Validity of problem posing as assessment

Abstract

This article aims to explore the construct validity of problem posing as an assessment method. The article proposes a framework of factors contributing to the validity of problem posing as assessment. For convergent validity these factors are the complexity of the problem, solvability of the problem and the coverage of the learning goals. For discriminant validity there is only one factor, namely whether the problem covers at least one learning goal. Further, this article explores whether it makes a difference for the validity whether the problem posing task is structured or unstructured. We have analyzed 86 problems posed by 21 secondary education students as part of an advanced mathematics course. The results showed that all previously mentioned factors contribute to the validity of problem posing as an assessment and that taking the students’ answer key into account in assessment contributed to the convergent validity as well. Therefore, the answer key is added to the proposed framework of factors contributing to the validity of problem posing. Furthermore, the problems posed from structured tasks had more diversity in complexity of the problems, allowing the teacher to distinguish the mathematical abilities of students better. Therefore, the structured tasks are more convergent valid than the unstructured tasks. The main implication of the results is that problems posed from structured tasks that are rated on complexity, solvability, students’ answer keys and coverage of the learning goals are a valid way of assessment.