Patricio Herbst

TL;DR: In this paper, the authors provide a historical count for how proving evolved as a task for students in school geometry, starting from the time when geometry became a high school subject and continuing to the time that proof became the centerpiece of the geometry curriculum.

TL;DR: For example, the authors argues that knowledge-in-action and reflection-inaction are common to people who perform the same job, yet they are not all part of the explicit regulations that describe this job.

TL;DR: In this paper, the authors examine students' perspectives on the public work of proving in American high school geometry classes and propose a model of how proving is shared by teacher and students, and show how the activity of proving is a site in which complementarity as well as contradiction can be observed between what makes sense for students to do for particular mathematical tasks and what they think they are supposed to do.

TL;DR: The authors argue that comics can be semiotic resources in learning to teach and suggest how information technologies can support experiences with comics in university mathematics methods courses that help learners see the mathematical work of teaching in lessons they observe, allow candidates to explore tactical decision-making in teaching, and support preservice teachers in rehearsing classroom interactions.

TL;DR: In this article, a teacher's work is analyzed in two classes with an area problem designed to bring about and prove a conjecture about the relationship between the medians and area of a triangle.