Although there is consensus on the relevance of the feedback given to student teachers, few instances in the literature have addressed this topic. Even less is said about feedback to mathematics lesson plans and how to characterize it. Lesson plans are artifacts that help establish a link between theory and practice, relate to a broader sense of assessment, beyond merely assigning grades, and keep the mathematics of the lesson as a central component. Focusing on the opportunities to think and reason that students will have on the lesson, the anticipatory work done when establishing a goal, selecting a task and declaring teaching practices, makes the concept of cognitive demand to emerge. Teachers should be able to plan high cognitive demand lessons and implement them in ways that preserve this demand. Mathematics teacher educators, therefore, have a valuable opportunity when providing feedback to the cognitive demand of student teacher lesson plans. This research addresses the characterization of the feedback giving process of two Chilean Mathematics teacher educators, and eventual shifts that might have happened after a professional development workshop focused on cognitive demand of goals and tasks in a mathematics lesson plan, and the effects that certain teaching practices could have to this demand. Results suggest that the overall experience of reflecting about the cognitive demand of a mathematics lesson elicited different kinds of shifts at different stages of the research for both participants, who were able, at the end, to use the concepts of cognitive demand to articulate their feedback to student teacher mathematics lesson plans.
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