When reading "The History of the Word Problem Genre" I was shocked at how similar the word problems look to what I have taken in high school along with calculus at UBC, overly complex, filled with unnecessary words and almost like solving a puzzle. I have always found it interesting when teachers, students etc. reference the idea that word problems are "real world" situations but many of the word problems outlined in the reading and ones I have done myself represent nothing close to what I have used mathematics in the real world for. Given my studies for the last four years (Finance) have revolved around mathematics it would seem logical that I would be an advocate for word problems but in reality the problems I have solved on the job or in daily life using mathematics have either been fairly straight forward and have non-complex language making it much simpler to solve or alternatively the problems are not laid out or described and rather must be developed by myself or another individual to even begin solving them.
Although math problems we see today are complex and abstract they are not as abstract as the Babylonian problems I believe this largely has to do with the fact they did not poses a refined system like algebra that we have now adopted and is used daily. Rather they had to represent math in real life situations and likely situations they had seen previously and have had trouble solving.
Applied mathematics is obviously important as it allows students to use real world applications and solve problems in an ideal manner and hopefully easily. Pure mathematics on the other hand though complex and less logical is still very important as it develops a way of solving much more complex problems that you may not see everyday but could potentially run into; furthermore, pure mathematics is becoming ever more prevalent with the development of technology and the advancement of society.
Thanks Winston! I like your examples comparing actual real-life mathematical problems, from finance and elsewhere, to the strange convolutions of textbook word problems. I'm not sure whether you've really grasped what it is that mathematicians call 'pure math' (it is very logical!), and the development of technology uses applied math (or applies pure math) to real life invention. Mind you, the supposed distinction between pure and applied math is not always that clear...
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