This study describes students’ conceptual understanding in solving mathematical problems. Conceptual understanding is an important component in learning mathematics. By learning mathematics students are able to apply concepts and think logically. The qualitative research took students of SMP Negeri 1 Gatak Sukoharjo Indonesia. There were 59 students who were tested to find out the conceptual understanding. All students are categorized into 16 students with high mathematical ability (Subject S-1), 25 students with moderate ability (Subject S-2), and 18 students with low mathematical ability (Subject S-3). Data collected through tests, video recordings, field notes, and interviews. Data analysis techniques include data reduction, data presentation, and drawing conclusions. The validity of the data is obtained through validation and triangulation. Subjects with high mathematical ability can solve mathematical problems correctly. Subjects with moderate mathematical abilities are able to solve the given problem but not all indicators on understanding the concept fulfilled. Subjects with low mathematical abilities are not able to solve problems precisely. Research contributes as a new reference to the theory of conceptual understanding.

The integration of learning models and software is a trend in mathematics courses. However, no existing learning model for geometry courses involves the students in the making of a tool or media project. The researchers noticed the potential of the project-based learning (PjBL) model and GeoGebra in analytical geometry courses. This study revealed differences in the influence of the Geo-PjBL and PjBL models on students’ achievement. The subjects consisted of 137 prospective mathematics teachers. The Basic Geometry Instrument (BGI) was used to measure the subjects’ initial ability in basic geometry, and the Geometry Analytic Instrument (GAI) was used to evaluate the model and prospective teachers’ performance. The Geo-PjBL and PjBL classroom activities lasted for 15 weeks. Both classrooms received the same content; the difference between the Geo-PjBL and PjBL classrooms was the tools used to present the problems and the project results. An analysis of covariance (ANCOVA) was conducted to analyze the data (α = 0.01). The Geo-PjBL model is more effective in applying analytical geometry subjects that require precision and accurate visual illustrations. Meanwhile, in the range of algebraic operations, the Geo-PjBL model is as effective as the PjBL model.

<p class="JRPMAbstractBody">Kondisi Negara Kesatuan Republik Indonesia yang dilanda oleh pandemi virus corona telah memicu pemerintah untuk bertindak lebih responsif. Salah satu upaya dalam ranah pembelajaran yaitu diterbitkannya Surat Edaran Menteri Pendidikan dan Kebudayaan Nomor 4 Tahun 2020 Tentang Pelaksanaan Kebijakan Pendidikan dalam Masa Darurat Penyebaran Corona Virus Disease (COVID-19). Penerapan media komunikasi secara online dalam pembelajaran rupanya berdampak secara siginifikan terhadap kondisi psikologis siswa. Dominasi paham tingkatan berfikir dalam teori Van Hiele terhadap geometri memberikan kesempatan pada psikologi warna untuk memainkan perannya, namun demikian warna kerap kali masih disalahpahami nilainya dalam pembelajaran. Penelitian ini difokuskan untuk mengetahui relevansi penerapan psikologi warna terhadap praktik pembelajaran geometri pada siswa kelas VIII SMP/MTs secara online. Adapun metode yang digunakan dalam penelitian adalah kualitatif dengan pendekatan studi literatur. Artikel ini berargumentasi bahwa psikologi warna tidak relevan dengan pembelajaran geometri pada siswa kelas VIII SMP/MTs secara online. Hal ini bisa terjadi karena dominasi <em>platform</em> yang diakses oleh siswa bukanlah <em>platform</em> edukasi serta minimnya penggunaan fitur warna bahkan dalam platform yang dikhususkan untuk geometri, yaitu geogebra.</p>

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<p><strong>Abstract: </strong>The aim of this research was to reveal the effect of TGT cooperative learning model with talking chips technique, TGT cooperative learning model, and direct learning model to the mathematics achievement in polyhedron subject viewed from mathematics communication ability. The type of this research was a quasi-experimental by 3x3 factorial design. The population was the eighth grade of Junior High School students at Wonogiri regency on academic year 2013/2014. The sample was taken by using stratified cluster random sampling technique. The instruments used for collecting data were mathematics achievement test and mathematics communication ability test. Analysis of the data used was unbalanced two-way analysis of variance. The conclusion of this research shows that TGT cooperative learning model with talking chips technique gives the same achievement as TGT cooperative learning model, but gives better achievement than direct instruction model, and TGT cooperative learning model gives better achievement than direct instruction model. It shows the same result in each categories of mathematics communication ability. Another conclusion shows that students with high mathematics communication ability have the same achievement as students with middle mathematics communication ability but they have better achievement than students with low mathematics communication ability, and students with middle mathematics communication ability have better achievement than students with low mathematics communication ability. It shows the same result in each learning model.<strong></strong></p><strong>Key words</strong>: TGT, Talking Chips, and mathematics communication ability