In too many classrooms, mathematics is viewed as a subject of fixed ability—a gatekeeper that sorts students into those who “get it” and those who don’t. This mindset is not only limiting, but it’s fundamentally untrue and unethical.
Imagine a maths classroom where every student is treated not as a learner, but as a mathematician. A place where high expectations aren’t a burden, but a badge of honour. This subtle shift in perspective is the key to unlocking profound mathematical growth for all students, ensuring a more ethical and equitable learning environment.
The Ethical Imperative of High Expectations
The decision to set high expectations for all students is fundamentally an ethical one. When teachers presume that some students (often those from marginalised groups) are incapable of rigorous mathematical thinking, they perpetuate systemic inequities. Treating every student as a mathematician, regardless of their background or prior performance, is an act of educational justice.
High Expectations as an Ethical Practice:
Combating Deficit Thinking: It actively rejects the notion that a student’s lack of prior success is due to inherent deficits. Instead, it places the responsibility on the instructional design to meet the students where they are and propel them forward.
Ensuring Access to Power: Mathematical literacy is a powerful tool for civic engagement and economic mobility. Offering every student challenging, meaningful maths grants them access to this power.
Promoting Intellectual Respect: Students are respected as intellectual contributors whose ideas are valued, debated, and built upon, rather than passive recipients of facts.
Oracy and Vocabulary: Tools for Equitable Participation
A true mathematician doesn’t work in silence; they articulate their thinking, justify their claims, and critique the reasoning of others. Oracy (the ability to express oneself fluently and grammatically in speech) and precise mathematical vocabulary are foundational to treating every student as a mathematician and to ensuring equity.
The achievement gap is chiefly a knowledge gap and a language gap.
It can be greatly ameliorated by knowledge-based schooling
Why Knowledge Matter – E. D. Hirsh, Jr
A child who has the relevant domain-specific background knowledge will understand the passage and get the right answer fast without conscious strategising. A child who does not have the enough information relevant knowledge will have to use special glosses in the test and consciously apply strategies; that child won’t finish the test and will get many answers wrong.
Why Knowledge Matter – E. D. Hirsh, Jr
Promote Mathematical Talk (Oracy for Equity)
Structured maths talk ensures that the class discussion isn’t dominated by a few voices, which is key to ethical teaching.
Structured Discourse: Use techniques like “Think-Pair-Share” or “Mathematical Socratic Seminars” to ensure every voice is heard and every student practices expressing complex ideas.
Equalising Participation: Utilising Accountable Talk Stems provides the linguistic scaffolds necessary for students who may be English Language Learners or who lack confidence in speaking:
“I respectfully disagree with [Name] because…”
“My strategy is efficient because…”
“Can you restate that using the term congruent?”
Valuing Non-Verbal Reasoning: Recognise and respect that some students’ mathematical understanding is best expressed through models, diagrams, or gestures. Always follow up, asking them to verbally connect their model to a concept.
2. Mastering Mathematical Vocabulary (Access and Clarity)
Precise language is the key to precise thought. High expectations demand that students use the correct mathematical terms—not just colloquialisms.
Vocabulary is Access: Explicitly teaching terms like coefficient, variable, perimeter, and trapezium demystifies the language of mathematics, which often acts as a barrier to understanding.
Bridging Everyday and Academic Language: Help students transition from common words to their mathematical counterparts (e.g., from “the distance around” to perimeter; from “steepness” to gradient or slope).
Interactive Glossaries: Ensure key terms are visible and accessible. These tools provide a low-stakes reference point, reducing the anxiety associated with using technical language incorrectly.
Shiftingthecurve 