# Mathematical Modeling in Chemistry Education

## Theory and reality

*Contact person: Dr. Ines Goldhausen*

*supported by: Chemical Industry Fund*

For the explanation of scientific phenomena as well as for problem solving in natural sciences, it is often necessary to use mathematical models (such as equations, functions, graphs, geometric figures, coordinates, etc.). They can be used to describe and link the corresponding scientific facts mathematically as well as to interpret the resulting mathematical formulations from a scientific point of view. In addition, a mathematical analysis of chemical processes can help to facilitate and deepen chemical understanding.

Of particular importance is a more conscious use of mathematical models, which is required by the so-called mathematical modelling. In this process, mathematical models are developed by the learners themselves in order to explain chemical facts or to solve problems. The modelling process does not only include the development or justified choice of a chemical and a mathematical model, but also their validation based on the results obtained.

A model was developed that shall serve as a basis for a differentiated consideration of this process and its relevance for learning chemistry. It is supposed to clarify which sub-steps the modeling process actually consists of. This enables to determine which problems the process is faced with specifically while learning chemistry.

In order to investigate students’ difficulties associated with the use of modeling tasks in chemistry classes, a video study was conducted to provide insight into the learners' thinking processes during mathematical modelling in chemistry classes. As a diagnostic tool for this purpose, a task format (graded learning aids) was developed that allows a detailed analysis of the students' thinking processes. The study shows that, at least for the selected example, the students' difficulties are particularly located in the areas of independent selection or development of a model, basic chemical knowledge as well as filtering out essential information regarding the real situation, rather than in mathematical work. When comparing this with the current ‘task culture’, which could be analyzed with the help of textbooks, a-level tasks, and subject teacher interviews (Goldhausen 2015), it can be determined that students’ difficulties are specifically occuring at the points that are rather less important in the current chemistry lessons.

Furthermore, the problem areas that are perceived individually could be located in the area of mathematics by the teachers. Due to this inaccurate location, there is a resulting lack of support for the students with regard to the actual difficulties.

Currently, however, there are no reliable studies on the influence of the teaching culture or the task structures used on comprehension in the area of mathematical modeling processes in chemistry. In particular, it is unknown to what extent student competencies in the area of mathematical modeling in chemistry classes can be influenced by the increased use of modeling tasks.

Moreover, in contrast to the use of other models (cf. Gilbert 2004), there are currently no indications from research on how mathematical modeling can be taught in chemistry.

Based on the findings from mathematics education (Blum & Borromeo Ferri 2009), we will now first investigate how the use of tasks that aim equally at the development of a chemical and a mathematical model affects the modeling competencies of the learners. One focus of the study is the independent execution of chemical experiments compared to the use of given and idealized values for situation modeling. Currently, corresponding tasks are being developed and the results of the video study are being validated with regard to their transferability to other examples with the help of a second video study.

Based on these results, action-oriented research focusing on participation and education will then be used to investigate how mathematical modeling can be taught in chemistry and how the understanding in the area of mathematical modeling processes can be optimally promoted in chemistry.

**Literature**

Blum, W., Borromeo Ferri, R. (2009). Mathematical Modelling: Can It Be Taught And Learnt? In *Journal of Mathematical Modelling and Application* 1/1, 45-58.

Gilbert, J. K. (2004) Models and Modelling: Routes to more authentic science education. In *International Journal of Science and Mathematics Education* 2, 115-130.

Goldhausen, I. (2015): *Mathematische Modelle im Chemieunterricht*, Berlin: uni-edition.