Tracing Creativity in Mathematical Modelling: An Event-Level Learning Analytics Study of Modelling Processes

In the world of mathematics education, there is a long-held belief that the true measure of a student's ability lies in the final answer they write down. When a student solves a problem, teachers often look only at the result to judge their skill. However, a growing number of educators and researchers are beginning to ask a different question: what happens in the mind of the student while they are working? This line of inquiry focuses on the journey rather than the destination. It suggests that creativity is not just a spark that appears at the end, but a process that unfolds over time, filled with false starts, sudden insights, and moments of rethinking. Understanding this process is particularly important in mathematical modelling, a type of problem-solving where students must take a messy, real-world situation and turn it into a mathematical story. Unlike standard textbook exercises with clear instructions, these tasks require students to decide what information matters, how to represent it, and how to check if their solution makes sense. The challenge for researchers has been to see this invisible thinking process clearly, moving beyond the final product to watch the creative act as it happens.

A team of researchers at The Hong Kong Polytechnic University has developed a new way to watch this process in action. They set out to understand how creativity emerges as students work through a mathematical modelling task, not by looking at the finished work, but by analyzing the digital footprints left behind as the students worked. The study involved 88 eighth-grade students who had never done this type of modelling before. These students sat in a classroom with digital tablets and spent an hour solving a complex, open-ended problem. As they worked, the computer system recorded every single action they took, from the moment they started reading the problem to the moment they finished. The system saved a snapshot of their work every fifteen seconds, capturing their handwriting, their drawings, and their clicks. This created a massive stream of raw data, a digital trail of every pause, every edit, and every backtracking move the students made.

The researchers faced a significant hurdle: a list of clicks and pauses does not automatically tell a story about creativity. A student might pause because they are thinking deeply, or because they are confused, or simply because they are distracted. To make sense of this, the team built a detailed workflow to translate these raw digital traces into meaningful events. They broke the students' hour-long work session into distinct moments, or events, and sorted each event into one of five stages of the modelling process. These stages ranged from understanding the problem and simplifying the situation, to creating mathematical representations, interpreting results, and finally, posing new questions based on their findings. They then looked at each event to see if it contained a "creative move." A creative move was defined not just as doing something new, but as doing something new that was also mathematically sound and relevant to the real-world situation. They scored these moves based on how original they were and how well they fit the context, creating a clear picture of when and where creativity happened.

Once the data was organized, the researchers compared the students who showed high levels of this process-based creativity with those who showed lower levels. They were looking for patterns in how the students moved from one stage of the task to another. They found that both groups of students followed a very similar path. Whether a student was highly creative or less so, they tended to spend time understanding the problem, then building a mathematical model, and then checking their work. The high-creativity group did show some extra pathways, moving more often between building their model and explaining their ideas, but the fundamental structure of how they worked was the same for everyone. This suggests that there is no single, unique "creative path" that looks completely different from the standard way of solving a problem. Instead, creativity seems to be woven into the same general process that everyone uses, just with a few extra connections between the steps.

The most striking finding, however, was about when the creative moments happened. The researchers discovered that creativity was not evenly distributed across the hour. It was not a constant stream of ideas. Instead, creative moves were heavily concentrated in specific parts of the process. The students were most likely to have a creative breakthrough when they were first trying to understand and simplify the problem, or when they were at the very end, thinking about how to pose a new question based on their work. In contrast, the middle phase, where students were busy writing down the actual mathematical equations and calculations, was the least likely time for a creative move to occur. This tells us that creativity in modelling is deeply tied to the specific task the student is doing at that moment. The nature of the work changes the likelihood of a creative spark.

The study also tested a common assumption in digital learning: that certain observable actions, like pausing, editing a previous answer, or going back to a previous step, are direct signs of creative thinking. Many educators assume that if a student stops to think or changes their mind, they are being creative. The data from this study, however, did not support that idea. When the researchers accounted for which stage of the task the student was in, these isolated actions no longer predicted whether a creative move would happen next. A pause could mean the student was stuck, or it could mean they were having a brilliant idea, but the action itself did not tell the difference. The context of the work mattered far more than the specific action. A pause during the "understanding" phase might be part of a creative process, but the same pause during the "calculation" phase might just be a moment of confusion.

These findings offer a new perspective for how we understand and support learning. They suggest that to truly see creativity, we cannot simply count the number of times a student edits their work or stops to think. We must look at the substance of what they are doing at that moment. Creativity in mathematical modelling is not a separate skill that happens in a vacuum; it is a response to the specific demands of the task at hand. The researchers' method of turning raw digital data into a story about the modelling process provides a powerful tool for educators. It allows them to see that creativity is most likely to flourish when students are defining the problem or reflecting on the solution, rather than when they are simply crunching numbers. By focusing on the context of the work, rather than just the surface-level actions, we can better understand how young minds engage with complex problems and where the seeds of innovation are most likely to take root.