AbstrakSalah satu metode pencarian solusi SPL yang dipelajari di pendidikan tinggi adalah metode Gauss-Jordan. Berdasarkan data penelitian, mahasiswa melakukan kesalahan dalam melakukan operasi baris elementer (OBE), membentuk ke dalam matriks yang diperbesar, dan bahkan pemahaman mendasar mengenai reduksi baris dan ini berpengaruh dalam menentukan solusi suatu SPL. Untuk itu perlu dianalisis hambatan belajar yang terjadi dalam menentukan solusi SPL menggunakan metode Gauss-Jordan. Peneitian ini merupakan penelitian kualitatif dan merupakan bagian dari Didactical Design Research (DDR). Penelitian ini dilaksanakan di salah satu universitas di Nusa Tenggara Timur (NTT) dengan subjek penelitian merupakan 20 mahasiswa calon guru matematika. Teknik penelitian ini adalah tes diagnostik dan wawancara. Hasil penelitian menunjukkan beberapa hambatan yang dialami mahasiswa adalah keterbatasan pemahaman pada OBE, pengklasifikasian MEBT, dan merepresentasikan MEBT ke dalam solusi SPL. Rekomendasi dari penelitian ini adalah pengajar hendaknya membuat suatu bahan ajar yang dapat meminimalisir hambatan belajar yang dialami mahasiswa. AbstractOne of many methods of finding solution of a system of linear equations (SLE) studied in higher education is the Gauss-Jordan method. Based on the research, students made mistakes in performing elementary row operations (ERO), forming into augmented matrices, and even basic understanding of row subtraction and this has an effect on determining the solution of an SLE. For this reason, it is necessary to analyze the learning obstacles that occur in determining the solution of LES using the Gauss-Jordan method. This qualitative research is part of the Didactical Design Research (DDR). This research was conducted at a university in East Nusa Tenggara (NTT) involving 20 students as preservice mathematics teacher. The technique of this research is diagnostic test and interview. The results show that some of the obstacles faced by students are insufficient understanding of ERO, classifying reduced row-echelon form (RREF), and representing MEBT into SPL solutions. This study recommends that teachers create teaching materials that minimizes learning obstacles experienced by students.
Abstrak. Penelitian ini bertujuan untuk menganalisis hambatan didaktis pada pertidaksamaan kuadrat. Pilihan didaktis sering didasarkan pada intuisi guru akan kompleksitas dan ketidaklengkapan informasi akan sebuah pendekatan. Melalui analisis didactical obstacles, guru dapat menghindari atau setidaknya berhati-hati pada suatu pendekatan yang terlihat sederhana dan mudah, tetapi menuntun pada terjadinya hambatan belajar. Penelitian menggunakan pendekatan kualitatif dengan paradigma interpretif dalam kerangka penelitian desain didaktis. Penelitian dilakukan pada 105 siswa kelas IX dan satu orang guru pada salah satu Sekolah Menengah Atas di Bandung. Pengumpulan data dilakukan melalui soal tes pertidaksamaan kuadrat, analisis buku pegangan guru, wawancara siswa dan guru. Hasil pekerjaan siswa atas soal pertidaksamaan kuadrat dianalisis untuk melihat cara mengetahui siswa dan pemahaman siswa. Cara mengetahui ini akan dibandingkan dengan pilihan didaktis yang digunakan guru. Hasil penelitian menunjukkan terdapat didactical obstacles dalam pertidaksamaan kuadrat. Hambatan didaktis tersebut adalah penggunaan metafora pembuat nol sebagai konsep utama dalam penyelesaian pertidaksamaan kuadrat. Pembuat nol ini merupakan implikasi dari penggunaan pendekatan sign chart. Untuk itu guru perlu berhati-hati menggunakan pendekatan garis bilangan dan metafora pembuat nol sebagai pilihan pendekatan didaktis. Penggunaan pendekatan dengan lintasan belajar yang dimulai dari pendekatan fungsi, dapat dipertimbangkan guru dalam pembelajaran pertidaksamaan kudarat.
Preservice mathematics teachers (PSMTs) need to master teaching material besides pedagogical competence. This knowledge is a combination of conceptual and procedural knowledge. Teachers should possess the ability to explain a concept, the reason for the concepts used, and the relationship among several concepts clearly and effectively to identify why the concept is used. This study aimed to identify the conceptual and procedural knowledge of PSMTs in Linear Algebra courses. Data collection was carried out through tests and interviews. The interview was conducted with several participants to clarify their test answers. The participants' interview answers revealed that they had difficulty in choosing the proper concept answering modified questions. Also, the participants tried to answer the question using a procedural approach. According to the findings, it is vital to construct appropriate teaching materials appropriate for the learning objective and material map concept.
The background of this research is the learning obstacles that arise on the topic of determining the solution of a system of linear equations (SLE) in applying elementary row operations (ERO). From these findings, it is necessary to formulate a hypothetical learning trajectory (HLT) that can guide the flow of thinking in designing didactic situations in the learning process. HLT expect to anticipate learning obstacles (LO) that arise. This research is a preliminary design of a series of didactical design research. The steps taken in compiling the HLT are 1) reviewing the lesson plan, the methods used to convey the material to determine SST solutions, and the textbooks used; 2) reviewing students' thinking processes conceptually and procedurally regarding theoretically determining SLE solutions; 3) reviewing design plans didactic. HLT is formulated into five types of student responses. It integrates into didactic situations by explaining the relevance of the elimination method in high school with three operations on ERO and then by explaining matrix material before SPL material. From this didactic situation, it can be formulated in teaching material that can accommodate emerging LO.
The purpose of this research was to know there was any difference in student’s mathematical communication ability in cooperative learning Think TalkWrite (TTW) type and Numbered Head Together (NHT) type. The population was all students at SMP Negeri 1 Lubuk Pakam. The sample was two classes which each consist of 36 students, VII A as experimental class I which taught by TTW and VII B as experimental class II which taught by NHT. The sample was taken by cluster random sampling. Collecting data technique of this research was mathematical comunication ability essay test that was given in the end of learning either in experimental class I or experimental class II. From the data analysis of each of experimental class were obtained that the average of posttest score in TTW classroom was higher than in NHT classroom. It was also obtained that score of mathematical communication indicators in TTW classroom was higher than in NHT classroom. From the data analysis of posttest score by using t-test with significance level α = 0.05, it was obtained that tcount = 4.687 and ttable = 1.667. It means that tcount > ttable then H0 was rejected and Ha was accepted. So, it can be concluded that there was difference of student’s mathematical communication ability who taught by cooperative learning model type TTW with NHT at SMP Negeri 1 Lubuk Pakam.
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