The emerging of formal mathematical proof is an essential component in advanced undergraduate mathematics courses. Several colleges have transformed mathematics courses by facilitating undergraduate students to understand formal mathematical language and axiomatic structure. Nevertheless, college students face difficulties when they transition to proof construction in mathematics courses. Therefore, this descriptive-explorative study explores prospective teachers' mathematical proof in the second semester of their studies. There were 240 pre-service mathematics teachers at a state university in Surabaya, Indonesia, determined using the conventional method. Their responses were analyzed using a combination of Miyazaki and Moore methods. This method classified reasoning types (i.e., deductive and inductive) and types of difficulties experienced during the proving. The results conveyed that 62.5% of prospective teachers tended to prefer deductive reasoning, while the rest used inductive reasoning. Only 15.83% of the responses were identified as correct answers, while the other answers included errors on a proof construction. Another result portrayed that most prospective teachers (27.5%) experienced difficulties in using definitions for constructing proofs. This study suggested that the analytical framework of the Miyazaki-Moore method can be employed as a tool to help teachers identify students' proof reasoning types and difficulties in constructing the mathematical proof.
Pengajuan dan pemecahan masalah merupakan pemicu keterampilan berpikir kritis maupun berpikir kreatif yang sesuai dengan tujuan kurikulum saat ini. Kedua konsep tersebut perlu diimplementasikan dalam pembelajaran, sehingga para guru perlu dibekali keterampilan merancang pembelajaran tersebut sekaligus memahami konsep masalah, pemecahan dan pengajuan masalah. Untuk mencapai tujuan tersebut, diperlukan program pelatihan guru untuk memantapkan pemahaman guru tentang pemahaman konten dan desain pembelajaran berbasis pengajuan dan pemecahan masalah matematika. Guru yang terlibat adalah 22 guru SMP yang ditugaskan oleh Dinas Pendidikan Kabupaten Magetan. Metode pelaksanaan terdiri dari tahap persiapan dengan melakukan koordinasi dengan mitra dan tim pelatih untuk merancang instrumen dan materi pelatihan. Tahap pelaksanaan terdiri dari kegiatan tatap muka dan kegiatan mandiri dengan diawali pemberian angket untuk analisis awal (pra-tes), pemberian materi pelatihan, praktik penyusunan soal, presentasi, dan kegiatan mandiri merancang perangkat pembelajaran. Tahap selanjutnya evaluasi dan tindak lanjut dilakukan dengan pemberian angket akhir pelatihan (pasca-tes) dan angket refleksi kegiatan. Hasil pelatihan menunjukkan 81,8% guru mampu memahami konsep dan mendesain pembelajaran berbasis pengajuan dan pemecahan masalah. Hasil evaluasi kegiatan guru menunjukkan 95,45% guru cenderung mengatakan baik dan menyarankan kegiatan perlu ditindaklanjuti.
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