Search

The observation that high school students often do not recognize the contributions of other subjects such as applied mathematics or informatics to chemistry may be countered by introducing appropriate mathematical modelling in chemistry class. It should be focused on topics which are typically part of the regular curricula. Here chemical kinetics is employed within the introduction of the nucleophilic substitution as an example allowing conjunctions to mathematics and informatics. In this context, kinetics is deepened by quantitative considerations as well as simulations. The time laws for the kinetics of first and second order are derived using mathematical methods that are typically included in present mathematics curricula. In addition, two quantitatively analyzable model experiments can be used to allow a playfully understanding of the differential equations and their solutions. Furthermore, these model experiments can be transformed into concise computer algorithms. In this way, students learn the different methods experiment, analytical derivation, and simulation for gaining chemical knowledge.

In high school and beyond students regard the subjects often isolated from each other. In contrast, every subject always requires contributions from other subjects. The subject chemistry requires, besides others, mathematical skills. In order to illustrate the relation between chemistry and applied mathematics the principles of mathematical modelling can already be introduced in high school. Here a practical example is employed to show how it is possible to simulate a standard experiment in high school chemistry, namely the titration of monoprotic strong and weak acids with a strong base. The mathematical derivation is merely based on mathematical skills, which are typically taught in 9th grade. The topic fits well in the chemistry curricula as a deepening. This approach of implementing mathematics in chemistry also aims to counteract the possible estrangement of the high school subject chemistry from the university subject chemistry. The mathematical derivations are detailed with focus on the traceability and should be adjusted for application in high school. The way of deriving the equations also allows to teach general methods of mathematical modelling in natural science.

The observation that high school students often do not recognize the contributions of other subjects such as applied mathematics or informatics to chemistry may be countered by introducing appropriate mathematical modelling in chemistry class. It should be focused on topics which are typically part of the regular curricula. Here chemical kinetics is employed within the introduction of the nucleophilic substitution as an example allowing conjunctions to mathematics and informatics. In this context, kinetics is deepened by quantitative considerations as well as simulations. The time laws for the kinetics of first and second order are derived using mathematical methods that are typically included in present mathematics curricula. In addition, two quantitatively analyzable model experiments can be used to allow a playfully understanding of the differential equations and their solutions. Furthermore, these model experiments can be transformed into concise computer algorithms. In this way, students learn the different methods experiment, analytical derivation, and simulation for gaining chemical knowledge.

In high school and beyond students regard the subjects often isolated from each other. In contrast, every subject always requires contributions from other subjects. The subject chemistry requires, besides others, mathematical skills. In order to illustrate the relation between chemistry and applied mathematics the principles of mathematical modelling can already be introduced in high school. Here a practical example is employed to show how it is possible to simulate a standard experiment in high school chemistry, namely the titration of monoprotic strong and weak acids with a strong base. The mathematical derivation is merely based on mathematical skills, which are typically taught in 9th grade. The topic fits well in the chemistry curricula as a deepening. This approach of implementing mathematics in chemistry also aims to counteract the possible estrangement of the high school subject chemistry from the university subject chemistry. The mathematical derivations are detailed with focus on the traceability and should be adjusted for application in high school. The way of deriving the equations also allows to teach general methods of mathematical modelling in natural science.

While quantum chemistry is the standard model for treating a chemical bond in chemical science for about one hundred years, its application in secondary education is still limited. Especially the introduction of wave properties of matter is often neglected. The complexity of this topic makes it necessary to treat it exemplary. Simple models with infinitely high potential walls and vanishing potential energy inside can serve as suggestion for teachers to teach the subject. The mathematical modeling is restricted to the sinus function and therefore suitable for the upper secondary level. The foundation of bond formation is the interference of electronic wave functions taking place when waves come close as atoms approach. Interference then leads to a redistribution of the charge. In case, this redistribution takes up more space than available before, the kinetic energy decreases. In addition, the redistribution of the charge leads to changes in the potential energy. This is the background for a series of rules and effects in high school chemistry that are often introduced without relation to each other. Even though the topic is rather located in upper secondary education, in middle secondary education the wave property of matter can be introduced phenomenologically equivalent to particle properties in a preparatory manner.