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Improving mathematical proof based on computational thinking components for prospective teachers in abstract algebra courses Nurlaelah, Elah; Pebrianti, Aneu; Taqiyuddin, Muhammad; Dahlan, Jarnawi Afgani; Usdiyana, Dian
Jurnal Infinity Vol 14 No 1 (2025): VOLUME 14, NUMBER 1, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i1.p85-108

Understanding and constructing mathematical proofs is fundamental for students in abstract algebra courses. The computational thinking approach can aid the process of compiling mathematical proofs. This study examined the impact of integrating computational thinking components in constructing mathematical proofs. The researcher employed a sequential explanatory approach to ascertain the enhancement of algebraic proof capability based on computational thinking through the t- test. A total of 32 prospective teachers in mathematics education programs were provided with worksheets for seven meetings, which were combined with computational thinking components. Quantitative data were collected from initial and subsequent test instruments. Moreover, three prospective teachers were examined through case studies to investigate their mathematical proof capability using computational thinking components, including decomposition, abstraction, pattern recognition, and algorithmic thinking. The study's findings indicated that CT intervention enhanced students' logical reasoning, proof-writing abilities, and overall engagement with abstract algebra concepts. The findings illustrate that integrating computational thinking into learning strategies can provide a framework for developing higher-order thinking skills, especially in proving, which are essential for studies in mathematics education programs.

Didactic Transposition of Straight-Line Equations: from Scholarly Knowledge to Knowledge to be Taught Suarsana, I Made; Suryadi, Didi; Nurlaelah, Elah; Jupri, Al; Pacis, Estrella R.
Plusminus: Jurnal Pendidikan Matematika Vol. 4 No. 2 (2024): July
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/plusminus.v4i2.1528

Penelitian ini bertujuan untuk mengkaji proses transposisi didaktik materi persamaan garis lurus dari scholarly knowledge ke knowledge to be taught. Penelitian menggunakan framework didactical design research dengan pendekatan kualitatif dan desain fenomenologi hermeneutik. Sumber data adalah scholarly knowledge berupa buku geometri analitik di perguruan tinggi dan dokumen knowledge to be taught berupa kurikulum dan buku pelajaran matematika SMP kelas VIII. Beberapa temuan permasalahan yang dapat menjadi potensi munculnya hambatan belajar yaitu pernyataan bentuk umum persamaan garis lurus , pendefinisian gradien sebagai rasio jarak atau rasio perubahan, serta penggunaan konteks yang tidak memenuhi asumsi realitas matematika. Temuan ini dapat dijadikan acuan bagi noosfer agar lebih berhati-hati dan melakukan antisipasi dalam merancang kurikulum dan buku pelajaran tentang persamaan garis lurus. This research examines the didactic transposition process of straight-line equation material from scholarly knowledge to knowledge to be taught. The research uses a didactical design framework with a qualitative approach and hermeneutic phenomenological design. The data sources are scholarly knowledge in the form of analytical geometry books at universities and knowledge-to-be-taught documents in the form of curriculum and grade VIII middle school mathematics textbooks. Some of the problem findings that could potentially create barriers to learning include stating the general form of the straight-line equation y=mx+c, defining gradient as a distance ratio or change ratio, and using contexts that do not meet the assumptions of mathematical reality. These findings can be a reference for the noosphere to be more careful and anticipate when designing curricula and textbooks about straight-line equations.

The effect of experiential learning and directed instructions assisted by augmented reality on students' self-regulated learning Maulida, Aya Shofia; Wahyudin, Wahyudin; Turmudi, Turmudi; Nurlaelah, Elah
Jurnal Infinity Vol 13 No 2 (2024): VOLUME 13, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v13i2.p553-568

In the last decade, augmented reality has been one type of virtual reality technology. AR can be applied to mobile learning, improving efficiency and effectiveness in education, even for learning mathematics. The study aims to analyze and describe comprehensively the effect of experiential learning and direct instruction assisted by augmented reality on the acquisition and improvement of students' mathematical reasoning abilities. This research uses quantitative methods with a quasi-experimental, one-group pretest-posttest design and a pretest-posttest control group design. The sample in this study consisted of 50 students in the eighth grade at one of the secondary schools in Bandung, Indonesia. The instrument in this study is a set of mathematical reasoning ability tests. The results of this study concluded that 1) Based on the standard of the deviation, the descriptive spread of scores for achieving mathematical reasoning abilities of students learning with experiential learning assisted by augmented reality (more widespread); 2) Cohen's d value on the output paired samples effect sizes was 14.003 with a point estimate of (large) so the value of the effects sizes obtained shows that the implementation of experiential learning assisted augmented reality has a major effect on the acquisition of mathematical reasoning abilities; 3) The mean achievement of mathematical reasoning abilities of students studying with experiential learning assisted by augmented reality was 60.38 relatively lower than the mean achieving mathematics reasoning abilities of students who studied with directed instructions assisted by augmented reality, 70.33; 4) The effect size value shown by the value is -3.50, and this value is less than 0.2, so based on Cohen's d criterion, then the effect of experiential learning assisted by augmented reality on the acquisition of mathematical reasoning abilities students are in the small category. The findings combine experiential learning and directed instructions assisted by augmented reality, influencing students' reasoning ability mathematically.

Improving mathematical proof based on computational thinking components for prospective teachers in abstract algebra courses Nurlaelah, Elah; Pebrianti, Aneu; Taqiyuddin, Muhammad; Dahlan, Jarnawi Afgani; Usdiyana, Dian
Jurnal Infinity Vol 14 No 1 (2025): VOLUME 14, NUMBER 1, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i1.p85-108

Understanding and constructing mathematical proofs is fundamental for students in abstract algebra courses. The computational thinking approach can aid the process of compiling mathematical proofs. This study examined the impact of integrating computational thinking components in constructing mathematical proofs. The researcher employed a sequential explanatory approach to ascertain the enhancement of algebraic proof capability based on computational thinking through the t- test. A total of 32 prospective teachers in mathematics education programs were provided with worksheets for seven meetings, which were combined with computational thinking components. Quantitative data were collected from initial and subsequent test instruments. Moreover, three prospective teachers were examined through case studies to investigate their mathematical proof capability using computational thinking components, including decomposition, abstraction, pattern recognition, and algorithmic thinking. The study's findings indicated that CT intervention enhanced students' logical reasoning, proof-writing abilities, and overall engagement with abstract algebra concepts. The findings illustrate that integrating computational thinking into learning strategies can provide a framework for developing higher-order thinking skills, especially in proving, which are essential for studies in mathematics education programs.

Does students' thought structure in object configuration patterns follow cognitive verbs in learning outcomes? Dahlan, Jarnawi Afgani; Nurlaelah, Elah; Bariyah, Nusrotul; Kristiani, Yasinta Dian
Jurnal Infinity Vol 14 No 2 (2025): VOLUME 14, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i2.p551-570

This study aims to comprehensively investigate students' learning approach in identifying, predicting, and generalizing object and number configuration. A qualitative method was applied with as many as 28 participants from eighth-grade students in Bandung, Indonesia. Students’ ability to recognize, predict, and generalize the configuration of objects and numbers was assessed. At the same time, the approaches employed in the process were analyzed. The research showed that students used different approaches to figure out the pattern of objects and number configuration. These approaches were: descriptive, operational, visual-descriptive, visual-operational, and descriptive-visual-operational. Keywords were typically employed in the descriptive approach to predict unknown objects or numbers. However, the descriptive approach could not accurately predict specific patterns. Therefore, students employed other approaches, including operational, visual-descriptive, visual-operational, and descriptive-visual-operational approaches. Unfortunately, all approaches have proven inadequate for formulating generalizations (general rules) independently. These results showed that when teaching students how numbers and objects are configured, they should be encouraged to try different ways of seeing patterns, such as descriptive, visual, operational, or a combination of the three.

The effect of experiential learning and directed instructions assisted by augmented reality on students' self-regulated learning Maulida, Aya Shofia; Wahyudin, Wahyudin; Turmudi, Turmudi; Nurlaelah, Elah
Jurnal Infinity Vol 13 No 2 (2024): VOLUME 13, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v13i2.p553-568

In the last decade, augmented reality has been one type of virtual reality technology. AR can be applied to mobile learning, improving efficiency and effectiveness in education, even for learning mathematics. The study aims to analyze and describe comprehensively the effect of experiential learning and direct instruction assisted by augmented reality on the acquisition and improvement of students' mathematical reasoning abilities. This research uses quantitative methods with a quasi-experimental, one-group pretest-posttest design and a pretest-posttest control group design. The sample in this study consisted of 50 students in the eighth grade at one of the secondary schools in Bandung, Indonesia. The instrument in this study is a set of mathematical reasoning ability tests. The results of this study concluded that 1) Based on the standard of the deviation, the descriptive spread of scores for achieving mathematical reasoning abilities of students learning with experiential learning assisted by augmented reality (more widespread); 2) Cohen's d value on the output paired samples effect sizes was 14.003 with a point estimate of (large) so the value of the effects sizes obtained shows that the implementation of experiential learning assisted augmented reality has a major effect on the acquisition of mathematical reasoning abilities; 3) The mean achievement of mathematical reasoning abilities of students studying with experiential learning assisted by augmented reality was 60.38 relatively lower than the mean achieving mathematics reasoning abilities of students who studied with directed instructions assisted by augmented reality, 70.33; 4) The effect size value shown by the value is -3.50, and this value is less than 0.2, so based on Cohen's d criterion, then the effect of experiential learning assisted by augmented reality on the acquisition of mathematical reasoning abilities students are in the small category. The findings combine experiential learning and directed instructions assisted by augmented reality, influencing students' reasoning ability mathematically.

Improving mathematical proof based on computational thinking components for prospective teachers in abstract algebra courses Nurlaelah, Elah; Pebrianti, Aneu; Taqiyuddin, Muhammad; Dahlan, Jarnawi Afgani; Usdiyana, Dian
Jurnal Infinity Vol 14 No 1 (2025): VOLUME 14, NUMBER 1, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i1.p85-108

Understanding and constructing mathematical proofs is fundamental for students in abstract algebra courses. The computational thinking approach can aid the process of compiling mathematical proofs. This study examined the impact of integrating computational thinking components in constructing mathematical proofs. The researcher employed a sequential explanatory approach to ascertain the enhancement of algebraic proof capability based on computational thinking through the t- test. A total of 32 prospective teachers in mathematics education programs were provided with worksheets for seven meetings, which were combined with computational thinking components. Quantitative data were collected from initial and subsequent test instruments. Moreover, three prospective teachers were examined through case studies to investigate their mathematical proof capability using computational thinking components, including decomposition, abstraction, pattern recognition, and algorithmic thinking. The study's findings indicated that CT intervention enhanced students' logical reasoning, proof-writing abilities, and overall engagement with abstract algebra concepts. The findings illustrate that integrating computational thinking into learning strategies can provide a framework for developing higher-order thinking skills, especially in proving, which are essential for studies in mathematics education programs.

Does students' thought structure in object configuration patterns follow cognitive verbs in learning outcomes? Dahlan, Jarnawi Afgani; Nurlaelah, Elah; Bariyah, Nusrotul; Kristiani, Yasinta Dian
Jurnal Infinity Vol 14 No 2 (2025): VOLUME 14, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i2.p551-570

This study aims to comprehensively investigate students' learning approach in identifying, predicting, and generalizing object and number configuration. A qualitative method was applied with as many as 28 participants from eighth-grade students in Bandung, Indonesia. Students’ ability to recognize, predict, and generalize the configuration of objects and numbers was assessed. At the same time, the approaches employed in the process were analyzed. The research showed that students used different approaches to figure out the pattern of objects and number configuration. These approaches were: descriptive, operational, visual-descriptive, visual-operational, and descriptive-visual-operational. Keywords were typically employed in the descriptive approach to predict unknown objects or numbers. However, the descriptive approach could not accurately predict specific patterns. Therefore, students employed other approaches, including operational, visual-descriptive, visual-operational, and descriptive-visual-operational approaches. Unfortunately, all approaches have proven inadequate for formulating generalizations (general rules) independently. These results showed that when teaching students how numbers and objects are configured, they should be encouraged to try different ways of seeing patterns, such as descriptive, visual, operational, or a combination of the three.

Exploration of Students' Mathematical Creative Reasoning Based on Extraneous Cognitive Load in Geometry Learning Agusti, Fardatil Aini; Suhendra, Suhendra; Nurlaelah, Elah
International Journal of Multidisciplinary Research of Higher Education Vol 8 No 3 (2025): (July) STEM, Education, Religion Studies, Social Sciences and Economic Developmen
Publisher : Islamic Studies and Development Center in Collaboration With Students' Research Center Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ijmurhica.v8i3.386

Creative reasoning and cognitive load management are two essential aspects in learning mathematics because they directly affect students' ability to understand concepts, develop solving strategies, and produce innovative solutions to mathematical problems. This study aims to explore the relationship between extraneous cognitive load and creative reasoning ability of elementary school students in solving geometry problems. This research used a qualitative approach with a case study design. The research subjects were 27 elementary school students who have learned the material of building space. Data were collected through extraneous cognitive load questionnaire, mathematical creative reasoning test, and interviews. Data analysis was done descriptively and thematically with reference to three indicators of creative reasoning, namely mathematical foundation, plausibility, and novelty, as well as five indicators of extraneous cognitive load: split attention, redundancy, transiency, advanced learner, and inadequate prior knowledge. The results showed that the higher the extraneous cognitive load experienced by students, the lower the creative reasoning score they achieved. Students with low extraneous cognitive load were able to understand information, develop logical strategies, and produce original solutions. In contrast, students with high extraneous cognitive load had difficulty understanding instructions, made mistakes in choosing strategies, and did not show flexible thinking skills. These findings reinforce the importance of learning design that takes into account students' cognitive working capacity. The implication of this research leads to the importance of teachers designing geometry lessons that have minimal instructional load, using effective visual media, and composing questions that are in accordance with students' abilities so that the creative thinking process can develop optimally.

Penerapan Model Pembelajaran Kooperatif Tipe CRH (Course, Review, Horray) Untuk Meningkatkan Kemampuan Pemahaman Matematis Siswa SMP Auliya, Risma Nurul; ., Darhim; Nurlaelah, Elah
Pasundan Journal of Mathematics Education Vol. 4 No. 1 (2014): Pasundan Journal of Mathematics Education
Publisher : Program Magister Pendidikan Matematika, Pascasarjana, Universitas Pasundan in collaboration with Asosiasi Guru Matematika Indonesia (AGMI) and Indonesian Mathematics Educators' Society (IMES)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23969/pjme.v4i1.2499

The aim of research are examining the application of cooperative learning model with CRH (Course, Review, Horray) type to improve student’s mathematical understanding ability. The research utilized a quasi experimental design. The population in this research are students in grade eight from one of junior high school in South Jakarta. As concern, the sample comprised of 32 students in CRH class (experiment group) and 34 students in conventional class (control group) which choosed by using purposive sampling technique. The problems are to improve mathematical understanding ability The quantitative analysis is used independent sample t-test, while qualitative analysis used a descriptive one. The result shows better increasing mathematical understanding ability by cooperative learning model applied CRH than by conventional teaching.

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