A Linguistic and Narrative View of Word Problems in Mathematics Education

 By

SUSAN GEROFSKY

Summary

This article explores the way mathematical word problems are structured and understood. For many students, word problems are like nightmares and they face difficulties when they  transfer it into arithmetic or algebra. The author wants to analyze mathematical word problems as a a linguistic genre rather than just math exercises. She plans to examine how these problems are structured in terms of pragmatics (how language is used in real-life communication) and discourse features .

By comparing word problems to other types of writing—such as stories or spoken conversations,she aims to uncover the hidden assumptions behind why and how word problems are used in teaching. Essentially, she wants to make us think about word problems differently, questioning whether they are truly effective as a teaching tool or if they serve more as a rigid tradition in math education.

Word problems and their three component structure

1)A "set-up" component, establishing the characters and location of the putative story. (This component is often not essential to the solution of the problem itself)

2) An "information" component, which gives the information needed to solve the problem (and sometimes extraneous information as a decoy for the unwary)

3) A question

Many students have found that these word problems are really difficult and it is not even related to their daily lives. For those students who have difficulty in word problem solving, Johnson(1992)advises the following steps:

• Identify the Question: Look for the question at the end of the problem.
• Break the Problem into Two Parts: set up the unknowns (define what you don’t know) and provide the necessary equation information (give numbers and relationships)
• Translate Words into Symbols: Convert the problem step by step into mathematical expressions.
• Solve the Equation

The author analyzes word problems in mathematics using J.L. Austin's speech act theory, which looks at how language functions in communication. She explains that word problems have three aspects: locutionary force (the literal meaning of the words), illocutionary force (the intention behind the problem, such as solving for X), and perlocutionary force (the effect on students, such as motivation or confusion). She argues that while word problems appear to be small stories, they do not actually describe real-life situations. They lack true storytelling elements like characters, emotions, or meaningful plots, making them more about decoding math hidden in words than about solving real-world problems. Gerofsky explains that students learn to solve word problems mechanically by ignoring the story, finding numbers, and following a set process to get one correct answer. She argues that since teachers and textbooks rarely encourage students to question the real-world meaning of these problems, educators should rethink their approach to teaching math and focus on real problem-solving skills.

She explains the truth value of problems: that word problems are not real-life situations but made-up scenarios for students to solve. She says they do not follow the rule that statements must be either true or false because their stories are fictional and can be changed without affecting the math. She also looks at how tense is used in word problems and finds that it is often inconsistent or unrealistic, proving that these problems are not about real events. Since word problems do not follow real-world logic, students and teachers understand that the goal is not to think about the story but to find the math and solve the problem.

She also explores the idea of word problems as parables but finds the comparison weak. Unlike parables, which offer open-ended lessons, word problems focus on a single correct answer and lack deeper meaning. While some word problems have lasted for centuries, she suggests this may be due to the conservatism of mathematical tradition rather than their educational value. She encourages educators to rethink their use of word problems and explore new ways to teach problem-solving that are more meaningful for students.

stop 1

A water tank has two taps, A and B Line A on the graph shows how the tank drains if only tap A is open line B shows how the tank drains if only tap B is open

a) How long does it take to drain if only tap A is open?

b) How long does it take to drain if only tap B is open?

c) Use the graph to find out how long it would take to drain

the tank if both taps were open [Kelly et al , 1987, 213]

Pinder writes of the father of one of her students who complained that his child wasn't being taught problems like the one above (which he had studied in school)(p.41)

Pinder’s reflection raises important concerns about the relevance of certain word problems in math education. The problem highlights a disconnect between mathematical exercises and practical situations, prompting the question of whether such problems are truly useful for students. But, parents always give importance to these kinds of problems because they think it is "real math". As educators, it’s crucial to focus on problems that are grounded in real-life scenarios, as this not only helps students see the value of math but also encourages critical thinking and problem-solving skills. Rather than simply manipulating symbols, students should engage with problems that allow them to apply math meaningfully, such as understanding water management or responding to emergencies like climate problems, floods or displacement of people, which offers more tangible learning experiences for them.

stop 2

"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)

In India, where rote learning and memorization were often prioritized, many students including myself were taught to solve equations or word problems by following set procedures without truly understanding the underlying concepts or knowing how to use them in practical situations. For instance, we would memorize formulas for calculating speed, distance, and time, but we didn’t always get to explore situations where these calculations would be practically useful, like planning travel time for a family trip or determining the best route between two places.

As a teacher now, I want to ensure that students not only learn the procedural steps but also understand when and why these steps are useful. For example, in the context of nursing, knowing how to calculate medication dosages and understanding rates of change is vital. Similarly, in everyday life, knowing how to budget, plan for a trip, or manage time efficiently all require mathematical thinking.

Question

As educators, have you ever used math problems in scenarios that are related to students' real lives?