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.

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.

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.

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.

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