In teaching science, you often need to decide on how far to introduce students to topics from an
abstract scientific and mathematical perspective. Considering this question, we developed and
tested educational materials on Particle Physics and Cosmology for students of grade 9 to 12 at
secondary and upper secondary level, and for gifted students in special courses or academies, like
Deutsche Schülerakademie or competitions like Jugend forscht, building on their prior knowledge.
Our material also contains experiments supported by DESY and the University ofWuppertal. The
theoretical parts of our course material cover electromagnetism and quantum mechanics up to
Maxwell’s equations, the Schrödinger equation and the Klein-Gordon equation, which require
basic knowledge in differential equations and group theory. Some course participants were
introduced to geometrical path lengths, tensors, and symmetries (according to Ellwange, 2012; Wong, 2013).
The evaluation of the results, the material, and the courses from a cognitive as well as a psychological
point of view unfolds possibilities and necessities to elaborate on different parts of
exercises and projects on different levels, and revealed new relations between these parts. Students’
perception of physics and mathematics, their beliefs in understanding something and their
workout of projects indicated relationships different from our expectations ([10], [11]). Results in
connection with different types of courses are described below for experiments on (i) Differential
Equations, (ii) Path Length and (iii) Symmetries. The topics are described in connection with
courses, activities, or students’ projects.