Performance Assessment to Measure Student’s Mathematical Proving Ability Based on the Abductive-Deductive Approach


This study provides an overview of performance assessment instruments to measure students’ mathematical proving abilities based on the abductive-deductive approach. This is descriptive qualitative research of performance assessment instruments and their rubrics in measuring students’ mathematical proving abilities. The research method was literature study. The performance assessment instrument consists of essays designed to identify the mathematical proving abilities of students in mathematics courses. In this article, the examples are given for the Real Analysis class. The items of performance assessment were arranged referring to the abductive-deductive reasoning approach which has a pattern containing three main questions: 1) “What conditions can be obtained from the conclusion?” which was answered with abductive reasoning, 2) “What are the consequences that can be obtained from known facts?” which can be answered with deductive reasoning, and 3) “What conditions connect the conditions of conclusions and the implications of premise?” which can be answered with a key process of the mathematical statement proving process.

Keywords: performance assessment, mathematical proving ability, abductivedeductive approach

1] Selden, A. and Selden, J. (2003). Validations of Proof Considered as Texts: Can undergraduates Tell Whether an Argument Proves a Theorem? Journal for Research in Mathematics Education, vol. 34, issue 1, pp. 4-36.

[2] Epp, S. (2003). The Role of Logic in Teaching Proof. The American Mathematical Monthly, vol. 110, issue 10, pp. 886-899.

[3] Lee, J. K. (2002). Philosophical Perspective on Proof in Mathematics Education. Philosophy of Mathematics Education Journal, vol. 16. Retrieved from lee.pdf.

[4] Douek, N. (1999). Some Remarks about Argumentation and Mathematical Proof and Their Educational Implications. In I. Schwank (Ed.), Mathematics Education I: Volume I. Osnabrück: Forschungsinstitut für Mathematikdidaktik and ERME.

[5] Dickerson, D. S. (2008). High School Mathematics Teachers Understandings of the Purposes of Mathematical Proof (Dissertation). New York: Syracuse University.

[6] Maya, R. (2011). Mathematical Understanding and Proving Abilities: Eksperiment With Undergraduate Student by Using Modified Moore Learning Approach. IndoMS. J.M.E., vol. 2, issue 2, pp. 231-250

[7] Lee, K. (2011). Students Logical Reasoning and Mathematical Proving of Implications (Dissertation). Michigan: Michigan State University.

[8] Stylianides, A., Stylianides G. and Philippou G. (2004). Undergraduate Students Understanding of The Contraposition Equivalence Rule in Symbolic and Verbal Contexts. Educational Studies in Mathematics, vol. 55, pp. 133-162.

[9] Kusnandi. (2008). Pembelajaran Matematika Dengan Strategi Abduktif-Deduktif Untuk Menumbuh kembangkan Kemampuan Membuktikan Pada Mahasiswa (Disertasi). Bandung: Universitas Pendidikan Indonesia.

[10] Arnawa, I. M. (2006). Meningkatkan Kemampuan Pembuktian Mahasiswa dalam Aljabar Abstrak Melalui Pembelajaran Berdasarkan Teori APOS (Disertasi). Bandung: Universitas Pendidikan Indonesia.

[11] Uhlig, F. (2002). The Role of Proof in Comprehending and Teaching Elementary Linear Algebra. Educational Studies in Mathematics, vol. 50, issue 3, pp. 335-346.

[12] Yerison. (2011). Peningkatan Kemampuan Pembuktian dan Kemandirian Belajar Matematik Mahasiswa Melalui Pendekatan M-Apos (Disertasi). Bandung: Universitas Pendidikan Indonesia.

[13] Tall, D. (1998). The Cognitive Development of Proof: Is Mathematics Proof for All or Some? Presented at Conference of the University of Chicago School Mathematics Project, Chicago, United States of America.

[14] Balik, I. W. (2012). Pengaruh Implementasi Asesmen Autentik Terhadap Prestasi Belajar Matematika dan Motivasi Berprestasi (Eksperimen pada Peserta Didik Kelas VIII SMP Negeri 3 Gianyar). Jurnal Penelitian dan Evaluasi Pendidikan, vol. 2, issue 2, pp. 1-14.

[15] Slavin, R. E. (2011). Psikologi Pendidikan Teori dan Praktek, Terjemahan Marianto Samosir. Jakarta: Indeks.

[16] Nitko, A. J. (2008). Educational Assessment of Students (3rd ed.). New Jersey: Prentice-Hall.

[17] Chong, H. Y., DiGangi, S. and Jannasch, A. (2008). The Role of Abductive Reasoning in Cognitive Based Assessment. Elementary Education Online, vol. 7, issue 2, pp. 310-322.

[18] Ruseffendi, E. T. (2006). Pengantar Kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajaran Matematika untuk Meningkatkan CBSA. Bandung: Tarsito.

[19] Johnson, R. S. J., Mims-Cox, S. and Doyle-Nichols, A. (2010). Developing Portofolios in Education: A Guide to Reflection, Inquiry, and Assessment. Los Angeles: SAGE Publication.

[20] Arends, R. I. (2013). Belajar untuk Mengajar, terjemahan Made Frida Yulia. Jakarta: Salemba Humanika.

[21] Setiadi, H. (2006). Penilaian Kinerja. Jakarta: Puspendik Balitbang Depdiknas.