Papers by Ahmad Wachidul Kohar
This article describes primary teachers’ beliefs, knowledge, and performance regarding mathematic... more This article describes primary teachers’ beliefs, knowledge, and performance regarding mathematical problem-solving. An explorative descriptive research was undertaken involving 80 teachers from East Java Province, Indonesia. Data were obtained through questionnaires and problem-solving tasks. The results of this study indicate that
the teachers have a sufficient understanding of the knowledge of problem-solving as instruction and problem-solving in teaching practice. However, they have less understanding about the knowledge of problem-solving strategies and the meaning of mathematical problems. It can be explained from the teachers’ performance in problem-solving tasks, indicating that their incorrect answers were found to be a manifestation of their difficulties in applying problem-solving strategies. Analysis of teachers’ beliefs shows that the teachers tend to view mathematics as an instrumental tool, while they tend to view teaching mathematics as a learner focused task and students should learn mathematics as an autonomous exploration of students’ own interest, which is aligned with a problem-solving view.
This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i... more This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem-solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were
selected from an interview using a belief-related task from purposively selected teachers in
Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem-solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. The analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem-solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem-solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both Platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving
The urgency of improving Indonesian mathematics teachers lead to the consideration of developing ... more The urgency of improving Indonesian mathematics teachers lead to the consideration of developing innovative Teacher Profesional Development (TPD) within PMRI (Pendidikan Matematika Realistik Indonesia) or Indonesian version of realistic mathematics education. PMRI as a promising mathematics learning approach developed in Indonesia has been disseminated through a number of stratified workshops (local and national levels) which regards to the requirement of a good TPD. In this paper, we argue that innovative TPD within PMRI provides a model of sustainable professional program. In particular, we describe some experiences from PMRI workshops to investigate the unique characteristics of TPD within PMRI. It considers the characteristics of PMRI such as considering teacher as active learners instead of passive receiver, facilitating teachers in designing and implementing PMRI lesson, and organizing sustainable follow up workshops to strengthen mathematics teachers' community. The analysis shows that there are some improvements on teacher's conception toward mathematics teaching, practical teaching, mathematics content knowledge, and the use of learning media.
Journal of Physics: Conference Series, 2016
Weaknesses on problem solving of Indonesian students as reported by recent international surveys ... more Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers' responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers' work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
Considering the low performance of Indonesian students in PISA (Programme for International Stude... more Considering the low performance of Indonesian students in PISA (Programme for International Student Assessment) survey in the period 2000-2012, the need of PISAlike tasks promoting mathematical literacyis important to be developed as learning resource for practisioners. For these reasons, this study aims to produce a set of PISAlike mathematics tasks which are valid, practical, and has the potential effect as well as explain the process of developing those tasks. Thus, we used the preliminary stages, and prototyping using formative evaluation (self evaluation, expert review, one-to-one, small group, and field test). A total of 67 students of senior high school students at Palembang and 12 experts were involved in the prototyping phase. Data collection techniques used are walkthrough, documentation, questionnaire, test results, and interviews. This study produced a set PISA-like math tasks as many as 12 items in the category of content, context, and process. The validity came from the experts who reviewed the prototype at this stage, while the practicality, particularly, obtained from the revised tasks in the steps of both ‘one-to-one’and ‘small group’. From the field test, we conclude that the tasks also potentially effect to the students’ mathematical literacy in activating the indicators of each FMC, i.e, communication, reasoning and argumentation, representation, mathematising, problem solving, and using formal/symbolic language and the students’ interest and seriousness when solving the tasks.
Abstrak. Literasi matematika, kemampuan seseorang dalam merumuskan, menerapkan, dan menafsirkan m... more Abstrak. Literasi matematika, kemampuan seseorang dalam merumuskan, menerapkan, dan menafsirkan matematika ke dalam berbagai konteks telah menjadi isu penting dalam survei internasional PISA dalam beberapa tahun terakhir ini. Sebuah kerangka telah dirancang oleh dewan pelaksana PISA sebagai landasan dalam mengembangkan konsep literasi matematika sekaligus menyusun soal PISA beserta profilnya untuk digunakan pada survei tahun 2012. Dalam tulisan ini, peneliti menyajikan proses pengembangan soal berbasis literasi matematika dengan menggunakan kerangka PISA 2012 sebagai rujukan utama. Soal dikembangkan dengan alur formative evaluation, yang terdiri dari tahap self evaluation, one-to-one, expert review, small group, dan field test dengan melibatkan 8 ahli dari pakar PMRI, 2 ahli dari tim PISA Australia, dan 67 siswa SMA usia 15 tahun di kota Palembang. Hasil penelitian menunjukkan soal yang dikembangkan memenuhi kriteria valid dan praktis berdasakan analisis hasil one-to-one, expert review, dan small group dan mempunyai efek potensial berdasarkan analisis field test yang menunjukkan keterlibatan siswa secara aktif dalam memunculkan indikator kemampuan dasar matematika yang disebutkan oleh kerangka PISA. Kata Kunci: pengembangan soal, literasi matematika, kerangka PISA 2012, kemampuan dasar matematika.
1 Modul Olimpiade Matematika SMP M M Ruang lingkup materi yang akan diujikan pada Olimpiade Sains... more 1 Modul Olimpiade Matematika SMP M M Ruang lingkup materi yang akan diujikan pada Olimpiade Sains Nasional disesuaikan dengan silabus Olimpiade Sains Nasional yang disusun oleh Direktorat Pembinaan SMP, Direktorat Jenderal Pendidikan Dasar, Kementerian Pendidikan Nasional. Adapun ruang lingkup materi adalah sebagai berikut. Raih Juara Olimpiade Matematika 3 Modul Olimpiade Matematika SMP M M BAB 1 PEMECAHAN MASALAH MATEMATIKA (MATHEMATICS PROBLEM SOLVING) A. Langkah-Langkah Pemecahan Masalah Matematika Untuk menyelesaikan masalah dalam olimpiade matematika dengan menggunakan pendekatan pemecahan masalah, kita akan mengikuti langkahlangkah dari Polya (1988) yang telah disusun secara hirarkis, yaitu: Langkah 1 : Memahami masalah (PAHAMI) Untuk dapat memahami masalah, hal-hal yang bisa dilakukan adalah 1. Identifikasi apa yang diketahui dan apa yang ditanyakan (dibuktikan) 2. Memperkenalkan notasi yang cocok PAHAMI RENCANAKAN JALANKAN PERIKSA KEMBALI SOLUSI Raih Juara Olimpiade Matematika 5 Modul Olimpiade Matematika SMP M M Ternyata kita melihat ada pola baru yang mengingatkan kita pada koefisien ekspansi binomial atau segitiga Pascal untuk mengetahui banyaknya elemen dari tiap-tiap himpunan bagian. Oleh karena itu, banyak himpunan bagian S dari n elemen adalah banyak himpunan bagiannya yang dapat dinyatakan dalam 2 n .
SEA DR Conference 2013
This study is motivated by the theory of multiple intelligences which reveal that a student will ... more This study is motivated by the theory of multiple intelligences which reveal that a student will be able to learn mathematics well, if it is delivered in accordance with the intelligence that matches with his/her intelligences. Because the intelligences of students in the classroom are diverse, teachers need to use a variety of ways so that the students can also be facilitated in accordance with the intelligences they have. Therefore, it is needed mathematics learning instruments integrating multiple intelligences. This is a developmental research that uses a model of Plomp development consisting of preliminary investigation, design, realization, and phase of the test, evaluation, and revision. The objectives of this research are to describe the process and results of developing mathematics learning instruments, as well as acquire it which integrates multiple intelligences on topics of cuboid and cube for the eighth grade students of Junior High School. The instruments were trialed on 25 students at grade VIII of SMP Negeri 1 Bojonegoro year 2010/2011. The results showed that the learning instruments are categorized as good learning instruments. The instruments consisting lesson plan, student's book, student's worksheet, assessment sheet are valid. They are also practical shown by the average of the experts stated that it can be used by little revision, and the average of learning implementation is categorized as a good implementation. They are also effective, shown by the student's activity of multiple intelligences involvement is effective, student's learning outcomes is classically successful, and student's response is positive.
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Papers by Ahmad Wachidul Kohar
the teachers have a sufficient understanding of the knowledge of problem-solving as instruction and problem-solving in teaching practice. However, they have less understanding about the knowledge of problem-solving strategies and the meaning of mathematical problems. It can be explained from the teachers’ performance in problem-solving tasks, indicating that their incorrect answers were found to be a manifestation of their difficulties in applying problem-solving strategies. Analysis of teachers’ beliefs shows that the teachers tend to view mathematics as an instrumental tool, while they tend to view teaching mathematics as a learner focused task and students should learn mathematics as an autonomous exploration of students’ own interest, which is aligned with a problem-solving view.
selected from an interview using a belief-related task from purposively selected teachers in
Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem-solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. The analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem-solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem-solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both Platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving
the teachers have a sufficient understanding of the knowledge of problem-solving as instruction and problem-solving in teaching practice. However, they have less understanding about the knowledge of problem-solving strategies and the meaning of mathematical problems. It can be explained from the teachers’ performance in problem-solving tasks, indicating that their incorrect answers were found to be a manifestation of their difficulties in applying problem-solving strategies. Analysis of teachers’ beliefs shows that the teachers tend to view mathematics as an instrumental tool, while they tend to view teaching mathematics as a learner focused task and students should learn mathematics as an autonomous exploration of students’ own interest, which is aligned with a problem-solving view.
selected from an interview using a belief-related task from purposively selected teachers in
Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem-solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. The analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem-solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem-solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both Platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving