September 23, 2024 Exit Slip

"EXERCISE 4.4.2. 

a) Susan's class on mathematics history has students posting on their blogs for various topics and readings, as a way to get her students to engage with the material. One day, Susan's TA Erica wonders, "I wonder how many blog posts will be made throughout the course." If there are 17 students in the course, and Erica estimates that around 20 blog posts are to be written by each student, how many blog posts will be written?

b) Susan can read and evaluate around 5 blog posts per hour while Erica can read and evaluate around 7 blog posts every 2 hours. If the two sit down on the last few days before the term ends to grade every blog post, how long will it take for the two of them to process every blog post?"

This was my attempt at making a word problem by basing the contents and story off a hypothetical sequence of events that my instructor and her TA would go through. Right off the bat, there are some questions to be raised. How would we be sure about our answers if the given information is just in estimates? Why would the professor and her TA wait until the last minute to grade everything, which is not true considering that there will be feedback checkpoints? Of course, the teacher isn't looking for this kind of thought, but instead is simply looking for an answer that is based on the assumption that the estimates are accurate and precise, every premise is valid and sound, and so forth.

Such word problems are within the realm of what I have experienced. Although word problems have mostly phased out by the end of Calculus I in university, every course in mathematics from grade 12 to before had me solving the woes of various constructed entities with problems ranging from the mundane to the utterly bizarre. I am also well aware of the meme that refers to "the guy in the math problems", which is used whenever there is a scenario with outlandish numbers (for example, a picture with a man pushing a shopping cart with 50 boxes of Twinkies at Wal-Mart). While some of these problems are likely applicable to the average student, the fact is that most of them lie in domains foreign to them. In an attempt to make word problems seem "realistic" to a wider audience, they end up feeling contrived and off the mark for almost everyone despite having some plausibility. That being said, I think it's possible to lean into the bizarre nature of some word problems. Why not fully commit to the insanity? Why not make unrealistic premises? I'm also a fan of using names from pop culture and other recognizable sources in word problems, so why not do that too? Although I hope the word problem I presented piqued your interest, I think that such wild word problems could equally pique the interests of students, much like they did for me. A sense of humour is always welcome after all.

Additionally, the concept of a word problem dates back millennia, and in class I've learned that these problems were enjoyed by people all over the world as a form of problem solving, idea sharing, and even riddling one another. Along the Silk Road, cultural melting pots formed at inns where they would share their word problems, sometimes only to flex their mathematical prowess. I think we can gather some inspiration from the enthusiasm of these days and incorporate them into our own classes. Currently, the word problem implementation in textbooks and classrooms is vaccine-like. We set up sterile targets for students to shoot down, and they are, again, contrived. There is a missing element of creativity that we can introduce. Why not encourage students to make their own word problems out of the stories and struggles in their lives? I could see myself setting aside time for students to form and exchange their word problems in class, which could be beneficial in terms of promoting creativity, collaboration, and most importantly: application to real life that the students would care about. I do want to note that it's okay if the questions they come up with seem contrived; even then, there's a fun storytelling element that allows the mathematics to embrace a written art form, whether fictional or non-fictional. Thus, I also believe that by allowing students to write their own mathematical stories, we can introduce an artistic flair that would pique many interests. In short, I would like to use word problems in my own teaching to promote collaboration, artistic and historical thinking, and the standard intents of practicality and realism.

To address the second question on the prompt for this blog post, the first thing that comes to my mind is simply bringing awareness to the history of word problems! Many students likely haven't even considered that there's a rich history to word problems, instead believing that they are a psyop intended to confuse and torture them under the guise of "real world connection". I'm assuming that mathematicians, math teachers and historians have compiled a bank of word problems throughout the ages -- I understand that they are already being used in our textbooks, and we can continue using them, except this time we'd acknowledge where, who, and when they came from, or what the problem was used for. My belief is that kids generally love harmless fun facts, and with enough repeated sightings of things like names, eras, civilizations, etc., they will start to recognize the rich history behind the problems they are solving. 

Another idea is to incorporate assignments where students simply search for historical word problems and inquire about them on their own, with a list of resources and starting points provided, of course. In these assignments, they could happen once a sufficient number of concepts have been taught such that students have a greater scope to find a relevant question from. Although I haven't gotten too deep into working on Assignment 1 for this course yet, I suspect that such an assignment (give starting points, ask students to solve their question in modern and ancient ways to build appreciation for both, and extend) could be replicated in a high school classroom. I look forward to hearing about more ideas on how to connect with the history of these word problems to our students, and hope that I was able to offer some fun ideas of my own! Even though I struggled through them in high school, I recognize their importance and do not wish for them to be thrown away, ending a tradition of millennia.