Today, hundreds of studies on mathematics learning have been found in various literature, supported by the use of GeoGebra software. This meta-analysis aims to determine the overall effect of using GeoGebra software and the extent to which study characteristics moderate the study effect sizes to consider the implications later. This study analyzed 36 effect sizes from 29 primary studies identified from ERIC documents, Sage Publishing, Google Scholar, and repositories from 2010 to 2020, and a total of 2111 students. In order to support calculation accuracy, a Comprehensive Meta-analysis (CMA) software was used. The effect size is determined using the Hedges equation, with an acceptable confidence level of 95%. It is known that the overall effect size of using GeoGebra software on the mathematical abilities of students is 0.96 based on the estimation of the random-effect model, and the standard error is 0.08. These findings indicate that, on average, students exposed to GeoGebra-based learning outperformed math abilities, which was initially equivalent to 82% of students in traditional classrooms. This study considers the five characteristics of the study. It showed that the GeoGebra software used was more effective in sample conditions less than or equal to 30. Providing classrooms with sufficient numbers of computers allowed students to use them individually, which was necessary to achieve a higher level of effectiveness. GeoGebra software is more effective when the treatment duration is set to less than or equal to four weeks. These findings help educators consider the characteristics of studies that moderate effect sizes using the GeoGebra software in the future.

The purpose of this study was to (1) assess the impact of using Dynamic Geometry Software (DGS) on students’ mathematical abilities, (2) determine the differences in effectiveness based on study characteristics in order to help educators decide under what conditions the use of DGS would be suitable in improving students' mathematical abilities. This meta-analysis study investigates 57 effect sizes from 50 articles that have been published in journals, international and domestic proceedings from 2010 to 2020 using the Comprehensive Meta-Analysis (CMA) tool as a calculation tool. Meanwhile, the Hedges coefficient is applied to the calculation of the effect size at the 95% confidence level. Based on a random effect model with a standard error of 0.09, the analysis results have found an overall effect size of 1.07. This means that learning using DGS has a high positive effect on students' mathematical abilities. The effect size of 1.07 explains the average student who uses DGS exceeds 84% math ability of those in conventional classes that are initially equivalent. Analysis of the study characteristics found significant differences in terms of sample size, student to computer ratio, and education level. This research showed the DGS used was more effective under certain conditions. First, it is very effective in sample conditions less than or equal to 30. Second, it provides classrooms with a sufficient number of computers, allowing students to use them individually, which is required to achieve higher effectiveness levels. Third, DGS is effective in high schools and colleges than in junior high schools. These facts can help educators in deciding on the appropriate sample sizes, student to computer ratios, and future levels of education in using DGS.

The aim of this study is to describe the formal thinking process of students in solving algebraic problems. This study is descriptive qualitative, with two 7th grade subjects taken using a purposive sampling technique. The main instrument in this study is the researchers own judgment, Test of Logical Operations instruments, and algebraic problem-solving tests. The data were collected from various sources using the think-aloud approach. Data were analysed, classified based on students’ cognitive development types (concrete, transitional, and formal) and transcribed into data presentation. The study found that, at the stages of understanding the problem and implementing the plan to solve the problem, the subjects successfully carried out the process of thinking assimilation and abstraction. On the other hand, at the stages of planning and re-examining answers, the subjects able to perform the assimilation process of thinking.

This research is based on the presence of obstacle in learning mathematics on inverse function. This research aims to analyze the learning obstacle, to know the types of error that is suffered by the students in learning inverse function. Kind of this kualitative research descriptive with data triangulation. The research subjects are high school students which is contained of 74 students and was taken 6 students to be main sample. The data of students' error is obtained from the writen test result, the students' false answers are identified into the type of error. Then it was chosen several students to be interviewed. Which the analysis result finding data in this research showed there are 4 types of errors, which are concept error, procedure error, counting error and concluding error. An obstacle which appear in learning inverse function is influenced by two factors, i.e internal factor and eksternal factor. Internal factor is showed by the students' motivation in following learning and students' skill in receiving learning material. While the eksternal factor is showed by the curriculum which applied in school with acceleration class caused many narrow learning time, teaching materials that is less complete with the discussion of question sample. Keywords: Inverse Function, Learning Obstacle, Learning Process. AbstrakPenelitian ini didasarkan pada keberadaan hambatan dalam pembelajaran matematika materi fungsi invers. Tujuan penelitian ini adalah untuk menganalisa hambatan belajar dan jenisnya, sebagaimana dialami siswa saat mempelajari fungsi invers. Penelitian ini menggunakan metode deskriptif kualitatif dengan triangulasi data. Subjek penelitian ini adalah 74 siswa sekolah menengah atas dan diambil 6 siswa sebagai sampel utama untuk diwawancara. Tes digunakan untuk memperoleh data kesalahan siswa, selanjutnya tipe kesalahan diperoleh dari identifikasi jawaban yang salah. Berdasarkan hasil temuan, diperoleh 4 tipe kesalahan yaitu kesalahan konsep, kesalahan prosedur, kesalahan perhitungan, dan kesalahan penyimpulan. Hambatan yang muncul dalam mempelajari fungsi invers dipengaruhi 2 faktor, yaitu eksternal dan internal. Faktor internal terlihat dari motivasi siswa dalam mengikuti pembelajaran dan kemampuan siswa menerima materi pembelajaran. Sedangkan faktor eksternal adalah penerapan kurikulum kelas akselerasi yang diterapkan sekolah mengakibatkan pendeknya waktu belajar, bahan ajar yang kurang lengkap dalam mendiskusikan contoh soal.

This study aimed at identifying the obstacles of mathematics-teacher-students based on Boero’s proving model. This study was conducted using a mix method by applying sequential explanatory strategy. The stages of the research were carried out by taking the quantitative data and revealing the qualitative data using semi-structured interviews. In the result of this study, it was found that most of mathematics-teacher-students had difficulties in constructing geometrical proofs of each Boero’s proving model. Even in the phase of writing formal proof, there were only 6.67% of students could write fully in the cases of indirect proving. There were 13.33% of students in the cases of direct proving. This study concluded several obstacles which students faced in constructing the geometrical proofs formally in each phase of Boero’ proving model. The obstacles included: the difficulty in making a diagrammatic sketch of conjecture which was completely made with the correct geometrical notation; the difficulty in knowing of cause-effect of geometrical problems to be proved, if it involved some conditional sentences; inability to write a conjecture made in the form of geometrical symbols, formulas and axiomatic deduction; the difficulty in selecting a valid statement of the conjecture made and the difficulty in writing formal proof.