Learning to Diagnose Primary Students’ Mathematical Competence Levels and Misconceptions in Document-Based Simulations

Abstract

Analyzing students’ documents (e.g., their homework) can serve as a basis for diagnosing students’ learning status and thus also for adaptive teaching. When making diagnostic judgments about students’ learning status in mathematics, teachers may benefit from using theoretical models of mathematical competence because such models illustrate what tasks students should have mastered on each level of competence. Based on students’ documents and a model of mathematical competence at the primary level, we developed a simulated learning environment for (1) analyzing and (2) supporting pre-service teachers’ diagnostic processes and results. When working in the simulated environment, pre-service elementary teachers are asked to assess virtual third graders’ learning status by diagnosing their mathematical competence levels as well as their misconceptions (e.g., misconception regarding multiplication) based on the competence model. To do so, pre-service teachers analyze students’ solutions to mathematical problems that they can select from a set of problems varying in content and difficulty. First data analyses suggest that the environment can capture differences in pre-service teachers’ diagnostic processes. A better understanding of these processes can serve as a basis for further developing the learning environment.