Analysis of Middle School Mathematics Teachers' Evaluations of Skill-Based Questions within the Framework of Mathematical Competencies

The purpose of this study is to examine the solution methods developed by middle school mathematics teachers for skill-based mathematics questions and their evaluations within the framework of mathematical competencies. Mathematical competency demands are defined as communication, devising strategy, mathematizing, representation, using symbols, operations and formal language, and reasoning and argument. Thirteen middle school mathematics teachers (7 female, 6 male) participated voluntarily in the study. They were asked to solve twelve skill-based questions, followed by the examination of their solutions, and then semi-structured interviews were conducted with each of them. During the interviews, the teachers were presented with semi-structured questions, and their evaluations were examined within the scope of mathematical competencies. The study results indicated that teachers apply different solutions in solving the questions and that mathematical competencies emerge at different levels within these solutions. Considering the determined levels of solutions, other competencies, except for communication competency, appeared to be at similar levels based on teachers' evaluations. The competency of using symbols, operations, and formal language stood out as an essential factor in selecting among strategies. It was found that teachers could create appropriate models according to the level of demand for mathematizing competency, yet they did not evaluate the structural relationships between variables within the scope of mathematizing competency. Regarding representation competency, the most striking point was that the majority of teachers identified and used visual information. However, only a few teachers were successful in manipulating representations in a solution-appropriate manner. It was also discovered that as the demand level increases in using symbols, operations, and formal language competency, the increase in the number, type, and procedures of operations used is not always correct with these solution methods. Teachers could not identify the mathematical deductions utilized in the solution process. The majority addressed them at a lower demand level in their evaluations.