Key question I chose

How can I incorporate mathematical modelling into my teaching practice?

As a Grade 11 Statistics and Probability teacher, I realized that mathematical modelling is not an “extra topic” that I squeeze in when I have time. It is a way of teaching the subject itself, because Statistics is already the mathematics of real situations with uncertainty. When I model, I start from a real question, translate it into mathematical language, solve it, then return to the situation to check if the answer makes sense.

One idea that stayed with me is that modelling is basically the translation of a real-life problem into mathematical form so it can be represented and solved more clearly. The reading describes this translation as the modelling process itself. This matters to me because many students think math begins only when symbols appear on the board. Modelling flips that. Math begins when a real question is stated precisely, with variables and assumptions.

How I understand the modelling process

What I like about the modelling reading is that it makes the process explicit. It describes modelling as studying some part of a real-life problem in mathematical terms and converting a physical situation into mathematics under suitable conditions. It also emphasizes that models simplify reality, so assumptions and approximations are unavoidable, and the real test is whether results make reasonable sense when interpreted back in context.

In my own teaching, I now think of modelling as a cycle. I begin with assumptions, create a formulation, do the solution steps, interpret the output, and validate it against what we know. If it does not fit, I revise and try again, not because I “failed,” but because the situation is complex and my first model was too rough. This cycle idea is shown clearly in the flowchart that goes from assumptions to formulation to solution to interpretation to validation, then asks if I am satisfied or if I need to iterate.

Why modelling fits naturally in Statistics and Probability

In the invention–discovery discussion, I resonated with the view that mathematics is both a science of patterns and an art of solving problems (Pogonowski, 2021). Modelling is exactly where those two meet. In Statistics, we look for patterns in data, but we also create problem-solving structures that help us make decisions. Even the choice of a model is partly creative, because I decide what variables matter, what to ignore, and what assumptions are acceptable.

Historically, this also makes sense to me. Early mathematics grew from practical needs like land measurement, taxation, and record-keeping in early civilizations (The Institution for Science Advancement, 2018). So when I teach modelling, I am not “making math more applied.” I am reconnecting math to one of its oldest purposes.

How I will incorporate modelling in my Grade 11 class

I plan to embed short modelling routines inside my regular lessons, not as a separate unit. Here are concrete ways I can do it.

First, I will treat statistical investigations as modelling tasks. For example, in the competency M11/12SP-IVe-1 (formulating the appropriate null and alternative hypotheses on a population proportion), I can frame the lesson around a real school question like “What proportion of Grade 11 students can correctly interpret a graph of a function after an intervention?” Then the modelling steps become natural. I define the parameter p, decide how to sample, choose a probability model (often a binomial model under clear assumptions), compute a test statistic, and interpret the decision in the context of teaching and learning. The most important part is not the formula. It is the interpretation and validation. Does the conclusion match what I observe in class, and what limitations might be affecting it.

Second, I will use the modelling process structure explicitly in class language. I will train students to say, in their own words, something like We understood the problem, we identified variables, we built a mathematical description, we solved it, then we interpreted it back to reality. This mirrors how the reading describes the modelling process moving from formulation to solution to interpretation and validation.

Third, I will incorporate simple model validation even in small activities. If students compute a regression line, I will ask them to check residuals informally, look for outliers, and explain whether the model is “good enough” for the purpose. The reading emphasizes that when a model is not accurate enough, we identify shortcomings and may need a new formulation, which makes modelling iterative. This is a mindset I want my students to learn early. A model is not automatically “true.” It is useful or not useful depending on the question and evidence.

Fourth, I will be intentional about technology as part of modelling, not just as a calculator. The technology–mathematics reading highlights that the relationship is reciprocal. Modern technology relies on mathematics, and mathematics also relies on technology, especially as we use computers not only for calculations but also for tasks like validation and searching for counterexamples (Hansson, 2020).

In practice, this supports my plan to use spreadsheets or simple simulation tools for probability (like sampling distributions), and to emphasize that using technology is still mathematical thinking when students can explain the inputs, outputs, and assumptions.

What I hope changes in my students

My goal is that students stop seeing Statistics as a list of disconnected procedures. I want them to experience it as “thinking with data.” When modelling is part of the lesson, students see why we define variables, why we need assumptions, and why interpretation matters as much as computation. They also learn a healthy habit of questioning results. If an answer looks unreasonable, that is not the end, it is a signal to revisit assumptions and improve the model, just like the modelling cycle suggests.

In the end, modelling is how I can make Statistics and Probability feel honest.

Real life is messy, so our mathematics must be both disciplined and flexible.

I think that is a powerful lesson to bring into a Grade 11 classroom.

References

Hansson, S. O. (2020). Technology and mathematics. Philosophy & Technology, 33(1), 117-139.

Pogonowski, J. (2021). ON THE INVENTION-DISCOVERY DILEMMA. Philosophy of Mathematics Education Journal, (38).

The Institution for Science Advancement. (2018, March 3). The story of maths, part I: From prehistoric to pre‑classical era. IFSA.