For many years, teaching mathematics mostly meant teaching computation: you learned a technique, you applied the formula. It made sense when calculating quickly and accurately was worth something. It is still important to develop students’ ability to reason, but in real life, a calculator solves an equation instantly, Excel takes care of the rest, and AI can now write the analysis for you. What we care about is whether students, both hospitality and business students, can understand a situation well enough to know what to calculate in the first place, and why.
This is one of the reasons why we redesigned our mathematics lessons for the preparatory year at EHL. Our students do not start with abstract equations but with hospitality problems.
A hotel wants to know how its distribution channels affect profitability, or an operator needs to estimate future energy consumption. None of these situations comes with an equation attached, just uncertainty and several variables interacting at the same time.
So instead of asking students to apply a formula from a textbook, we ask them to translate a real situation into a mathematical representation. Solving equations is still part of the course, but the focus is on helping them understand how equations emerge from reality and how to model reality themselves. Yes, future managers must be able to interpret outputs and identify mistakes, but the computation itself is no longer the main competitive advantage. In fact, the challenge is much more about framing and modeling problems to make better decisions.
Applied Mathematics & Tools for Hospitality is built around a simple idea: before any calculation, students need to translate words into equations. A manager receives a situation, such as revenue is decreasing, costs are soaring, customer satisfaction is flatlining, distribution channels are changing and competitors are becoming more aggressive. Before doing anything else, somebody has to determine what matters, what does not, and which variables are likely to explain the situation. This is where many students struggle the most. If students are given the equation they can generally solve it because they learned it in high school. The challenging part is deciding which equation should be used in the first place. We see it very clearly when we ask the same question twice, first with numbers and then with variables. Remember these letters in your equations? Many students find the answer in a few minutes with the numbers, then get stuck when they need to write the generalized formula.
In our course, students start by identifying the variables that explain a phenomenon, how they relate to each other, and what we can compare them to. One of our favorite examples is how you can express a profit and the goal behind it. Let's compare profit to revenue (or selling price): we have what's called a return. A return is a great way to analyze the performance of profit. Let's compare profit to cost: we have a markup, which is a great way to set a selling price. This difference has a tremendous impact on how we apply this in a mathematical equation, and we often see students mix up the two. Once this representation exists, we can introduce the mathematical techniques, and the equation simply becomes a formal way of writing a relationship that students have already identified.
Spreadsheets play a central role in this process, mainly because they lay bare the student’s reasoning. The quality of students’ reasoning becomes visible as soon as they start building a model. Every assumption has to appear somewhere, and every relationship has to become a formula. The spreadsheet forces students to translate a situation into variables, variables into equations, and equations into formulas. What was initially a hunch, or intuition, became an explicit representation that can be tested and discussed. The objective is to move from a situation to a model that supports analysis and decision-making, and that can be automated. The model still does not make the decision for them. When Excel returns a number of housekeepers or cooks that is not an integer for calculating the resources needed, students either copy it as is or don’t know whether to round it down or up, without asking themselves what it means in terms of operations for a hotel. With time, they understand what it finally means: round it up if you have full-time employees, or to a certain number of decimal places if it is part-time or a specific scheduling need.
As students progress through the course, the situations become increasingly ambiguous. This is intentional because real business problems rarely arrive with complete information. Students start with percentages, ratios, weighted averages and simple equations, then combine several mechanisms through systems of equations and successive growth rates. But even if these subjects seem simple in theory, the complexity lies in the two factors we already discussed: translation and modeling. A typical case is removing a tip that is already included in a bill. Many students simply take the percentage off the total, while the tip was calculated on the amount before it was added!
Little by little, students discover that mathematical reasoning is often less about calculating and more about building a useful representation of reality. Mathematics becomes the first language through which they learn a broader method of reasoning. Future managers will spend most of their careers trying to understand situations and represent problems in a way that helps them make wise decisions, and this is exactly what we are trying to do with our students. Mathematics provides the framework, hospitality provides the context, and spreadsheets—with a few games sprinkled in here and there—bring the reasoning to life.
The future development of this course will involve how we think about AI. Most discussions about AI in math teaching focus on its ability to solve problems. In our own work, we have observed a significant difference in the quality of the output produced by the same AI system depending on the broader instruction system surrounding it, including the prompt, memory, conversation history, and other contextual inputs. But once the necessary context is available, providing more information does not necessarily produce the greatest improvement. Explicitly defining the steps that transform the input into the output can have a much stronger effect. This observation led us to an interesting question: if articulating these steps improves the way we work with AI, could learning to articulate a method also help students better understand their own reasoning?
This might be true because AI systems require detailed instructions. When students try to guide an AI through a problem, they quickly discover that they must first have a clear understanding of their own reasoning process. Before they can tell the AI what to do, they need to understand what they would have done themselves by hand. In many cases, the challenge is no longer building a model, but articulating the method used to build it. The objective is to help them transform a specific solution into a transferable process applicable to new situations.
We are only beginning to explore this idea, but it looks promising. Nevertheless, future managers must still learn how to move from a complex situation to an explicit model that can be questioned. More fundamentally, the course tries to rebuild mathematical foundations based on understanding rather than rote memorization. The tools we use for this will continue to evolve. Excel was created 40 years ago, changing the way we interact with numbers; 4 years ago, it was the case with this generation of AI; more than likely, the tools in 20 years will be different. But the need to reason does not change with the tool: whether students work with a friend, a colleague, Excel, AI, or a future tool, they must still identify what matters, structure the problem, and explain how to move from the input to the output. AI may simply become another tool in students’ tool box.