Problem-solving and problem-posing have become important cognitive activities in teaching and learning mathematics. Many researchers argued that the traditional way of assessment cannot truly reveal what the students learnt and knew. Authentic assessment was used as an alternative method in assessing the students' mathematical learning. A performance rubric is an appropriate tool in examining students' ability to solve and pose mathematical problems.

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In mathematics classrooms, teachers use multiple representations to help students explore and develop abstract concepts. Students are engaged in problem solving as they manipulate objects as they search for a solution. They also can enhance their profound knowledge when posing a scenario problem that matches to the appropriate manipulatives. The integration of manipulatives during teaching and learning can conceptually support students' acquisition of symbols and mathematical language.

Previous research has shown knowledge, perceptions, and attitudes are essential factors during mathematics classroom instruction. The current study examined the effects of a 3-week fraction instructional unit using concrete models, problem-solving, and problem-posing to improve elementary preservice teachers' knowledge, perceptions and attitudes towards fractions. A quasi-experiment design was implemented to gather data via closed-ended, open-ended, and essay tasks from a convenience sampling of 71 female elementary preservice teachers during pre-and post-assessments. The study discovered that the select preservice teachers were weak in the content knowledge specifically on unit-whole, part-whole, equivalent area, arithmetic operations, and ordering fractional values. In contrast, the incorporation of concrete models, problem-solving and problemposing was effective in improving the preservice teachers' level of pedagogical content knowledge, perceptions and attitudes towards fractions. Implications of the results and suggestions are discussed. AbstrakPenelitian sebelumnya menunjukkan bahwa pengetahuan, persepsi, dan sikap merupakan faktor penting dalam pembelajaran matematika. Penelitian saat ini meneliti tentang pengaruh dari pembelajaran pecahan selama kurun waktu 3 minggu menggunakan model konkret, pemecahan masalah, dan problem-posing untuk meningkatkan pengetahuan, persepsi, dan sikap calon guru sekolah dasar terhadap materi pecahan. Sebuah desain eksperimen semu diimplementasikan untuk mengumpulkan data melalui permasalahan dalam bentuk soal closed-ended, open-ended, dan uraian dari pengambilan sampel yang representative dari 71 calon guru wanita sekolah dasar selama pra dan pasca penilaian. Studi ini menemukan bahwa calon guru terpilih lemah pada konten materi pecahan, khususnya pada unit-whole, part-whole, area yang sama, operasi aritmatika, dan nilai pecahan berurutan. Sebaliknya, penggabungan model konkret, pemecahan masalah, dan problem-posing adalah efektif dalam meningkatkan level pengetahuan konten pedagogis calon guru, persepsi, dan sikap terhadap materi pecahan. Implikasi hasil dan saran lebih lanjut dibahas dalam tulisan ini.