The role of PWWs in helping students to prove the cosine of a sum

Abstract

In learning mathematics, students learn to compile a mathematical argument and proof. However, the objects studied in mathematics are abstract objects. Sometimes, the visualization of the object is required to make students easier in understanding it so that they can prove it. Proofs without Words (PWWs) is an image media that has the opportunity to play a major role in learning mathematics from the basic education level to higher level. This study aims to explore how third-year students majoring in mathematics education in prove the cosine of the sum with the help of PWWs. This study uses a qualitative approach. Forty five third-year college students majoring in mathematics education were shown the PWWs images. Then, they were given the related questions of the drawing to assist the students in understanding the formula of cosine of the sum. The analysis on the students 'answer showed that PWWs provide visualization of the abstract mathematical concepts. However, in the process they need to be reminded about polar coordinate concept and the concept of distance between two points on the Cartesian coordinates to answer the questions. PWWs can be used to assist them in constructing an understanding and proof of the cosine of the sum. Nevertheless, it depends on the students' prior knowledge which is the basis for the concept.