General relativity in high school: a comparative analysis of the physics curriculum in Brazil, Colombia, Scotland and NorwayAbstract
In line with recent discoveries related to black holes and the detection of gravitational waves, researchers and educators have become interested in bringing content related to General Relativity (GR) to undergraduate and graduate courses and, although still timidly , into basic education. With interest limited to high school, this paper aims to analyze, from a comparative perspective, the Physics curriculum documents of two South American countries, Brazil and Colombia, and two European countries commonly ranked highly in educational rankings, Scotland and Norway, to evaluate the inclusion of GR at the basic education level. Qualitative documentary research of normative curriculum documents was carried out, highlighting the conceptual, epistemological, and pedagogical aspects described in each one of them. The results showed that there is a curricular proposal for teaching GR in Scotland and Norway, but without specifying what content to include or how to implement it at these levels. The Brazilian curriculum assumes the teaching of concepts associated with Astronomy without explicitly mentioning the approach of Einstein’s theory. As for Colombia, there is no structured provision for GR content in the Physics curriculum, which indicates a need for updates, necessarily accompanied by funding, infrastructure, and adequate teacher training to include Astronomy and GR concepts, and thus achieve greater contextualization in teaching and learning.
Keywords:
Basic Education; Comparative Studies; Curriculum; General Relativity; Physics Education
1. Introduction
Education is a fundamental right for all people and is known as a permanent, personal, cultural, and social process [1]. To achieve people’s education, each government, through its public policies, establishes a series of guidelines that direct and regulate educational services, including curricular programs. In Colombia, the law that establishes the general norms for regulating the Public Education Service defines the curriculum as:
a set of criteria, syllabi, methodologies, and processes that contribute to the comprehensive formation and the building of national, regional, and local cultural identity. It also includes the human, academic, and infrastructural resources to implement the policies and carry out the institutional educational project [2, p. 17].
Regarding the syllabi, they set the goals by level, grade and field, the methodology, the time distribution, and the evaluation and administration criteria necessary to provide an educational service. In the case of science education, each government issues a series of normative documents that answer questions like: Why teach science? And, what to teach?
This last question is oriented toward selecting content, including the structuring concepts of each scientific discipline of the natural sciences. Physics is a discipline based on theories that allow us to understand natural phenomena. Among these theories are those that emerged in the early twentieth century, such as quantum Physics and the theory of relativity.
The theory of relativity was formulated by the German physicist Albert Einstein in 1905, in his publication “On the Electrodynamics of Moving Bodies”. In his work, he showed that measurements in space and time, two inseparable entities, depend on motion [3]. A decade later, Einstein proposed a new theory of gravity, called the theory of General Relativity (GR), in which he stated that the curvature of space-time, produced by the presence of masses results in gravity [4].
Despite the revolutionary nature of the theory, the lack of experimental evidence and some counterintuitive results led to its rejection by some physicists of the time. Currently, there is enough empirical evidence supporting this theory, such as the detection of gravitational waves in 2015 [5] and the first image of a black hole obtained in 2019 [6]. Even some technological applications have been developed based on Einstein’s relativity, such as the Global Positioning System (GPS).
These results show that the theory of relativity provides new concepts and allows us to understand phenomena that Newtonian mechanics cannot explain, like the question of why gravity exists. In addition, its validity and importance in understanding certaind phenomena are evidence of the great value in teaching this theory in elementary or high school, and how it can help students understand some of the new technological advances.
Aside from the importance of this theory for understanding discoveries in the field of Astrophysics, its discussion in school makes it possible to address aspects associated with the nature of science (NOS), understood as encompassing epistemology and sociology of science [7,8,9], which is crucial for achieving strong scientific and technological literacy (ST) [10,11,12].
However, despite the well-known importance of studying relativity, this subject is rarely taught in elementary or middle school because its concepts are considered too difficult and advanced for students to understand [13]. In most countries, including Colombia and Brazil, this leads to a lack of curriculum designs that can help establish guidelines for introducing GR at these educational levels.
This is evident when analyzing documents like the Basic Competency Standards (EBC) in Colombia and the Common National Curriculum Base (BNCC) in Brazil, and it has pedagogical and didactic implications since teachers decide whether to teach it or not. In Colombia, particularly, the Institutional Educational Projects (PEI) of each Educational Institution are built based on these documents, and the teaching of Physics is limited to classical mechanics. Implications in science teacher training programs are to be expected, given the limited interest in bringing the concepts of relativity to secondary education. On this, [14, p. 3] states that
Teacher training programs curricula and syllabi poor in these topics have closed the doors to Modern Physics at school. It is because the poor preparation of teachers makes them feel neither competent nor confident to approach these topics, and since the school curriculum does not demand it either, they simply choose not to “make more noise about the subject” and end up omitting it.
Despite the absence of content about GR in the official documents related to the physical sciences curriculum, the conceptual and practical importance of this theory is recognized. Therefore, it is necessary to propose initiatives to allow its teaching and to bring the non-scientific population closer to these new concepts. Currently, there is a global interest in including relativity in high school as an introduction to modern Physics [13, 15]. Although research on its teaching is at an early stage [16], and didactic strategies for teaching Einstein’s theory are still scarce [17].
In several countries, such as Norway and Scotland, GR is part of the upper high school Physics curriculum, allowing students at these levels to have a first conceptual approach to this theory. Thus, the objective of this article is to analyze these documents, looking for points of convergence and divergence concerning the Physics curricula of Colombia and Brazil to propose reflections for the incorporation of conceptual, epistemological, sociological, and pedagogical-didactic elements for the teaching of GR in the two South American countries. Therefore, the following research questions are posed: In order to understand the state of affairs, what similarities and differences regarding conceptual or disciplinary, pedagogical-didactic, epistemological, or sociological aspects can be found in the normative curriculum documents for Physics teaching in Colombia, Brazil, Scotland, and Norway? Consequently, what would be the boundary and viability conditions for the full development of teaching General Relativity in the Brazilian and Colombian curricula?
It is important to emphasize that this paper offers a comparison between different curricular objectives of four countries (two from South America and two from Europe) regarding the teaching of GR in secondary education. Although it does not claim to be on a large scale of analysis, it is important to highlight that Brazil and Colombia, together, represent more than 60% of the population of the respective continent; in addition, they have similarities – among themselves and among the other countries in the region – in terms of geography, economy, climate, social and cultural aspects, which make them good elements for analysis. On the other hand, the comparison with two European countries recognized worldwide for the quality of their basic education represents an important reference. Thus, the sample of countries is sufficiently representative of the comparative overview to analyze in detail the situation of the curricula of basic schools in relation to GR education especially if we consider how binding and comprehensive these documents are intrinsically [18].
2. Method
The research developed is characterized: a) by its nature, basic and applied (it aims to build knowledge and apply it to the interpretation and solution of a problem); b) by its qualitative approach (i.e., it seeks to interpret and search for meanings regarding the phenomenon of interest); c) with exploratory objectives (to increase familiarity with the object and enable the construction of consistent hypotheses) and descriptive objectives (which seek to characterize the phenomenon
and highlight correlations between variables); and d) by its procedurally documentary nature, since it consists of the search, analysis and substantiation in documents that have not yet been systematically analyzed to answer the questions presented [19].
This methodological design seeks to materialize the possibilities of investigation of the research questions presented, especially by allowing an in-depth understanding of the object and the consequent construction of a category suggestive of the implementation of curricular changes with potential qualification of the teaching of GR in Brazil and Colombia.
For this research, priority was given to searching for information in the official curricular documents that determine the Physics content prescribed for secondary education in Brazil and Colombia, comparing them with the analogous documents of two European countries, Scotland and Norway, which include the teaching of GR at the same educational level. The normative and prescriptive nature of this type of documentary basis in the four countries analyzed ensures that the chosen sources are capable of providing structural elements for the analysis and development of the postulated research problems.
The contents of the chosen documents provide access to the categorical elements necessary and sufficient for the exploration and description of the object of investigation. Through them, it is possible to access the organization and systematization of nuclei of meaning (themes, concepts and meanings) and the conditions of research production [20, 21].
The research then is based on a model for document research [22, 23] consisting of the five phases described in Chart 1: preparatory, descriptive, interpretative, interpretative by thematic nucleus, and global theoretical construction.
These phases refer to some concepts, such as the thematic nuclei, which are the subtopics that delimit the contents; the analysis units, which are the individual texts such as books, articles, essays, and theses; and the factors, which are the relevant elements to distinguish in the analysis units. Each of these factors displays items called indicators [22].
3. Preparation of the Study
GR in Physics curricula is defined as a subject during this phase of the research. To achieve this, three thematic nuclei corresponding to the conceptual or disciplinary, pedagogical-didactic, epistemological, and sociological elements of the curriculum are proposed, and the factors and indicators are established based on these thematic nuclei, as shown in Chart 2.
For this research, the analysis units are the official normative documents of natural-physical sciences in the four countries (Brazil, Colombia, Scotland, and Norway), as described in Chart 3.
The education stage chosen for the analysis of each document is the last level of basic education (which, for Colombia and Brazil, is high school – also called secondary education), because Physics content is usually addressed in greater depth at these levels. In Colombia, secondary education consists of two grades, 10 and 11; in Brazil, a minimum of three years. For Norway, a document directed to upper secondary education was chosen because it proposes to address GR. This level lasts for three years and consists of general or vocational studies. General studies include the Basic Course (first year), Advanced Course I (second year), and Advanced Course II (third year). For Scotland, the teaching of GR is proposed for the higher level S6. This level is for those students who wish to remain in school and want to pursue further higher and advanced higher studies. Figure 1 shows the levels of education in the four countries chosen for the analysis.
4. Results by Thematic Nucleus
This section corresponds to the interpretative phase by thematic core of the document research model [22, 23]. Each thematic nucleus defined in the preparatory phase is taken separately. The conceptual, pedagogical-didactic, epistemological, and sociological elements of the curriculum, mentioned in each official document used for teaching Physics in school, are described.
4.1. Conceptual or disciplinary elements of the curriculum
The DBA presenting an outlook on the Natural Sciences teaching in Colombian educational institutions appeared in 2016. These are a set of structuring learnings for a particular grade and field, formed by three central elements: the statement, which refers to the structuring learning for the field; the learning evidence, which is the signs shown by the student indicating that he/she is achieving the learnings expressed in the statement; and the example, which reinforces the learning evidence. For Physics teaching in secondary education, in particular, the statements that will guide learning at this educational level can be found in the DBA, as seen in Chart 4, which shows that the contents are focused on mechanics, wave motion, electrostatics, and electrodynamics.
Likewise, the EBC in Colombia contains a series of concrete actions of thought and production, broken down into three columns. The left column refers to the way of approaching knowledge as a social or natural scientist, where concrete thinking and production actions are described. In the right column are the actions associated with the development of personal and social commitments, which include the responsibilities acquired by people when discoveries and advances in science are known and critically evaluated. In the middle column, we find the information related to the management of social or natural sciences knowledge, where actions based on specific knowledge appear. This column presents some subdivisions that seek to account for those actions related to the specific knowledge developed by these sciences. Natural sciences are divided into a living environment, the physical environment, and the relationship between science, technology, and society. For grades 10 and 11, the physical environment column is subdivided into chemical and physical processes. The latter includes the competencies associated with the subject of Physics.
Chart 5 describes in detail some thinking, and production actions found in the field of management of natural sciences knowledge related to the concept of gravity.
Concrete thinking and production actions related to conceptual and disciplinary aspects. Taken from [26].
If we look, however, at the BNCC for secondary education in Brazil, we can see that the curriculum for Natural Sciences and its Technologies is divided into thematic units called Matter and Energy, Life and Evolution, and Earth and Universe. Each of these units contains conceptual knowledge connected to a set of competencies and skills. Chart 6 shows the respective conceptual knowledge for secondary education in Brazil found in the Origin of Life unit, which includes a description of the contents associated with gravity and Astronomy.
It should be noted that, in the BNCC, the contents of Physics, Chemistry, and Biology are grouped in the same field of Natural Sciences and its Technologies. Table VI shows the inclusion of contents related to Astronomy, stellar evolution, and gravitation. However, it is important to point out that each state in Brazil has the autonomy to establish some aspects (such as: details, emphasis and articulations) of its own curricular guidelines. For example, in the state of Paraná, the 2024 Educational Itineraries Booklet establishes secondary education content related to robotics, energy, and Astronomy. Meanwhile, for the Federal District, the curriculum for high school establishes parameters for the teaching of Astronomy but does not include robotics.
In Norway, the contents described in the PPSG [24] are divided into three core elements: energy and energy transfer, forces and fields, matter, time and space. Chart 7 shows the competency objectives for Physics 2 related to the contents associated with gravity, including the GR.
In Scotland, the official AHPCS document [25] shows the structure of the Physics course in terms of units, conceptual knowledge, and the skills addressed in each one of them. In the Rotational Motion and Astrophysics unit, the knowledge associated with gravity and GR appears, as illustrated in Chart 8.
4.2. Pedagogical-didactic elements of thecurriculum
Several pedagogical aspects oriented to science education are described in the Colombian EBC. The document asks for consideration of the student’s previous knowledge, what it consists of, and how it is organized in their thinking so that the student can have an approach to scientific knowledge.
In the same document, but in the EBC section of How to Guide Science Education in Basic and Secondary Education, some guidelines are given for science teaching, to avoid returning to the old conceptions of science as a finished product and the teacher as a transmitter of knowledge. These guidelines focus on aspects such as the value of meaningful learning, a pedagogy that considers levels of complexity in learning, working from an interdisciplinary perspective, the importance of student participation in their learning process, collaborative work in the classroom, and an evaluation that does not only consider scientific knowledge but also interdisciplinarity, the ways of proceeding scientifically and the accepted personal and social commitments [26].
Chart 9 describes some actions that consider the pedagogical-didactic aspects.
Concrete thinking and production actions related to pedagogical-didactic aspects. Taken from [26].
In Brazil, the BNCC [27] seeks to promote the inquire learning approach in which the student is the protagonist of his/her learning process and allows him/her to approach the procedures and instruments of science. For example, to identify problems, formulate questions, use measuring instruments, carry out experimental activities, etc. But all this stems from open and contextualized problems with the aim of stimulating curiosity and creativity.
This document not only proposes reflections around discussions on the use and impact of technology in science and society, also proposes to address different contents, such as stellar evolution and gravitational interactions, from the use of digital devices and applications (software, simulation and virtual reality, among others).
An aspect to highlight is found in competency 3, described in the BNCC. It has to do with the ability that the student must acquire to evaluate information published in different media, as described below:
To interpret popular science texts that address Natural Science topics, available in different media, considering the presentation of data, both in text form and in equations, graphs and/or tables, the consistency of the arguments and the coherence of the conclusions, with the objective of building strategies to select reliable sources of information [27, p. 559].
This ability to analyze information of different natures and origins, especially the one disseminated in digital media, seems to be important for the student to learn how to select information, analyze it critically and evaluate the sociocultural impacts that scientific and technological knowledge can cause.
In the case of Norway, Chart 10 shows the competency objectives for Physics 2 that are related to pedagogical-didactic aspects. It is established there, and in other sections of the PPSG, that the use of programming languages, experiments, theories and models is important for understanding physical phenomena. In particular, it is stated that the teacher should encourage student participation, based on a more practical, exploratory, and collaborative work.
On the other hand, Scotland proposes a unit called investigating science, which emphasizes an experimental and investigative approach to developing knowledge and understanding of Physics concepts, as set out in Chart 11. Furthermore, Scotland’s AHPCS document points out that the Physics course provides opportunities for learning to be collaborative and independent within familiar and unfamiliar contexts.
As in Brazil, this Scottish curriculum describes that the student, after viewing the course, will be able to critically reflect on scientific publications and media reports.
4.3. Epistemological and sociological elements of the curriculum
In Colombia, a description of the conception of science that guided the construction of this document can be found in the EBC. There, it can be observed that science is considered as an enterprise undergoing permanent change, where its theories are constantly reviewed and reformulated. They quote Thomas Kuhn [28] to explain that the so-called “scientific truth” is simply a set of provisional paradigms, which can be reevaluated and replaced by other paradigms [26].
In relation to the people who do science and how they do it, the EBCs emphasize that scientific research is a social practice, in which scientists work in teams, share experiences, and submit their research to the scientific community; a different conception from the solitary scientist locked in his/her laboratory and disconnected from reality. Chart 12 shows some actions related to epistemological and sociological aspects in the areas of approaching knowledge as a social or natural scientist and to the development of personal and social commitments.
Concrete actions of thinking and production related to epistemological and sociological aspects. Taken from [26].
On the other hand, in Brazil’s official document, the BNCC proposes to work on content related to the history and philosophy of science. The social, historical, and cultural character of science and technology is highlighted, allowing science and technology to be understood as a human and social enterprise. The importance of historical contextualization is also valued, not only to know the names of scientists and important dates, but also to emphasize that scientific knowledge is a collective construction influenced by political, economic, technological, environmental, and social conditions of each place, time and culture. In this contextualization, the BNCC proposes to show the explanatory limits of science by comparing different scientific explanations proposed in different times and cultures.
The Norwegian Physics curriculum document highlights that Physics allows an understanding of how technological development affects the individual and society, i.e., sociological issues external to science and technology are discussed in this document [10]. Furthermore, it emphasizes that Physics should contribute to developing critical thinking and to understanding (and developing) aspects of science such as tentativeness, its empirical nature, creativity, and its social character, giving importance to the value of collaboration and exchange of ideas in scientific work, as described in Chart 13.
Finally, in Scotland, the importance of fostering critical thinking and understanding the tentativeness of Physics is emphasized. To this end, the importance of having an open mind and recognizing alternative points of view is promoted. The document also highlights that the course provides opportunities for students to understand the impact of Physics in their context and to critically reflect on scientific publications and media reports.
5. Analysis of Results
This section corresponds to the interpretative phase by a thematic core of the document research model [22]. The information described for each of the thematic cores is analyzed.
In the case of the conceptual and/or disciplinary elements of the curriculum, the incorporation of contents associated with Astronomy and stellar Physics at higher levels of education is observed in the curricula of Brazil and Scotland. This is noteworthy because some authors have already found that Astronomy and Einstein’s theory are contents that interest and improve students’ attitudes towards Physics [29,30,31,32].
This is important, especially in these times of crisis that science teaching and learning are going through, which is evidenced by the decrease in student performance in science in international tests [33] and in the disinterest in science-related courses or careers [34].
However, it is important to highlight that in Scotland, these gravitational and astronomical studies are complemented by GR content. Even in the curricula of lower levels of schooling in this European country (S3–S4) there is an interest in including concepts associated with GR, such as gravitational waves [35].
In Brazil, GR content is not explicitly described in its curricula. However, another Brazilian curriculum document, called “Complementary Educational Guidelines for National Curricular Parameters” – PCN+ EM [36, p. 79] can be found in thematic 6, units 2 and 3, the following guidelines:
To know the theories and models proposed for the origin, evolution and constitution of the universe, in addition to the current ways of investigating it and the limits of their results in order to broaden their vision of the world.
To understand aspects of the evolution of scientific models to explain the constitution of the universe (matter, radiation and interactions) through time, identifying specificities of the current model.
As can be seen, these orientations open possibilities for including GR in secondary education, as one of the current theories for understanding the universe and for explaining how scientific theories evolve. For example, one can find Brazilian works, such as [30], who propose a didactic intervention for the teaching of Astronomy, but based on GR. This interest in addressing concepts of GR at the secondary school level in Brazil, even from the teaching of Astronomy, can also be seen in some master’s degree works [37, 38].
Like Scotland, Norway includes GR in its curricular guidelines, but what will be taught from this theory? The documents of both countries describe, without much clarity, the incorporation of GR at higher levels. Furthermore, these documents do not clarify whether the approach to this theory is conceptual, mathematical, or both. In this regard, there is a debate about whether the inclusion of GR in secondary education is best approached conceptually or including its mathematical developments [39, 40]. In this way, it is necessary to assess whether or not curricular insertion is predominantly positive (by giving relative freedom to the education system and teachers) or negative (by not establishing the obligation and the way of implementation, causing uncertainties or asymmetries).
Now, with reference to the pedagogical-didactic elements of the curriculum, one can find in both the Brazilian and Norwegian curricula, an interest in including programming language, technological and digital knowledge in the teaching of science. This is because science and technology maintain an important link. In this regard [41], they state that:
In today’s society, science and technology are closely linked. New ideas and applications of science influence technological innovations and productions, and technology provides science with new research tools and procedures that advance it (p. 13).
In this regard, [42] argues that GR offers the opportunity to reflect on the role of technology in science, which is evident today with the discovery of gravitational waves and the capture of the first image of a black hole, since sophisticated laboratories and advanced programming algorithms were used for this purpose.
Also described in the curricula of Brazil, Colombia and Scotland is the interest in developing in students the ability to analyze information published in different media. For the case of research related to GR, the analysis of scientific news published by the media seems appropriate, since it allows, among other things, to relate what students learn at school and current scientific advances. For example, some authors have already analyzed the benefits of including news published in digital newspapers, not only to achieve this contextualization of knowledge, but also to address aspects of the NOS from contents associated with the RG [42, 43].
Finally, in the epistemological and sociological elements of the curriculum, it was possible to identify that the four curricular documents emphasize the importance of specifying the social character and the changing nature of science. These aspects are included in the approach that the literature calls “consensus view” of NOS and have to do with the idea that science is embedded in social and cultural contexts and that scientific knowledge is tentative [44].
There are other approaches that also consider the technological impact on science and society. That is why, for some authors, the acronym NOS expands its meaning to be called Nature of Science and Technology (NOS&T) [10]. Precisely, in Brazil, Norway, and Colombia there is evidence of an interest in keeping in mind the technological tools in science learning, and that students can evaluate their social and ethical implications.
In addition, the documents show an interest in fostering critical thinking in students, which is one of the objectives of science education and that learning aspects of NOS can contribute to this purpose, since this thinking is necessary for students to be able to evaluate the impact of science on society, technology, and other disciplines.
6. Final Considerations
This phase corresponds to the global theoretical construction [22] and seeks to answer the research question.
The present study aimed to analyze the Physics curriculum documents of four countries, Colombia, Brazil, Scotland, and Norway, looking for points of convergence and divergence among them, with the purpose of, from a comparative analysis, establishing guidelines for the inclusion of GR in the official curricular orientations of the two South American countries.
An analysis of the different curricular documents for the teaching of Physics in the four countries shows that there are similarities between them, but also some singular differences.
Regarding the similarities found in the conceptual and disciplinary elements, it can be seen that all the curricular documents analyzed propose the teaching of classical gravity theory, regardless of whether GR is addressed or not. Although Einstein’s theory breaks with some of the paradigms of Newtonian Physics [45], classical gravity allows predicting the behavior of many things, such as the fall of an apple, as well as calculating the orbit that a satellite should reach. Therefore, from a practical point of view, it is still a very useful and necessary theory to understand phenomena that occur in low gravitational fields, such as those produced by the earth or the moon.
Regarding the epistemological elements, it is evident in each of the documents an interest in taking into account aspects of NOS for its teaching at the educational levels, such as the tentativeness of science and the social character of science. It is necessary to do it since some authors have pointed out that including aspects of NOS in school contributes for example to the development of argumentative skills [46] and allows the student to better understand the processes by which scientific knowledge is produced [47, 48]. However, today, little of this is done, and it is evident that students still have an insufficient and inaccurate understanding of NOS, which remains a major challenge for science teachers [49, 50].
Although some aspects of NOS are present in the analyzed documents, they have little impact on students’ learning. This possibly has to do with the fact that the teacher does not consciously address these aspects in his or her planning. Because of this, several authors recommend the use of an explicit reflective approach to teaching NOS because it is an effective method to improve students’ understanding [51, 52]. For this, teachers should prepare their lessons explicitly, clearly and intentionally to address these principles, either, for example, from historical narratives [53] or socio-scientific issues [52], among others.
In the case of the pedagogical-didactic contents, the curricular documents of the four countries also show an interest in proposing science teaching that fosters collaborative and participatory work by students. That means, the student is encouraged to become the protagonist of his/her own learning. To attain this end, the analyzed curricula specify that Physics teaching should be oriented with a more investigative and practical approach.
Now, if we analyze the differences found in the curricular documents, in terms of pedagogical-didactic elements, Brazil describes the importance of including technology in the teaching of Physics, with greater insistence than the other three countries. This is interesting because today we see a much closer dependence between science and technology [54], taking into account that research nowadays requires much more sophisticated instruments to test theories, either in the micro world of phenomena associated with quantum mechanics or in distant places of the universe where the consequences of GR are evidenced.
In addition, the use of technology and programming languages in these educational levels of elementary and middle school is also appropriate to complement the learning of students and minimize the difficulties that can bring, for example, the approach of the GR due to its mathematical structure and abstract concepts, making it more visual and interactive. For the case of teaching GR, teachers could explain the two scientific collaborations that are revolutionizing contemporary science and have to do with the Laser Interferometric Gravitational-Wave Observatory (LIGO) and the Event Horizon Telescope (EHT) project to give context to students on the way science is done today, not only for the use of technological tools for scientific findings, but also to show the importance of collaborative work and international cooperation for the development of new knowledge.
Another important aspect of these pedagogical-didactic elements has to do with a teaching that takes into account the formulation of questions. In the Colombian EBC, it is proposed that one of the thinking actions is that students formulate specific questions about applications of scientific theories. This exercise of formulating questions can also serve to bring to the classroom some of the guidelines described in this curriculum document, since it allows students to participate in their learning and to make it meaningful and critical [55].
In relation to the conceptual and/or disciplinary element, it is evident in both Brazil and Scotland that Astronomy is part of the curricular orientations in middle and upper secondary education, emphasizing stellar Physics and gravitation, which is not the case in Colombia and Norway. These Astronomy topics open the possibility of including concepts, principles, and applications of GR at these educational levels, since understanding the universe that the James Webb Space Telescope and the EHT are showing today requires an understanding of Einstein’s theory, at least at a basic level. For example, in Brazil, although the BNCC does not explicitly incorporate the contents of the GR, it allows teachers to reflect on its contents, principles, and applications, such as black holes and gravitational waves [30].
On the other hand, if the GR content is analyzed in both the Scottish and Norwegian curriculum documents, it is unclear what will be taught. However, two aspects can be raised that may justify this choice of content for the Colombian and Brazilian curricula.
First, identify the key concepts and applications of the theory to carry out both qualitative and quantitative analyses. One of the fundamental concepts is that of curved space-time, since most of the phenomena associated with GR are a consequence of assuming a curved 4-dimensional universe [56]. Regarding the applications of GR [56, 57], it is recommended to begin courses with the most important concepts of GR for several reasons, including time constraints, so that regardless of where the course ends, students have the opportunity to understand basic physical phenomena. It is also argued that starting with applications is easier for students. Furthermore, presenting the content in this order, says the author, allows enough time to propose courses with different emphasis, for example, on black holes, gravitational waves, cosmology, or experimental tests.
Secondly, for this choice of content, the student’s context is important. For this, it is suggested to make use of current journalistic news about the study of gravitational waves and images of black holes, since they would allow epistemological and sociological reflections on science and evaluate the role of technology in science.
For the Colombian case, it is evident that the curricular documents are focused on the teaching of classical Physics. Although these are also contents that can be contextualized and are important for various professional careers, they do not respond to the demands that current science requires. Furthermore, considering the low interest that students are showing in science-related careers, it is necessary to update the Physics curriculum and the analysis performed above allows us to conclude that introducing content associated with Astronomy favors student interest and motivates them to possibly pursue careers in STEM [29]. Additionally, if this Astronomy learning is complemented with GR content, it would allow the student in some way to understand some of the current technological developments that are characterized by providing more reliable and accurate instruments [54].
Although in Scotland and Norway, the teaching of concepts associated with GR is addressed in their curricula, it is also true that it is done for higher levels that are not offered in Brazil and Colombia. On the contrary, it is for students who wish to continue their university studies or who are focused on a more scientific education. Therefore, it is necessary to continue to reflect on the possibilities of including GR in the basic levels of compulsory education, but this is something commit with which not only governmental entities, but also faculties of education, teachers and researchers in science didactics should commit themselves.
Acknowledgments
National Council for Scientific and Technological Development of Brazil (CNPq).
Data Availability
The entire data set supporting the results of this study was published in the article itself.
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Edited by
-
Editor-Chefe:
Marcello Ferreira https://orcid.org/0000-0003-4945-3169.
Publication Dates
-
Publication in this collection
21 July 2025 -
Date of issue
2025
History
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Received
27 May 2025 -
Accepted
18 June 2025
