Medium Mathematical Ability Research Articles

The effects of gradual release of assistance instruction on students’ heuristics, confidence, and attitude toward independent problem-solving

The 'Gradual Release of Assistance (GRA) instruction' was implemented among pre-service teachers in a problem-solving course designed to reduce students' resistance to independent problem-solving. This approach aimed to enhance students' heuristic skills, confidence, and attitudes toward problem-solving. The GRA instruction encompassed activities with progressively decreasing levels of instructional support across three stages: the maximum assistance stage, the medium assistance stage, and the independent problem-solving stage. Utilizing an embedded multiple-case design and a simple time-series analysis of six individual cases, this research explored how pre-service teachers applied heuristics and their confidence and attitudes toward problem-solving. The study revealed improvements in heuristic application among cases with high and medium mathematical abilities, as well as increased confidence and positive attitudes toward problem-solving within this cohort. However, there were no notable improvements in using different heuristics among cases with low mathematical ability. The findings discussed the observed changes and consistencies, offering plausible explanations that underscore the significance of GRA instruction in alleviating students' reluctance to engage in independent problem-solving.

Proses Berpikir Kreatif Siswa SMP dalam Menyelesaikan Masalah Matematika Open-Ended Ditinjau dari Kemampuan Matematika

Future challenges that are increasingly complex require the competence of graduates who are not only skilled, but also creative. The process of creative thinking has four stages, namely synthesizing ideas, building ideas, planning the implementation of ideas, and implementing ideas. Open-ended math problems are a medium that teachers can use to find out students' creative thinking processes. The purpose of this research is to describe the process of creative thinking of junior high school students in solving open-ended math problems in terms of mathematical abilities. This research is a qualitative descriptive study conducted in 7th grade of SMP Muhammadiyah 2 Taman. The research subject was one student from each category of high, medium and low mathematical ability. Data collection methods used are test and interview methods. The results obtained were that at the stage of synthesizing ideas, subjects with high, medium, and low mathematical abilities did so based on experience in class with known formulas. At the stage of building ideas, subjects with high mathematical abilities considered convenience, subjects with mathematical abilities considered other ways, and subjects with low mathematical abilities considered logic. At the stage of planning the implementation of the idea of a high ability subject and is doing it smoothly and productively, the low math ability subject is doing it inefficiently. As well as at the stage of applying the idea, the subject of high mathematical ability fulfilled the creative thinking aspects of fluency, flexibility, and novelty, the subject of medium mathematical ability fulfilled the aspect of flexibility, and novelty, the subject of low mathematical ability only fulfilled the aspect of flexibility.

CREATIVE THINKING ABILITIES OF PROSPECTIVE MATHEMATICS TEACHERS IN SOLVING OPEN-ENDED TRIGONOMETRY PROBLEM

The current technological developments require students to have creative thinking skills. One of the four thinking skills needed in the 21st century is creative thinking skills which is still lacking in students. The purpose of this study was to describe prospective mathematics teachers’ creative thinking skills in solving open-ended trigonometry problems. This research is descriptive qualitative research. This study involved 40 prospective mathematics teachers who were then reduced to four subjects based on high and medium mathematical abilities which were studied in more depth in solving open-ended trigonometry problems. The research instruments used in this study were the researcher, interview guide, and open-ended trigonometry questions. The results of collegers work were analyzed based on aspects and levels of creative thinking skills. In this study, the data analysis phase includes data reduction, data presentation, and conclusion. Then triangulated the data in describing the results of the study. The results of this study are that first colleger with high mathematical abilities meet the aspects of fluency and novelty and the second fulfills the aspects of fluency and flexibility. First colleger with medium abilities fulfill the flexibility aspect and the second fulfills the novelty aspect. So, it can be concluded that collegers with high and medium mathematical abilities were solving open-ended trigonometry problems have a creative level and quite creative.

ANALISIS PROSES BERPIKIR KRITIS SISWA DALAM PEMECAHAN MASALAH MATEMATIKA PADA POKOK BAHASAN POLA DAN BARISAN BILANGAN

This study aims to analyze how students’ critical thingking processes in solving mathematical problems on the subject of patterms and sequences of numbers of students at SMP N 3 Fatuleu Tengah Satap. This study used a qualitative descriptive approach. Class VIII at SMP N 3 Fatuleu Tengah Satap, in solving patern and number sequence material questions the instrument provided in this study were 1) Critical Thingking test sheets, 2) Interviews, 3) Documentation. Documentation data analysis in this study,namely, 1) Data reducation, 2) presentation of data, 3) drawing conclusion/verivication based on data analysis, it can be concluded that 3 students with high mathematical abilities can go thourgh 4indicators and stages of the critical thingking process consisting of clarification (understand the problem), analysis (analysis the problem). Completion strategies (solving problems), and inference (making conclusions) on medium mathematical abilities students only go through the clarification and analysis stages but do not fulfill the strategy and inference stages and students with low mathematical abilities, namely students who interprect critical thingking on the answer sheet but are incomplete in answering.

STUDENTS' GEOMETRY THINKING ON CIRCLE MATERIAL BASED ON VAN HIELE'S THEORY

The purpose of this study was to describe students' geometric thinking skills on circle material based on Van Hiele's theory (Visualization, Analysis, Informal Deduction, Deduction, Rigor). The subjects of this study were 3 students of class IX-A SMP Hang Tuah 4 Surabaya based on their initial mathematical abilities (high, medium, and low). The initial mathematical ability data was obtained from data on report cards for the even semester of the 2021-2022 academic year and based on the considerations of the mathematics teacher for class IX-A. This type of research is descriptive qualitative research. Collecting data in this study used tests and interviews. The test instrument used in this study was a circular geometry test in the form of mathematical questions with circle material arranged based on the Van Hiele indicator without stage 4 (Rigor) with the consideration that the research was conducted in class IX SMP so students have not been able to understand the material at stage 4 (rigor). Student with high initial mathematical abilities, geometric thinking abilities is already at stage 2 (informal deduction). Student with medium mathematical abilities, geometric thinking skills is at stage 2 (informal deduction). Student with low mathematical abilities, geometric thinking skills is at stage 0 (visualization).

The distance between students’ concept image and quadrilateral object definition based on students’ mathematical ability

Students learn mathematics through practical applications without applying it. Consequently, the concept images and definitions that students offer do not match. This study examines the gap in mathematical ability between the concept images of professionals in mathematics education and students' concept images of content, including quadrilaterals. This study employed a qualitative approach with a hermeneutic phenomenology method. Sixty-two seventh-grade students were involved in conducting this study. Some instruments, such as quadrilateral-related tests and semi-structured interview questions, were used to collect the data. The results of quadrilateral-related tests and interviews revealed that most students with high mathematical ability, some with medium mathematical ability, and a small number with low mathematical ability have a concept image that matches the definition but cannot produce proof of the properties of a quadrilateral. In addition, a small number of students with high mathematical talents, some with medium mathematical abilities, and a large number of students with low mathematical abilities were unable to completely explain each rectangle's formal definition and properties. This indicates that there are some students whose concept image is low. So, several alternatives and effective mathematics learning should be implemented to facilitate students in enhancing students concept image.

IDENTIFICATION OF HIGH SCHOOL STUDENTS' COMPUTATIONAL THINKING SKILLS IN SOLVING BINOMIAL PROBABILITY PROBLEMS

This study aims to identify the computational thinking skills of high school students in solving binomial probability problems. This research uses a case study method with a descriptive qualitative approach. The subjects of this study were three students of class XI, where each student represented each category of mathematical ability in general, namely: low, medium, and high. Data collection using test and interview methods. Based on the results of data analysis using computational thinking stages, that found: 1) Students with high mathematical abilities can fulfill the stages of computational thinking skills in each given problem. 2) Students with medium mathematical abilities can’t always fulfill the stages of computational thinking. When unable to solve problems, students with medium mathematical abilities have problem formulation and abstraction skills. 3) Students with low mathematical abilities are not as good as students with medium or high mathematical abilities. Students with low mathematical ability cannot fulfill all stages of computational thinking when they cannot solve problems.

Students' Mathematical Literacy Ability in Calculus Courses in Online Learning at the University of Semarang

Learning calculus in an online class is very challenging for students. This type of research is qualitative with the aim of explaining students' mathematical literacy skills in calculus courses. The sample for this study were three students out of 38 students who took electrical engineering courses. The students consisted of different levels of initial mathematical ability, namely high (score 80), medium (scores between 50 to 80) and low (less than 50) in calculus courses. Test and interview methods were used to collect data. The results showed that students with high mathematical abilities (S1) were at level 4 of their literacy skills and the percentage score reached 78.3%. Students with medium mathematical abilities (S2) are at level 3 of mathematical literacy skills with a score percentage reaching 62.5% and for students with low mathematical abilities (S3) are at level 2 literacy skills and the percentage score reaches 46.6%.

PROFIL PENALARAN MATEMATIS SISWA SMP DALAM PEMECAHAN MASALAH ARITMETIKA SOSIAL BERDASARKAN KEMAMPUAN MATEMATIKA

Mathematical reasoning is the ability to think about mathematical problems, namely by thinking logically about mathematical problems to get conclusions about problem solutions. There are several factors that can affect students' mathematical reasoning, including mathematical abilities. Dissimilarity of students' mathematical abilities allows for dissimilarity in their mathematical reasoning abilities. So, this research intends to describe students' mathematical reasoning abilities in solving social arithmetic problems based on dissimilarity in mathematical abilities. The purpose of this research was to describe qualitative data about the mathematical reasoning abilities of students with high, medium, or low abilities in solving social arithmetic problems. The instrument used was the Mathematical Ability Test to determine the three research subjects, followed by a Problem Solving Test to get qualitative data about students' mathematical reasoning abilities, then interviews to get deeper data that was not obtained through written tests. Thus, the research data were analyzed using mathematical reasoning indicators. From the result of data analysis, it was found that all students understood the problem well. Students with high and medium mathematical abilities are determining and implementing problem solving strategies properly, namely writing down the step for solving them correctly and making accurate conclusions by giving logical argumens at aech step of the solution. However, students with low mathematical abillities have difficulty in determining and implementing problem solving strategies because they do not understand the concept, thus writing the steps to solve the problems incorrectly and not giving accurate conclusions about the correctness of the solution.
 Keywords: mathematical reasoning, problem solving, mathematical abilities

ANALYTICAL THINKING PROCESS OF STUDENTS IN SOLVING MATHEMATICAL PROBLEMS OF QUADRATIC FUNCTIONS

Analytical thinking is an ability to observe objects thoroughly and solve facts comprehensively. This study is set to describe students' analytical thinking processes in solving mathematical problems, especially in quadratic functions. It employs a qualitative approach with qualitative descriptive research. The subjects in this study are one student with high mathematics ability, one student with medium mathematics ability, and one student with low mathematics ability of Tenth Grade of State Islamic Senior High School 3 Tulungagung. Data collection are carried out through task-based interviews. Meanwhile, data analysis technique are data reduction, data presentation, and conclusion Based on the results of data analysis and discussion, it is concluded that (1) The student with high mathematical ability pass several stages, namely differentiating, and organizing, he/he can solve the quadratic function problem properly according to the problem solving steps. (2) The student with medium mathematical ability can go through differentiating and organizing stages. But at the attributing stage, he/she are less able to solve problems based on the objectives. (3) The student with low mathematical ability tends not to pass differentiating, organizing, and attributing analytical thinking stages. He/she are less able to solve quadratic function problems according to the solving steps.Keywords: Analytical thinking process; problem solving; quadratic functions

STUDENTS' MATHEMATICAL COMMUNICATION SKILLS IN SOLVING STORY PROBLEMS BASED ON MATHEMATICAL ABILITIES

The research aims to describe the students' mathematical communication skills in solving story problems based on mathematical abilities. This research is descriptive qualitative research. Subjects in this research involved 3 students tenth-grade science in one of the senior high schools in Sidoarjo. Based on the mathematics scores in the last report card, I obtained one student with high mathematical abilities, medium mathematical abilities, and low mathematical abilities. The research data were obtained from mathematical communication skills tests and interviews based on a communication skills test. The results showed that students' mathematical communication skills are in line with their ability to solve problems on story problems because they are influenced by the level of mathematical ability of each student who is different in written and oral communication skills.

Students’ Mental Construction in Cube and Cuboid Concepts Based on Mathematical Ability Differences

Understanding of cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies of students’ understanding of these concepts have posited a gap between the students’ surface area and volume conceptions of its and students’ understanding. The study aims to describe the students’ mental constructions in APOS (Action, Process, Object, and Schema) theory framework. This study used analysis of students as subject to three junior high school students who have differences in mathematical abilities with a qualitative approach. Data were collected by the task sheet and interview. The result of this study evidences that subject who has high mathematical ability could solve problems about cube and cuboid concepts correctly in the action stage. In the process and object stage, subject could provide detailed explanations of how steps to assess the surface area and volume of cube and cuboid. She compared two shapes with different sizes of cube and cuboid. In the schema stage, she made systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject who has medium mathematical ability explained her mental construction in action and process stage well, despite the error in the process stage. Next stage, she had compared two different shapes of cube and cuboid to found their ratio. The last stage, she had not completed her explanation. The subject has low mathematical ability could solve the problems about cube and cuboid concepts. At the process, object, and schema stage, she had not completed its indicators to show cube and cuboid concepts.

PROFIL PENALARAN ANALOGI SISWA DALAM PEMECAHAN MASALAH MATEMATIKA DITINJAU DARI KEMAMPUAN MATEMATIKA

Analogy reasoning is the process of thinking logically and analytically in drawing conclusions based on the similarities between the two things being compared. The purpose of this study is to describe the analogy reasoning of students in solving mathematical problems in terms of high, medium, and low mathematical abilities. This research is a descriptive study with a qualitative approach. Data collection was carried out in class IX-H of SMP Negeri 5 Surabaya in the 2019/2020 school year by 33 students and each subject was selected for each category of mathematical ability. The results of the analysis of Problem Solving Tests and interviews show that students with high, medium, and low mathematical abilities mention information that is known and what is asked for logical reasons on the source and target problem, and explain the relations between the information. This indicates that each subject has an encoding process. Each subject also mentions and explains the concepts used to solve source problems, which means each subject has an inferring process. The difference is, subjects with high mathematical ability mention the same concepts between the source problem and the target problem and explain the concepts used to solve the target problem, then students can complete the target problem. This means that the subject is doing two other processes, namely mapping and applying. Subjects with medium mathematical abilities are mentioning the same concept between the source problem and the target problem but cannot explain the concept used in the target problem. However, the subject only did one of the two indicators in the mapping process, so the analogy reasoning process carried out by the subject was encoding and inferring. While students with low mathematical abilities are stopped in the encoding and inferring processes. Keywords: Analogy Reasoning, Mathematical Abilitiy

Algebraic Thinking Profiles of Junior High Schools’ Pupil in Mathematics Problem Solving

Algebra is one of concept that must be learned by pupils. It is because the algebraic concept can be used in all areas of mathematics. One of the ways that is used to develop pupils' algebraic abilities is to think algebraically. While one of the ways to develop pupils' algebraic thinking skills is to adapt pupils with mathematical problem solving. The purpose of this study is describing algebraic thinking profiles of junior high school pupils in mathematical problem solving. The description of pupils' algebraic thinking profiles is explained based on six indicators namely generalization, abstraction, analytic thinking, dynamic thinking, modeling and organization. This research is a qualitative study using test and interview methods. The research subjects consisted of one student in each student with high mathematical abilities, medium mathematical abilities and low mathematical abilities. The results showed that there were differences in algebraic thinking of junior high school pupils in solving mathematics in terms of mathematical abilities. Based on research data shows that pupils with high mathematical abilities always think algebraically in each problems solving are given, while students with medium and low ability do not always think algebraically in each of problem solving.

Profil Pemahaman Konseptual Mahasiswa Calon Guru Matematika tentang Grup Ditinjau dari Kemampuan Matematika

Many students have not mastered the concept of group theory well. Hence, the researcher intended to describe the conceptual understanding of group theory based on the student’s mathematical abilities. The implementation of this research begun with the students studied about Group Theory classically. Next, to examine the mathematical abilities of students, the researcher administered the questionnaire to obtain the data about the GPA (Grade Point Average) of students. Then, the researcher chose the participants of this study based on the high, middle, and low GPA. The selected research subjects were then given test questions that had been validated by the experts. Data was analyzed using the indicators of conceptual understanding, namely: (1) explaining or restate the group concept, (2) providing an example and a nonexample, (3) using group concept to solve the problem. The results showed that the students with high mathematical abilities reached three indicators of conceptual understanding perfectly. Students with medium mathematical abilities reached two indicators of conceptual understanding but it was not perfect, she did not write the answer completely. In addition, students with low mathematical abilities could not do the test at all, he could not write the group correctly. He did not reach any indicators of conceptual understanding, thus, it can be concluded that the students with low mathematical abilities did not understand the concept well.

Profil Berpikir Aljabar Siswa SMP dalam Memecahkan Masalah Matematika Kontekstual Ditinjau dari Kemampuan Matematika

Algebra is one of the important concepts in mathematics and began to be taught in class VII of junior high school. One way to find out students' thinking and reasoning abilities algebraically is to algebraic thinking. Algebraic thinking is a mental activity consisting of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. The means that can be used to explore students' algebraic thinking is problem solving. The problem used in this research is contextual mathematical problems. Algebraic thinking in each student in solving contextual mathematical problems varies based on the level of mathematical abilities. The purpose of this research is to describe the algebraic thinking’s profile of junior high school students in solving contextual mathematical problems based on mathematical abilities. This research uses a qualitative approach with methods of collecting data through tests and interviews. The subjects of this research were one student with high mathematical abilities, one student with medium mathematical abilities, and one student with low mathematical abilities. The results of this research indicate algebraic thinking of student with high mathematical abilities, consists of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. Algebraic thinking of student with medium mathematical abilities, consists of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. Algebraic thinking of student with low mathematical abilities, consists of generalization, dynamic thinking, and organization.Keywords: algebraic thinking, problem solving, contextual mathematical problems, mathematical abilities

Mathematics Metacognitive Skills of Papua’s Students in Solving Mathematics Problems

This research focuses on the analysis of mathematics metacognitive skills of Papua’s students in School of Indonesian Children in solving mathematics learning problems. The research was conducted to provide a good quality education for Papuan students, so the research start the research from the metacognitive skills especially in mathematics. The respondents of the research are 6 students from grade VII in School of Indonesian Children. Those respondents are represent of higher mathematical ability, medium mathematical ability, and lower mathematical ability. The research used descriptive qualitative research method. Data collection procedures used in this research was in-depth interview and participant observation as well as documents related to metacognitive process in solving the problems in learning mathematics. The in-depth interview was with the respondents, the Principal, the mathematical teacher and the Character Building teacher. For documents related to metacognitive process in solving the problems in learning mathematics such as the result national exam in elementary, the result daily test of math, the result of quiz or homework. In general, the students in Papua were lack of mathematics metacognitive ability such as, lack of cognitive knowledge and cognitive regulation, sometimes they cannot perform the activities that reflects conscious metacognitive such as mathematics problem solving. The research result indicates that the structure metacognitive ability of students in Papua influences their problem solving ability in learning mathematics. This metacognitive ability is also influenced by the fact that it becomes their characteristics background as respondents from Papua.

Mathematics Metacognitive Skills of Papua’s Students in Solving Mathematics Problems

This research focuses on the analysis of mathematics metacognitive skills of Papua’s students in School of Indonesian Children (SIC) in solving mathematics learning problems. The research was conducted to provide a good quality education for Papuan students, so the research start the research from the metacognitive skills especially in mathematics. The respondents of the research are 6 students from grade VII of SIC. Those respondents are represent of higher mathematical ability, medium mathematical ability, and lower mathematical ability. The research used descriptive qualitative research method. Data collection procedures used in this research was in-depth interview and participant observation as well as documents related to metacognitive process in solving the problems in learning mathematics. The in-depth interview was with the respondents, the Principal, the mathematical teacher and the Character Building teacher. For documents related to metacognitive process in solving the problems in learning mathematics such as the result national exam in elementary, the result daily test of math, the result of quiz or homework. In general, the students in Papua were lack of mathematics metacognitive ability such as, lack of cognitive knowledge and cognitive regulation, sometimes they cannot perform the activities that reflects conscious metacognitive such as mathematics problem solving. The research result indicates that the structure metacognitive ability of students in Papua influences their problem solving ability in learning mathematics. This metacognitive ability is also influenced by the fact that it becomes their characteristics background as respondents from Papua.