The article deals with a special kind of modelling tass. These problems are used for learning and researching as well. So the results of an empirical study on mathematical modelling of pupils in secondary schools are presented. Pupils of forms 8-10 were observed working on open, realistic problems. These observations were recorded and evaluated. The goal of the presented part of the study is a detailed look at the control processes of modelling problems. In this context changes between real life control and mathematical control during the control phases are studied and evaluated. We describe in detail the sub phases of controlling and explain their connection with modelling process. The problems used in this project can also be used in math lessons, so this kind of research can put teachers and researchers together. These tasks are suitable to support ongoing in-service development and teacher education.

The article deals with a special kind of modelling tass. These problems are used for learning and researching as well. So the results of an empirical study on mathematical modelling of pupils in secondary schools are presented. Pupils of forms 8-10 were observed working on open, realistic problems. These observations were recorded and evaluated. The goal of the presented part of the study is a detailed look at the control processes of modelling problems. In this context changes between real life control and mathematical control during the control phases are studied and evaluated. We describe in detail the sub phases of controlling and explain their connection with modelling process. The problems used in this project can also be used in math lessons, so this kind of research can put teachers and researchers together. These tasks are suitable to support ongoing in-service development and teacher education.

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.