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

Influence of prerequisite concepts understanding and mathematical communication skills toward student’s mathematical proving ability

This study aims to describe the influence of prerequisite concepts understanding and mathematical communication skills on the mathematical proving ability of Mathematics Education Program students in the Faculty of Mathematics and Science, State University of Jakarta (FMIPA UNJ). The method used in this study was a survey and correlational techniques. The study population was all students of the Mathematics Education Program FMIPA UNJ in 2018. The study sample was taken with a simple random sampling technique, there were 50 students in total. In this study, the dependent variable was mathematical proving ability (Y) and the independent variables were the prerequisite concepts understanding (X1) and mathematical communication skills (X2). This study based on the inferential statistical analysis of research data by using multiple regression analyses to test the effect of independent variables on the dependent variables. The results obtained were: 1) the prerequisite concepts understanding had a positive effect and significant on students’ mathematical proving ability, 2) mathematical communication skills had a positive effect and significant on students’ mathematical proving ability, and 3) prerequisite concepts understanding and mathematical communication skills simultaneously had a positive effect and significant on mathematical proving ability with effect size of 69.3%. Pengaruh pemahaman prerequisite concepts dan kemampuan komunikasi matematis terhadap mathematical proving ability mahasiswaAbstrakPenelitian ini bertujuan untuk memperoleh informasi tentang pengaruh pemahaman prerequisite concepts dan kemampuan komunikasi matematis terhadap kemampuan membuktikan matematis mahasiswa Pendidikan Matematika di Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Jakarta (FMIPA UNJ). Metode yang digunakan dalam penelitian ini adalah metode survei dan teknik korelasional. Populasi penelitian adalah seluruh mahasiswa Program Studi Pendidikan Matematika FMIPA UNJ tahun 2018. Sampel penelitian diambil dengan teknik simple random sampling sebanyak 50 mahasiswa. Variabel terikat dalam penelitian ini adalah kemampuan membuktikan matematis (Y) dan variabel bebasnya adalah pemahaman prerequisite concepts (X1) dan kemampuan komunikasi matematis (X2). Penelitian ini berdasarkan analisis statistik inferensial atas data penelitian dengan menggunakan analisis regresi ganda untuk menguji pengaruh variable-variabel bebas terhadap variabel terikat. Hasil yang diperoleh adalah: 1) pemahaman prerequisite concepts berpengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa, 2) kemampuan komunikasi matematis berpengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa, 3) pemahaman prerequisite concepts dan kemampuan komunikasi matematis secara bersama-sama (simultan) memberikan pengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa dengan besar pengaruh sebesar 69,3%.