Honors Geometry: Writing Proofs with Ms. Shapiro

In this article, SASS board member Gloria K. ('22) interviewed Honors Geometry instructor Ms. Shapiro. We hope that this article will help current and future Honors Geometry students in their academic journey!

What is your favorite thing about teaching Honors Geometry?

My favorite part is teaching students proof writing. Honors Geometry is the first class many students take that introduces them to proof writing, which is so important later on in math and develops critical thinking.

What challenges students the most in Geometry? How would you recommend that students overcome these challenges?

I think that proof writing fits in both of these categories. It’s one of the most interesting topics in geometry, but it’s also the most difficult. Often, students come out of Algebra with an exact method for solving an equation in mind. Proof writing is challenging because there is no exact algorithm for students to follow, and you really have to explain what you do.

The best way to overcome this is to come in with a very solid foundation in algebra and previous math courses.

What types of students do well in Geometry?

Students do well in Geometry when they are prepared, those who have a solid foundation in algebra to help with proof writing as well as the equations that come up.

What does the average workload for each week look like?

In MathXL, there are two small exercise sets as well as a weekly homework. Every two weeks, there is a problem set. After each unit, there is a written exam, MathXL exam, or both. This would add up to an average of 2 or 3 hours per week.

How do you recommend that students prepare for exams in Geometry?

I would encourage students to keep up with the material as it comes and to reach out to me if they have questions as the semester progresses. They can send me emails and come to office hours. Other than that, the best way to succeed in exams is to review past homework assignments and problem sets. Extra practice problems can also be found in MathXL and the textbook if there is a particular topic you want to review.

How is the participation grade for Geometry determined?

The participation grade for Geometry is determined by the two sets of exercises.

How is a student’s overall grade in Geometry determined? What percentage of a student’s overall grade is determined by exams, homework, quizzes, participation, etc.?

Participation is 5%, MathXL homework is 10%, problem sets are 15%, unit quizzes are also 20%, the midterm is 20%, and the final counts for 30% of the overall grade.

What materials do students use in the course (textbooks, lectures, online resources, etc.)?

We use the lectures that students are expected to watch before class, MathXL for school—that’s the online component, and there is also the physical textbook that many students use for reference.

Are students expected to be on camera for the entire class?

No, only when they come on mic to contribute to a problem.

Have you had any experiences with students in Geometry that could encourage those who think they cannot excel at the material to take the class?

Definitely! I’ve had a number of students discouraged that they struggled in algebra, but geometry is really different and they really found their footing in it. For some students, the visual-spatial is where their comfort level is. I would strongly encourage students to take geometry as it lays the foundation for trigonometry and more advanced proof writing.

What about Geometry interests so many students?

I think the visual-spatial aspect of it. Proof writing is certainly integral, but the visual-spatial aspect of it can be fascinating, like solving a puzzle. Visually inclined or artistic students often especially enjoy this part. There are also many application problems, for example finding the height of a tree outside. These really are what geometry is all about.

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