Croatia: Mathematics and human body

Description of the Activity

The main aim of the Mathematics and the Human Body Lighthouse activity is for participants to:

• Revise their school-acquired knowledge of functions (exponential and trigonometric) and sequences.
• Gain an appreciation of the prevalence and importance of mathematics in real life.
• Be introduced to the relevance of mathematics in a scientific context beyond physics, challenging the common preconception that mathematical modeling is limited to physics-related problems.
• Explore the role of mathematics in medicine, biology, and pharmacy, and reflect on its applications.
• Identify mathematical modeling procedures and apply them to real-life problems.

This activity focuses on the topic of health. Participants should have a basic understanding of functions and be familiar with specific types such as linear, exponential, and trigonometric functions.

Course of the Activity

The activity begins with a motivating example: the modeling of stents using differential equations. Although this example involves higher-level mathematics, making it unsuitable for high school students, it effectively demonstrates the real-world relevance of mathematics in science and medicine, introducing the concept of biomedical mathematics.

Next, participants engage in problem-solving tasks, working in pairs with guidance from activity leaders if needed. These tasks are designed to highlight the role of mathematics in medicine, biology, and pharmacy. Participants apply their calculation skills and basic knowledge of functions (e.g., using an exponential function to model drug concentration in the bloodstream) while exploring and discussing mathematical relationships between different human body measurements. They interpret their results in real-world contexts and make health-related recommendations.

Each task is discussed with the activity leaders. The aim of these discussions is not only to verify the accuracy of solutions but also to transition from specific problems to the broader mathematical modeling procedures used in their solutions.

The activity continues with exercises focused on drawing conclusions from graphs. This is a group-based heuristic dialogue, where students analyze and interpret given graphs (e.g., vessel diameter, average blood pressure, or the relationship between height and age). During this phase, participants examine different model characteristics, such as whether they are discrete or causal, and discuss concepts like the differences between linearity, correlation, and causality.

Description of the Implementation Process

This activity was designed by members of the Faculty of Science at the University of Zagreb and was conducted in one of the faculty’s lecture halls, with a duration of 120 minutes.

The main leaders of the activity were Prof. Dr. Sc. Željka Milin Šipuš and Dr. Sc. Matija Bašić, both members of the Department of Mathematics at the Faculty of Science. Their role was to introduce participants to the topic, coordinate their activities during the problem-solving process, and guide them through heuristic discussions following the completion of each task. Additional support in organization, coordination, and logistics was provided by Petra Vidović (HMD) and Renata Švedrec (HMD).

A total of 11 participants took part in the Lighthouse activity. Most of them were 17 years old (age range: 16 to 18) and were accompanied by a mathematics teacher. The participants played an active role throughout the session. They were encouraged to ask questions, leading to thought-provoking discussions. Some of the questions raised included:

• “Is it possible to analyze the geometry of a stent? How? How is this done professionally?”
• “How can we derive an algebraic expression to model drug concentration? What if multiple drugs are involved? Which professions analyze such problems?”

Since the activity was structured as a series of heuristic conversations, participants were prompted with guiding questions such as:

• “How does the increase in drug concentration in the blood behave? What type of dependency does it follow?”
• “What is the meaning of a mathematical model? What defines a linear model? What is the difference between linearity, correlation, and causality?”

These discussions encouraged participants to actively engage, reason critically, and justify their answers. They employed various problem-solving strategies, and one of the most interesting aspects was observing the evolution of their reasoning. Because the tasks were embedded in real-world contexts, the problems initially appeared to be biological in nature. As a result, participants first relied on their knowledge of biology (e.g., capillaries, arteries). However, as the activity leaders posed further sub-questions, it became evident how their reasoning gradually shifted from biology to mathematics, illustrating the interdisciplinary nature of the topic.

Final Remarks

Health literacy and responsible behavior are becoming increasingly important, particularly in relation to medication use. Mathematics, often perceived as abstract, gains real-world relevance through interdisciplinary approaches, such as modeling drug concentration in the bloodstream.

While certain simplifications (e.g., assuming a 25% daily drug excretion rate) are necessary, they provide opportunities for discussions on data accuracy, physiological variations, and the role of scientific modeling. Expanding on this topic could include student-led research, model comparisons, and the use of technological tools to deepen understanding.

This well-structured activity effectively connects mathematics to real-world applications and holds significant value for future implementation.