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Critical Thinking of Students with High and Low Mathematics Efficacy PISA Problem: A Case of Algebraic Task Yanto, Arfan Dwi; Wijaya, Muhammad Avicenna Wahyu; Kohar, Ahmad Wachidul
Journal of Mathematical Pedagogy (JoMP) Vol. 3 No. 2: July 2022
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jomp.v3n2.p68-80

Abstract

This study aims to describe students' critical thinking on PISA problems on algebra content in terms of high and low mathematics efficacy. This descriptive qualitative research involves two junior high school students with high and low mathematics efficacy in one of the junior high schools in Jombang Regency. Data collection techniques were carried out by administering a mathematics efficacy questionnaire, Algebraic Content PISA Problems (ACPP), and interview guidelines. Data analysis was based on indicators of critical thinking ability (interpretation, analysis, evaluation, inference, explanation, and self-regulation). From the results of data analysis, critical thinking in the interpretation aspect shows that only students with high mathematics efficacy can write what is known and asked. Likewise, in the analysis aspect, it shows that only students with high mathematics efficacy can create a mathematical model of the given problem.  In the evaluation aspect, students with high and low mathematical efficacy can write complete problem-solving. Likewise, in the inference aspect, students with high and low mathematics efficacy were able to draw conclusions logically. Likewise, in the explanation aspect, students with high and low mathematical efficacy can write down the final results and provide reasons for the conclusions drawn. Meanwhile, in the aspect of self-regulation, students with high and low mathematics efficacy have conducted a review. Therefore, understanding students' critical thinking is very important for students and teachers to improve students' ability to solve PISA problems.
Students' Deductive Reasoning in Evaluating Solutions to Geometry Problems Rahmah, Aulia; Dewi, Silvia Kumala; Kohar, Ahmad Wachidul
Journal of Mathematical Pedagogy (JoMP) Vol. 4 No. 2: July 2023
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jomp.v4n2.p74-83

Abstract

Deductive reasoning is very important in learning mathematics and is one of the formal goals that emphasizes the arrangement of reasoning. This is a qualitative research that aims to describe the deductive reasoning abilities of junior high school students in evaluating problem solutions in geometry material. The subjects of this study were two junior high school students in Gresik who had high mathematical abilities and were of different genders. The instrument used was task-based interviews. The task in question is a deductive reasoning ability test in which there are problems and their solutions. Data analysis was carried out using three indicators of deductive reasoning according to Sumarmo: carrying out calculations based on certain formulas, conducting proofs, and drawing conclusions. The results showed that the deductive reasoning abilities of female and male students were relatively the same. In solving the problem, Both male and female students had similar initial idea by making an example of the length of the side of the given object. However, male students are more capable of proving and considering more effective strategies for solving problems. Therefore, students and teachers need to improve their deductive reasoning abilities and consider all effective strategies for solving problems.
Students' New Concept Construction Process Based on APOS Theory: Introvert versus Extrovert Mahfudhoh, Mahfudhoh; Saniya, Saasa; Kohar, Ahmad Wachidul
Journal of Mathematical Pedagogy (JoMP) Vol. 4 No. 2: July 2023
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jomp.v4n2.p84-96

Abstract

This study aims to describe the process of constructing new concepts for students with introverted and extroverted personalities. The research subjects were two students of grade VI in one of the elementary schools with different personalities (introverts and extroverts). Data collection techniques using personality test questionnaires, tests, and interviews. Analysis of the data from the proportion concept test results refers to the APOS indicator (Action, Process, Object, Schema). The results showed that there were differences between introverted and extroverted students in the process of constructing students' new concepts on proportion concept. At the Action stage, they can solve problems related to the concept of worth comparison. The two subjects used a similar strategy, namely the multiplication operation. At the Process stage, introverted subjects can interpret the value comparison problem into various representations, both tables and graphs, and can explain its characteristics. While the extrovert subject is only able to represent the problem of value comparison in the form of a table only and experiences doubts in explaining its characteristics. At the Object stage, they can provide other examples of the concept of value comparison, but introverted subjects are more creative in this regard. In addition, they are also able to classify whether a problem includes the concept of valued comparison or not. At the Schema stage, they can define worth comparison and can infer its relationship with several concepts even though the extroverted subject has not fully concluded its relationship with the classification of comparison. This description can be used as input for teachers in choosing learning methods or strategies to convey material that is well received by each student.
Developing pre-service mathematics teachers’ curriculum knowledge for designing mathematics lesson: A professional development model Ekawati, Rooselyna; Palupi, Evangelista Lus Windyana; Kohar, Ahmad Wachidul; Putri, Hani Rizkia
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 8 Issue 1 January 2023
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v8i1.2295

Abstract

This paper aims to describe an innovative Teacher Professional Development Program (TPDP) to develop pre-service mathematics teachers’ curriculum knowledge. The participants of this study were eighteen pre-service mathematics teachers who have not learned about curriculum as a course in their teacher education program. Two different instruments to measure Pre-Service Teacher Curriculum Knowledge in the domain of statistics and algebra were delivered before and after the TPDP. The innovative TPDP for pre-service teachers in this study considered the current school mathematics curriculum as an entry object of learning. Furthermore, the triangle object such as the development of curriculum among countries, essential mathematics content, as well as designing lessons were elaborated in the model. The developed TPDP and pre-service teachers' lesson designs were described and analyzed qualitatively to see the pre-service teachers' curriculum knowledge. The result of the study shows that there is an improvement in Pre-Service Teachers' Curriculum Knowledge in almost all the components of Curriculum Knowledge, except basic skills and concepts. This implies that for designing a lesson plan, pre-service mathematics teachers need to carefully understand the school mathematics structure as a whole in a brief before the basic competence is reviewed.
Mathematics teacher educators’ noticing of pedagogical content knowledge on hierarchical classification of quadrilateral Rooselyna Ekawati; Ahmad Wachidul Kohar; Tatag Yuli Eko Siswono; Agung Lukito; Kai-Lin Yang; Khoirun Nisa
Jurnal Infinity Vol 12 No 2 (2023): VOLUME 12, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v12i2.p261-274

Abstract

This study aims to investigate mathematics teacher educators’ (MTE) knowledge in noticing preservice teachers’ pedagogical content knowledge (PCK) on the hierarchical classification of the quadrilateral. A multiple case study was conducted to analyze the responses of ten MTEs in an online moderated-forum group discussion (M-FGD) from their written work on the MTE-PCK test completed prior to the M-FGD. The PCK test consisted of two tasks: the task that examines MTEs’ knowledge to predict pre-service teachers’ reason in representing the hierarchical classification of quadrilateral in Venn diagrams, and the task that examines MTEs’ knowledge in making a flowchart as a recommendation to mathematics teacher to analyze the validity of quadrilateral classification. Results show that the MTEs indicate two considerations of noticing pre-service teachers’ PCK on the quadrilateral classification: by definition and properties of quadrilaterals and by the visual appearance of quadrilaterals. Despite this, 20% of them were indicated to perform a lack of understanding of the hierarchical classification of quadrilaterals, as indicated by invalid flowcharts of validating the hierarchical classification of the quadrilateral.
Prospective teachers’ design of numeracy tasks using a physical distancing context Kohar, Ahmad Wachidul; Rahaju, Endah Budi; Rohim, Abdur
Journal on Mathematics Education Vol. 13 No. 2 (2022): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v13i2.pp191-210

Abstract

Physical distancing, which is widely practiced limiting the spread of COVID-19, is recognized to contain mathematical thoughts that can be harnessed as a context for prospective teachers’ practices of mathematical problem posing. The goal of this study is to investigate the profile of mathematical tasks posed by prospective mathematics teachers using the context of physical distancing that meets the criteria of numeracy tasks. Data were collected from 66 mathematical tasks posed by thirty-three prospective teachers at a public university in Surabaya, Indonesia, attending an assessment course of numeracy based on a problem-posing task. To analyze, the posed tasks were first identified as solvable or unsolvable tasks and then further categorized into the domains of the level of context use and the level of cognitive processes. Results show that the level of context use embedded in the posed tasks varies from zero to first order, with only a few of the posed tasks being coded as having second-order context. Regarding the levels of cognitive processes, most of the posed tasks reach the level of understanding, with only a small number of reasoning tasks identified. Interestingly, all the tasks coded to contain second-order context are classified as reasoning tasks. Some implications regarding designing numeracy tasks using physical distancing and interventions in teacher education related to numeracy task design are discussed.
Aligning numeracy task design with SDG goals: Nutrition facts as a context for prospective mathematics teachers' problem posing Sari, Yurizka Melia; Kohar, Ahmad Wachidul; El Milla, Yulia Izza; Fiangga, Shofan; Rahayu, Dwi Shinta
Journal on Mathematics Education Vol. 15 No. 1 (2024): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v15i1.pp191-206

Abstract

Nutrition facts are the details on food packaging that describe its nutritional value, including serving size, calories, macronutrients like carbohydrates, protein, and fat, and micronutrients such as vitamins and minerals. These facts have mathematical concepts that can be utilized as a context for prospective teachers to create mathematical problems. By leveraging this real-world data, educators can contribute to multiple Sustainable Development Goals (SDGs), particularly SDG 3 (Good Health and Well-being), by promoting nutritional awareness, and SDG 4 (Quality Education) by enhancing student engagement and understanding through relatable examples. This study examines the profile of mathematical tasks created by prospective mathematics teachers using nutrition facts as a context that meets numeracy task criteria. Data were collected from 62 mathematical tasks created by 31 prospective teachers attending a realistic mathematics education course on numeracy based on a problem-posing task at a public university in Surabaya, Indonesia. The posed tasks were categorized into solvable or unsolvable tasks and the domains of the level of context use and the level of cognitive processes. Results revealed that the level of context use in the posed tasks varied from zero to second order. Surprisingly, most of the tasks were in the first-order level context. Most posed tasks reached the application level, with only a few identified as reasoning tasks. Interestingly, some tasks coded as second-order context were classified as reasoning tasks. The study provides implications for designing numeracy tasks using nutrition facts and interventions in teacher education related to numeracy task design.
Deductive or inductive? Prospective teachers’ preference of proof method on an intermediate proof task Siswono, Tatag Yuli Eko; Hartono, Sugi; Kohar, Ahmad Wachidul
Journal on Mathematics Education Vol. 11 No. 3 (2020): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.
Students’ cognitive processes in solving problem related to the concept of area conservation Ekawati, Rooselyna; Kohar, Ahmad Wachidul; Imah, Elly Matul; Amin, Siti Maghfirotun; Fiangga, Shofan
Journal on Mathematics Education Vol. 10 No. 1 (2019): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area conservation test. Results indicate that both samples performed more cyclic processes on formulating solution planning, regulating solution part and detecting and correcting error during the problem-solving. However, it was found that the high achiever student performed some processes than those of low achiever. Also, while the high achiever student did not predict any outcomes of his formulated strategies, the low achiever did not carry out the thought process after detecting errors of the initial solution gained. About the concept of area conservation, the finding also reveals that within the samples’ cognitive processes, the use of area formula come first before students decided to look for another strategy such as doing ‘cut-rotate-paste’ for the curved planes, which do not have any direct formula. The possible causes of the results were discussed to derive some recommendation for future studies.
FUNSTATION (FUN STATISTICS EDUCATION) SEBAGAI ALTERNATIF UNTUK MENINGKATKAN PEMAHAMAN STATISTIKA SISWA SEKOLAH MENENGAH PERTAMA Fadlilah, ChusnuL; Meilina, Dika Dwi; Hasanah, Ika Nur; Kohar, Ahmad Wachidul
Galois: Jurnal Penelitian Pendidikan Matematika Vol 1 No 1 (2022): Galois : Jurnal Penelitian Pendidikan Matematika
Publisher : Program Studi Tadris Matematika Fakultas Ilmu Tarbiyah dan Keguruan UIN Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/gjppm.v1i1.1043

Abstract

In the era of the industrial revolution 4.0 and society 5.0, the world's development became very fast and unlimited. Therefore, to face these challenges, it is necessary to have quality human resources who are competent, ready to compete and compete. Quality human resources can be developed through both formal and non-formal education. The better quality of education will encourage the realization of a comprehensive understanding of students so as to form a young generation that is intelligent, critical, creative, innovative and accomplished. The development of quality human resources is needed at all levels of education, one of which is the junior high school level. However, junior high school students still have difficulty in learning statistics. To overcome these difficulties, an innovative product was developed in the form of statistical learning media FUNSTATION (Fun Statistics Education). Development research was conducted to develop FUNSTATION (Fun Statistics Education) statistical learning media based on the ADDIE model (Analyze, Design, Develop, Implement, Evaluate). The results showed that the assessment met the criteria of validity, practicality and effectiveness. Validity is fulfilled based on an assessment by a media expert lecturer. Meanwhile, practicality and effectiveness were obtained based on the results of questionnaires on junior high school students. The results of the questionnaire and trial test showed that the use of FUNSTATION (Fun Statistics Education) from 10 students stated that it was practical and effective. So it can be concluded that the learning media FUNSTATION (Fun Statistics Education) has met the three assessments that can improve statistical understanding. ABSTRAK Pada era revolusi industry 4.0 dan society 5.0 perkembangan dunia menjadi sangat cepat dan tak terbatas. Oleh karena itu untuk menghadapi tantangan tersebut diperlukan kualitas sumber daya manusia yang memiliki kompetensi, siap bersaing dan berkompetisi. Sumber daya manusia yang berkualitas dapat dikembangkan melalui pendidikan baik formal maupun nonformal. Kualitas pendidikan yang semakin baik akan mendorong terwujudnya pemahaman siswa secara komprehensif sehingga terbentuk generasi muda yang cerdas, kritis, kreatif, inovatif dan berprestasi. Pengembangan kualitas sumber daya manusia yang berkualitas diperlukan dalam semua jenjang pendidikan salah satunya jenjang sekolah menengah pertama. Namun, siswa sekolah menengah pertama masih mengalami kesulitan pada materi pembelajaran statistika. Untuk mengatasi kesulitan tersebut dikembangkan produk inovatif berupa media pembelajaran statistika FUNSTATION (Fun Statistics Education). Penelitian pengembangan dilakukan untuk mengembangkan media pembelajaran statistika FUNSTATION (Fun Statistics Education) berdasarkan model ADDIE (Analyze, Design, Develop, Implement, Evaluate). Hasil penelitian menunjukkan bahwa penilaian memenuhi kriteria kevalidan, kepraktisan dan keefektifan. Kevalidan dipenuhi berdasarkan penilaian oleh dosen ahli media. Sementara kepraktisan dan keefektifan diperoleh berdasarkan hasil kuesioner pada siswa SMP. Hasil kuesioner dan tes uji coba menunjukkan bahwa penggunaan FUNSTATION (Fun Statistics Education) dari 10 siswa menyatakan praktis dan efektif. Sehingga diperoleh kesimpulan bahwa media pembelajaran FUNSTATION (Fun Statistics Education) telah memenuhi ketiga penilaian yang dapat meningkatkan pemahaman statistika.