There’s no doubt that problem solving is central to mathematics, but its pedagogical value is amplified when teachers deliver intentional instruction.

Intentional teaching is not casual inquiry; it’s purposeful modelling of strategies, carefully designed scaffolds, and explicit metacognitive talk that guides students from supported practice to independent problem-solving.

What the research tells us

Research on inquiry-based and scaffolded approaches shows intentional teaching brings clear benefits. For example, inquiry-oriented professional literature (Beswick, 2021) and recent models for scaffolding problem solving (DP model literature) confirm that when teachers explicitly teach strategies and plan fadeable supports, students show improved transfer and confidence in tackling non-routine problems.

How can I strengthen intentional teaching in my classroom? 

Knowing the theory is one thing, but putting abstract complexities to use in your classroom can feel overwhelming. It doesn’t need to be!

A few simple methods for making your maths worded problem lessons more intentional may include: 

• Modelling your thinking aloud. When you solve a problem, narrate decision points: “I’ll re-read to see what’s being asked, then I’ll underline numbers that matter.” Modelling signals process over speed.
• Designing tasks with clear cognitive demand. Use tasks that have a clear learning goal (e.g., interpreting the question structure, representing relations) and multiple access points. Low-floor/high-ceiling tasks let every child participate but still stretch higher thinkers.
• Scaffolding strategically. Offer supports targeted to your students’ needs: worked examples for novices, heuristic prompts for emerging solvers, and open challenges for extensions. Scaffolding should be gradually withdrawn.
• Using purposeful questioning. Ask “Why did you choose that method?” or “How could you check that?” Questions should push reasoning, not just retrieval.
• Making assessment formative and diagnostic. Use observations of strategy choice and reasoning to guide next teaching steps – not just correctness.

The theory in practice

Taking the above practical methods into account, here’s what a classroom sequence of an intentional lesson on worded maths problems could look like:

• Hook/context: provide a short real-world scenario to grab students’ interest.
• Model: you as the teacher thinks aloud solving a similar problem.
• Guided practice: students attempt a related problem with prompts.
• Collaborative practice: students work in pairs explaining their steps.
• Independent task and reflection: Students solve a variant and write or discuss the strategy used.

Classroom culture matters

Intentional teaching thrives in classrooms where struggle is normalised and strategy-sharing is celebrated. Create routines: a “strategy wall,” sentence starters for explanations, and weekly “method swap” sessions where students present alternative approaches. Over time, students internalise the metacognitive routines you model and become independent, flexible problem solvers.

References

Beswick, K. (2021). Inquiry-based approaches to mathematics learning, teaching, and mathematics education research. Journal of Mathematics Teacher Education, 24, 123–126. doi.org/10.1007/s10857-021-09494-4

Tay, Y. & Toh, T-L. (2023). A model for scaffolding mathematical problem-solving: From theory to practice. Contemporary Mathematics and Science Education. 4. ep23019. DOI:10.30935/conmaths/13308