Mathematics

Biology

Operating system

Mathematics education

Political science

Paleontology

Artificial intelligence

Management

Psychology

Economics

Set (abstract data type)

Judgement

Programming language

Context (archaeology)

Computer science

Task (project management)

Decimal

Process (computing)

Selection (genetic algorithm)

Arithmetic

Frontiers in Education

Teachers’ diagnostic competences are regarded as highly important for classroom assessment and teacher decision making. Prior conceptualizations of diagnostic competences as judgement accuracy have been extended to include a wider understanding of what constitutes a diagnosis; novel models of teachers’ diagnostic competences explicitly include the diagnostic process as the core of diagnosing. In this context, domain-general and mathematics-specific research emphasizes the importance of tasks used to elicit student cognition. However, the role of (mathematical) tasks in diagnostic processes has not yet attracted much systematic empirical research interest. In particular, it is currently unclear whether teachers consider diagnostic task potential when selecting tasks for diagnostic interviews and how this relationship is shaped by their professional knowledge. This study focuses on pre-service mathematics teachers’ selection of tasks during one-to-one diagnostic interviews in live simulations. Each participant worked on two 30 mins interviews in the role of a teacher, diagnosing a student’s mathematical understanding of decimal fractions. The participants’ professional knowledge was measured afterward. Trained assistants played simulated students, who portrayed one of four student case profiles, each having different mathematical (mis-)conceptions of decimal fractions. For the interview, participants could select tasks from a set of 45 tasks with different diagnostic task potentials. Two aspects of task selection during the diagnostic processes were analyzed: participants’ sensitivity to the diagnostic potential, which was reflected in higher odds for selecting tasks with high potential than tasks with low potential, and the adaptive use of diagnostic task potential, which was reflected in task selection influenced by a task’s diagnostic potential in combination with previously collected information about the student’s understanding. The results show that participants vary in their sensitivity to diagnostic task potential, but not in their adaptive use. Moreover, participants’ content knowledge had a significant effect on their sensitivity. However, the effects of pedagogical content and pedagogical knowledge did not reach significance. The results highlight that pre-service teachers require further support to effectively attend to diagnostic task potential. Simulations were used for assessment purposes in this study, and they appear promising for this purpose because they allow for the creation of authentic yet controlled situations.

Selecting Mathematical Tasks for Assessing Student’s Understanding: Pre-Service Teachers’ Sensitivity to and Adaptive Use of Diagnostic Task Potential in Simulated Diagnostic One-To-One Interviews