Math Applications — Taking it Personally

Contextualized math is a current theme in our profession; some courses are taught strictly working from context — the story is the thing, and only the mathematics that relates to that story is developed.  Other courses emphasize context, while many of us take a moderated approach in which we blend context and abstraction.  Whatever the mix, these contexts are experienced as ‘applications’ or word problems by our students.  Do applications (or context) present issues of equity in our developmental math classes?

I would like to tell you about what two of my students (beginning algebra) are experiencing this semester.  First, a student to be called Mary.

Mary: (looking at a typical ‘distance’  problem about two cars)  I don’t know how to write the algebra for this, but I can figure out the answer.
Instructor: Okay, so tell me more about that.  How do you figure it out?
Mary: Well, the problem says that one car is going 10 miles per hour faster, so I put myself in that situation; I know that the speed limit is 70 miles per hour, so that must be the faster car.  The other car must have been going 60.
Instructor: I see.  What part of the problem told you that the cars were on a highway with a speed limit of 70?
Mary: The problem did not say that, but the only way I can understand the problem is to put myself in to it.

The second student will be called John (whose native language is Arabic).

John: (looking at a problem about a tree and a flag pole dealing with their heights)  This problem is really hard.
Instructor: What makes it hard?
John: Everything in the problem … I need to translate it into my language; it does not make sense to me.
Instructor: Are you talking about the individual words?
John: Yes, yes … they are confusing.

The prognosis for Mary is not as good as the prognosis for John.  They are both taking the applications personally; the difference is that Mary thinks that she has to see herself in the problem for it to make sense, while John thinks that he will understand the problem once he knows all of the words.

This experience made me think of some research I saw a few years ago dealing with how word problems in mathematics might raise issues of equity.  The research suggested that students from a ‘lower class’ (this was British research) get distracted by the details of the applications as they relate to their personal life.  My student, Mary, was doing exactly that.  Her learning skills, and her life experiences, provided a limited view of applications; some problems dealt with objects or situations with which she had no experience, and she did not know what to do … other problems activated related but not worthwhile information (like the car problem).   Clearly, we will need to work together (Mary, the class, and me) to help broaden the view and provide more resources.

Taking an application personally can create difficulties in forming a solution strategy; taking it personally highlights information (which might be trivial) and causes us to possibly ignore other information critical to a solution.  This situation deals with perception and motivation.  For those of us who are using high-context classrooms, I wonder if you are finding that the approach is equally accessible to all of your students.

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