The Investigation of students' mistakes in simplifying algebraic expressions, and finding the source of these mistakes from the viewpoint of Mathematics teachers

Mathematics is one of the courses that is contained in the curriculum for students in all fields. One of the concerns of educators and math teachers is that middle school mathematics students have many problems when faced with algebraic topics. In Iran, all students need to study algebra and teachers must help them build a deep and lasting understanding and skills for high school math. Hence, an important goal for teachers is to be aware of the mistakes in order to help students to understand concepts and procedures correctly. However, unfortunately, some teachers do not have enough knowledge to identify and correct the existing mistakes and their origin. So perhaps recognizing mistakes and their origins and informing teachers about these mistakes can help students succeed in learning algebra. Thus, the purpose of this research was to investigate the students' mistakes in simplifying the algebraic expressions and finding the origin of making such mistakes from the mathematics teachers’ viewpoint.

This research is one of an “applied research” type and due to its purpose is considered as “qualitative research”. The research sample includes 14 math teachers of the middle school of Kerman province with teaching experience between 12 to 29 years who were selected by the targeted sampling method. Because teachers who had experience teaching algebra in middle school had to be selected. To collect the data, we first designed a test about simplifying algebraic expressions for eighth-grade students and extracting erroneous cases, through a semi-structured interview with math teachers. The qualitative content analysis method was used for data analysis.

The findings of this research showed that from the viewpoint of mathematics teachers, 22 types of mistakes were made by students of middle school when simplifying algebraic expressions including exponentiation, positive and negative sign, addition, subtraction, multiplication of integers, conjoining, a variable related operating, use of brackets, similar terms, and the order of operations. The findings also showed that teachers believe that the causes of students' mistakes in simplifying algebraic expressions are as follows: The lack of understanding, misunderstanding or incomplete understanding of concepts such as variables, exponent, brackets, and similar terms; ignoring of algebraic symbols; students' self-made rules in dealing with exponent and brackets; interference of previously learned algebraic concepts with current learning and vice versa; and incorrect calculation of addition, subtraction, and multiplication of integers, causes making mistakes when simplifying algebraic expressions.

Today, students are no longer isolated in a desert where the math teachers are the oasis of knowledge, but rather floating in an ocean of information. However, teachers are still needed to help them understand algebra in a meaningful way. In algebra, the concepts are formed hierarchically and the learning of each concept depends on the students' understanding of the prerequisite concepts, so, if teachers attend the algebra class fully aware of the reasons for students' mistakes, they attempt to make the prerequisite concepts understandable to the students correctly, and without any misunderstandings and errors. This helps students to make fewer mistakes in solving algebraic problems, increase their self-confidence, and ultimately, perform better.