How mathematical modeling combined with ICT technologies revolutionizes teaching and problem-solving in mathematics, chemistry, and biological sciences.
Explore MoreModern biology, chemistry, and mathematics face the challenge of describing extremely complex systems - from the spread of viruses to chemical reactions in cells. Mathematical modeling has become an indispensable tool that allows not only understanding these phenomena but also predicting their development and testing hypotheses without the need for costly and time-consuming experiments 1 .
Using equations and algorithms to represent complex natural systems with accuracy.
Combining digital technologies with modeling for interactive and engaging learning experiences.
Solving real-world problems in biology, chemistry, and medicine through computational models.
The process of creating abstract representations of real-world systems using the language of mathematics.
A mathematical model is a simplified description of a real phenomenon or system, expressed in the language of mathematics. As sources indicate, a model is "a set of equations, functions, or algorithms that describe the properties of a system we are interested in" 1 . It is always an intentional simplification - focusing on the essential features of the studied phenomena while omitting less important aspects for a given problem .
Whether it's a parabola as a model of projectile trajectory or differential equations describing the spread of an epidemic, these are examples of mathematical models we encounter in both education and everyday life. A good model does not reproduce reality in all its complexity but captures the essence of the studied phenomenon, allowing for its analysis and behavior prediction under different conditions .
Defining the problem in the language of the specific knowledge domain (biology, chemistry)
Defining symbols, variables, and relationships between them
Formulating calculation algorithms using defined quantities
Performing calculations using appropriate computer applications
Presenting the solution in the language of the original domain
Verifying correctness by comparing with real phenomena
| Stage | Activities | Example in Biology Teaching |
|---|---|---|
| Problem Formulation | Defining model goals and scope | Modeling bacterial population growth |
| Model Building | Selecting variables and parameters, defining relationships | Defining variables: time, population size, growth rate |
| Computational Implementation | Using ICT tools for simulations | Using spreadsheets or specialized software |
| Validation | Comparing with experimental data | Comparing with bacterial culture results in the laboratory |
| Application | Using the model for predictions | Predicting population doubling time |
In biology and medicine, mathematical models play a key role in understanding the dynamics of life processes. During the COVID-19 pandemic, epidemiological models were crucial for planning preventive actions and predicting the development of the situation 1 .
In biology teaching, models allow students to understand the mechanisms governing nature - from simple population growth models to complex trophic networks in ecosystems.
Models of cancer development, simulations of processes occurring in cells, or analyses of gene spread dynamics in populations - these are just some examples of applications of mathematical modeling in modern biology and medicine 1 . For students, working with such models means the possibility of actively exploring the complexity of the living world without the need to conduct long-term experimental research.
In chemical sciences, modeling finds applications in simulating chemical reactions, designing new molecules, and optimizing industrial processes 1 . At the educational level, computer models allow students and pupils to visualize molecular structures, predict reaction products, and analyze the kinetics of chemical processes.
ICT technologies enable the creation of interactive visualizations of molecular structures, simulations of collisions between reagents, or modeling of energy changes during reactions. These tools significantly support the learning process, allowing the understanding of abstract chemical concepts through direct interaction with models.
Population dynamics, epidemiology, genetics
Reaction kinetics, molecular design, process optimization
Disease spread, drug interactions, treatment efficacy
Ecosystem dynamics, species interactions, climate impact
Modern education in the field of science is increasingly using information and communication technologies (ICT) as integral tools supporting the process of mathematical modeling 2 3 . These include:
The use of ICT in teaching mathematical modeling brings tangible benefits: it makes classes more attractive, increases student engagement, enables personalization of the teaching process, and provides tools for visualizing complex concepts 3 .
Digital technologies open up new possibilities in terms of a personalized approach to education. Educational applications offer "the ability to adapt tasks to each student's current abilities" 2 . In the context of mathematical modeling, this means that students with different predispositions and skills can work with models tailored to their level of understanding, gradually developing competencies in building and analyzing more complex systems.
Particularly valuable is the use of ICT in working with students with special educational needs. As sources indicate, "the use of information and communication technologies proves particularly useful in working with children with special educational needs" 3 . For these students, digital tools can be the only chance to partially acquire knowledge, eliminating barriers resulting from disabilities.
| Tool Category | Examples | Application in Modeling |
|---|---|---|
| Educational Platforms | Moodle, Google Classroom, Microsoft Teams | Sharing models, organizing remote work, monitoring progress |
| Simulation Software | PhET, NetLogo, Python with scientific libraries | Creating and testing mathematical models |
| Visualization Tools | GeoGebra, Desmos, interactive whiteboards | Visualizing models and simulation results |
| Mobile Applications | Khan Academy, Labster | Learning through interaction with models anywhere |
To illustrate how mathematical modeling and ICT technologies can be used in educational practice, consider a school research project involving modeling the spread of a hypothetical disease in a school community.
Understanding by students the mechanisms of infectious disease spread and factors influencing epidemic dynamics.
The educational experiment allows students to observe characteristic features of epidemic development, including the herd immunity threshold effect and the nonlinear relationship between model parameters and process dynamics.
| R0 Coefficient | Peak Infection Rate | Time to Peak (days) | Total Infected |
|---|---|---|---|
| 1.5 | 15% | 45 | 58% |
| 2.5 | 28% | 28 | 89% |
| 3.5 | 36% | 20 | 94% |
| 5.0 | 42% | 14 | 96% |
Analysis of simulation results allows students to understand how small changes in model parameters (such as the R0 coefficient) translate into significant differences in the course of an epidemic. Discussion about the causes of these phenomena leads to a deeper understanding of both the mathematics behind the models and the biology of epidemic processes.
NetLogo, Excel with macros, Python - enables model implementation and simulation
GeoGebra, spreadsheets with chart functions - serves to present results graphically
SIR model and its variants - constitute a formal description of studied phenomena
Introductory materials to modeling, software instructions - support the learning process
The integration of mathematical modeling with ICT technologies in teaching science subjects contributes to the development of key competencies for the modern world. Students not only acquire subject knowledge but also develop the ability for critical thinking, solving complex problems, teamwork, and proficient navigation in the digital environment 4 .
However, this requires appropriate teacher preparation. As sources indicate, "to effectively use ICT in education, teachers should receive appropriate support on the topic" 2 . Courses and training on the use of ICT in education provide teachers with practical knowledge about tools and technologies they can use in their daily work 2 5 .
Despite enormous potential, the use of mathematical modeling and ICT technologies in education faces certain challenges. Creating models requires not only knowledge of mathematics "but also a deep understanding of the studied system" 1 . Challenges include selecting appropriate assumptions, validating results, and interpreting obtained data 1 .
Additionally, models can be limited by incomplete knowledge or measurement inaccuracies 1 . In education, an important challenge is also ensuring equal access to technology and appropriate preparation of less digitally skilled students and teachers.
The integration of mathematical modeling with information and communication technologies creates a powerful didactic tool that can revolutionize the way mathematical, chemical, and biological sciences are taught. Instead of dry facts and abstract equations, students receive interactive, engaging tools allowing for independent discovery of the principles governing the natural world.
In the era of rapid development of science and technology, "the ability to create and interpret mathematical models is highly valued both in the scientific environment and in the job market" 1 . Investing in the development of these competencies among students is an investment in the future - both of individual units and the entire society, which will be able to more effectively respond to the complex challenges of the modern world.
The future of science education lies in the skillful combination of traditional knowledge with modern technologies, creating an educational space where theory and practice, mathematics and nature, humans and technology meet to jointly build a deeper understanding of the world around us.