A Linguistic and Narrative View of Word Problems in Mathematics Education

By

SUSAN GEROFSKY

Susan Gerofsky's paper analyzes mathematical word problems from the perspective of linguistics and discourse analysis. Author highlights that while word problems appear to tell stories, they actually follow a pattern based on arithmetic and algebraic formulas rather than real-world stories. Susan first describes the three general components of a word problem which include:

1. A 'set up' component typically viewed as a narrative and generally non-essential

2. An 'information' component providing information to solve the problem

3. The question

Though some believe narratives are engaging, students tends to disregard them, focusing only on analysing them.

Susan takes into account the language features of word problems, their absence of empirical relevance in the world, and so they are indeterminate in the sense of locutionary force (i.e., what they literally mean). She outlines how there is a requirement for students to do some kind of "pretend" reading, reading fictionalized hypotheticals as if they were real, but completely fabricated. The study also discusses verb tense inconsistencies, showing how math word problems mix up grammatical tenses in ways not found in ordinary speech or storytelling.

Susan concludes the paper by explaining David Pimm's idea that word problems can be considered parables. Although they share some things in common, she wonders if this is an accurate comparison. Her general thesis is that we must critically examine the role of word problems within mathematics education and re-look at why they continue to be used so prevalently.

Stop 1

"You can't go out and use them in daily life, or in electronics, or in nursing. But they teach you basic procedures which you will be able to use elsewhere."(p.38

From my childhood experience I learned word problems following specific steps, without showing how the steps worked to solve problems related to real life. It led me to question whether the students were simply being taught to memorize steps to solve problems rather than to think.

While learning processes is important, I felt like not relating them to real applications made math seem less applicable. Students can possibly do math problems, but maybe not understand how they can utilize those skills in their future occupations or daily life.

If mathematical problems were related to the real world, students would be able to recognize how mathematics functions in their world. For example, understanding mathematics in nursing or electronics would allow students to visualize the relevance of their studies in real-life situations. The realization would allow students to be critical and understand the application of mathematics in life.

Stop 2

That delineating the boundaries of the word problem genre can allow us to play with those boundaries in interesting ways(p.g.43)

I stopped at this quote because in my opinion we can identify new ways to use the word problems by delineating the boundaries. We can use open-ended questions and by creating word problems more interesting to the students can help them to explore math beyond just applying formulas. Moreover, by connecting word problems to real life, we can encourage students to think critically rather than treating it as simple exercises. As a result, students recognize that math is relevant and useful.

One of the experiences that remain in my memory is when I witnessed how my students solved a division word problem. I knew that traditional word problems have the effect of making students think about calculations and not so much about thinking. But when I altered the problem a bit—by asking questions, allowing different answers, and making it real-life related—the students started thinking more deeply. This opened my eyes to the fact that as teachers, we can make word problems more than just exercises. We can use them to help students explore and understand math on a deeper level.