Hawksley, A. J. (2015). Exploring ratios and sequences with mathematically layered beverages. In Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (pp. 519–524). Tessellations Publishing.
Stop 1:
My first stop was Hawksley’s observation that people rarely think of cooking as "inherently mathematical," even though ratios and proportions are its foundation. In our current graduate courses, we have discussed the importance of building capacity before introducing formal language. Hawksley’s workshop honors this by letting students start with the intuitive sensation of sweetness. By testing their calculations, if the layers mix, the math was incorrect, they use their physical senses to refine their understanding of density and fractions. It turns a dry lesson into a self-correcting, hands-on exploration.
Stop 2:
I paused again at the concept of Fibonacci Lemonade. Hawksley explains that if the sugar in layer n follows the Fibonacci number Fn and the lemon juice follows Fn-1, the ratio of sugar to juice approximates the golden ratio as the layers progress. This is a profound shift in perspective. Instead of the golden ratio being an abstract decimal (1.618...), it becomes a "tastable example" of mathematical harmony. This aligns with our discussions on how "everything connects" - the Fibonacci sequence is not just a pattern on paper, but a recipe for flavor.
Stop 3:
I Wonder
Hawksley mentions that this workshop is effective for all ages. I wonder: if we replaced our standard introductory lessons on sequences with a "sensory lab" like this, would the physical memory of the "Fibonacci sweetness" lead to better long-term retention of the underlying limit theorems and recurrence relations than a standard lecture?
Hi Kabula,I really love the direction mathematics teaching and learning is taking! Your question about replacing standard introductory lessons with a 'sensory lab' is a powerful one. I was amazed by the use of beads in the Fisher article, and now, applying this to beverages makes the math feel incredibly close to our daily lives.I believe that starting with this sensory approach is exactly what leads to better long-term retention. When we lead with the 'Fibonacci sweetness,' we give students a physical memory to 'attach' the theory to later. Often, we start with abstract formulas like $F_n = F_{n-1} + F_{n-2}$, which can feel distant. But if the very first thing a student does is taste the recurrence, the limit theorems we teach afterward aren't just empty rules—they become the language used to explain an experience they’ve already had.
ReplyDeleteHi Kabula, thanks again for your summary and reflection. I actually did an assessment where students played with ratios and proportions to make lemonade. We called it Menu Math. My biggest regret was not being able to have students actually make and taste the lemonade. The assessment focused on students’ ability to manipulate ratios and proportions, and I worried that having them make the lemonade on the spot might have given away the answers.
ReplyDeleteAnother constraint was that I had a class of 38 Grade 8 students squeezed into a small classroom. I suppose I could have made the lemonade myself and had students try it, but that also feels like it would remove some of the fun and ownership for them. I know my students probably do not remember that assessment, but they would have definitely remembered if they had made and drank lemonade in math class.