Why was this CIP important to the growth of our academic program?

When I arrived at Emma Willard 11 years ago, the geometry class was a light revision of Exeter’s problem-based course—a sequence of well-designed, multi-concept problems leading toward concept evolution—with light guidance from the teacher and an emphasis on student presentation, writing, and discussion. Over time, the original curriculum was substantially abridged, impacting its careful sequencing.

While appreciating the original course’s Harkness-style emphasis on student discussion in a math classroom, I had been concerned for some time with the absence of hands-on, physical “building” in the geometry curriculum. If students don’t get to touch mathematical tools and models in geometry, they may never experience the pleasure of connecting the physical and the theoretical. 

Additionally, I wanted the course to provide all our students with a solid understanding of the concept of mathematical proof. One of the distinctive aspects of mathematics is the fact that we can speak of absolute truth if we take the opportunity to prove assertions along the way. And in the process, it can also be a magnificent game!

Why did you want to be the one to redesign the geometry curriculum? 

I offered to rework the course for several reasons, the first of which was a sense of responsibility, both to our students and to a subject I care very much about.

Second, over the course of my mathematics-teaching career, I have never before designed a complete course. I have repeatedly inherited other teachers’ courses, then modified them by introducing labs, explorations, and applications that reflect my own interests and thoughts on how to make the material stimulating and intriguing, also drawing on my training and first career as an engineer and researcher. 

Finally, I am privileged to be the mentor for young mathematics teachers beginning their careers, and this tends to put me in a mindset of specifying what is needed to make teaching the class as clear as possible for a new teacher. Any new course will involve some learning and modification on the fly. That’s fertile ground for conversations with young teachers who are learning and who also bring fresh eyes and perspectives.

What was your approach to researching possibilities for the course design?

Because geometry is a basic component of high school math education, most of my colleagues have taught it at some point in time. Thus, I began my CIP journey with an in-depth listening tour of the Mathematics Department. What have my perceptive colleagues valued or been concerned about in teaching geometry? What kind of learning materials have they found helpful? What would they love to see? 

Many echoed my desire for a course that was rigorous but also experiential, designed to stimulate curiosity and develop comfort with physical tools and models. Two colleagues independently recommended a textbook that is out of print but offers fine explanations and a variety of problems for additional practice and challenge. 

I then arranged visits to geometry classes at three very different high schools—one a regional high school with an entirely project-based geometry curriculum, one a highly-regarded public school, and one a peer boarding/day school. The first school excelled at conveying geometry in action, hands-on, with tools in students’ hands every single day. The second demonstrated incredibly thoughtful structure and support of students in how it organized and conveyed a very substantial body of geometry material, while blending it with algebraic concepts to help students keep those skills sharp. The third used a textbook—the same one my colleagues had praised from their previous experience!—very effectively, combining book problems with small-group explorations that emphasized collaboration. I can’t say enough about the generosity and welcome that I was met with at these schools; a footnote on my syllabus thanks all my teacher hosts by name. 

What elements will you keep from the current course design?

We’ll continue to use the online DeltaMath system for low-stakes weekly mastery checks of key skills, as well as weekly assessments (some quizzes, some tests) for rapid feedback. We have found that small-group work with paper handouts and board work keeps students focused and talking to each other, and we will continue with a binder system that helps train organization (especially important for our younger students). 

What will be different about the course?

Substantial differences this year will include beginning each class with a short exploration, construction, or “puzzle” that connects to the unit, and the use of both handouts and textbook—yes, the excellent textbook that just kept coming up as I talked to teachers in multiple schools!—to give students multiple resources for practice. 

You will see geometry tools in our students’ hands—compasses, rulers, tools for building angles and polygons, and manipulative shapes. Items as simple as strings and as droll as hula hoops can light up students’ recognition of the geometry in the world that surrounds them. I hope our students will leave this course feeling they have played as much as they have learned.

The Mathematics Department will also assemble a lending library of geometry texts to ensure that there are no barriers to students being able to obtain the books they need.

What have you learned throughout the process?

I’ve recognized how much uninterrupted time I needed in my own space to really think about lesson content and the “flow” within a course. The course release Emma Willard provides for new course development is absolutely critical. 

The interplay between learning from conversations with other educators and having the space to synthesize on my own has been productive and incredibly rewarding. I know there will be revisions as the course takes flight, and I am so looking forward to working with my geometry course colleagues here at Emma as we both implement and improve.