A Reflection on Discourse Analysis and Mathematics Education

 by

 David Pimm

David Pimm, a researcher from the University of Alberta, explores the connection between discourse analysis and mathematics education. Discourse analysis is a method of studying language that looks at connected speech or writing beyond individual sentences. His paper marks the 25th anniversary of a key review article, Language and Mathematical Education by Austin and Howson, published in 1979.

Some features of discourse and their mathematical and mathematical education

versions

• Voice and Agency – How mathematical ideas are presented, including pronoun use, references, and the role of the speaker or writer in shaping meaning.
• Meta-discourse – How people express opinions, politeness, and uncertainty in mathematical communication.
• Temporal Structure – Using verb tense and sequence markers to show the flow of mathematical reasoning.
• Style and Genre – The different ways math is written and spoken, including specific styles used in education and research.

Here, Pimm discusses the first 3 features.

1.Voice

Voice shows how the speaker or writer positions themselves in a conversation. It shows whether they are asserting authority, being informal, or addressing the audience directly. In math problems, phrases like "Let us consider" or "We can observe" suggest the speaker is guiding the reader.

2. Meta-Discourse

In mathematical communication, meta-discourse refers to elements of language that reflect the speaker or writer’s attitude toward their statements. A key aspect of meta-discourse is hedging—using language to soften assertions and manage uncertainty.

3. Temporal Structure

Mathematics is often described as “timeless,” meaning that its truths do not change over time. Temporal structure looks at how time is shown in a text. It focuses on how events are ordered—whether they happened in the past, are happening now, or will happen in the future. In math problems, the tense helps clarify when things are happening, making the problem easier to understand.

Stops

1)"Word problems have no truth value: the people and the events are fictional. Yet by using the names of real girls from the class in this problem, there may have been some interaction between the problem authors’ real and fictional worlds."(p.9)

As a math teacher, this quote reminds me that while word problems may be fictional, they become more meaningful when they incorporate students' names, familiar situations, or cultural traditions. This approach makes math more engaging and helps students connect with the problems on a personal level. At the same time, students bring real-world thinking into these problems such as figuring out how to create a perfect design for a flower mat by dividing a circle into six or eight equal parts. This highlights the importance of integrating diverse cultural experiences in math, such as Onam Pookkalam (flower mat designs), Indigenous drum making, or Mi'kmaq patterns, when we teach geometry or drawing circles, equal division of circles, ensuring that all students see themselves reflected in their learning. Moreover, the way problems describe students can shape their identity, so as educators, we must be mindful to present diverse and inclusive representations, avoiding stereotypes and fostering a sense of belonging.

Mi'kmaq Patterns

                                 

                                                            Pookkalam (flower Mat)

2) "This complex and problematic switch of tenses from present to past to present to past to present and the presumed, created context of the problem makes this hard to rationalize." (p. 8)

This quote made me think about how switching between different tenses in word problems can make them harder to understand. In math, clarity is important, and tense changes can confuse students about the order of events or the problem's meaning.

 I noticed this in my own teaching when a word problem about a student planting flowers used both past and future tense in the same sentence. Some students got confused about whether the action had already happened or was going to happen, which distracted them from solving the math when they are too concerned about the tense and grammar. This reminded me that using consistent verb tenses in math problems helps students focus on the math itself instead of struggling with the wording.

How often do we think about the language we use in math problems? Is language a barrier to learning math for students from diverse backgrounds?

Could making the wording simpler help more students focus on the math?