Scoring reasoning tasks on a napkin

Wouldn't it be handy to have a method for gauging their potential effectiveness? I thought

Exec summary

Not all maths tasks promote reasoning equally - some are more effective, some are less effective.

Wouldn't it be handy to have a method for gauging their potential effectiveness? I thought.

So I decided to come up with a simple 'Reasoning Potential Rubric' - the kind you could scribble on a napkin - that scores five key dimensions:

1. justification
2. multiple approaches
3. generalisation
4. cognitive demand
5. discussion.

This article introduces the rubric, provides two worked examples, and offers practical strategies to modify tasks for greater reasoning potential.

Why score the reasoning potential of a task?

Tasks may look like they promote reasoning but, in reality, they only require students to follow a set method or recall a fact. Alternatively, a task might have great reasoning potential, but without the right prompts, questions, or discussions, students won’t get the full benefit.

This is where a Reasoning Potential Rubric comes in - a simple framework for assessing the reasoning demands of a task. By scoring tasks against key criteria, we can:

? Identify whether a task promotes deep reasoning or just surface-level understanding.

? Pinpoint ways to improve reasoning within a task.

? Help teachers make intentional choices when selecting or designing reasoning-rich activities.

Disclaimer - This is my starting point. I'm not saying it's the highest fidelity measuring instrument but it got me further ahead than when I started.

Remember that this rubric scores a task's potential to foster student reasoning based on the task and planned follow-up questions; it's not an in-class assessment tool.

The Reasoning Potential Rubric

My framework scores tasks across five dimensions, each rated from 1 (low) to 3 (high).

Each task is given a Reasoning Potential Score (RPS) by adding up the scores across the five dimensions:

• 5-7 → Low Reasoning Potential (mainly recall or procedural)
• 8-11 → Moderate Reasoning Potential (some reasoning but limited justification)
• 12-15 → High Reasoning Potential (rich reasoning, generalisation, and discussion)

By applying this rubric, I can evaluate the depth of reasoning in a task and make adjustments accordingly. If a task scores low, small modifications - such as adding a justification prompt or allowing for multiple solution methods - can increase the reasoning potential.

Example scoring

To see the rubric in action, I'll apply it to some real tasks and assess their Reasoning Potential Score (RPS).

Task 1: Always, Sometimes, Never

Let's see how the always/sometimes/never true task might score:

This task has a high degree of reasoning potential because it requires justification and naturally leads to discussion, but I think there are still ways to increase the RPS.

? Encourage Multiple Approaches (Increase from 2 to 3)

Add: "Can you use a visual model (e.g., number line or diagrams) to support your answer?"

Ask: "How would an algebraic approach help justify your choice?"

? Promote Generalisation (Increase from 2 to 3)

Add: "Can you create a general rule for when multiplying by a fraction makes a number smaller?"

Challenge students: "What other types of numbers (e.g., negatives, zero, fractions greater than 1) might behave differently?"

? Increase Discussion & Debate (Maintain 3, but deepen engagement)

Introduce: "Swap answers with a partner—can you convince them to change their mind?"

Ask: "Are there any misleading examples that might make someone tick the wrong box?"

Task 2: Comparing Fractions

Let's see how this comparing fractions task might score:

The task is well-structured for reasoning, as it requires justification rather than a simple answer, but there is limited opportunity for generalisation - students will need to compare more than one pair of fractions to form broader rules about fraction comparison.

So here's how I might improve its reasoning potential.

? Encourage Multiple Approaches (Increase from 2 to 3)

Add: “Find at least two different ways to compare these fractions. Which method do you prefer, and why?”

Introduce visual models (fraction bars, number lines) and ask: “Does a diagram make the comparison clearer?”

? Promote Generalisation (Increase from 1 to 2 or 3)

Add: “Can you find another pair of fractions where the fraction with the larger denominator is actually greater? What do you notice?”

Challenge students: “Can you come up with a rule for when the cross-multiplication method might be misleading?”

? Increase Discussion & Debate (Increase from 2 to 3)

Pose a provocative statement: “Fractions with larger denominators are always smaller. Do you agree? Convince someone who disagrees.”

Ask: “Is there ever a case where two different methods give different answers? Why or why not?”

How teachers can use this rubric in lesson planning

Checking the reasoning potential of a task is like tuning an instrument; sometimes it’s slightly off-key, and a few adjustments (like adding a discussion prompt or requiring justification) can bring it into harmony. The Reasoning Potential Rubric isn’t just a tool for evaluating existing tasks; it’s also a practical guide for lesson design.

By embedding reasoning evaluation into lesson planning, we can ensure students experience tasks that challenge their thinking, encourage discussion, and develop a deeper understanding of maths.

Summary: what’s next?

Developing reasoning in maths requires more than just choosing the right tasks. It’s about creating opportunities for students to explain, justify, and connect ideas. The Reasoning Potential Rubric provides a structured way to assess, refine, and enhance reasoning tasks, helping me make deliberate choices in lesson planning and resource creation.

In the next article, I’ll explore how Don Steward’s resources embody these principles so effectively. What makes his tasks so rich in reasoning, and what can we learn from his approach?