Mistakes Made by Freshman Students of Science Teaching and Their Reasons during the Proving Process.

IntroductionThinking is a process required for understanding new situations. In other words, it is the conceptualisation, implementation, analysis and criticism of the knowledge obtained by observation, experience, sense, and many other ways (Ozden, 1997: pp. 79). One of the most important tools that improve thinking is mathematics (Tural, 2005). Mathematics can be defined as a process that explains the relationship that constitutes the essence of surrounding situations and it is beneficial in making decisions on both the current situation and the future. Mathematics is a process that starts with looking for patterns, discovering relationships and ends with a formal process such as 'proof (Dreyfus, 1991).The proof process holds a key role in the field of mathematics (Lakatos, 1976) and it is necessary for doing and understanding mathematics. It does not consist only of finding the answers of theorems, it also provides students with logical reasoning, which is required for mathematical understanding and reasoning (Polya, 1981). Mathematical proof may be used at all levels, including elementary, secondary etc.One of the basic levels that requires using proof is the high school level. The high school years are those during which the process of abstract thinking develops and during these years the methods of deduction and induction methods are formed. Conversely, use of geometric proofs commonly takes part in the geometry curriculum related to high school (Altiparmak & Ozis, 2005). Geometric proofs are the opportunity to educate students on the foundations of mathematical principles. Therefore, teachers tell students in the lower levels of mathematics that they will prove why the sum of the interior angles of a triangle is 180 degrees (Jones, 1994). In this framework, students should be able to understand mathematical proof within both mathematics and geometry courses at high school. However; many students have difficulty in understanding the process of proof. Consequently; these students lack proving skills when they come to university, whereas proofs are also central to university level mathematics courses such as 'General Mathematics' and 'Algebra'. In this context, students in mathematics programmes should be able to understand and construct mathematical proofs. The process of proving is also seen in mathematics courses related to science programmes. Students in science programmes can also use proof to verify or explain a statement with various methods in 'General Mathematics I or II'. While some students use the method of induction proof, some use the method of deductive proof. Conversely, some students give special examples for justifying an argument in the process of proof.Virtually, Methods of Proof' is an important topic that explains the process of reasoning, finding the true value and using it. Therefore, it has an undeniable function in the practice of university mathematics (Hemmi, 2010). However; many university students may not see the functions (meaning, purpose and usefulness) of proof (de Vilhers, 1999) and may not completely use the methods (induction, deduction, etc.) of proof. One of the most important factors regarding using these methods of proof correcdy is the foreknowledge of students. Both students in mathematics and science programmes may not make the use of proof, since they do not exactly learn the methods of proof in high school.There are many studies on the students and prospective teachers at the Mathematics Departments in Turkey. However; with the exception of Aydin, (2011), Gokkurt and Soylu (2012) and Gokkurt, §ahin, and Soylu (2014), litde research has been done on students in Science Departments. These studies have also studied science students' abilities of making proof or their views to prove it. However; in Turkey, there is not any studies on what students' mistakes are in the process of making mathematical proof and on the reasons of these errors. But the mistakes while science students are making mathematical proof and to investigate the reasons of these mistakes are important. …