$Mathematical symbols forming a cityscape$

Decoding Math: How Understanding Its Language Can Unlock New Worlds

Avery Sinclair in Mind & Education August 2025 • 4 min read.

"Explore how viewing mathematics as a discourse can transform our understanding and application of it in everyday life, challenging traditional perceptions."

Mathematics is often perceived as a cold, abstract discipline, a realm of numbers and equations detached from the messiness of human experience. However, what if we began to see mathematics not just as a tool for calculation, but as a discourse—a language with its own grammar, syntax, and cultural context? This perspective invites us to reconsider the role of mathematics in shaping our realities, actions, and even our political landscapes.

The traditional view of mathematics emphasizes its objectivity and universality, suggesting that mathematical truths exist independently of human interpretation. This is the Platonist view. Yet, a discursive approach challenges this notion, arguing that mathematics is deeply intertwined with human practices and social structures. This means acknowledging that mathematical knowledge is constructed, negotiated, and applied within specific contexts, influencing how we understand and interact with the world.

In this article, we'll embark on a journey to explore mathematics as a discourse, uncovering its hidden dimensions and challenging conventional perceptions. We'll delve into how mathematics shapes our possibilities, rationalities, structures, and authorities, and how it can even influence what we overlook. By adopting this lens, we can gain a more nuanced and critical understanding of mathematics and its impact on our lives.

Mathematics as a Language: More Than Just Numbers

Mathematical symbols forming a cityscape

To understand mathematics as a discourse, we must first recognize its key components. According to Ole Skovsmose, interpreting mathematics as a discourse involves three core claims: that mathematics involves transitions between mathematics and reality, that it includes actions, and that it possesses a political dimension. These claims challenge the traditional view of mathematics as a purely objective and neutral tool.

The idea that mathematics involves transitions between mathematics and reality suggests that mathematical concepts are not simply abstract ideas, but are actively involved in shaping our understanding of the world. This means that when we use mathematics to model or analyze real-world phenomena, we are not just passively describing reality, but actively constructing it.

Shaping Possibilities: Mathematics provides the blueprints for technological advancements, defining what is possible in the realm of engineering and innovation.
Forming Rationality: Mathematical models structure economic arguments and policy decisions, influencing our understanding of what is considered rational.
Creating Structures: From the design of everyday objects to the organization of production processes, mathematics shapes the structures that govern our lives.
Establishing Authority: Claims presented with numerical data and mathematical models often carry more weight, influencing policy and public opinion.

Furthermore, recognizing the political dimension of mathematics means acknowledging that mathematical practices are not always neutral or benign. Mathematics can be used to reinforce existing power structures, exclude certain perspectives, or justify social inequalities. By understanding these hidden dimensions, we can begin to critically evaluate the role of mathematics in shaping our world.

Beyond the Equation: A Call for Critical Reflection

Adopting a discursive perspective on mathematics is not just an academic exercise; it's a call for critical reflection. By understanding how mathematics shapes our realities, actions, and political landscapes, we can begin to challenge its hidden biases and limitations. This means promoting a more inclusive and equitable approach to mathematics education, one that empowers individuals to critically engage with mathematical knowledge and use it to create a more just and sustainable world. It also means critically examining the role of ethnomathematics, ensuring that it, too, is subject to careful analysis and reflection.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1590/1980-4415v29n51a02, Alternate LINK

Title: (Ethno)Mathematics As Discourse

Subject: Education

Journal: Bolema: Boletim de Educação Matemática

Publisher: FapUNIFESP (SciELO)

Authors: Ole Skovsmose

Published: 2015-04-01

Everything You Need To Know

According to Ole Skovsmose, what are the core claims for interpreting mathematics as a discourse, and how do these challenge the traditional view?

Mathematics as a discourse, as described by Ole Skovsmose, involves transitions between mathematics and reality, actions, and a political dimension. The transitions between mathematics and reality suggest that mathematical concepts actively shape our understanding of the world rather than passively describing it. This active construction influences how we model and analyze real-world phenomena. The element of action indicates that mathematics is not just theoretical but also involves active engagement and application. The political dimension recognizes that mathematics can influence power structures and social inequalities, which means that mathematical practices aren't always neutral.

How does the discursive approach to mathematics differ from the traditional, Platonist view of mathematics, and what implications does this have for our understanding of mathematical knowledge?

The traditional, Platonist view of mathematics emphasizes its objectivity and universality, suggesting that mathematical truths exist independently of human interpretation. In contrast, a discursive approach challenges this view by asserting that mathematics is intertwined with human practices and social structures. This perspective acknowledges that mathematical knowledge is constructed and negotiated within specific contexts, which influences how we understand and interact with the world. The discursive approach calls for critical reflection on how mathematics shapes realities and actions, while the Platonist view focuses on its independent existence.

In what specific ways does mathematics shape our possibilities, rationality, structures, and authority, according to the text?

When we say mathematics shapes possibilities, it means mathematical blueprints define what is achievable in engineering and innovation. When we say mathematics forms rationality, it implies mathematical models structure economic arguments and policy decisions, influencing what is considered rational. When we say mathematics creates structures, it explains how mathematics shapes the designs of everyday objects and the organization of production processes. And when we say mathematics establishes authority, it highlights how claims presented with numerical data and mathematical models often carry more weight, influencing policy and public opinion. The article mentions possibilities, rationality, structures, and authority without exploring things like ethics, bias in algorithms or uncertainty in data, which are other critical dimensions.

What is ethnomathematics, and why is it important to apply critical analysis and reflection to it?

Ethnomathematics is the study of the relationship between mathematics and culture. The importance of critical analysis and reflection in ethnomathematics lies in the need to ensure that this field is also subject to careful scrutiny to avoid reinforcing biases or limitations. While ethnomathematics seeks to incorporate diverse cultural perspectives into mathematics, it's essential to critically evaluate these perspectives to promote a more inclusive and equitable approach. The article stresses that all mathematical practices, including ethnomathematics, should be examined for their potential impacts and biases.

Why is it important to understand how mathematics shapes our realities and actions, and what does this understanding allow us to do?

By understanding how mathematics shapes possibilities, rationalities, structures, and authorities, we can critically evaluate its role in reinforcing power structures and social inequalities. This understanding allows us to challenge hidden biases and limitations within mathematical practices. It promotes a more inclusive and equitable approach to mathematics education, empowering individuals to critically engage with mathematical knowledge and use it to create a more just and sustainable world. This involves questioning the assumptions and values embedded in mathematical models and algorithms.