Analysis of the Mathematical Proof Skills of Students of Science Teaching

Mathematics and proof are two closely related concepts. Mathematics not only shows what is right or wrong, but it also teaches that it is not enough to know the latest formulas and results should be explained with causality. In this context, students learn the underlying meaning behind what mathematicians do by way of proofs. Accordingly, this study aims to analyse the mathematical proof skills of students studying science teaching. The study group is composed of 50 first-year college students studying science teaching in the academic year 2011-2012. The study employs case study method as a form of qualitative research and six open-ended questions are used for data gathering purposes. The obtained data show that students successfully employ mathematical proof methods (induction, deduction etc.), but the majority of the students accepted the technique of giving a numerical value as a method of proof.IntroductionOne of the most important functions of education systems is to develop the reasoning skills of students (Fitzgerald, 1996). So, it is necessary to organize mathematical proof activities and take proof to the center of mathematics education in order to enable students to develop their mathematical reasoning skills from the very first years of their education life (National Council of Teachers of Mathematics [NCTM], 2000; Schoenfeld, 1994; Stylianides, Stylianides, & Philipppou, 2007). In the most general sense, proof is the act of establishing the truth of a statement or a result by way of showing adequate evidence (Yildinm, 1996). In other words, it is a systematic and complex problem-solving activity where hypotheses are formulated and tested (Shipley, 1999). Bell (1976) defines proof as a process occurring as a result of some stages, and emphasizes that verification (verification of a statement), explanation (demonstrating why the statement is true), and systematization (organizing statements, axioms and theorems in an inductive system) are the significant stages of this process. Mathematics and proof are two closely related concepts because mathematics not only shows what is right or wrong (Hanna, 2000), but it also teaches that it is not enough to know the latest formulas and results should be explained with causality (Guven, Celik, & Karataj, 2005). In this context, students learn the underlying meaning behind what mathematicians do by way of proofs (Imamoglu, 2010).Proof has a significant role in establishing, developing and conveying mathematical knowledge (Stylianides, 2007). Proof presents new problem-solving methods, tools and strategies to students (Rav, 1999) and also helps students in developing their critical thinking abilities (Fawcett, 1938). Moreover, it enhances their mathematical understanding by aiding them to get a better grasp of concepts (Hanna, 1990; Hanna, 2000; Hersh, 1993). While proof has an important position in establishing mathematical knowledge, proof process is considered as a hard, meaningless and reluctandy done activity by students in mathematics courses (Alibert, 1998; Almeida, 2003; de Villiers, 1990; Hemmi, 2010; Jones, 2000; Knuth, 2002; Raman, 2003).One of the basic levels that requires using proof is high school level. During the years of high school, the process of abstract thinking develops and during these years the mathematical proof methods of deduction and induction methods are formed. In addition, use of geometric proofs commonly take part in geometry curriculum related to high school (Dreyfus, 1999). In this framework, students should be able to understand mathematical proof within both mathematics and geometry courses at high school. However, most of students have difficulty in understanding the process of proof. Consequendy, these students lack proving skills when they come to university. In this context, students who were studying at the Department of Mathematics Teaching should be able to understand and construct mathematical proofs. …