Grade 11 students’ interconnected use of conceptual knowledge, procedural skills, and strategic competence in algebra: a mixed method study of error analysis

The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students’ difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly selected grade 11 students in an urban school in Ontario, Canada. Ten students were later interviewed. In this paper, we discuss the solutions and interviews of five students. The results showed that the majority of university/college stream mathematics students were in the transition stage from arithmetic to algebra. Another prominent feature of these students’ problem solving process was their overuse of procedures without being able to critically evaluate whether these procedures would work or not. They also demonstrated lack of relational, application, and structural abilities when solving instructional problems. We emphasize that, in order to be successful, all components of problem solving (procedural work, local focus, strategic skills, and algebraic reasoning) should work together in a coherent manner, as the main learning challenge in problem solving remains keeping cohesion between its multiple interconnected components. Therefore, it is necessary that to show them the arithmetic-algebraic connection in problem solving and to facilitate them to systematically check their answers in the context of a general strategy.