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Mathematical Critical Thinking: Analysis of Middle School Students' Thinking Processes in Solving Trigonometry Problems Tajuddin, Annas Tasyah; Sujadi, Imam; Slamet, Isnandar; Hendriyanto, Agus
Mosharafa: Jurnal Pendidikan Matematika Vol. 12 No. 4 (2023): October
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/mosharafa.v12i4.1185

Abstract

Kemampuan berpikir kritis siswa dalam matematika saat ini masih lemah. Penelitian ini bertujuan untuk mengidentifikasi karakteristik kemampuan berpikir kritis matematis siswa dalam menyelesaikan masalah trigonometri. Metode penelitian yang digunakan adalah studi kualitatif dengan desain fenomenologi, melibatkan peneliti sebagai instrumen utama. Penelitian ini menggunakan tes (masalah trigonometri), pedoman wawancara, dan observasi sebagai instrumen non-tes. Subjek penelitian terdiri dari tiga siswa kelas X yang dipilih dengan teknik purposive sampling. Uji keabsahan dilakukan melalui triangulasi metode dan teori, serta analisis data menggunakan teknik induktif. Hasil penelitian menunjukkan bahwa siswa dengan kemampuan berpikir kritis cenderung lebih efektif dan cepat dalam menyelesaikan masalah trigonometri. Mereka memiliki pendekatan unik dalam memecahkan masalah dan fokus pada pencarian jawaban. Pemikiran kritis matematis juga mempengaruhi kemampuan siswa dalam memahami dan menghubungkan informasi yang ada dalam soal. Selain itu, pemikiran kritis matematis berdampak pada pemikiran logis dan daya ingat yang baik, sehingga siswa lebih mudah dalam menentukan formula pemecahan masalah. Students' critical thinking skills in mathematics are currently still weak. This study aims to identify the characteristics of students' mathematical critical thinking abilities in solving trigonometry problems. The research method used is a qualitative study with a phenomenological design involving researchers as the main instrument. This study uses tests (trigonometry problems), interview guidelines, and observation as non-test instruments. The research subjects consisted of three class X students selected by purposive sampling technique. The validity test was carried out through method and theory triangulation and data analysis using inductive techniques. The results showed that students with critical thinking skills tended to be more effective and faster in solving trigonometry problems. They have a unique approach to solving problems and focus on finding answers. Mathematical critical thinking also affects students' ability to understand and relate the information contained in the problem. In addition, mathematical critical thinking impacts logical thinking and good memory, so students find it easier to determine problem-solving formulas.
The Autoregresiive Integrated Moving Average and Fuzzy Time Series Cheng Hybrid for Predicting Stock Price Neyun, Ignasia N.G.; Sulandari, Winita; Slamet, Isnandar
Jurnal Bumigora Information Technology (BITe) Vol. 5 No. 2 (2023)
Publisher : Universitas Bumigora

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30812/bite.v5i2.2972

Abstract

Background: PT Telkom Indonesia Tbk is the largest company in the telecommunications sector in Indonesia. PT Telkom's share price always rises every year, attracting investors to invest. In investing, it is very important to analyze shares in order to know the situation and condition of the shares. Objective: This research aims to predict the share price of PT Telkom Indonesia Tbk. Methods: The method used is the Autoregressive Integrated Moving Average (ARIMA)-Fuzzy Time Series Cheng hybrid method. Cheng's FTS model is able to overcome nonlinearity problems in ARIMA model residuals. In this research, the first modeling uses the ARIMA model, where the data is divided into two, namely January to November 2019 data used as training data, and December 2019 data used as testing data. Next, residual modeling was carried out with FTS Cheng. Hybrid forecasting is obtained by adding up the results of ARIMA and FTS Cheng forecasts. Result: Model evaluation is based on MAPE values and in this study the MAPE value of the ARIMA-FTS Cheng hybrid model was obtained at 1.03\% for training data and 1.09\% for testing data. Conclusion: The hybrid model has a MAPE value of less than 10\%, so it can be concluded that the ARIMA-FTS Cheng hybrid model can predict PT Telkom Indonesia Tbk stock closing price data accurately.
Pengembangan Modul Berbasis Pendidikan Matematika Realistik untuk Meningkatkan Kemampuan Berpikir Kritis Siswa SMA Tajuddin, Annas Tasyah; Sujadi, Imam; Slamet, Isnandar
Prosiding SNPBS (Seminar Nasional Pendidikan Biologi dan Saintek) 2022: Prosiding SNPBS (Seminar Nasional Pendidikan Biologi dan Saintek)
Publisher : Universitas Muhammadiyah Surakarta

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

Abstract

Media pembelajaran yang dapat digunakan dalam pembelajaran matematika adalah modul. Guru dapat mengembangkan modul berdasarkan pendekatan pembelajaran yang sesuai dengan perkembangan dan kebutuhan pembelajaran matematika. Pendekatan tersebut harus dapat menarik perhatian siswa pada proses pembelajaran dan melibatkan partisipasi aktif mereka. Selain itu, harus mampu mengoptimalkan suasana belajar untuk menciptakan kegiatan belajar yang bermakna bagi siswa. Salah satu pendekatan yang dapat memberikan makna dan terkait dengan realitas kehidupan siswa adalah Pendidikan Matematika Realistik. Pembelajaran matematika juga didukung oleh penguasaan keterampilan berpikir kritis siswa, yaitu proses berpikir efektif untuk membantu siswa membuat sesuatu, mengevaluasi, dan menerapkan keputusannya sesuai dengan apa yang diyakini atau dilakukan. Penerapan modul berdasarkan Pendekatan Pendidikan Matematika Realistik pada pembelajaran matematika dapat melatih keterampilan siswa dalam menghubungkan, memanipulasi, dan mentransformasikan pengetahuan dan pengalaman yang telah dimilikinya untuk berpikir kritis dalam rangka mengambil keputusan dan memecahkan masalah. Proses pembelajaran berlangsung secara alamiah dimana siswa melakukan aktivitas dan memperoleh pengalaman bukan menerima pengetahuan yang ditransfer dari guru. Artikel ini ditulis dengan menggunakan metode studi kepustakaan dengan teknik analisis isi dari artikel ilmiah dan referensi lain berupa media cetak dan elektronik yang relevan.Berdasarkan analisis terhadap beberapa artikel dan referensi ilmiah yang relevan, ditemukan bahwa penerapan pendekatan Pendidikan Matematika Realistik di SMA menghasilkan peningkatan hasil belajar dan kemampuan berpikir kritis.
Analysis of junior high school students' refractive thinking process in solving numeracy problems Janah, Rahmawati Fatkhul; Sujadi, Imam; Slamet, Isnandar
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 12 No 3 (2024)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v12i3.18446

Abstract

The purpose of this study is to examine how junior high school students use refractive thinking to solve algebraic problems based on their mathematical skill levels, specifically high and low. Refractive thinking involves a phase where students rethink and modify their approaches to solving algebraic problems. This qualitative study employs interviews and observational methods, with participants consisting of students with both high and low mathematical abilities. The results indicate that students with high mathematical ability navigate the stages of refractive thinking more effectively, including problem identification, strategy formulation, and evaluation. These students are often able to quickly identify errors and experiment with multiple strategies to arrive at better solutions. In contrast, students with low mathematical ability struggle with problem identification and tend to persist with initial, less effective approaches. These findings highlight significant differences in the refractive thinking processes of the two groups, underscoring the need to develop instructional strategies that foster reflective thinking skills, particularly for students with lower mathematical aptitude.
The Impact of Intelligence (IQ) and Learning Styles on Mathematics Learning Motivation and Achievement in Secondary School Students Prayitno, Hadi; Sujadi, Imam; Slamet, Isnandar; Pramesti, Getut
Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika Vol. 9 No. 1 (2025): JRPIPM SEPTEMBER 2025
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jrpipm.v9n1.p101-117

Abstract

This study aims to examine the influence of intelligence quotient (IQ) and learning styles on students’ learning motivation and mathematics achievement among tenth-grade high school students. The research employed a quantitative approach using an ex post facto design. A total of 83 students participated in the study, selected through a census sampling technique, as the entire population of tenth-grade students was included. Instruments used in this study included an IQ test, a learning style questionnaire (covering auditory, visual, and kinesthetic styles), a motivation questionnaire, and a mathematics achievement test. Data analysis involved instrument validity and reliability testing, classical assumption tests (normality and homogeneity), and multivariate analysis (MANOVA) to assess both the direct and interaction effects of IQ and learning styles on learning motivation and mathematics achievement. The results showed that IQ had a significant effect on mathematics achievement (p < 0.05), but no significant effect on learning motivation. Learning styles did not significantly influence either mathematics achievement or learning motivation. Furthermore, there was no significant interaction between IQ and learning styles in relation to either outcome. The coefficient of determination (R²) indicated that the model explained 26.3% of the variance in mathematics achievement and 16.5% of the variance in learning motivation. It can be concluded that IQ contributes to students’ success in mathematics, while learning motivation and performance are also shaped by other factors beyond IQ and learning styles. These findings highlight the importance of instructional strategies that consider students’ intellectual capacities along with affective and contextual factors
FORECASTING STATIONARY CLIMATE DATA USING AUTOREGRESSIVE MODELS AND HIGH-ORDER FUZZY Kayyisa, Alfien Diva; Sulandari, Winita; Slamet, Isnandar
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0313-0324

Abstract

Forecasting is essential for improving aviation safety, with air humidity being a critical factor influenced by air temperature. This study analyzes daily humidity data from I Gusti Ngurah Rai Airport, one of Indonesia’s busiest air stations, using two time series modeling approaches: Autoregressive (AR) and high-order fuzzy modeling. The objective is to evaluate and compare their forecasting accuracy. Historical daily data from the Meteorology, Climatology, and Geophysics Agency of Indonesia were used to build the forecasting models. The optimal linear AR model served as the foundation for constructing the AR high-order fuzzy model, which incorporates linguistic rules to capture nonlinear patterns. Both models were implemented and evaluated using the Mean Squared Error (MSE) metric. Results show that the AR(2) model outperforms the AR high-order fuzzy model, achieving a lower MSE of 13.23. This suggests that the AR(2) model provides more accurate humidity forecasts over the observed period. These findings offer practical insights for policymakers and decision-makers in forecasting daily humidity levels and supporting aviation operations. While the study confirms the effectiveness of traditional AR modeling, it also highlights limitations of the fuzzy approach, particularly its sensitivity to parameter tuning and data sparsity. The integration of high-order fuzzy modeling represents a novel contribution to this domain, though further refinement is needed to enhance its forecasting performance.
Markov-switching and noise-to-signal ratio approach for early detection of currency crises Sugiyanto, Sugiyanto; Nirwana, Muhammad Bayu; Slamet, Isnandar; Zukhronah, Etik; Parahita, Syifa’ Salsabila Gita
International Journal of Advances in Applied Sciences Vol 15, No 1: March 2026
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijaas.v15.i1.pp42-54

Abstract

Economic instability can easily lead to a currency crisis. Therefore, observing a number of crisis indicators is crucial for building an early warning system (EWS). However, selecting the indicators most responsive to the crisis is the best choice. For this purpose, the noise-to-signal ratio (NSR) method was used. Monthly data from 1990-1925 were used in the autoregressive moving average (ARMA), generalized autoregressive moving average with generalized autoregressive conditional heteroscedasticity (GARMACH), and Markov-switching (MS)-GARMACH hybrid models to explain the crisis. Model interpretation indicates that there will be no crisis from May 2025-April 2026.
The Comparison of Cooperative Learning Model Viewed from Students’ Emotional Intelligence Junaedi, Ahmad; Budiyono, Budiyono; Slamet, Isnandar
International Journal of Science and Applied Science: Conference Series Vol 2, No 1 (2018): International Journal of Science and Applied Science: Conference Series
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1048.6 KB) | DOI: 10.20961/ijsascs.v2i1.22734

Abstract

This research aimed to know the different influence of each learning model, emotional Intelligence, and interaction between those two elements toward the students’ achievement in mathematic. This is an experimental study within the 3x3 factorial design. The populations of this study were VII grade students of State Junior High Schools (SMP) in Surakarta city in academic year of 2016/2017. The samples of this study were students of SMPN 8 Surakarta, SMPN 16 Surakarta, and SMPN 20 Surakarta which were taken by stratified cluster random sampling. The instruments to collect the data were achievement test, questionnaire and documentation. The technique to analyze the data was variance analysis of two ways with different cell. Based on the result, it can be concluded that: (1) TGT model produced the same good result as well as TAI model, TGT model produced the better achievement than the direct learning, and TAI model produced the better achievement than direct learning in the algebra material. (2) Students having high emotional intelligence are better than students having low and medium emotional intelligence in term of achievement in mathematics. The students having medium emotional intelligence are as low as students having low emotional intelligence in term of achievement in algebra material. (3) In each category of emotional intelligence, TGT model produced higher achievement than TAI model and direct learning model, TAI and direct learning model produced the equal result in algebra material. (4) In each learning model, students’ achievement of those who have high emotional intelligence are higher than those who have medium and low emotional intelligence, and students who have low and medium intelligence produced the equal achievement in algebra material.
Perbandingan Metode Seasonal Autoregressive Integrated Moving Average (SARIMA) dan Extreme Learning Machine (ELM) pada Peramalan Peredaran Uang Kartal di Indonesia Pratiwi, Afita Ulya; Zukhronah, Etik; Slamet, Isnandar
Indonesian Journal of Applied Statistics Vol 7, No 2 (2024)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.13057/ijas.v7i2.83128

Abstract

Money is generally accepted as legal tender in fulfilling an obligation. Money circulation is very important to be considered and controlled, to have a positive impact on the economy. Control of money circulation is usually emphasized on the type of cash, which is in the form of paper and metals. One of the ways that can help in controlling cash is by forecasting. This study aims to compare the accuracy of forecasting results on cash circulation data using the SARIMA and ELM methods. The data used is the circulation cash from January 2011 to April 2022. The SARIMA method is a method for forecasting time series data containing seasonality, while the ELM method is a method on artificial neural networks that can do forecasting. The best SARIMA model obtained is SARIMA (1,1,0)(0,1,0)12. The best ELM architecture obtains 12 input layer neurons, 45 hidden layer neurons, and 1 output layer. The measure of forecasting error to determine the best model is using MAPE. The results show that the SARIMA method has a training data MAPE of 2,3270% and testing data of 2,2772%, while the ELM method has a training data MAPE of 4,2548% and testing data of 3,8615%. Therefore, the SARIMA method is better than the ELM method at forecasting the circulation of cash in Indonesia.Keywords: cash; extreme learning machine; seasonal autoregressive integrated moving average.  
PENGEMBANGAN MODUL PEMBELAJARAN DENGAN PENDEKATAN DISCOVERY LEARNING PADA MATERI LIMIT FUNGSI ALJABAR KELAS X DI SMA INSAN CENDEKIA SUKOHARJO TAHUN AJARAN 2015/2016 Wulandari, Setyati Puji; Budiyono, Budiyono; Slamet, Isnandar
Journal of Mathematics and Mathematics Education Vol 7, No 1 (2017): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v7i1.20236

Abstract

Abstract: The aims of this research were to: 1) determine the validity of the results of the development of learning modules with discovery learning approach on the material of limit algebra functions; 2) determine the practicality of the development of learning modules; 3) determine the effectiveness of the development of learning modules; 4) determine whether students achievement in the material of limit algebra functions using learning modules is better than the students who don’t use it. The development of the modules was done through the modified Four D, namely define, design, development, and disseminate. Data were analyzed using descriptive analysis. Validity analysis was based on an expert assessment. Practicality analysis was based on implementation of learning module. Effectiveness analysis was based on student response after using the module. Analysis of student achievement was based on t-test hypothesis. The result concluded that: 1) learning modules with discovery learning approach to the material limit algebra functions declared fit for use by experts with the validity score of 3.44 and be in very good criteria; 2) learning modules expressed practical use in learning with the practicality score gained from the sheet of implementation of learning is 0.919 and be in very good criteria; 3) learning modules is effective for use in learning with the scores of effectiveness obtained from the sheet of student's response to the module is 3.03 and be in good criteria; 4) learning achievement of students who use the learning module is better than students who don’t use it, but isn’t significant.Keywords: learning module, discovery learning, limit algebra functions.
Co-Authors Abda Abda Adi Wicaksono, Nanda AHMAD JUNAEDI Anggraini, Putri Nurika Aprilia, Nabila Churin Aulia Ar Rakhman Awaludin Ayuningrum, Retna Azhar, Zenitha Amalia B Budiyono Budiyono Budiyono Budiyono, Budiyono Ek Ajeng Rahmi Pinahayu Fachry Abda El Rahman Fhadilla, Nahdatul Fitriana, Laila Fitriana, Laila Nur Getut Pramesti Hadi Prayitno, Hadi Handajani, Sri Sulistijowati Heldy Ramadhan Putra P Hendriyanto, Agus Heritin, Anisak Hermawati, Evi Hodiyanto, Hodiyanto Husna Afanyn Khoirunissa Ikrar Pramudya, Ikrar Imam Sujadi Imam Suryadi, Imam Indra Raditya , Dionisius Indra Setyawan Irwan Susanto Irwan Susanto Isnaini, Bayutama Janah, Rahmawati Fatkhul Kadar, Jimmy Abdel Kayyisa, Alfien Diva Lintang Fitra Utami Mardiyana Mardiyana Meilasari, Venty Meilasari, Venty Muhammad Riza Naufalia Nuraya, Naufalia Neyun, Ignasia N.G. Ningrum, Sri Adiningsih Utami Nirwana, Muhammad Bayu Nugraha, Titis Jati Nugroho, Muhamad Asif Cahya Aji Nur Hasanah Nurfauziyyah, Nuha Parahita, Syifa’ Salsabila Gita Pardede, Hilman Ferdinandus Permatasari, Nisa Permatasari, Nisa Pitra Dwiningsih, Pitra Pratama, Yulian Surya Pratiwi, Afita Ulya PUJI LESTARI Raditya, Dionisius Indra Ratri, Aninda Puspa Respatiwulan, Respatiwulan Sari, Putri Permata Shanti Indah Lestari, Shanti Indah Sri Subanti Suci Irawati Sugianto Sugianto Sugiyanto - Sugiyanto, Sugiyanto Sulandari, Winita Susanti, Sarah Wahyu Susilotomoa, Dhestahendra Citra Tajuddin, Annas Tasyah Tririnika, Yuliana Valentino, Yohanes Felix Vera Rosalina Bulu Wahyu Kurniawan Winita Sulandari Wulandari, Setyati Puji Wulandari, Setyati Puji Yudi Pramono Pawiro, Yudi Pramono Yuliana Susanti, Yuliana Zukhronah, Etik