The Energy of Math Talk: What Happens When Students Are Free to Share

“Eureka! Look what I found, Miss! It is the Indus Valley Zebu Bull!” exclaimed one excited learner, holding up a newly discovered artefact.

“I’m not able to find the Sphinx, Miss. This is very frustrating, and I’m tired,” shared another learner, visibly worn out after searching for the artefact without success.

These were just two of the many moments that made our MYP 1 archaeological dig site activity memorable. As part of our Individuals & Societies unit, What Can We Learn from Different Civilisations?, learners stepped into the shoes of archaeologists, getting their hands dirty as they excavated, observed, and documented their findings of artefacts from the past.

As their Individuals & Societies facilitators, we paused the activity and invited the learners to reflect on something we often take for granted: the time, patience and effort involved in archaeological discoveries. We spoke about how our knowledge of ancient civilisations has been shaped by archaeologists who painstakingly excavate sites, document their findings and piece together clues left behind by people who lived thousands of years ago. Without their work, our understanding of the past would be far more limited.

The learner who had been frustrated by the elusive Sphinx was suddenly re-energised. With a renewed sense of purpose, they returned to the excavation, ready to try again. 

Through this invigorating activity, our MYP 1 learners at The School of Raya explored how we can reconstruct the past when we cannot travel back in time? Rather than beginning with a textbook or a list of historical facts, learners stepped into the role of archaeologists. Working in teams, they explored an excavation site designed to introduce them to the methods used to uncover and study evidence from the past.

Each team worked with a designated excavation area and carefully established a grid using labelled stakes and twine. This introduced learners to the importance of mapping and recording the precise location of archaeological finds. Equipped with soft brushes and small trowels, learners carefully excavated their assigned squares. The excitement of calling out “Eureka!” when an artefact was discovered added to the sense of adventure. 

However, the activity was about much more than finding objects. The most meaningful part of the experience came after discovery. Learners were encouraged to move beyond simply identifying an object and begin interpreting what it might reveal.

They considered questions such as:

• What does this object suggest about the daily lives of people in the past?
• What materials or techniques might have been used to make it?
• What can its location tell us?
• Which conclusions can we draw from the evidence, and what remains uncertain?

These questions introduced learners to an important distinction in historical inquiry: the difference between an observation and an inference. While an observation describes what we can see, an inference is an interpretation based on the available evidence.

Through the activity, learners developed a foundation for investigating ancient civilisations such as the Indus Valley, Mesopotamia, Egypt and Greece. They began to understand how material remains can provide clues about technology, craftsmanship, trade, settlement patterns and everyday life. An object that might initially appear ordinary could offer valuable insights into the knowledge, creativity and priorities of the society that produced it. A meaningful example is the Code of Hammurabi, an ancient Babylonian law code inscribed on a stone stele. At first glance, it may appear to be just a stone monument covered in writing. However, it reveals that the Babylonians developed a written system of laws to regulate society, resolve disputes and establish punishments for different offences. For instance, the principle of “an eye for an eye” reflects how punishments were linked to the nature of the offence. 

The archaeological dig supported the development of several important learning skills. Learners practised research and inquiry by asking focused questions and investigating evidence, while observation and interpretation enabled them to record details accurately and draw evidence-based conclusions. They developed critical thinking by distinguishing between what the artefacts revealed and what they inferred from the evidence. Through teamwork and shared responsibility for the excavation, learners strengthened their collaboration skills. Finally, by documenting their discoveries in field logs and explaining their interpretations clearly, they developed their communication skills

The archaeological dig was a reminder that meaningful learning often begins with curiosity. A grid of soil, a carefully uncovered object and a series of questions became an opportunity for learners to investigate the past using the methods of historians and archaeologists.

After all, every artefact has a story to tell. The challenge is learning how to uncover it.

Recently, in my Grade 9 Chemistry class, we were exploring the real-world impact of mining. We had arrived at this discussion on our quest to understand the world of elements and our study of the Periodic Table. As we explored both the advantages and disadvantages of mining elements for our gadgets, technologies and industrial needs, someone quipped, “A disadvantage would be increased greenhouse gas emissions due to mining machinery.” Almost immediately, another voice followed: “Yes, that means global warming!” And right on its heels came a loud blurt from across the room: “Arctic ice melting!”

Then, just as quickly as the ideas had tumbled out, the classroom fell still.

The connections seemed to settle in. One idea had led to another, and suddenly the consequences of mining extended far beyond the mine itself. Then, from one corner of the room, came a gentle question:

“Does that mean we are mining for precious elements in the Arctic?”

And there it was, the moment when a chemistry lesson stopped being just about elements and the Periodic Table. It became a question about the world around us.

This, among many other ways, is the power of learning in an IB context. Concepts and theories taught within different subject disciplines take on centre stage roles when students are given opportunities to connect them with the real world. Through case studies, newspaper article analysis, industry expert talks, field visits and even model Shark Tank sessions, learners encounter real-world, real-time situations that invite them to ask questions, make connections and consider the impact of what they are learning.

Some lessons begin from the lens of a real-world situation and then work backwards.

‘What is happening here? Why is it happening? What do we need to understand to explain it?’

The direction of learning shifts. Instead of beginning with a concept and asking students where they might use it, students begin with real world scenarios that exist and discover the concepts they need to understand it.

There are moments when this leads to something quite powerful—an epiphany. In the Chemistry classroom I began with, my students began to see that Chemistry is not confined to formulae, symbols and the pages of a textbook. The elements they study are part of the technologies they use, the resources societies depend upon, the environmental challenges communities face and the choices that shape our future. My students didn't need to be told that mining connects Chemistry to climate, geography, technology and sustainability—they discovered the connections themselves.

They begin to see why what they are learning matters.

In effect that is the full-circle moment, real world impacts around us impact the ways in which we learn and what we learn, in turn, helps us make better sense of the world around us.

Cox_skates is undefeated, top of the leaderboard; in real life, he's never once stood on an actual skateboard. Hand him one, and he lasts about four seconds before gravity takes over!

It's a strange little contradiction, but it's not really about skating. It's about two very different things that both feel like knowing how to do something until one asks which one actually holds up once the screen is gone.

In the language of learning research, this gap has a name: surface learning versus deep learning, first described by researchers Ference Marton and Roger Saljo back in the 1970s. Surface learning is about reproducing something: the fact, the move, the correct answer; "knowing" it well enough to recognize or try repeating it. Deep learning is about actually using the "understanding" to build it into something one can use: adjust, explain, apply somewhere new, do it again under pressure. Both can look identical from the outside. Only one of them survives contact with reality.

Recognizing the right answer is cognitively lower order. Our brain barely has to work; it just matches what's in front of us to something familiar. That's what the screen skating game gives us: the feel of mastery, minus the actual physical effort of falling, wobbling, catching yourself, falling again. Real skating asks our body to build balance the slow way, through failure. The screen game skips straight to the reward.

"Winning" in the screen game means timing the button press. "Winning" on real skates means our body learned to balance, to fall well and overcome fear. Same word — completely different thing being measured.

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I often see students describe this with honesty, if you listen attentively. When a child is asked to explain/write out their thinking, rather than just pick the right answer, and you'll often hear some version of: ahhh!! no!! it's a lot… It hurts my brain. That's not a complaint to brush off, it's an accurate report. Writing, explaining, and working something out from scratch are what researchers call "generative" acts. One has to produce the thought themselves, rather than just recognize it. That's genuinely harder. The discomfort during generative tasks isn't a sign something's gone wrong. It's a sign that real work is happening.

This shows up well past academics, too. A young dancer can watch a routine once and describe every step back perfectly and still stumble the moment she may have to actually perform it, because naming the steps and performing them physically are two very different things. A student can hum a melody back note-for-note after listening to it once, and still be nowhere close to actually playing it. In every one of these, there are two things that feel like competence: recognizing what mastery looks like, and being able to produce it on one's own, in real situations. Only the second one is real.

Today, answers, techniques, "how it's done", are all one search away, in a form fluent enough to feel like understanding. It isn't. It's familiarity showing up like understanding.

It takes a bridge to move from knowing to understanding and “effort” is that bridge. Crossing it feels uncomfortable, even like failing, at first. But it's persistence that carries one across, until what once felt shaky starts to feel like solid ground.

That's the whole difference between Cox_skates and a real skater. It's just about the will to try, fall first and get back up, which, it turns out, is most of what learning looks like!