Antoinette Villarin teaches mathematics at Borel Middle School in San Mateo, California. This lesson was recorded in an eighth-grade geometry class. Nineteen students were invited to be in this zero-period (first-of-the-day) class, based on whether they wanted to take two math classes as an eighth grader. At the time, students were concurrently taking Algebra. All attend Borel except for one student who comes for this class before attending another nearby school. Antoinette also has been videotaped for an Inside Mathematics lesson on perimeter, area and proof and a lesson on constant rate of change with different groups of students. She has also reflected on the value of authentic mathematics teaching alongside others who provide lessons on Inside Mathematics.
In this lesson, Antoinette works with students on justifying their mathematical thinking using coordinate geometry. Students read a scenario multiple times, and they generate possible problems that could be asked of the scenario. Then the students work with a problem set to identify strategies and justify their strategies to the group. Specific connections that Antoinette makes to geometric concepts include:
- “The student understands the importance of logical reasoning, justification, and proof in mathematics.”
- “The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.”