Babylonian word problems - response

Within the chapter, I paused at the mention of how many math workbooks today aim to provide “real word” examples, yet include ones that are so contrived that they actually become meaningless for the student. This makes me think of many examples I encountered in my own time in grade school where the class would laugh at some word problem that consists of an individual buying a few hundred watermelons and the like. While it was clear what concept these word problems were trying to get at, they were not necessarily achieving the goal of showing us the use of math in real life, unless you could look beyond the numbers and see the broader concept, such as something like "math may be used in calculating costs." However, it was interesting to see that perhaps word problems were still very contrived even at the time when the Babylonians were doing math. These word problems seem to have the same goal of aiming for the concept of using math to calculate things like area and such, but, just as in the modern day, may be forced to use strange values and situations for the sake of learning that does not necessarily keep them realistic.

I also found interesting the suggestion that this may point to there being no clear divide between pure and applied mathematics, and that we may need to question whether any true “real-life” problems exist or if all must contain certain features that make situations perfect and unrealistic compared to real situations, such that math can be applied easily for student learning. While requiring a bit of a stretch, this point made me wonder about how we attempt to separate math classes into streams at the secondary level. In particular, these courses are often separated as some being more “real-world” or applied, and thus better for students who plan to immediately enter the “real world” post-secondary. If it appears that we struggle to actually teach something real about the world through our word problems, I just wonder how well we are connecting course content in such foundations or apprenticeship style math classes or the curriculum at large to concepts or problems they may genuinely encounter in life. In particular, it makes me wonder how truly beneficial these math classes are for these students and also if there truly is any clear line to be drawn between the streams that focus more on abstract/pure math vs applied.

In general, I also noticed that most of the problems likely struggle with this true real-world connection because they are being written to be solvable by the students so that they can learn the math tools, and the chapter includes the point that it thus may not be out of any inherent interest in the topic being connected. I do think this may suggest there is a time and place for the more contrived word problems that are being used out of pure utility to help students pick up on the math concepts, and a time when we should encourage students to do projects or research into genuine real-world applications of math, to gain some personal insight on how math is played out or applied in some area of their interest.

One other concern I have with the more contrived word-problems in students' workbooks today is the kind of habits it might be causing. Namely, we often urge students to read word problems more carefully and to identify all important pieces of information and their relationship to each other before beginning their solution, to ensure minimal errors. However, the more contrived the values or situations get, while still using the same general format, it makes me wonder if this only further encourages students to skip over many of the words or supposed “real-world” situation of the problem and jump right into applying the formula to the numbers. I think this particularly happens if they encounter a lot of the exact same format of word problem, just with some new crazy scenario and new values, and so they come to disregard the words and race to apply the formulas instead, possibly causing them to miss important information when the word problem format actually does change. Perhaps if each word-problem was produced with more care and to be more realistic and more unique from others, students would be less likely to develop this habit of jumping over the provided information, necessary for solving the problem.