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Blog post

Play and direct teaching in mathematics education: strengthened through supportive climate

Vicky Zhao, Secondary mathematics teacher at Trumpington Community College

In classrooms worldwide, teachers often ask: Do students learn best through playful exploration or (see also Bächtold et al., 2024)? This question assumes a divide that may not exist. My research and classroom experience as a state secondary maths teacher in England suggest these approaches are more alike than different, especially when delivered in a climate of warmth, responsiveness and trust.

Direct teaching involves modelling procedures, which I apply in graph plotting by demonstrating how to substitute values, calculate coordinates and plot points, followed by individual practices. A play-based approach, conversely, begins with real-world scenarios – such as tracking the cost of a flight ticket – and guides students to discover relationships through experimentation and reflection.

Two separate studies were carried out to examine how learning environments shape the effectiveness of different pedagogical approaches. The first study collected longitudinal home-based observational data on 1,000 children in Germany (Zhao & Gibson, 2023). The second drew on from approximately 1,000 students across Kenya, Ghana and Colombia. Together, these studies show that the effectiveness of playful and direct-teaching approaches depends not just on the method, but on the climate in which it is delivered. When teachers foster warmth, responsiveness and curiosity, students engage more deeply, regardless of whether the activity is playful or guided.

‘When teachers foster warmth, responsiveness and curiosity, students engage more deeply, regardless of whether the activity is playful or guided.’

Safety matters

In this blog post, safety refers to emotional and psychological security, an environment where students feel confident to take risks, make mistakes, and engage without fear of judgment or overwhelming stress. Both play and direct teaching, if implemented successfully, can create safety: play through emotional rehearsal, direct teaching through clarity. Play ‘makes children masters of the situation’ (Freud, 1961, p. 11), as symbolic rehearsal helps children process and prepare for real-life. Moran et al. (2023) that children who practised breathing techniques with the Sesame Street Muppets used them more often in emotionally charged situations. The playful context of familiar characters and low-stakes scenarios made it safe to experiment, helping children internalise coping strategies.

Direct teaching can also offer safety through predictability. The gradual release model, ‘I do, we do, you do’, begins with teacher modelling, moves into guided practice, and then leads to independent practices. Students are reassured that success is achievable and repeatable. De Bruin et al. (2025) found that predictable teaching helps students .

Scaffolding is key

Vygotsky (1978) described learning as occurring in the ‘zone’ between what a child can do alone and with help. In play, support is often subtle: adults pose questions that help children extend exploration without taking over. In direct teaching, scaffolding is described as more explicit in the gradual release model, as highlighted by the . Drawing from the graph plotting example, I start with full modelling, then progress towards partial scaffolding (see figure 1). As a student’s accuracy improves, a teacher would fade their support and allow students to start working independently. In both methods, the teacher gradually transfers responsibility for managing the task and applying independently (see also Zhao & Gibson, 2023).


Figure 1. Fading of scaffolding

The missing ingredient: Climate

My research involving a longitudinal observational study of 1,000 German families (see above) shows that a supportive climate unlocks the potential of both play and direct teaching. I found that mathematically rich play predicted stronger outcomes only when adults were warm, responsive and attuned to children’s cues (Zhao & Gibson, 2023). Engagement depended on interaction quality, not play alone.

The second referenced earlier, drawing on 1,000 students from 25 Colombian, 70 Ghanaian and 70 Kenyan schools, extends this finding into predominantly direct-teaching environments: students engaged more when teachers fostered respect, curiosity and belonging through collaboration and real-life connections. Without such a climate, neither play nor direct teaching reaches its potential. With it, both become powerful tools for learning and wellbeing.

Play and direct teaching may differ in form, but they can be argued to rest on the same foundations: psychological safety and scaffolding. While this interpretation highlights shared principles, other perspectives may emphasise distinction in purpose, structure and student’s autonomy. Drawing on my dual role as a teacher and researcher, I advocate that research and practices should focus more on the climate in which it is delivered. When teachers create environments of warmth, responsiveness and trust, these shared principles come alive, enabling students to engage deeply, take risks and thrive. Rather than viewing play and direct teaching as pedagogical opposites, future research could examine whether these foundations hold across diverse contexts, and explore how variations in classroom climate influence the effectiveness of play and direct teaching, which are important for designing pedagogies that are both adaptable and inclusive.


References

Bächtold, M., Papet, J., Barbe Asensio, D., & Ngoua Ondo, A. (2024). Direct instruction or active learning? The spectrum of first‑year university teaching practices. Higher Education Research & Development, 43(8), 1704–1720.

Freud, S. (1961). Beyond the pleasure principle. Norton.

Vygotsky, L. S. (1978). Mind in society. Harvard University Press.

Zhao, V., & Gibson, J. L. (2023). Early home learning support and home mathematics environment. Child Development, 94(6), e377–e392.