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Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes Matitaputty, Christi; Nusantara, Toto; Hidayanto, Erry; Sukoriyanto
Journal on Mathematics Education Vol. 13 No. 3 (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.v13i3.pp393-414

Abstract

Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world. Therefore, this study aimed to examine in-service mathematics teachers' pedagogical content knowledge (PCK) to determine students’ mistakes in solving permutations and combinations problem and their teaching strategies to eliminate these errors. Data were collected by distributing vignettes, CoRe, and PaP-eRs to thirteen mathematics teachers from ten provinces in Indonesia after they finished an online professional teacher education program to determine their PCK in teaching permutations and combinations. The data collected were analyzed qualitatively using a content analysis approach to obtain categories inductively. The result showed that PCK of in-service mathematics in teaching permutations and combinations was observed by identifying student mistakes conceptually and procedurally, even though some could not determine their mistakes in permutations. On the other hand, the knowledge of instructional strategies can engage all students in active learning, but most of them only give general answers. Furthermore, an in-depth understanding of permutations and combinations topic is needed to support the development of teachers’ pedagogic competencies sustainably. The contribution of this research will be of interest to curriculum development and mathematics educators.
How mathematics teachers' special knowledge changing: A case study in the Professional Teacher Education program Matitaputty, Christi; Nusantara, Toto; Hidayanto, Erry; Sukoriyanto
Journal on Mathematics Education Vol. 15 No. 2 (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.v15i2.pp545-574

Abstract

The COVID-19 pandemic has catalyzed the widespread adoption of distance learning, necessitating a comprehensive understanding of how teacher knowledge evolves within the context of Teacher Professional Education (TPE) programs. Some research endeavors may employ evaluation methodologies that inadequately capture the nuanced dimensions of knowledge, highlighting the necessity for greater incorporation of evidence-based approaches in the formulation and assessment of teacher development initiatives. This study employs a qualitative methodology to explore the evolution of Mathematics Teachers' Specialized Knowledge (MTSK) within the framework of a TPE program. Data were gathered through the engagement of three educators in the preparation and execution of lessons on permutation and combination via a Learning Management System (LMS), coupled with in-depth interviews. The findings underscore the TPE program's role in fostering collaborative learning environments through participation in online educational communities. Teachers are shown to be increasingly integrating technology into their pedagogical practices, albeit with varying degrees of proficiency. The presence of Professional Learning Communities (PLCs) is identified as instrumental in supporting educators in refining instructional strategies to enhance teaching effectiveness. Nevertheless, there remains a subset of teachers necessitating more profound and more comprehensive content knowledge about their subject matter. These insights emphasize the importance of designing TPE programs that offer sustained and adaptable professional development opportunities to facilitate continuous growth among educators. Consequently, it is recommended that online learning communities geared toward addressing the diverse learning requirements of students be established, thereby aiding in the identification and resolution of pedagogical challenges.
Effect of recitation method on mathematical reasoning ability and student self confidence Mohammad Dadan Sundawan; Toto Nusantara; Subanji Subanji; Erry Hidayanto
Premiere Educandum : Jurnal Pendidikan Dasar dan Pembelajaran Vol. 13 No. 1 (2023)
Publisher : Universitas PGRI Madiun

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25273/pe.v13i1.19144

Abstract

Mathematics is one of the basic sciences that has an important role in the world of education. In general, the purpose of learning mathematics is to help students prepare themselves to be able to face changing circumstances in life and in an ever-evolving world, through practicing acting on the basis of logical, rational and critical thinking and preparing students to be able to use mathematics and a mathematical mindset. in everyday life and in studying various sciences. The aims of this study were (1) to determine the effect of the use of the recitation method on the mathematical reasoning abilities of grade VI elementary school students; (2) to determine the effect of using the recitation method on the self-confidence of VI elementary students. The method that researchers used in this study was quasi-experimental (quasi-experimental). Sampling in this study using purposive sampling technique, while for data analysis researchers used the normality test, homogeneity test, correlation analysis, simple linear regression analysis and t test. The results showed that there is an effect of the recitation method on students' mathematical reasoning abilities of 19.7% and the average value of mathematical reasoning abilities in the experimental class is better than the average value of mathematical reasoning abilities in the control class. There is an effect of the recitation method on students' self-confidence of 51.2%.
DISSECTING STUDENT MISCONSTRUCTION IN TRANSFORMATIONAL ACTIVITIES SOLVES PROBLEMS THAT ALLOW COGNITIVE CONFLICT TO OCCUR Rosimanidar Rosimanidar; Purwanto Purwanto; Erry Hidayanto; I Made Sulandra
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 13, No 3 (2024)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v13i3.9457

Abstract

The transformative activity was crucial for problem-solving. In resolving problems, cognitive conflicts could arise, characterized by construction errors marked by deviations or differences from scientific concepts. Eight of the 106 students who experienced cognitive conflicts made construction errors in transformative activities. These errors were categorized into four groups. This research aimed to describe students' construction errors in transformative activities when solving problems that might lead to cognitive conflicts. The research design was phenomenological, with four subjects selected and one student from each group. Student responses and interview results served as research data, analyzed through narrative text analysis. The research findings revealed four forms of construction errors in students during transformative activities in problem-solving that might lead to cognitive conflicts: (1) pseudo construction "correct," occurring when students provide a correct answer to a problem, but upon closer examination, it was found that the clarification of the answer was incorrect; (2) pseudo construction "incorrect," happening when students gave an incorrect answer to a problem, but upon closer examination, the students had a correct thought process and could provide the right answer; (3) hole construction errors, occurring when there were inconsistencies in the construction process of concepts in students' minds; and (4) mis-analogical construction errors, occurring when students made errors in analogizing a problem with representations of other concepts. These four construction errors occurred in transformative activities based on incomplete rule-based systems. Examining these construction errors allowed instructors to improve students' transformative thinking activities according to linear equations with one variable.Aktivitas transformasional sangat penting dalam menyelesaikan masalah. Dalam penyelesaian masalah kemungkinan terjadi konflik kognitif, yaitu kesalahan konstruksi yang ditandai ada penyimpangan atau perbedaan dengan konsep ilmiah. Mahasiswa mengalami konflik kognitif sebanyak 106 orang dan 8 mahasiswanya telah melakukan kesalahan konstruksi dalam aktivitas transformasional. Penelitian ini bertujuan untuk mendeskripsikan kesalahan konstruksi mahasiswa dalam aktivitas transformasional menyelesaikan masalah yang memungkinkan terjadi  konflik kognitif. Jenis penelitian ini adalah fenomenologi dengan dipilih 4 subjek penelitian yang masing-masing 1 mahasiswa dari setiap kelompok tersebut. Jawaban mahasiswa dan hasil wawancara digunakan sebagai data penelitian. Data penelitian dianalisis melalui analisis teks naratif. Temuan penelitian diperoleh bahwa ada empat bentuk kesalahan konstruksi mahasiswa yang dibedah dalam aktivitas transformasional menyelesaikan masalah yang memungkinkan terjadi konflik kognitif, yaitu (1) pseudo construction “benar” yang terjadi saat mahasiswa memberikan jawaban benar terhadap suatu permasalahan, namun ketika ditelusuri, ternyata mahasiswa salah dalam memberikan klarifikasi jawaban; (2) Kesalahan pseudo construction “salah” yang terjadi saat mahasiswa memberikan jawaban salah terhadap suatu permasalahan, namun ketika ditelusuri mahasiswa mempunyai cara berpikir yang benar dan dapat memberikan jawaban yang benar; (3)Kesalahan lubang konstruksi (hole construction) yang terjadi saat proses konstruksi konsep dalam pikiran mahasiswa ada yang tidak sesuai;  dan (4) kesalahan mis-analogical construction yang terjadi saat mahasiswa membuat kesalahan dalam menganalogikan masalah dengan representasi konsep lain. Keempat kesalahan konstruksi tersebut terjadi pada aktivitas transformasional berbasis aturan tidak lengkap (incomplete rule-based). Penelaahan kesalahan konstruksi ini dijadikan dasar bagi dosen untuk memperbaiki aktivitas berpikir transformasional mahasiswa sesuai konsep persamaan linier satu variabel
PRE-SERVICE TEACHERS’ SYMBOLIC-VISUAL REPRESENTATION SKILLS IN ADDING AND SUBTRACTING FRACTIONS Arwan Mhd. Said; Purwanto Purwanto; Erry Hidayanto; Rustanto Rahardi
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 13, No 3 (2024)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v13i3.10233

Abstract

The current study attempted to describe pre-service teachers’ symbolic-visual representation skills in adding and subtracting fractions. It specifically aimed to analyze the teachers’ ability to construct either a symbolic or visual representation in fraction operations. A case study was conducted by involving 17 fifth-semester students who were enrolled in a teacher training course at one of universities in Ternate, Indonesia. The participants consisted of two males and fifteen females. The study data were gathered using a fraction problem-solving test. The results showed that: 1) the majority of participants succeeded in performing fraction operations and making representations by adding and subtracting fractions; 2) the participants demonstrated proficiency in executing fraction operations but showed poor ability in generating different representations of fractions; 3) the participants were more successful in creating visual representation for fraction addition compared to fraction subtraction. The participants also excelled in constructing circle models as visual representations, outperforming other visual representation models such as number lines, rectangular models for transition situations, and numerical representations of mixed fractions.
KECERDASAN LOGIS MATEMATIS SISWA DALAM MENYELESAIKAN MASALAH KONTEKSTUAL Dwi Aldi Hidayatulloh; Erry Hidayanto; Santi Irawati
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 13, No 4 (2024)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v13i4.9058

Abstract

Seringkali siswa masih kesulitan memecahkan masalah kontekstual. Hal ini terungkap dari hasil studi pendahuluan ditemukan bahwa sebagian besar siswa belum mampu melakukan penalaran deduktif untuk menemukan solusi. Oleh karena itu, diperlukan penelitian untuk mengeksplorasi bagaimana kecerdasan logis matematis siswa dalam menyelesaikan masalah kontekstual. Tujuan penelitian ini yaitu untuk mendeskripsikan kecerdasan logis matematis siswa dalam menyelesaikan masalah kontekstual. Penelitian ini menggunakan pendekatan kualitatif dengan metode analisis deskriptif. Penelitian dilaksanakan di SMP Negeri 3 Batu tahun ajaran 2023-2024. Terdapat 31 responden dan dipilih tiga subjek penelitian yang mewakili masing-masing satu siswa dari kategori kecerdasan logis matematis. Instrumen penelitian terdiri dari angket persepsi kecerdasan logis matematis, tes kecerdasan logis matematis dan pedoman wawancara. Data tersebut dianalisis menggunakan teknik triangulasi. Hasil penelitian menunjukan siswa dengan persepsi kecerdasan logis matematis tinggi mampu memenuhi semua indikator kecerdasan logis matematis dalam menyelesaikan masalah kontekstual. Siswa dengan persepsi kecerdasan logis matematis sedang memenuhi indikator mampu mengidentifikasi informasi yang terdapat pada permasalahan dengan lengkap, mampu melakukan operasi numerik dan mampu membuat kesimpulan jawaban dari permasalahan dan cukup mampu melakukan penalaran secara deduktif. Siswa dengan persepsi kecerdasan logis matematis rendah hanya mampu memenuhi indikator mengidentifikasi informasi yang terdapat pada permasalahan. Often students still have difficulty solving contextual problems. This was revealed from the results of the preliminary study which found that the majority of students were not able to carry out deductive reasoning to find solutions. Therefore, research is needed to explore how students' mathematical logical intelligence in solving contextual problems. The aim of this research is to describe students' mathematical logical intelligence in solving contextual problems. This research uses a qualitative approach with descriptive analysis methods. The research was carried out at SMP Negeri 3 Batu in the 2023-2024 academic year.   There were 31 respondents and three research subjects were selected representing one student each from the mathematical logical intelligence category. The research instrument consisted of a mathematical logical intelligence perception questionnaire, a mathematical logical intelligence test and an interview guide. The data was analyzed using triangulation techniques. The research results show that students with a high perception of mathematical logical intelligence are able to fulfill all indicators of mathematical logical intelligence in solving contextual problems. Students with the perception of moderate mathematical logical intelligence meet the indicators of being able to identify the information contained in the problem completely, being able to carry out numerical operations and being able to draw conclusions about answers to problems and being quite able to carry out deductive reasoning. Students with a perception of low mathematical logical intelligence are only able to fulfill the indicators of identifying the information contained in the problem.
Kemampuan Berpikir Kritis Siswa SMP dalam Menyelesaikan Masalah Geometri Wulandari, Monika Retno; Hidayanto, Erry; Kusumasari, Vita
Jurnal Gantang Vol 10 No 1 (2025): Jurnal Gantang
Publisher : Universitas Maritim Raja Ali Haji

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31629/jg.v10i1.7197

Abstract

This study aims to describe the critical thinking skills of junior high school (SMP) students in solving geometry problems. A descriptive qualitative approach was used, involving six eighth-grade students selected through purposive sampling. The subjects consisted of two students from each category of mathematical ability: high (  & ), medium (  & ), and low (  & ). The six students were selected based on their performance in the written test and their verbal communication skills, as observed during the pre-research phase, to ensure a more accurate representation of the population. Data were collected through written tests consisting of two essay questions and semi-structured interview guidelines developed based on Facione’s critical thinking indicators: interpretation, analysis, evaluation, and inference. The research data collected were written test results and interviews, which were then analyzed based on critical thinking indicators. The results showed that interpretation was the indicator most easily achieved by all subjects, analysis was optimally achieved only by students with high mathematical ability, while evaluation and inference were the most difficult indicators to fulfill. The study concludes that students’ critical thinking skills in solving geometry problems are generally low, primarily because of insufficient mastery of the underlying material.
Literasi Matematis Siswa Extrovert dalam Menyelesaikan Masalah Tidak Terstruktur (Ill-Structure Problem) Gestiani, Anggun; Erry Hidayanto; Sukoriyanto
Indiktika : Jurnal Inovasi Pendidikan Matematika Vol. 7 No. 2 (2025): Indiktika : Jurnal Inovasi Pendidikan Matematika
Publisher : Universitas PGRI Palembang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31851/indiktika.v7i2.17135

Abstract

Penelitian ini bertujuan mendeskripsikan bagaimana literasi matematis siswa extrovert dalam menyelesaikan ill-structure problem. Subjek penelitian merupakan siswa kelas VIII yang dipilih menggunakan teknik purposive sampling untuk dilakukan wawancara yaitu dengan memilih siswa yang memiliki kemampuan literasi matematis yang tinggi dan dengan tipe kepribadian extrovert. Teknik pengumpulan data terdiri dari pengisian angket tipe kepribadian, tes literasi matematis dan wawancara. Teknik analisis data dilakukan dengan reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa subjek mampu memenuhi indikator formulate (merumuskan), yaitu mampu mengidentifikasi informasi serta variabel penting dalam permasalahan, dan menyusun model matematis yang sesuai. Namun, subjek belum mampu memenuhi indikator employ (menggunakan) karena tidak menerapkan model yang telah disusun untuk menemukan solusi. Selain itu, subjek juga belum memenuhi indikator interpret (menafsirkan) karena tidak menafsirkan hasil matematis yang diperoleh dalam konteks masalah.
Reversible thinking in solving mathematics problems in terms of cognitive style Fauzan, Hakmi Rais; Hidayanto, Erry; Chandra, Tjang Daniel
Al-Jabar: Jurnal Pendidikan Matematika Vol 15 No 2 (2024): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v15i2.24527

Abstract

Background: Reversible thinking, the ability to think bidirectionally, is a crucial component of mathematical problem-solving. Differences in cognitive styles, particularly field-dependent and field-independent characteristics, play a significant role in students' reversible thinking, necessitating a deeper exploration of these relationships.Aim: This study aims to describe students' reversible thinking processes in solving mathematical problems based on their cognitive styles, focusing on field-dependent and field-independent traits.Method: A qualitative descriptive approach was applied to 32 eighth-grade students from a junior high school in Malang City, Indonesia. Data were collected using the Group Embedded Figures Test (GEFT), a reversible thinking test, and semi-structured interviews. Students were categorized into field-dependent and field-independent groups using GEFT before undertaking a reversible thinking test. Semi-structured interviews were conducted to gain deeper insights into their problem-solving approaches.Results: The findings indicate that students with field-independent cognitive styles exhibit better performance in the aspects of negation and reciprocity. They carefully apply problem-solving strategies, consistently reverting to initial values after achieving correct solutions. Conversely, students with field-dependent cognitive styles are more prone to errors, particularly in changing operation signs and applying the concept of reciprocal equivalence.Conclusion: This study highlights significant differences in reversible thinking between students with field-dependent and field-independent cognitive styles. The results suggest the need for tailored teaching methods to enhance reversible thinking based on cognitive styles. Further research is recommended to explore barriers and additional factors influencing reversible thinking.
Literasi Matematis Siswa Extrovert dalam Menyelesaikan Masalah Tidak Terstruktur (Ill-Structure Problem) Gestiani, Anggun; Erry Hidayanto; Sukoriyanto
Indiktika : Jurnal Inovasi Pendidikan Matematika Vol. 7 No. 2 (2025): Indiktika : Jurnal Inovasi Pendidikan Matematika
Publisher : Universitas PGRI Palembang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31851/indiktika.v7i2.17135

Abstract

Penelitian ini bertujuan mendeskripsikan bagaimana literasi matematis siswa extrovert dalam menyelesaikan ill-structure problem. Subjek penelitian merupakan siswa kelas VIII yang dipilih menggunakan teknik purposive sampling untuk dilakukan wawancara yaitu dengan memilih siswa yang memiliki kemampuan literasi matematis yang tinggi dan dengan tipe kepribadian extrovert. Teknik pengumpulan data terdiri dari pengisian angket tipe kepribadian, tes literasi matematis dan wawancara. Teknik analisis data dilakukan dengan reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa subjek mampu memenuhi indikator formulate (merumuskan), yaitu mampu mengidentifikasi informasi serta variabel penting dalam permasalahan, dan menyusun model matematis yang sesuai. Namun, subjek belum mampu memenuhi indikator employ (menggunakan) karena tidak menerapkan model yang telah disusun untuk menemukan solusi. Selain itu, subjek juga belum memenuhi indikator interpret (menafsirkan) karena tidak menafsirkan hasil matematis yang diperoleh dalam konteks masalah.
Co-Authors 'Azizah, Dewi Nur Abdur Rahman As’ari Afin Nur Latifa Agus Alamsyah Agus Yulianto Agus Yulianto Agustin, Nana Maulidah Aldino, Fals Ana Cholila Anggraini Eka Pramestasari Anggraini, Arika Dewi Annesa Eka Norman Anton Budi Jatmiko Arini, Kartika Ayu Dwi Ariza Husniyatul Ummah Arwan Mhd. Said Assegaff, Muhamad Farid Aynin Mashfufah Aziz Rizky Muhdiyanto Budiarto, Darum Cholis Sa’dijah Christi Matitaputty Darum Budiarto Dian Ratna Sari Dwi Aldi Hidayatulloh Dwi Cahyowati, Ety Tedjo Dwi Listyorini Dwi Susanti Dwiyana Dwiyana Edy Bambang Irawan Eko Prasetyo Elis Dwi Wulandari Ety Tedjo Dwi Cahyowati Ewan Gunawan Fadhil Zil Ikram Faiqatul ‘Athiyah Fals Aldino Faradina, Erta Fatmianeri, Yulia Fauzan, Hakmi Rais Gestiani, Anggun Handayaningsih, Rohyatun Henny Rismawatie Yusmarina Heri Prianto Hery Susanto Hidayanto, Sisworo I Ketut Suada I Made Sulandra I Nengah Parta Ikhtiar, Muhammad Awwalul Indayani, Nunik Intan Mahyastuti Khoerul Umam Khomsatun Ni'mah Laily Wijayanti Utami Lely Purnawati Lisrahmat, Mimin Nazura Makbul Muksar Mariana, Erna Maskanur Rezky Mirza Amelia Oktaviani Mohammad Archi Maulyda Mohammad Dadan Sundawan Muhammad Noor Kholid Muhammad Rizaldi Munika, Risa Dewi Nana Maulidah Agustin Nunik Indayani Nur Indah Permata Sari Nuratiqoh, Nuratiqoh Permadi, Hendro Puguh Darmawan Puji Astuti Purwanto Purwanto Purwanto Purwanto Purwanto Purwanto Purwanto Purwanto Purwanto Purwosetiyono, Fransiskus Xaverius Didik Putri Raznia Safira Putri, Intan Faraminda Qohar, Abd. Rachmalia Vinda Kusuma Refni Adesia Pradiarti Risna Zulfa Musriroh Rohmah, Riska Nur Rosimanidar Rosimanidar Rosimanidar Rosyidah, Ana Siti Rustanto Rahardi Saleh, Sitti Fithriani Sandie Sari, Nur Indha Permata SATRIYAS ILYAS Sisworo Siti Nurjanah Sitti Fithriani Saleh Subanji Subanji Subanji, S Sudirman Sudirman Sudirman Sudirman Sukoriyanto Susiswo Swasono Rahardjo Tasni, Nurfaida Taufiq Hidayanto Tjang Daniel Chandra Toto Nusantara Umi Fitria Ayu Ummah, Ariza Husniyatul Utami, Laily Wijayanti Uun Hariyanti Vita Kusumasari Wildan Hakim Wulandari, Monika Retno Yayon Adi Galung Sastria Yulianto, Sisworo Yundari, Yundari