A Linguistic and Narrative View of Word Problems in Mathematics Education – Susan Gerofsky
Summary
The author critically described word problems as linguistic genre considering its pragmatic structure and observed the problems associated with the use of word problems in mathematics education even though other writers such as Burton (1991) and Nester & Katriel (1997) supposedly found the value of word problems used in mathematics teaching and testing and encouraged students to become more proficient at solving them. The author talked about the three components structure of word problems though there may be variations, the question of truth value, linguistic and metalinguistic verb tense, Tradition: “I did them and my children should do it too” and word problems as parables.
Gerofsky claimed that the stories in word problems are hypothetical and does not necessarily mean they are real-life problems or could be such. The author got me interested in the ‘throwaway’ stories which seem to be quite useless in our time but somehow still found in our textbooks and used as exercises for practicing algorithms. In my opinion, I do not consider any mathematical question to be a ‘throwaway’ unless there’s Missing, Surplus or Contradictory Data Problems (MSCD) (Puchalska & Semadeni, 1987, p.10). Even with that, it generates a sort of debate among students for discussion, for children with little mathematical experience to analyze the story more carefully and older students to try and find a solution to the problem by trial and error (Puchalska & Semadeni, 1987, p.10).
Stop 1
Reading this article reminds me of how uncomfortable I always was when my teacher gives word problems, either his own set questions or from textbooks. Sometimes, the problem statement may be too long and incomprehensible. And before I finished reading, I had already forgotten the first sentences. My mathematics teachers taught us Mildred Johnson’s (1992) procedure and it helped most of us. How long should a word problem be in order not to distract students from the translation task at hand?
Stop 2
How has your experience been during your school days and now as a teacher in terms of word problems?
Stop 3
Do you consider any mathematical question to be a “throwaway” and made your students skip?
Stop 4
Would you consider a parent’s request to teach or give examples of supposedly ‘throwaway’ questions or what the parent learned in his time?
Thanks, Milli - and thank you for responding to this reading through our mix-up! I always find it interesting to hear the commonly held belief of: "I did them and my children should do them too." I most often hear this in relation to memorizing multiplication facts. I wonder this is such a commonly held belief by so many people? Is it based in nostalgia? Considering the amount of people that claim they are, "not a math person", or complain about not learning how to do their taxes in high school mathematics, why is there such a strong desire to have things stay the same?
ReplyDeletePart of my goal in my current practice around word problems is to help students pose their own problems. This in itself has been a 'trial and error' process for me over the past few years. I think the idea of story surrounding a problem can be the most powerful tool for young learners (and perhaps older students too). I wonder what the best way to approach this is? Do students need a lot of modelling in order to pose their own problems? Or could too much modelling of traditional questions create more 'textbook' type problems that might just perpetuate the problem?
If I do not think my students will understand what is going on in a word problem, it is unlikely that I would assign it, though I might adapt it. Unfortunately sometimes that is out of my control, especially during school or school board assigned tests (we still have a lot of standardized testing in Quebec). For instance, I still remember a question that was on a mathematics exam my grade twos had to take. The question was centered around the best unit of measurement to measure a telephone pole. There I was standing before the class, gesturing out the window to the telephone poles in the street that my students had no concept of. My students don't even understand landlines as these days everyone uses cellphones. And even if my students knew about telephone polls, in what situation would they EVER need to measure one?
ReplyDeleteLaura, in response to your question about having students think of their own questions: I think mathematical thinking is a huge component of this that we need to help our students develop. In one of our classes last term, Prof. Cynthia Nicol introduced us to "3 Act Math Tasks" (https://gfletchy.com/) which help students think about things mathematically. You can also ask Lyndsay as she has done them before in her practice.
I'm planning to introduce them into my practice when I return to the classroom next year and I hope that they will lead to my students being able to ask about things mathematically. I think if students can think and ask about things mathematically, this will strengthen their ability to formulate (and respond to) word problems better.
As far as I can remember, word problems were irrelevant and nonsensical in my own educational experience. I describe a bit of that in my comment to Laura's post this week. I hope to let those questions die.
Thanks for the link, Annie! I will check that out!
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