The Horizon Lesson

Welcome to the Horizon Lesson!

Representations of a problem-based lesson in which students investigate how far away the horizon appears when standing on a sandbar in the middle of the ocean. Using visualization and physical exploration of this natural setting, students pose questions and draw mathematical conclusions, applying the Pythagorean theorem to find unknown side lengths in right triangles and developing an understanding of circle properties such as radius and tangent lines.

This collection features two storyboards, each representing a version of the lesson developed by groups of teachers participating in StoryCircles—a collaborative process in which teachers design, share, and refine lessons together. Each storyboard illustrates how the Longitude Lesson might unfold in practice. Rather than serving as prescriptive teaching scripts, these storyboards are intended as resources that help teachers explore the instructional possibilities the problem offers and consider the range of decisions a teacher might make along the way. Specifically, you will have the opportunity to review the Foster Family, which consists of a collection of two artifacts:

• The first version, Angel Foster, was developed by educators from the state of New York along with mathematics educators from the University of Michigan to represent a lesson they participated in as part of a professional development about place-based education. See: Dimmel, J. K., & Milewski, A. M. (2019). Scale, perspective, and natural mathematical questions: Rethinking representations of the world in real-life problems. For the Learning of Mathematics, 39(3), 34–40.
• The second version, Bonnie Foster, was developed by a team of mathematics educators from the University of Michigan to help envision how that lesson could feasibly play out in a high school classroom.

You will have the opportunity to reflect on these lesson representations by adding annotations, reviewing annotations contributed by other teachers, and starting a discussion thread. 

Audience:

Highschool Mathematics Teachers, Teacher Educators, Students

Mathematics Domain:

Geometry

Key Features:

• View storyboards
• Annotate storyboards
• Read annotations from teachers around the world
• Compare annotations
• Start lesson focused discussion threads

Learning Objectives

• Examine two different representations of the Horizon lesson and discover different ways to teach this topic
• Refine your knowledge on teaching approaches by understanding different perspectives
• Initiate discussions with teachers on teaching approaches

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Sponsors:

National Science Foundation, James S. McDonnell Foundation