In this article Gerofsky discusses the reasoning behind including word problems in mathematics education. Most word problems, she mentions, are fictional and have a "false truth" aspect to them. It interesting that most of the time when we discuss why there should be word problems in math, it is because we want to make some sort of connection between the math and the world outside the classroom. More often then not, this "real world" is not real at all.
Gerofsky shows how word problems follow a basic formula involving 3 components. The first component creates the story, the second component provides information, and the third component identifies the goal. I take note of the fact that my students will almost always skip the first component, in search of the other two components. I find it especially astonishing when students can not figure which operation to use in the problem. By the time they have reached grade 5 many students, I would anticipate, understand that textbooks are broken up into chapters of content. If the class is learning about division, then you can safely guess that the word problem will involve division. Is it because they truly don't understand the question, or are they not interested in the problem at all?
It was interesting to read about that use of tense can also play a large role in word problems. It appears that in the English language many tense words are thrown around and used in all tenses. As someone whose first language is English I am able to get by despite these anomalies. However, I can imagine how hard it would be for an ELL student to understand a word problem. Even if they could read it fluently, it might not make an sense.
My questions are:
1) Do you think word problems should continue to be used in math curriculum? Why or why not?
2) Susan stated, "All this leads me to a question for which I have no answer as yet, the question of the purposes of word problems as a genre" (Gerofsky, 1996). My question for Susan is, after 20 years have you found an answer yet? Have you found purposes for word problems?
Dave,
ReplyDeleteWhen you mentioned that many of your students skip the first component, I thought back to the article I read on the new SAT word problems. In that article, a student remarked that her teacher told her to ignore the words/story and just look for the math. It seems as though it is almost encouraged for students to ignore the words! As you mention, students end up expecting what is needed for certain word problems based off of chapters in the textbook. What might be interesting though, is placing word problems out of context to see if students are actually reading what is going on. What I mean by this is, within an entire worksheet of word problems involving division, include one or two that need multiplication. Would students continue with the methods of previous problems or would they actually realize this problem is different from the others.
I don't think word problems should be completely removed from the curriculum, but I do think their correspondence to arithmetic should not be as strong as it is. There are a lot of great opportunities for word problems in the math curriculum, but I don't think they are being used to their full potential.
I've been debating your first question with two other educators all day. Everyone's gut reaction: of course we need word problems! How could we not?! That said, as we were folks primarily interested in higher education, we first needed to address the following: do we even really have word problems in university? Sure, in calculus and other over stuffed service courses, word problems - sometimes terrible ones - run rampant, but getting into third year plus, I think they largely disappear. There are application problems, but those are different: no longer structured in three components, context details cannot be ignored, and extra information is fair game.
ReplyDeleteWhile I don't think any of us will ever be completely convinced about a total removal of word problems, such descriptions seem to add fuel to the fire of accusations about students rarely being exposed to real mathematical activity. And if that's the case, perhaps a dramatic refocus (and perhaps rebranding?) is in order.