Penelitian ini bertujuan untuk menganalisis tahapan berpikir geometris yang dimiliki oleh siswa SMA dalam menyelesaikan masalah matematika. Penelitian ini merupakan penelitian kualitatif dengan siswa kelas X yang mempunyai nilai matematika di atas rata-rata sebagai subjek penelitian. Dalam penelitian ini, peneliti menggunakan lembar masalah sebagai instrumen pendukung untuk mengetahui tahapan berpikir geometris yang dimiliki siswa. Lembar masalah berupa pertanyaan yang berfungsi untuk merangsang munculnya tahapan berpikir geometris yang dimiliki siswa. Metode pengumpulan data yang digunakan dalam penelitian ini adalah wawancara, dokumentasi, catatan lapangan, dan lembar jawaban siswa. Teknik analisis data yang digunakan yaitu teknik analisis dari Miles & Huberman yang meliputi tiga aktivitas yaitu reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa ada suatu aktivitas yang belum masuk pada tahapan berpikir geometris menurut Van Hiele dan Musa. Aktivitas tersebut adalah menentukan rencana untuk menyelesaikan masalah matematika, dan dalam penelitian ini peneliti sebut sebagai level 1,5 yaitu mengorganisasi.

This study aims to develop elementary V class multimedia based on humanistic theory on integer competencies that is valid, practical, and effective. The development model is a 4D (define, design, development, disseminate) model. In the define stage there are interviews and observations to study the curriculum and the needs of teachers and students. In the design stage, draft I multimedia was designed using Adobe Flash Player. In the development stage, draft I is valid based on questionnaires from media and  material expert validators. Furthermore, the results of field notes and student and teacher response questionnaires indicate that draft II is practical. Then drat III was tested by independent t-test which resulted that draft III is effective. Draft III developed into a final product which was then disseminated at the disseminate stage with the delivery of products to teachers, training of teachers, and publications in national journals.

This study aimed to determine: (a) how the learning process of plane based on constructivistic learning theory; and (b) the effectiveness of such learning in improving learning achievement. The subject of this study was all of 5 th class of SD Negeri Purworejo. Data analysis technique in this study included qualitative descriptive technique, quantitative descriptive and quantitative t-test. After the preliminary analysis it was found that this constructivistic learning was done with multimedia Powerpoint, greenboard, and pencil-paper. Based on the field note and the observation of two teachers it was found that learning has been done according to constructivist learning theory. Teacher's response questionnaire generated a score of 39.5, as well as the t-test yielded t count = 2.016 > 1.645 = t table. This means that learning based on constructivist learning theory was significantly effective to improve learning achievement.