Babylonian Word Problems

     To me, practicality in mathematics means that the math learned in useful in day to day life. Most of the time, it is something that is so frequently used or thought about that we almost forget that it is math. Examples of this is calculating which box of chocolates is cheaper at the store, or planning how long you can sleep in the next day without being late for class. When I think about abstraction, I imagine math that can't be easily modeled in my head. For example, this would be something like the n-th dimension when thinking about linear algebra. I think that things that were once an abstract concept to someone can become concrete as they become more familiar with the topic and develop a deeper understanding. I would argue that pi is pretty abstract until you understand that it is the ratio between the circumference and the diameter. The same can be said for algebra, as the steps would seem meaningless if you didn't understand why it worked. The difference between 'pure' and 'applied' mathematics is more a difference in discipline than in the math itself'. I imagine 'pure' math as the theory behind math, or researching math itself to develop new concepts. 'Applied' math, is using math to create something concrete in the world, like building bridges or understanding cells. Yet the line between 'pure' and 'applied' is a fine one, as theoretical concepts can be applied, and a question seeming rooted in real world examples can be abstract and conceptual.

    One of the main themes in A man left Albuquerque heading east: Word problems as genre in mathematics education is the discussion of what constitutes a 'practical' math problem. When reading the example word problems from ancient Babylonian texts (pp.133), I had the thought that they were very similar to the word problems we give students in school. Questions that seemed as if they were rooted in real world examples as the topics were on things we do on the daily. Things such as buying food, dividing property, and calculating weight. However, I thought that the unknowns and numbers seemed forced in there to create a problem that someone could do in school, rather than something we would do in every day life. I've noticed this with word problems students often do in the modern classroom or in their textbooks. They detail events like Greg buying 500 watermelons, or Sam needing to find out how to feed the 90 cats he owns. Usually, we don't buy 500 watermelons, or own 90 cats.

    I think the reason I feel this way about the Babylonian math problems is because the importance of applying mathematics is stressed so much in teacher education. There is a bigger desire for math to be connected to real world scenarios so students will be more interested in math. However, artificially disguising a question to seem like it's connected to a real world situation doesn't accomplish much. When I did questions like those in high school, I would just scour the question for the numbers and it didn't really matter if I was adding money or scraps of paper. Another example of forced application, would be questions I've seen in textbooks that are superficially changed to incorporate Indigenous names or subjects. I think it's fine as long as changing the problem from calculating the area of a garden to the area of a longhouse isn't the only thing a teacher is doing to promote Indigenous learning in the classroom.