The Effect of Problem-Based Learning on Metacognitive Ability in the Conjecturing Process of Junior High School Students

This study aimed to analyze the effect of problem-based learning on metacognitive abilities in the conjecturing process of junior high school students. To reach this purpose, a mixed-methods design, which is a combination of quantitative and qualitative methods, was used. The quantitative method was used to analyze the metacognitive abilities of the students’ conjecturing process, while the qualitative method was used to explore observation and interview data. The subjects of this study consisted of 60 eighth-grade students. Two learning models were compared, namely the problem-based learning model and the conventional learning model. The metacognitive abilities of students’ conjecturing process were measured by a pattern generalization problem-solving test. After collecting the data and analyzing them through the independent-samples t-test, it was revealed that the PBL had a significant effect on the metacognitive abilities of students’ conjecturing process in solving pattern generalization problems. Finally, based on the results, some conclusions and implications were suggested.

The Emergence of the “FlexTech” Orchestration of Inferential Reasoning on Pattern Generalization

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.

Investigating Middle School Students Generalization of Number Pattern Based on Learning Style

Pattern generalization is an important aspect of mathematics contained in every topic in teaching. This study aims to investigate middle school students’ generalization of number patterns based on learning style. Descriptive qualitative, portraying or describing the events that are the center of attention (problem-solving abilities, student learning styles) qualitatively.This study explored 4 participants (12 to 13 years old) with their constructed number pattern they had generalized during individual task-based interviews. Questions that include indicators of the problem solving process in terms of student learning styles, and interviews. The data analysis used was namely data reduction, data presentation, drawing conclusions. We found that students who are converger, diverger, accommodator, and assimilator understands the problem by knowing what is known and asked and explains the problem with their own sentences. The converger and assimilator students look back without checking the counts involved, the diverger students do not see other alternative solutions and do not check the counts involved, accommodator students consider that the solutions obtained are logical, ask themselves whether the question has been answered, check the counts that are done, reread the question, and use other alternative solutions. The implication of this study indicated that students of the type of converger, diverger, accommodator, and assimilator are able to solve problems through the stages of implementing plans by interpreting problems in mathematical form, implementing strategies during the process and counting takes place. Based on several studies on pattern generalization, there have not been researchers who have revealed the number pattern generalization of high school students based on learning styles.

STRATEGIES OF PATTERN GENERALIZATION FOR ENHANCING STUDENTS’ ALGEBRAIC THINKING

Mathematics is seen as a science of pattern. Identifying and using patterns is the essence of mathematical thinking for children to improve algebraic thinking from their early schooling. The pattern is an arrangement of objects that have regularities or properties that can be generalized. Therefore, it is essential to know the strategies used by students in generalizing patterns and how students think in these processes. This study is descriptive research with a mixed quantitative-qualitative approach that aimed to investigate student’s algebraic thinking using various strategies to generalize the visual pattern. An instrument about the linear geometric growing pattern was administrated to 75 upper primary school students (grades 5-6) and 81 lower secondary students (grades 7-8) in two private schools in Semarang, Indonesia. The results showed that students used different pattern generalization strategies. The student generally preferred recursive, chunking, and functional approaches in each generalization task, whereas few used counting from drawing strategies to generalize patterns. The use of the recursive strategy decreased, whereas the chunking strategy and the functional strategy increased across grades 5-8 for the problems. The results also showed the student who used the recursive and chunking strategy preferred to change visual patterns into rows of numbers. Hence, they adopt a numeric approach by finding the common difference of visible pattern in each step.

PEMECAHAN MASALAH GENERALISASI POLA MATEMATIKA CALON GURU SEKOLAH DASAR DITINJAU DARI GAYA BELAJAR [THE PROBLEM SOLVING OF MATHEMATICAL PATTERN GENERALIZATION BY PROSPECTIVE ELEMENTARY SCHOOL TEACHERS BASED ON LEARNING STYLES]

<p>This qualitative research aims to describe the problem solving of pattern generalization in terms of visual, auditory, and kinesthetic learning styles. The subjects in this study were three primary school teacher candidates at the University of Mataram with visual, auditory, and kinesthetic learning styles. Data was collected by giving ELSA learning style tests and pattern generalization tests to the subjects and interviewing the subjects. Data was analyzed using descriptive method and classificationing. The results showed that the research subjects who had a visual learning style were able to perform the problem-solving stages better than the audio and kinesthetic learning styles. This is because the visual learning style likes reading or understanding written instructions which results in the visual learning style being capable of good and orderly coding and processing of information.</p><p><strong>BAHASA INDONESIA ABSTRACT: </strong>Penelitian kualitatif ini bertujuan untuk mendeskripsikan pemecahan masalah generalisasi pola ditinjau dari gaya belajar visual, auditori dan kinestetik. Subjek pada penelitian ini adalah tiga orang mahasiswa calon guru Universitas Mataram dengan gaya belajar visual, auditori dan kinestetik. Pengambilan data dilakukan dengan cara memberikan tes gaya belajar ELSA dan tes generalisasi pola dan wawancara. Data dianalisis dengan cara deskriptif dan klasifikasi. Hasil penelitian menunjukkan bahwa subjek penelitian yang memiliki gaya belajar visual mampu melakukan tahapan pemecahan masalah yang lebih baik dibandingkan gaya belajar audio dan kinestetik. Hal ini disebabkan karena gaya belajar visual memiliki sifat suka membaca ataupun memahami instruksi secara tertulis yang mengakibatkan gaya belajar visual memiliki sifat mampu melakukan pengkodean dan pemrosesan informasi yang baik dan teratur.</p>

Proses Berpikir Siswa dalam Memperbaiki Kesalahan Generalisasi Pola Linier

AbstrakMasih banyak kesalahan yang dilakukan oleh siswa dalam menggeneralisasi pola linier yang disebabkan fokus pada data numerik. Siswa-siswa yang mengalami kesalahan ini penting diberikan kesempatan kembali untuk memperbaiki kesalahan dalam menggeneralisasi pola linier. Untuk itu, tujuan penelitian ini adalah menganalisis proses berpikir siswa dalam memperbaiki kesalahan generalisasi pola linier. Sesuai dengan tujuan penelitian tersebut, maka penelitian ini merupakan penelitian kualitatif deskriptif dengan pendekatan studi kasus terhadap 2 siswa kelas VIII sekolah menengah pertama yang berhasil memperbaiki kesalahan generalisasi pola linier. Hasil penelitian menunjukkan bahwa terdapat dua jenis proses berpikir dalam memperbaiki kesalahan generalisasi pola linier, yaitu memperbaiki dengan menguji dan mencoba, serta memperbaiki dengan mengganti strategi generalisasi. Proses memperbaiki dengan menguji dan mencoba terdiri dari tiga tahap, yaitu: tahap mencari beda, tahap menguji, dan tahap mencoba. Proses memperbaiki dengan mengganti strategi generalisasi terdiri dari tiga tahap, yaitu: tahap mencari beda, tahap mengganti strategi generalisasi, dan tahap menemukan rumus suku ke-n. Cara yang paling efektif untuk memperbaiki kesalahan generalisasi pola linier adalah dengan cara mengganti strategi. Students Thinking Processes in Correcting Errors of Linear Pattern GeneralizationAbstractThere are still many mistakes made by students in generalizing linear patterns due to the focus on numerical data. It is important for students who experience this error to be given another opportunity to correct errors in generalizing linear patterns. For this reason, the purpose of this study is to analyze students' thought processes in correcting errors in the generalization of linear patterns. By the objectives of this study, this research is a descriptive qualitative study with a case study approach to 2 students of class VIII junior high school who succeeded in correcting errors in the generalization of linear patterns. The results showed that there are two types of thought processes in correcting errors in the generalization of linear patterns, namely repairing by testing and trying, and improving by replacing generalization strategies. The process of improving by testing and trying consists of three stages, namely: the stage of finding a difference, the testing stage, and the trying stage. The process of improving by replacing the generalization strategy consists of three stages, namely: the stage of finding a difference, the stage of changing the generalization strategy, and the stage of finding the formula for the nth term. The most effective way to correct linear pattern generalization errors is by changing strategies.