Why does telling remain such a charged issue in mathematics teaching? Reframing telling through its functions rather than its form offers a way forward.

Telling versus not telling ranks high among mathematics education’s most polarising dichotomies. For some educators, a learning sequence heavy on telling automatically signals direct instruction, while minimal telling represents discovery learning. This oversimplified and caricatured view¹ fails to capture the nuances of telling in effective teaching practice.

The debate around telling is evident in competing mantras. Some advocate “Never say anything a kid can say!”², pushing back against traditional transmission models. Others urge teachers to “Just tell them”³, emphasising the power of clear explanations. These opposing directives leave teachers caught between conflicting orthodoxies. In reality, teaching requires both explanation and exploration⁴. Telling is a vital strategy to both pedagogical camps—when we understand what it really means and how to use it effectively.

The form of telling in mathematics

Telling has traditionally been characterised by its form—stating or explaining information, demonstrating procedures, telling students if they are right or wrong. As we’ll explore later, this limited view misses the rich variety of ways teachers can “tell” in the classroom.

The clarity of mathematical explanations deserves more attention than it typically receives. I’ll touch here on two elements that have recently piqued my interest: vagueness and mazes. Vagueness terms are words or phrases indicating approximation, ambiguity, and lack of assurance, often stemming from insufficient understanding of the content. Mazes are false starts or halts in speech, redundantly spoken words, and tangles of words, perhaps due to insufficient planning.

To illustrate, consider the four contrasting examples below, taken from Land and Smith (1979). In this paper, the authors varied vagueness, mazes, and additional content, and examined the effect on student achievement.⁵

While avoiding vagueness and mazes addresses the basic mechanics of clear communication, we need a broader framework to understand what makes mathematical explanations truly effective. Charalambous et al. (2011) provide one such framework, stating that good explanations should:

1. Be meaningful and easy to understand
2. Define key terms and concepts appropriately
3. Draw on and highlight key mathematical ideas
4. Explain the thought process step-by-step without skipping steps
5. Make transitions between successive steps clear
6. Use language appropriate for the audience
7. Use suitable examples and representations appropriately
8. Clarify the question under consideration and show how it is answered

So far we have focused on the form of communication. But that doesn’t determine whether something counts as telling. Teachers can effectively “tell” through a series of carefully crafted questions, just as declarative statements can function as provocations that encourage student exploration. As Lobato et al. (2005) put it, “Defining telling in terms of form alone does not account for the times when questions tell and declarative statements question.” This suggests we need to look beyond form to understand the function of telling in mathematics teaching.

The function of telling in mathematics

In the past, I’ve asked pre-service teachers whether they are ‘telling’ or ‘teaching’. But this oversimplifies the rich variety of ways teachers can tell in the classroom. Rather than focusing solely on how teachers communicate (the form), we need to examine what their communications aim to achieve (the function). Lobato et al. (2005) frame telling as a phenomenon of verbal discourse with three main attributes: form, content, and function. While form refers to the grammatical structure of discourse (questions, statements, commands), and content refers to the mathematical ideas being conveyed, function captures the purpose of discourse in a situated activity. This function is simultaneously determined by a teacher’s intentions, the nature of the teaching action, and how students interpret those actions.

Building from this framework, Singleton (2015) conducted a case study examining how telling manifested in the discourse of one mathematics classroom over fourteen lessons. Through careful analysis of classroom interactions, he defined mathematical telling as discourse that contained mathematical content and served the function of inserting something new mathematically into the conversation. (He chose not to examine form directly.)

His analysis revealed seven distinct functions that telling can serve, ranging from the most to least obtrusive. I’ve drawn heavily from the paper here, but I’d encourage you to read his expanded definitions, many with illustrative examples.

1. Validate: Confirming whether student expressions of mathematics are correct or incorrect. While seemingly straightforward, validation represents a clear instance of inserting new mathematical information into the conversation—the truth value of a statement. Singleton found this type of telling occurred in more than half of mathematical conversations between teacher and students.
2. Disclose: Providing complete mathematical information about solutions, explanations, or conventions. Unlike other forms of telling, disclosure presents resolved and complete mathematical ideas rather than partial ones. Singleton observed four main purposes: amplifying student input, explaining mathematical concepts, modelling appropriate reasoning, and providing norms and expectations.
3. Guide: Supporting students as they develop solutions, construct justifications, discus concepts, or address errors, while leaving the mathematical substance it contributed partially incomplete or unresolved. This incompleteness requires students to take further action, yet still constitutes telling because it introduces new mathematical constraints or possibilities. Singleton observed four main purposes: focusing students toward or away from an idea, leading students into productive ways of thinking, addressing reasoning errors, and giving helpful hints and suggestions.
4. Clarify Task: Clarifying the mathematics of the task, question or activity without addressing the actual solution. While this might appear to simply set the stage for mathematical work, it constitutes telling because it introduces new mathematical meanings and prerequisites necessary for engagement. The two main purposes were providing basic instructions and clarifying mathematical meanings needed to engage in the task.
5. Qualify: Qualifying a mathematical part of a conversation in response to human experiences of mathematics. This surprising but important category shows how telling can shape students’ relationship with mathematics while introducing new perspectives on mathematical activity. For example, downplaying student errors to minimise embarrassment, attaching value to the activity or task, and acknowledging interesting contributions.
6. Interpret: Clarifying or characterising student utterances through rephrasing, summarising, generalising, condensing or inferring unspoken pieces of student thought. This counts as telling because, as Singleton notes, “Even though the teacher attributed such interpretations to students, they were nevertheless filtered through the teacher’s own conceptual grid of meanings and brought something new into play.” The teacher’s mathematical lens inevitably adds new elements to the original student ideas.
7. Assess: Making mathematically structured requests that go beyond simply eliciting student thinking. When teachers make such requests, they introduce new mathematical constraints or frameworks. Singleton gives the example of asking “Is that partitioning or iterating?” noting that the question imposes a new idea or constraint and is therefore a form of telling.

These different functions of telling rarely operate in isolation. A teacher might validate a student’s approach while interpreting their reasoning, or guide their thinking while clarifying aspects of the task. This aligns with what Baxter and Williams (2010) call ‘analytic scaffolding’—strategic teacher interventions that support mathematical discourse. Teachers might provide embedded explanations when student discourse alone isn’t sufficient, summarise lengthy discussions, connect sophisticated concepts to tasks, or suggest alternative strategies. Even in these moments of telling, skilled teachers prioritise student thinking.

Viewing telling in relation to its function ultimately challenges the traditional dichotomy between inquiry-based and explicit instruction. Rather than seeing telling as opposed to student-centred learning, we can recognise how different forms of telling can support and enhance student mathematical activity. The key lies not in whether to tell, but in understanding how different types of telling can serve different pedagogical purposes.

Importantly, telling works alongside questioning, listening, and other pedagogical moves to support student learning. As Singleton observes, “Mathematical telling practices should be viewed as one of many available instructional tools for creating structure and managing student activity.” Just as teachers weave together different pedagogical approaches to support learning, they also integrate different forms of telling—from validation to guidance to clarification—to respond to student needs in the moment.

Conclusion

We need to recast the dilemma of telling from whether we should tell, to when and how we should tell. This shift requires us to first acknowledge that telling has an emotional dimension that runs deeper than pedagogical preference—it touches on teachers’ fundamental sense of professional identity and efficacy. As Smith (1996) argues, telling can be deeply connected with how teachers view their professional competence. Through telling, particularly through disclosure and validation, teachers can demonstrate their mastery of content and trace a direct line from their teaching actions to student learning. When asked to move away from these forms of telling, that clear line becomes hazier, making mathematics teaching feel less certain and more fluid.

This emotional underpinning helps explain why shifting practice around telling is so challenging. Even teachers who intellectually accept the value of reducing certain types of telling may find it emotionally difficult to do so. Rather than asking teachers to abandon a core part of their professional practice and identity, we need to help them expand their repertoire of telling functions. A teacher who masters the full range of telling practices—from subtle guidance to strategic disclosure—can maintain their sense of efficacy while creating richer learning opportunities for students.

When we understand telling through its functions rather than its form, we see that it is more than mere transmission of information—it is a complex pedagogical tool essential to any orientation towards teaching. The art of teaching lies in knowing when different forms of telling will serve useful functions in the classroom. This requires careful observation of student thinking, awareness of mathematical goals, and the flexibility to adjust approaches based on student responses. By moving beyond simplistic debates about whether to tell, we can focus on developing this vital pedagogical skill—one that honors both teacher expertise and student learning.

References and further reading

Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26.

Charalambous, C. Y., Hill, H. C., & Ball, D. L. (2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441–463.

Chazan, D., & Ball, D. (1999). Beyond Being Told Not to Tell. For the Learning of Mathematics, 19(2), 2–10.

Land, M. L., & Smith, L. R. (1979). The Effect of Low Inference Teacher Clarity Inhibitors on Student Achievement. Journal of Teacher Education, 30(3), 55–57.

Lobato, J., Clarke, D., & Ellis, A. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36, 101–136.

Smith, J. P. (1996). Efficacy and Teaching Mathematics by Telling: A Challenge for Reform. Journal for Research in Mathematics Education, 27(4), 387–402.

Smith, L. R., & Land, M. L. (1981). Low-Inference Verbal Behaviors Related to Teacher Clarity. The Journal of Classroom Interaction, 17(1), 37–42.

Singleton, B. K. (2015). The telling dilemma: Types of mathematical telling in inquiry. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1070-1077).

Photo by Patrick Fore on Unsplash

1. Guy Claxton wrote: “Any kind of teaching can be done ‘badly’. Explicit teaching can be dull and disengaging, just as inquiry-based teaching can be unfocused or pitched inappropriately. It is intellectually lazy to promote a ‘good’ version of one by attacking a ‘weak’ or caricatured version of the other. In reality, the craft of teaching mostly involves a judicious and dynamic mixture of both explanation and exploration, depending on a whole variety of factors (prior knowledge, subject, purpose, age, aptitude, mood etc) to which good teachers are sensitive and responsive (see John Hattie’s work). To try to enforce a single template is bad education and bad science.” https://www.guyclaxton.net/post/the-sciences-of-learning-and-the-practice-of-teaching ︎
2. Reinhart, S. C. (2000). Never Say Anything a Kid Can Say! Mathematics Teaching in the Middle School, 5(8), 478–483. Free download: https://hybridalgebra.pbworks.com/f/Never+Say+Anything+a+Kid+Can+Say.pdf
   This is a great reading that I’ve included on many reading lists. ︎
3. Groshell, Z. (2024). Just tell them: the power of explanations and explicit teaching, John Catt Educational Ltd.
   I’m looking forward to reading this when it’s released in Australia in February 2025. ︎
4. See footnote 1. ︎
5. Thanks to Zach Groshell on X for originally introducing me to these concepts in this thread. ︎

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