In this article, Gerofsky describes how mathematical
word problems can fit under the umbrella of a linguistic genre. She uses “methods from pragmatics [the study
of language in use in particular contexts], discourse analysis [the study of
extended stretches of spoken or written text in terms of utterances and their
relationships], and genre studies [the study of ‘text types’ in terms of their
linguistic and contextual features].” (p.37)
A typical word problem, or story problem,
has a few defining characteristics. It
usually introduces the problem with some erroneous background information which
may or may not be useful, then it gives some values, and clues as to which
operations/algorithms you will need to use, and finally it will ask a
question. In my experience as a
classroom teacher, children need to consistently practice word problems. A give my class a word problem everyday and
we go over it as a class looking for these key features mentioned above. It is imperative that a student knows which
information is relevant and which information can be ignored. Often, students will skip to the question at
the end, and then look back at all the numbers, and then combine all of those
numbers into one or two operations that have recently been discussed in class. I find that being able to weed out the
unnecessary information and truly understand what is being asked is the key to
word problems.
Radatz (1984) mentions that students in
their elementary years, and who are knew to problem solving, tend to focus more
on the story, while older secondary school students will immediately look for
the math in the problem, rather than be concerned about the story.
Gerofsky also points out that often there
can be confusion when multiple tenses are used in word problems. Some languages do not have the same tense
structures as English. This would make
it very difficult for a student coming from another country, or even one from
Canada but perhaps has parents who speak another language at home, to translate
the problem in their head while they are reading it.
Another interesting point that is brought
up is how most story problems are fictitious.
Sometimes they are based on truths, but use words to make it seem
fictitious, such as “If the Lions Gate Bridge was 32 m above sea level. .
.” If we are talking about a factual
object, then we might as well use facts, and not use words such as ‘if’. If a story problem is meant to be fictitious,
then it should not be based on real things, and should actually be a
story.
In her summary, Gerofsky questions the use
of word problems in childhood mathematics programs, and wonders if there are
new ways to pose them. In essence, we
should be critical of the lessons that we learned as children, and be careful
to not blindly pass them on to the next generation.
You make a lot of good points, David; isn't it interesting how word problems are "boiled down"? I mean, they're essentially microcosms we've created by eliminating a host of variables in order to calculate particular characteristics of a certain situation. No wonder students (and here, professors) question the usefulness of word problems. Even in fictitious problems, there's no personal investment in the questions (and furthermore, possibly, no reason to solve them). I've recently been looking for a car to buy, and when it comes to assessing the value of the car, it would be impossible to assess a car JUST on the mileage or JUST gas consumption for, say, a rate problem. There are SO many variables that go into the decisions we make, that it would make more sense for students to pursue a line of inquiry, like the Schoenfield article - I wonder about project-based learning and pursuing rate calculations in that way: If students needed to assess five cars and calculate gas consumption, mileage, repair costs, insurance costs, and create a budget per month? Per year? To show the calculation from miles per gallon to litres per 100 kilometers? Then, justify why they think the car they pick, out of the five, is best? I might get started on designing a project right this minute!
ReplyDeleteAs a child, I always despised word problems. I considered them to be the bane of my mathematical existence. I think part of the reason might have been these fictitious situations that always seemed thoroughly unreasonable to me. I suppose that the pedagogical "point" of word problems is to provide some sort of "real world example of mathematics." Now, this phrase on its own bothers me. We tell our students "Ok....now here's a real world example." Aren't we somewhat implicitly implying that mathematics is somehow "not real," and all this "abstract" material is separate from human endeavours? Certainly, there are plenty of "word problems" that appear in appropriate contexts, such as the ones introduced in the article I read this week.
ReplyDeleteOn the other hand, I'm brought back to some of the articles we read in Ann's class regarding young children being able to work through "word problems" (verbally stated and using manipulatives though) and then the students struggling with an equivalent problem using symbolic notation. I suppose those problems are a bit less fictitious than some of the ones noted in this article. I'm looking forward to the discussion on Wednesday where we can connect all of our articles together..