Exploring Ratios and Sequences with Mathematically Layered Beverages
Andrea Johanna Hawksley
Stop #1: "Many recipes have fairly strict ratios of ingredients (for example, baked goods), while others, like those in beverages, allow for a great deal of flexibility" (Hawksley, 2015, p.519).
This made me think back to my CEGEP and early university years. We often talked about how the different sciences could compare to the kitchen. Chemistry was more like cooking, you could kind of eyeball some things or use less precise glassware for many experiments, whereas biology was so precise and the perfect amount of each chemical had to be used by using an insanely precise measuring tool. We said how chemistry was like cooking and biology was like baking! Interestingly enough, I studied chemistry in my undergrad, and as I sit here reflecting on the comparison I just made, I am thinking about myself when I cook vs. when I bake. I think I enjoy cooking more, because I love the flexibility of getting inspired by a recipe, then changing it and making it mine by adding whatever I have or love. Whereas when baking, I find it mildly annoying to always go back to the recipe, and then having to run to the store for that 1 missing ingredient, that will ruin your batch if you don't have it. All that to say, I love baked goods, but I love the flexibility of cooking.
Stop #2: "[...], if the bottom layer has 5 teaspoons of simple syrup per unit of volume, and the top had 3 teaspoons of simple syrup per unit of volume, then the sweetness ratio is 3:5" (Hawksley, 2015, p.519).
As I read this, I was waiting for the author to describe how they took white board markers and marked the ratios on the cups! But it was never said! (Sad face) So, for my stop #2, I am suggesting an extension! If or when this experiment is performed again, perhaps the students could identify their ratios and fraction with white board marks on each glass to be able to increase the practicality and effectiveness of using these beverages as visuals (and tastables) to gain a better understanding of fractions and ratios and their relationship. This could also perhaps lead to adding or subtracting fractions, using bigger and smaller cups for sums/differences!
Stop 3#: "Many students struggle with understanding fractions even though they are a crucial skill that is generally taught fairly early in the mathematics curriculum as a precursor to later skills. Fractions can seem illogical and hard to conceptualize (Hawksley, 2015, p.523).
This particularly stuck out to me this week. As Amanda and I are wrapping up our project (focusing on fractions) this is just another scholarly article discussing the same problem. Fractions are a topic that is touched across almost all grade levels (most topics do not stretch this far), yet it still seems to be one of the hardest concepts for students to grasp. It is our job as teachers, to find better ways to teach them, to perhaps spend more time on it younger, and to use these types of activities to help build the foundations and grow!
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).
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).
Taylor, I always thought about the two being opposite (chemistry = precise with grad cylinders, vs. biology = imprecise) but upon further reflection, you can’t generally dissect or do surgery.
ReplyDeleteI also really enjoy a little space to make things I do personal (even in baking with Double Chocolate Diablo Cookies!! https://chatelaine.com/recipe/desserts/tacofinos-chocolate-diablo-cookies/ ) Without this flexibility, I am constantly comparing myself to the example or my teammates which is a slippery slope to poor mental health. By making your project and math personal, they become unique and not in a realm capable of direct comparison as it wouldn’t make sense.
The origami grow-with-me clothes is such a brilliant find and solution to children clothing waste. My wife and I found that at the age of the most compact shape, children are not scraping their knees and ruining their clothing; they just don’t generate that much force. At around 5-7, they are wearing holes in their socks, knees, elbows, etc. So, this age range creates damage that perhaps culturally, we do not feel comfortable using as hand-me-downs to friends and family. This would create an abundance of baby clothes in society (as they keep making them!), and a constant need to replenish (or fix) child clothing. This origami outfit, if worn to its material limit, could move numbers from the baby clothing abundances past the toddler phase shifting the current equilibrium towards child.
Anyhow, we had many more examples of fibre arts rather than culinary arts (including the pi baking). I want to try and connect more with mathematical concepts, easily accessible, cheap children’s snacks/foods/cereals. What kind of culinary mathematics would be possible. Perhaps tapping into averages and ratios at the same time. Hear me out:
Buy 1 box of lucky charms.
Dump a small sample in each student group.
Count total. Count marshmellows. Generate ratio.
Average out the ratio. Convert to decimal. Convert to percentage.
Rewrite the box of cereal with mathematical facts for truth in advertising. “Lucky charms… now “32% marshmellows!” etc.
Buy another box of lucky charms.
Repeat procedure above.
Average out between two boxes. Is there a consistency between boxes?
Rewrite the box “Lucky charms… now between 30-32% marshmellows!”
Or choose a different cereal with fun bits and have students choose the ratios they like better.
Thanks for the thoughts Taylor!
These layered drinks sound visual, tasty and fun! I really like your extensions, writing on the cups and combining cups in different ways. I agree that many math concepts, like fractions, are not sticking with students even with exposure year after year. Maybe embodying fraction experiences will help to build a metaphoric foundation that can stick - I feel that layered drinks would be memorable!
ReplyDeleteI was also curious about food/culinary arts and maths. I checked out the review written by Pamela Gorkin (2017) for Eugenia Chen’s book, How to Bake [Pi] : An Edible Exploration of the Mathematics of Mathematics, that Susan posted in our extra resources links this week. (It is available through the UBC library, but only in print :( but may be worth checking out down road - I liked earlier videos we have watched by Eugenia Chen in our program.) It states, “cookbooks are good examples of how to write bad mathematical texts. As Cheng notes, recipe books are unsatisfying because they usually don’t explain why things work—they just provide an algorithm.” (p.102) This links to the idea that you and Olly have discussed about how cooking can be flexible, where you can start with a general direction but still get to put your own creative spin on things - whether this is to accommodate a taste, availability of ingredients or a sense of ownership over what you have made. “Cottage pie and Shepherd’s pie are just variations on a theme. Now ‘‘abstract’’ this: take an empty pastry shell, put in your desired filling, and use the topping of your choice. Abstraction is, she says, what makes mathematics mathematics and it is also what makes people think it is detached from real life.” (p. 102) So, maybe it is not about just introducing embodied experiences, but specifically experiences that link metaphorically this way? “Cheng points out that if you wanted to invent a recipe, you would probably start with a familiar one that you like, but that might be improved.” (p. 102) This reminds me of the foraging, analyzing, recreating, create new format from Vogelstein et al. (2019) and makes me think that students need to (1) have a recipe they are familiar with (2) know some foundational relationships within that recipe (ex - what ingredients will ruin the outcome if tampered with vs create an enjoyable variation. If you take the riser out of a muffin recipe it may not be successful, but if you change the flavour profile ingredients it may.) How long does it take to become familiar with a recipe? How many times do you need to make it before positioning students to be a creator of something new as opposed to replicating the recipe given to them? Do we not give (or have) enough time and practice to build this familiarity in school?