General Relativity and Cosmology in Secondary Level II/High School
The project focuses on developing course material and student activities on General Relativity and cosmology for high school pupils, accessible with conceptual and mathematical means at secondary level II.
This pedagogical project was launched on the occasion of the centenary of Einstein’s General Theory of Relativity (GR), aiming to introduce secondary school pupils to modern cosmology and General Relativity.
The main purposes of this project are the following:
- Consolidate and enlarge pupils’ existing knowledge in physics and mathematics while studying subjects they find fascinating and motivating. The main objective is then not to replace the subjects traditionally taught, but rather to complement and reinforce them.
- Develop teaching material for high-school students on General Relativity and cosmology to provide a more complete and deep understanding of the issues of modern cosmology. The existing teaching material on GR and cosmology is either basic, adapted for the general public or for primary school pupils, focusing on the qualitative or philosophical aspects but not allowing a complete understanding of the topics, or “expert” and far beyond secondary school level.
- Improve links between the high school and real research: students who learn physics up to the 19th century are often left with distorted ideas about the main issues in modern physics. A more accurate awareness of what constitutes contemporary physics research (and hence what options are available to pupils after school) can have a strong impact on their choices for further study. This can counterbalance the general loss of interest in the “hard” sciences
This project focuses on the introduction into high schools of subjects dealing with cosmology and GR: the study ROSE (Relevance for Science Education project, 2010) shows that subjects dealing with astrophysics, cosmology and extreme events in the universe are of significantly higher interest for pupils in many countries (Sjøberg & Schreiner, 2007; Sjøberg & Schreiner, 2010; Lelliott & Rollnick, 2010; Baram-Tsabari & Yarden, 2012). Furthermore, it has been shown that pupils having attended a course containing topics from modern physics in addition to the standard curriculum, can achieve a better learning of the classically taught contents (Newton’s mechanics, electromagnetism) than pupils who followed a standard course (Baumert et al., 1998).
Moreover, using an example relating to quantum mechanics, Levrini and Fantini (2013) highlight how over-simplification to make a subject more accessible can have negative effects on student comprehension. Therefore, in the SwissMAP project, the goal has been to simplify the notions at the mathematical level while maintaining a relatively high conceptual level for the intended audience. The originality here is that the targeted approach is then not exclusively qualitative: the teaching material also includes quantitative and/or semi-quantitative analysis.
Up to the beginning of the project (2015), the optional course of cosmology and GR had been successfully taught in the Geneva high school for four years with continuous feedback from pupils and teachers. The result was that, on one hand the learning achievement of this course was the same as the other optional courses (average 4.5/6 and standard deviation 0.7), and on the other hand this was the only physics optional course to have had a gender ratio girls:boys ≥1, and this for four years in a row.
The content and the structure of the course was validated and evaluated by many experts on cosmology, general relativity and physics education, as part of the publication of the course book and of related scientific reviews. Furthermore, the project provided many professional courses for teachers in Switzerland and France, with a general rate of teacher attendance of 3.9/4 and numerous conferences and workshops in Swiss secondary schools on the related subjects.
The project resulted in a course (in French) and a series of activities characterised by an intermediate level of difficulty. The course is divided into nine main chapters, from an introduction to astrophysics through to gravitational waves, covering subjects such as gravitational lensing, black holes, cosmological distances and the thermal history of the universe. Seven annexes complete the course, integrating and/or broadening the complementary notions that pupils may need for a complete understanding of the main chapters. Each chapter is related to a series of exercises and/or activities including model answers (reserved for teachers). The level of difficulty increases with the chapters, allowing a gradual immersion in the subjects:
- The activities of the first chapters do not require any knowledge specific to high school physics or mathematics. Instead, they revise some basic concepts from Secondary I including unit conversions, orders of magnitude and proportionality;
- Each chapter includes exercises and/or activities based on mechanics, waves, electricity, magnetism and thermodynamics of the general high-school physics curriculum;
- Some exercises in Chapters 7-9 require mathematical tools generally acquired in the final years of high school (such as derivatives, integrals or function analysis);
- A few exercises in the final chapters rely on basic knowledge of programming language (such as Python or Mathematica).
Moreover, several common themes can be followed through the chapters of the course, using an overarching subject that can be developed while increasing the level of difficulty. The order and selection of the activities concerning a specific theme are flexible and can be adapted to teaching constraints and the pupils’ level.
The material (in French only) is freely available on the SwissMAP website. The examples of answers for the exercises and activities are available for teachers only upon request.