Students errors in constructing mathematical proofs by direct method
Herizal Herizal (a*), Marhami Marhami (a), Nurul Akmal (b)

a) Program Studi Pendidikan Matematika, Universitas Malikussaleh, Jl. Cot Teungku Nie, Reuleut, Aceh Utara 24355, Indonesia
*herizal_mathedu[at]unimal.ac.id
b) Program Studi Tadris Matematika, IAIN Lhokseumawe, Jl. Medan-Banda Aceh, Alue Awe-Muara Dua, Lhokseumawe 24352, Indonesia

Abstract

In mathematics, there are two methods for proving mathematical statements which are direct method and indirect method. Both of the methods were included in mathematics curriculum in senior high school level as a learning topic. It implied that the teachers or preservice teachers must master in the methods. In addition to, learning advanced mathematics course also needed the ability of mathematical proving. Direct method was a method often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what the errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to thirteen college students. They were preservice mathematics teachers in one of public universities in Aceh, Indonesia and asked to prove the statements by direct method. The data were analysed by using Miles and Huberman step. The results showed that there were three main errors, they were (1) proving by example, (2) errors in algebraic manipulation, and (3) wrong in identifying the hypothesis or assumption and conclusion of a mathematical statements. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs.

Keywords: direct method- mathematical proof- mathematical proving

Topic: Mathematics Education