
d. The level of check the solution
At this stage, both students with low and high motivation still experience errors in the process of answering. Low student 1 (fig. 6) experienced an error in using the symbol flowchart. The symbol at the start should not be rectangular, but oval. Profit is a process that must be carried out by the program, not as data that must be input, therefore the symbol that must be given is rectangular. Besides, students also have not written answers to the end. Low student 2 (fig. 7) have understood the form of the flowchart symbol, but the data provided on the flow chart is incomplete. The input data should be written down what data should be inputted, the read and print data should also be written what should be read and printed.
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detail then the reading of the input data process is also needed, so after inputting the selling and buying prices it is necessary to read the data.
These data indicate that with different motivational conditions students will have an impact on the ability to solve mathematical problems. A summary of the motivations and abilities of the problems mastered in accordance with table 1 below.
4 CONCLUSION
The high-level motivation students were able to solve all of the mathematical problem-solving stages, whereas the low-level motivation students were able to solve drafting the solution plan stage only.
5 ACKNOWLEDGMENT
Thank you to the Chair of the Mathematics Education Study Program for allowing the place to carry out research and all the support given.
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REFERENCES
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TABLE1
RECORD MOTIVATION AND PROBLEM SOLVING ABILITY
Motivation Problem solving
Level 1 Level 2 Level 3 Level 4 Low Motivation able able unable unable High Motivation able able able able
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