Week 1: Using AI to Rehearse Counting Principles Lessons

Gelman & Gallistel (1978) Meets the Simulate → Reflect → Refine Method

---

Introduction: Why Link AI Rehearsal with Counting Principles?

At first glance, Gelman & Gallistel’s (1978) Counting Principles and the modern idea of using AI to rehearse lessons might seem worlds apart. One is a cornerstone of developmental psychology, the other a cutting-edge digital tool. But in practice, they answer the same teacher question:

👉 How can I predict the ways children will think — and stumble — before I walk into the classroom?

Gelman & Gallistel showed that children’s counting is not random. It develops around five principles — one-to-one, stable order, cardinality, abstraction, and order irrelevance. When children violate these principles, they aren’t being “wrong” so much as showing where their conceptual understanding is still forming.

Fast forward to today, and AI offers teachers something remarkable: the chance to rehearse lessons with virtual students, surfacing exactly these kinds of misconceptions in advance. By combining the two:

• The research tells us what to look for (the principles and their pitfalls).

• The AI rehearsal gives us a safe way to see those pitfalls in action — and refine lessons to address them.

This approach builds on our earlier discussion in Making Maths Meaningful Every Day, which highlighted how early maths learning is rooted in daily exposure and developmental progressions. It also extends the practical use of AI that we introduced in Week 1: Rehearse Your Lesson with Virtual Students.

The result? A teaching approach that is both evidence-informed and practically useful, helping teachers anticipate the classic early-years confusions around counting while reducing workload and stress.

---

1. One-to-One Principle

Each item must be counted once, and only once.

Simulate
Teacher to AI:

“You are 5-year-olds learning to count. Some of you will double-count, some will skip objects, and some will point too quickly.”

AI Dialogue Example:

• Teacher: “Let’s count 4 teddies.”

  • Student A: “1, 2, 3, 4.”

  • Student B: “1, 2, 2, 3, 4.”

  • Student C: points to two teddies at once “1, 2, 3.”

Reflect

• Misconception: children don’t yet coordinate pointing with number words.

• Ask yourself: Did I model slow, accurate pointing?

• AI prompt: “What strategies help 5-year-olds avoid double-counting?”

Refine

• Add explicit modelling: teacher counts slowly, touching each teddy.

• Refined activity: give children counters + picture cards. Teacher pretends to miscount, children “catch the mistake.”

---

2. Stable Order Principle

Number words must always be used in the same order.

Simulate
Teacher to AI:

“Role-play children reciting numbers. Some know the order, some mix them up, some get stuck.”

AI Dialogue Example:

• Teacher: “Count to 10.”

  • Student A: “1, 2, 3, 5, 4, 6…”

  • Student B: “1, 2, 3, 4, 5… um…”

  • Student C: “1, 3, 7, 9!”

Reflect

• Misconception: sequence isn’t yet stable.

• Ask yourself: Am I relying too much on rote counting without rhythm?

• AI prompt: “Suggest playful routines to strengthen stable order.”

Refine

• Add songs, chants, stepping-stone mats.

• Refined activity: children hop along a floor number line, chanting numbers in order. Peer correction if order breaks down.

---

3. Cardinality Principle

The last number said represents the total quantity.

Simulate
Teacher to AI:

“Role-play children who can count objects but give the wrong total when asked.”

AI Dialogue Example:

• Teacher: “Count these 6 blocks.”

  • Students: “1, 2, 3, 4, 5, 6.”

• Teacher: “So how many are there?”

  • Student A: “6.”

  • Student B: “5.”

  • Student C: “7.”

Reflect

• Misconception: children don’t grasp that the last number is the set size.

• Ask yourself: Do I emphasise the final number enough?

• AI prompt: “What questions reinforce the link between last number and total?”

Refine

• Add “circle the last number” activity.

• Refined activity: after counting, children clap or hold up fingers for the last number. Extension: “Show me 6 without the blocks.”

---

4. Abstraction Principle

Any set of objects can be counted — not just identical ones.

Simulate
Teacher to AI:

“Pretend to be children who resist counting sounds, actions, or mixed objects.”

AI Dialogue Example:

• Teacher: “Let’s count 3 claps.” claps hands 3 times

  • Student A: “That’s clapping, not counting.”

  • Student B: “1, 2, 3.”

  • Student C: “You can’t count sounds.”

Reflect

• Misconception: counting applies only to physical items.

• Ask yourself: Am I limiting counting to blocks and toys?

• AI prompt: “Give me playful ways to count sounds and actions.”

Refine

• Add varied examples: count claps, jumps, drum beats.

• Refined activity: “count your steps from the mat to the door,” then compare to counting blocks.

---

5. Order Irrelevance Principle

The order you count objects in doesn’t change the total.

Simulate
Teacher to AI:

“Role-play children reacting to the same 5 blocks rearranged in different shapes.”

AI Dialogue Example:

• Teacher: “Here are 5 blocks in a row. How many?”

  • Students: “5.”

• Teacher: moves blocks into a circle “How many now?”

  • Student A: “Still 5.”

  • Student B: “More — it looks bigger.”

  • Student C: “One disappeared!”

Reflect

• Misconception: spacing changes quantity.

• Ask yourself: Do I give enough chances for children to see number stays constant?

• AI prompt: “How can I make order irrelevance playful?”

Refine

• Add “predict → check” cycle: children guess first, then recount.

• Refined activity: children rearrange their own counters into lines, piles, towers, then prove the number is the same.

---

Why This Combination is Powerful

• Research-backed: Gelman & Gallistel identify the core concepts of counting.

• Practice-ready: The Simulate → Reflect → Refine method makes those principles teachable by surfacing real misconceptions.

• Workload-reducing: Teachers prepare strategies in advance rather than firefighting misconceptions mid-lesson.

• Engaging: Off-task play (building towers, mixing objects) is reframed into learning opportunities.

---

Final Thought

Counting is not just chanting numbers — it’s about mastering principles that underpin all later mathematics. AI rehearsal lets teachers preview how children might respond, so lessons are clearer, misconceptions are anticipated, and children’s playful energy is channelled into deep learning.

By linking classic developmental research with modern AI rehearsal, we equip teachers with the tools to be both evidence-informed and classroom-ready.