In this article, the author looks at the nature of word problems in mathematics education by using three methods. The three methods are pragmatics (the branch of linguistics dealing with language in use and the contexts in which it is used), discourse analysis (approaches to analyze written, vocal, or sign language use or any significant semiotic event), and genre studies (a branch of general critical theory in several different fields, including the literary or artistic, linguistic, or rhetorical). Among other structures of word problems, the author describes the break-up of generic word problems into three components ("set-up", "information", and "question").
This is how I generally tried to solve word problems. I wasn't interested in the problem set-up. I would try to find all the variables involved in solving the problem and then identify the relationship to find the answer. Once I come up with an answer, I would go to the back of the book to check the answer. If my answer was identical to the book's, I would move on. Otherwise, I would re-read the problem to find where I went wrong. Whether the problems were word problems or abstract algebraic problems, I employed the same techniques. This could be why I hated word problems. Whenever I tried to come up problems to solve in the class, the problems were often times identical to those found in textbooks. The author cites John Lave to describe this phenomenon.
Finally, the author goes on to wonder why word problems in mathematics have persisted for so long. I am curious to know if the author has found some answers to the purpose of word problems in mathematics education.
This is how I generally tried to solve word problems. I wasn't interested in the problem set-up. I would try to find all the variables involved in solving the problem and then identify the relationship to find the answer. Once I come up with an answer, I would go to the back of the book to check the answer. If my answer was identical to the book's, I would move on. Otherwise, I would re-read the problem to find where I went wrong. Whether the problems were word problems or abstract algebraic problems, I employed the same techniques. This could be why I hated word problems. Whenever I tried to come up problems to solve in the class, the problems were often times identical to those found in textbooks. The author cites John Lave to describe this phenomenon.
Finally, the author goes on to wonder why word problems in mathematics have persisted for so long. I am curious to know if the author has found some answers to the purpose of word problems in mathematics education.
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ReplyDeleteI think that lots of students follow the same steps as you did Murugan to this day. I believe that word problems bring life to mathematics education and are imperative to really see if the students understands the context of where mathematical topics are used, rather than just the pure application of computation. It is a definitely a skill in and of its self to extract the variables from the rest of the text, and this is a skill that needs a lot of practice. After reading Conrad's blog post as well, it seems really important to keep practicing the skills of not only problem solving but more so posing problems to allow students to explore a deeper understanding.
ReplyDeleteI agree with you Philippa, that so many students approach word problems in the way that Murugan does: as if their context was insignificant, and only the numbers were important. To help try to mitigate this issue, I once taught the geometry section of a math 9 class through carpentry. Having physical constructs that 'responded' to the results of our calculations seemed to emphasize the context in which we were solving the problem, and in turn, this context seemed to give rise to how these numbers might be put together. However, too often are the contexts, or the 'set ups,' of a word problem uninspired, or unnecessary. No wonder students don't seem to pay any credence to them!
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