Traditionally, Geometry class has sought to develop not just a student’s ability to work with shape and space but also their understanding of formal, axiomatic mathematics. The significance of axiomatic reasoning, however, frequently gets lost in the grind of memorizing precise definitions about shapes and then using those definitions to develop a more complicated proof about another shape (although ironically the proof is often about a claim in that is painfully obvious).
I have also become more and more convinced that the work done in math class must be about something more relevant and meaningful than a few trivial claims about shapes. In this case, there is an opportunity if not imperative to show students how the mathematical practice of developing definitions and exploring their implications can help them understand and interrogate their world.
Racism, for example, is often reduced to individual prejudice. But as Candis Watts Smith discusses in her TED Talk a “really narrow definition [of racism] can constrain our opportunities to produce a more racially egalitarian society.” She later posits that “maybe if we can come together and come to a shared and perhaps precise definition of what racism is, we can work toward a society where mothers like me aren’t in constant fear of their children’s lives.”
How we define, or fail to define, racism affects our ability to identify and dismantle it. In fact, just last year Merriam-Webster announced it was revising its definition of the word racism after receiving emails from Kennedy Mitchum, a recent college graduate. Merriam-Webster’s revised definition will be expanded to include systemic racism.
In All About Love bell hooks writes, “Definitions are vital starting points for the imagination…a good definition marks our starting point and lets us know where we want to end up.” She writes specifically of the dangers of defining love only as a nebulous mix of emotion and affection. Such a definition leads us to see love as a noun rather than a verb that requires action. It can also lead us to accept abuse and shame as part of love. She argues that this definition keeps us from loving fully. And she makes a challenging and compelling case for a more precise definition of love. Everyone should read the first chapter of All About Love at least once (probably more).
Watts Smith, Mitchum, and hooks exemplify exactly the type of thinking Geometry class hopes to develop: the practice of identifying definitions, understanding their implications, and revising them when needed. Their work also exemplifies a more expansive picture of mathematical practice, one directly connected to action and lived experience. Axiomatic thinking does not always come in two columns and is not only about trapezoids. Students deserve a bigger math. And surely understanding the implications of our definitions for love and racism is necessary work.
The slide deck below provides an outline for an interactive lesson built around these ideas. Beginning with student-developed definitions of five words (square, racism, circle, love, and pop), the lesson explores this type of mathematical reasoning in both traditional, Geometric contexts as well as more meaningful and relevant ones. Student will inevitability have incomplete definitions of square and circle, will likely have an individual prejudice definition of racism, and a wide variety of definitions for love and pop. The ambiguity in their definitions provides the jumping off point for discussion and work.
The deck also includes an extension lesson that examines how definitions shape arguments and a mini-project to help students explore the role definitions play in their life. These activities also could provide interdisciplinary connections: A Health or English class could concurrently study the first essay in All Above Love or a history/civics class could delve deeper into the politics and history of how racism is defined.
(also access the deck and read more detail in the speaker notes by clicking here)
