There has been more than one the solving process of the problem sometimes. It has been named an open-ended context when related to an approach, and in this study, purposed to use a geometric-function problem for analyzing each process that was experienced a student when they were conceptualizing the completion. Three students purposively who was a sample is registered by the senior high school in a science program at the region of West Jakarta, Indonesia. Student solved the problem in this explorative study, there were two choices of completion ways, technical or conceptual, but they used the procedural technique operational. Two conceptualizing process in solving the problem, it was constructing the algebraic representation of the function and organizing concepts. But, there is only one between the other where was effective and efficient of the process based on the perspective of the management theory. The first process was efficient by recognizing the function in algebraic and graphic representation. But, the second process affected the solution ineffective because all three students have been miss controlling the domain function concept even though it is a resource. So, an effective and efficient for learning is when students involving more conceptual knowledge.

Penelitian ini bertujuan untuk menganalisis konsepsi siswa pada bentuk bangun ruang limas terkait dengan panjang semua rusuk yang sama dan memiliki diagonal sisi. Penelitian ini merupakan survei kualitatif. Sampelnya adalah siswa kelas XII-IPS di satu Sekolah Menengah Atas Kabupaten Belitung tahun pelajaran 2018/2019. Siswa menyampaikan konsepsinya dengan cara menjawab pertanyaan survei. Analisis konsepsi siswa difokuskan pada pemahaman konsep dan objek mental bangun ruang yang ada dalam pikirannya. Hasil analisis dari respon siswa menemukan ada tiga tipe konsepsi yang teridentifikasi, yaitu konsepsi siswa yang menunjukkan kesiapan intelektual, konsepsi yang mengarah pada hambatan epistemologis, dan konsepsi yang menunjukan miskonsepsi. Pemahaman pada konsep dasar dan keluasan jaringan informasi konsep menjadi syarat untuk mempelajari konsep lanjutan suatu materi matematika, agar siswa terhindar dari miskonsepsi, sehingga pembelajaran mampu menghadirkan pengalaman konseptual dan perseptual.

Geometry mastery is a must for high school students, affected by several factors such as learning approach (LA), gender, level of basic geometry competencies (BGC) and level of mathematical self-efficacy (MSE) among others. The purpose of this study is to examine those factors that affect the geometry problem solving (GPS) abilities of the students. This study involved 101 Indonesian high school students. They were divided into two groups based on the implemented LA, namely the investigative learning group and the direct instruction group. Data were collected through three instrument types, namely test of BGC, GPS, and MSE. The MSE scale consists of two models namely mathematics test-taking self-efficacy (MTSE) and mathematical skill self-efficacy (MSSE). Data were analyzed using ANOVA techniques, path analysis, and error analysis. The path diagram is MSE, which mediates the BGC effect on GPS. Data analysis results revealed that the level of BGC, MTSE as well as interactions between LA and gender had a significant impact on the GPS capability of students. In this case, the BGC of the students impacted their MSE and thus impaired their GPS skills, which also moderated the gender and learning. There are phases in the process of solving problems that tend to hamper student performance. The visualization process appears to be done by female students, while male students make representations when they do. The researchers, therefore, suggest further research related to gender-based LA study in the geometry curriculum to improve the ability of the students.

The mathematical problem mostly has been involved in the measurement of student ability according to study objectives and data needs. In this study, geometric-function problem has been used to data collection, analyzed problem type, and students thinking levels based on their completion. The sample of this study was three student high school in a science programme in the region of West Jakarta who selected purposively. Based on data analyzed, the result was found that students view the problem as the task constructed algebraic function formula. The completion and solution that have been shown by students, categorized the problem in open-ended type. The finding of mathematical thinking levels analysis there was a different complexity of thinking process between students because the number of concepts applicate. According to van Hiele theory, student's geometry thinking levels was on abstraction level minimally, and the problem is not relevant for deduction thinking level criterion. For the analysis result about algebraic thinking levels, by the structure of the observed learning outcome (SOLO) taxonomy, students at the levels between relational and extended abstract. Students in these levels was a student high ability so it is appropriate with the background of the sample selected.

No abstract

By the characteristics of mathematics, which has the object of study is abstract, then the abstraction becomes an important part that can not be separated from mathematics. The development of abstraction theories, either directly or not, will be closely related to the process of learning mathematics in the classroom. Also, the rapid development of virtual manipulatives media in the world of mathematics education can bring a good influence on the learning process that takes place in the classroom. In this regard, this paper aims to examine theories of abstraction in mathematics and its possible implementation in mathematics education which is integrated with virtual manipulatives media to provide a choice to overcome various problems of learning mathematics. In the world of mathematics education, some abstract concepts in mathematics will be more easily learned through empirical abstraction processes such as introducing the concept of positive integers in students. However, when abstract concepts are not allowed to be empirically introduced to the students, the role of virtual manipulatives media can be one of the alternatives to choose from. Also, virtual media manipulatives can be utilized to facilitate the process of reflective abstraction and theoretical abstraction

Functional analysis has been of interest and the thinking of students should be prepared.  Analyzing the process of conceptualizing geometric function problem solving based on the dimensions of cognitive processes and knowledge was the purpose of this study. The subjects of this study were three students selected purposively from one of the secondary schools in Indonesia. Exploration of these studies with constant comparative techniques. The results of the data analysis show that the cognitive processes that operate and the knowledge applied by students focus on the conceptualization of algebraic representations. Based on the conceptualization process, students' conceptual systems are still fragmented because of the problem of the relationship between the concept and the basis of its relationship. As a result, procedural knowledge is more dominant.

Latar belakang penelitian ini adalah pentingnya kemampuan dan disposisi berpikir kritis matematiksiswa, sedangkan tujuannya untuk mengetahui perbedaan peningkatan kemampuan dan disposisi berpikir kritis matematik siswa yang mendapatkan pembelajaran berbasis-masalah dan pembelajaran konvensional. Penelitian ini merupakan penelitian eksperimen dengan disain kelompok kontrol non-ekivalen menggunakan teknik purposive sampling. Kelas eksperimen mendapat pembelajaran matematika berbasis-masalah dan kelas kontrol mendapat pembelajaran konvensional. Instrumen yang digunakan berupa tes kemampuan berpikir kritis, dan skala disposisi berpikir kritis. Penelitian ini dilakukan di salah satu sekolah menengah atas. Populasi penelitian ini adalah siswa SMA dengan sampel penelitian adalah siswa kelas X SMA Negeri di Tanjungpandan Bangka Belitung dengan responden penelitiannya adalah siswa kelas X sebanyak dua kelas yang dipilih secara acak dari enam kelas yang ada. Analisis data kemampuan dan disposisi berpikir kritis matematik menggunakan uji-t.Hasil penelitian menunjukkan bahwa peningkatan kemampuan berpikir kritis matematik siswa yang mendapat pembelajaran matematika berbasis-masalah lebih baik daripada siswa yang mendapat pembelajaran konvensional. Analisis data skala memperlihatkan bahwa peningkatan disposisi berpikir kritis matematik siswa yang mendapatkan pembelajaran berbasis-masalah tidak lebih baik daripada siswa yang mendapat pembelajaran konvensional. Pembelajaran berbasis-masalah memungkinkan sebagai alternatif pembelajaran untuk diimplementasikan di SMA.