The Characteristic of the Process of Students’ Metacognition in Solving Calculus Problems (original) (raw)

The Characterization Of Mathematics Students’ Metacognition Process In Solving Mathematical Problems

2016

It is an article as the result of a study to analysis happening of mathematical students’ metacognition changes in solving and describing the characteristic of mathematical problem. The metacognition is based on the changes of awareness, evaluation, and regulation as the components of it. To make known of them, the writer has determined the indicators of each of the components which are spelled out into descriptors in order the process of metacognition changes can be seen. The process of the study involved 23 Students of Mathematics Department who finished Differential Calculus lesson as the subjects of the study. The subjects of the study were given mathematical problems about the application of function derivation to make known of the maximum area of a field. The data of the study was obtained consists of mathematical problem worksheet, record, metacognition questionnaire, and interview transcript. Then, the data was analysed by using Glaser’s and Strauss’ constant comparative mod...

The Emergence of Students’ Metacognition in the Process of Mathematical Problem Solving

2018

Developing a problem-solving skill for important things which need to be paid attention is how the students' thinking process in solving a problem is. Thinking about what is thought in this term relates to students' awareness of their ability to develop various ways which may be taken in solving a problem is known as metacognition. The existence of metacognition is very important for students in solving mathematical problems. This is a qualitative study using the grade VII students having medium ability as the subjects. The results of the study obtained that through intervention conducted by the researchers in 5 meetings, metacognition capability emerged in the subjects so that with their own ability they are able to solve mathematical problems provided.

Metacognitive Strategies: Instructional Approaches in Teaching and Learning of Basic Calculus

The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students' learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.

The development of students’ metacognition in mathematical problem-solving

THE 2ND SCIENCE AND MATHEMATICS INTERNATIONAL CONFERENCE (SMIC 2020): Transforming Research and Education of Science and Mathematics in the Digital Age

Every student has different thinking abilities, such as thinking activities to receive and process information. The students' thinking ability is cognitive thinking ability or known as metacognition, such as monitoring and controlling each stage conducted. Therefore, teachers need to make efforts to improve students' metacognition by using probing prompting learning techniques. This technique can encourage students' metacognition abilities in solving mathematical problems. This study aims to determine the development of students' metacognition in mathematical problem-solving. This classroom action research applied a qualitative descriptive method which was carried out in five cycles, involving four out of 22 Year 7 students in one of the islamic junior high schools in Aceh Besar, Indonesia. Data analysis of students' metacognition development was investigated through metacognition question sheets which were carried out after solving mathematical problem solving problems. Students' and teacher's activities were investigated in each lesson. The results showed that the students' metacognition in mathematical problem-solving increased in Cycle I to V based on metacognition question sheets, students' activity sheets, and teacher's observation sheets in using probing prompting techniques. The development of students' metacognition can also be seen through other supporting aspects, such as students' activities and teacher's efforts in the learning, both increased in each cycle. The results also showed that students' metacognition increased with the increase in student activities and teacher teaching abilities.

Comparison of Metacognition Awareness of Mathematics and Mathematics Education Students Based on the Ability of Mathematics

International Journal of Trends in Mathematics Education Research

Awareness of metacognition is one of mental process that occurs when a person knows what he thinks, including the knowledge and awareness to do something or realize the reason that. The purpose of this study is (1) to describe how the metacognition awareness of mathematics student and mathematics education student based on mathematical ability, and (2) to know the difference metacognitive awareness between of mathematics students with math education students based on mathematical ability. This research subject are the Department of Mathematics and Mathematics Education students of Halu Oleo University Kendari, Indonesia. This research is ex post facto by the data analysis using descriptive and inferential approach. Descriptive approach used to describe the level of metacognitive awareness of mathematics students and mathematics education students based on his mathematical abilities, whereas inferential approach used to see the difference in metacognition awareness of mathematics stu...

Metacognitive awareness: how it affects mathematical problem-solving process

Journal of Physics: Conference Series, 2019

Problem-solving is one of the basic skills in learning mathematics where in the process needs awareness in every step. Metacognitive awareness means to be aware of how to think. This study aimed to know the effect of metacognitive awareness in the mathematical problem-solving process. This is a descriptive-qualitative study. The samples of this study are 10 students. Data of metacognitive awareness were collected using questionnaire adapted from Metacognitive Awareness Inventory (MAI) developed by Schraw and Dennison, data about mathematical problem-solving process were based on the test result. The MAI measures two components which include the knowledge about cognition and the regulation of cognition. The results indicate that the two components of metacognitive awareness, that is knowledge about cognition and regulation of cognition gave the effect to mathematical problem-solving students especially for regulation of cognition. The Student with high levels of regulation of cogniti...

The Relationship Between Students’ Metacognitive Awareness and their Solutions to Similar Types of Mathematical Problems

Eurasian Journal of Mathematics, Science & Technology Education, 2013

This study was designed to investigate the relationship between the metacognitive awareness of university students and their solutions to the similar mathematical problem types. Participants were 97 freshmen from department of mathematics at a state university in Turkey. Two different scales were used for data collection: “Metacognitive Awareness Inventory” and “Mathematical Problem Types Test’’. The results showed that there was a significant positive correlation between the students’ metacognitive awareness levels and their problem solving levels regarding routine and non-routine problems. There was no significant linear correlation between university students’ metacognitive awareness levels and their problem solving levels for “separation”, “combining”, and “multiplication” in routine problems. Multiple regression analysis was used to test if the metacognitive awareness significantly predicted participants’ levels of problem solving. The results of the regression indicated that metacognitive awareness significantly predicted problem solving levels and both predictors explained 45% of the total variance. Keywords: problem types, metacognitive awareness, problem solving, problem solving level

Metacognitive Analysis of Students in Solving Mathematics Problem

Al Khawarizmi: Jurnal Pendidikan dan Pembelajaran Matematika

This research is motivated by the lack of students' understanding of their thinking skills and students cannot determine the right strategy to overcome the problems encountered in solving mathematical problems. The purpose of this study was to find out how the metacognitive level of students in solving math problem solving problems in class IX.1 students of SMPN 26 Padang. This type of research is descriptive quantitative. The subject of this research is class IX.1 SMP Negeri 26 Padang. The instruments used are tests and interviews. The test is used to determine the metacognitive level of students in solving problem solving problems. Interviews were used to find out more about the metacognitive level in terms of students' understanding. The results showed that as many as 35.71% of students were at the metacognitive level of Tacit Use, as many as 35.71% of students had the metacognitive level of Aware Use, and as many as 28.58% of students had the metacognitive level of Strat...

3 4 1 Interactive Effect of Metacognitive Strategies-Based Instruction in Mathematics on Metacognitive Awareness of Students

2016

This paper attempts to ascertain the interactive effect of meta-cognitive strategies-based instruction in mathematics on student–outcomes. For this purpose, an intervention programme based on meta-cognitive strategies was developed for students of standard eighth. The intervention programme lasted for about 35 hours spread over eight weeks. The aim of the research was to ascertain whether meta-cognitive strategies instruction facilitates metacognitive awareness in students. Paper-pencil tests were used in study. The participants of the study included 135 students. The study consisted of one experimental group consisting of 69 students and one control group consisting of 66 students. The experimental group received the intervention programme and the control group received the traditional, lecture-based, teachercentred instruction. The data was analysed using the statistical technique of ANCOVA. Metacognitive awareness in form of knowledge about cognition and regulation about cognitio...

The errors of metacognitive evaluation on metacognitive failure of students in mathematical problem solving

Journal of Physics: Conference Series, 2018

Metacognitive activity is very important in mathematical problems solving. Metacognitive activity consists of metacognitive awareness, metacognitive evaluation and metacognitive regulation. This study aimed to reveal the errors of metacognitive evaluation in students' metacognitive failure in solving mathematical problems. 20 students taken as research subjects were grouped into three groups: the first group was students who experienced one metacognitive failure, the second group was students who experienced two metacognitive failures and the third group was students who experienced three metacognitive failures. One person was taken from each group as the reasearch subject. The research data was collected from worksheets done using think aload then followed by interviewing the research subjects based on the results' of subject work. The findings in this study were students who experienced metacognitive failure in solving mathematical problems tends to miscalculate metacognitive evaluation in considering the effectiveness and limitations of their thinking and the effectiveness of their chosen strategy of completion.