Culminating Project [DRAFT]: Mathematical Principles in Historical Swordplay

The Geometry of the Blade: Mathematical Principles in Historical Swordplay

By: Kristie Truell & Oliver Podwysocki

"Everyone, please choose your weapon of choice."
Photo by Inna Nasonova on Unsplash

Our Creative Process

Oliver has been teaching sciences, maths and the arts for 11 years. As a hobby, Oliver tries to learn skills that have been lost or are on the decline over time to keep them alive and sustain their presence in the wealth of collective knowledge of society. He has an athletic background and has recently taken up Italian swordplay through HEMA (Historical European Martial Arts). Oliver loves swordplay because it is meditative in that it requires the swordsperson to be fully present (mentally & physically) to deal with threats at high speeds with fluid and efficient motion.

Kristie has been teaching secondary science and math including Chemistry for 4 years. One of the things that made Kristie fall in love with Chemistry was the spatial geometry of molecules and how understanding that made all the other concepts fall into place. Kristie does not have a background in swordplay, but she enjoys yoga and diving which are both activities that rely heavily on body line and alignment. As a learner, her brain works best while moving and being able to look at problems from a different angle. 

Through swordplay, several mathematical connections are explored such as optimizing movement, forcing your opponent into larger geometries which take more time to execute, timing of attacks and striking distances to opponent, creating predictable striking patterns and breaking those patterns for advantage, leverage in sword-on-sword interactions, and so many more! In these lessons, we will explore very foundational concepts that require minimal personal protective equipment and skill to explore safely. All of these concepts could be taught with a pencil and paper, but come very intuitively when felt or embodied such as sword leverage or any concept related to distance (ie. choosing targets, measure/footwork).

Our lessons seek to provide students with a way to physically act out concepts that are typically understood in a very abstract manner. There is a danger of “black boxing” higher level math concepts by rushing to solving with algebra and a calculator. Our lessons allow students to view the math concepts “from the inside”. The shift in perspective required to represent their actions as a drawing, diagram, or notation can lead to deeper understanding (Smith, 2018).

It's both a sword AND a shield. Photo by Chris Linnett on Unsplash

Project Overview

Following the order and structures of Oliver’s teachers of longsword and rapier, the order of the lessons scaffold so that movements, offensive and defensive concepts build upon each other. A few fundamental concepts that are woven throughout are:

1. Footwork: using different types of steps, our footwork provides us with opportunities to get within a particular measure to execute a strike.

2. "The Three Advantages": to maximize advantages over your opponents sword, you must have true edge (edge corresponding to your knuckles) on top of your opponent’s sword, leverage of your forte (blade region closest to hand) against their debole (blade region close to tip), and crossing your blade over your opponent’s to maintain a threatening angle and displace their sword.

We start with footwork to gain a sense of being within range of attack; using the body as its own measurement tool, each individual will have a different amount of displacement with their steps. Then we learn how to strike once we learn how to get within range to attack. After learning how to strike, we can create combinations of sword movements that can flow using permutations that lead to rotational and reflective geometries. Finally, we learn how best to strike an opponent while maintaining control using measure and trigonometry inscribed within a circle. These lessons span a range of mathematical concepts and grade levels. 

Onto this we applied Abrahamson’s framework for embodied lesson design (2014). The components of this framework are:

1. Phenomenalize: Develop an activity that relies on the reasoning or solution strategy connected to the target concept. This requires conceptual anchoring, ensuring the activity is intentionally designed to elicit specific mathematical reasoning rather than simply mining a fun task for incidental connections.

2. Concretize: Introduce the formal models, diagrams, and/or symbolic representation of solution strategy. This step is necessary for reification of the mathematical concept and expanding mathematical vocabulary and notation skills. 

3. Dialog: Guide students in making connections between the embodied activity and formal solution models. This continues the reification process and prevents the embodied portion of the lesson from becoming “disembodied” from the formal notation by drawing out those students’ initial novice observations and bridging between the formal notation.

The Product

Link to instructional slide deck (it is a live working document that will change as we continue to develop it).
View-Only Link

"Armed and ready!"

Photo by Lance Reis on Unsplash