Learning paths in training mathematics teachers: goals, tasks and assessment.

SUMMARY

Inspired in Simon’s seminal idea of hypothetical learning trajectory, in this article we introduce the notion of learning path of a task. Based on this notion, we present a procedure for characterizing a learning goal. We show the usefulness of this kind of characterization in two aspects of mathematics teachers’ practice: analyzing the contribution of a task and of a sequence of tasks to the attainment of a learning goal; and collecting and analyzing information for learning assessment. We illustrate and reflect on these ideas and procedures in the context of secondary mathematics teacher education programs.