Investigating the procedural and structural conception of algebraic expressions of seventh, eighth, ninth grades students

Many international studies have been done in order to trace the intellectual path of students in manipulation with the concept of variables and algebraic expressions, as well as to examine and specify their functional problems. However, despite the importance of these two concepts, comprehensive research has not been conducted in the seventh, eighth and ninth grades in Iran, and research has often focused on how to manipulate and write algebraic expressions. Due to the change in Iran's mathematics curriculum in 2009 and the consequent change in mathematics textbooks, the need for a clear picture of students' understanding of these two concepts is doubled.Algebraic expressions are the important part of Algebra and its deep understanding is necessory for solving algebraic problems. The purpose of this study was to investigate grade 7th, 8th and 9th students' understanding of algebraic expressions.

400 students were selected by multistage cluster sampling from 7th , 8th  and 9th  grade students in Tehran. A researcher-made test was designed and implemented. Out of 400 students, 15 students were selected and semi-structured interviews were conducted in order to clarify and interpret students' perceptions.

The results of the test and interviews showed that most students have a poor structural understanding of algebraic expressions and they have understood them merely procedurally. Increasing academic bases did not almost improve structural understanding, but procedural understanding improves with increasing levels.

The results of this study showed that most students in algebraic expressions (simple and complex) have a purely procedural understanding, which means that they have understood algebraic expressions as a set of algorithms and processes. As it turned out from the interviews, these people, when it is necessary to perform an operation on the algebraic expression and consider the algebraic expression as a whole, only memorize the steps as a parrot because they have no understanding of the whole structure of the algebraic expression; and they focus only on the steps within an algebraic expression. In complex algebraic expressions, compared to simple algebraic expressions, the percentage of students who had a purely procedural understanding was reduced. The results of interviews with a number of students showed that this decrease was not due to an increase in students' structural understanding, but for reasons such as ignoring the distributive action, not understanding algebraic expressions, not understanding the process in complex algebraic expressions.