Probing students’ understanding of Einsteinian physics concepts: a study in primary and secondary Greek schools

Internationally, the need to modernize school curricula and introduce the concepts of modern physics into schools has been accepted in recent years. Research on introducing Einsteinian physics (EP) to the most effective school age is lagging. The present study aims to evaluate a short intervention in Einstein’s physics and determine the school level at which the concepts of EP are optimally comprehended. Therefore, a teaching intervention was carried out to 325 Greek students; 83 students in 6th grade (11–12 years old), 116 students in 9th grade (14–15 years old), and 126 students in 11th grade (16–17 years old). All students completed pre—and post—conceptual and attitudinal questionnaires. According to data analysis, the conceptual performance of students concerning EP improved significantly. In concrete, students of 11th grade have exceeded the conceptual scores, compared with general changes identified to the majority of school grades. Moreover, the study participants had a positive attitude towards science, mostly towards Einstein’s physics, before the teaching intervention, which remained at a high level after the intervention. The study generates useful results for introducing modern physics in primary and secondary education.


Introduction
The 20th century was a landmark in the history of physics, as quite a few of the most important theories were presented throughout it.Albert Einstein played a key role in the conceptual reconstruction of classical physics.Einsteinian physics (EP hereafter) is one of the foundations of modern physics, and it includes The theory of relativity and some theories about quantum physics (Kaur et al 2017a, Choudhary et al 2020).
Despite the new scientific theories, which have been proven almost a century ago, modern physics is considered a field for which less research has been conducted regarding its inclusion in science education (Levrini 2014, Kersting andSteier 2018).Adapting EP to an educational model capable of being integrated into modern curricula is challenging (Mannila et al 2002, Foppoli et al 2019).
Systematic research is necessary to conclude the appropriate ages for learning EP (Alstein et al 2020, Choudhary et al 2020, Kaur et al 2020).Learning and comparing classical physics with modern physics increases motivation, encourages students' interest, and improves their understanding of physics.This approach lies at the core of the present research, including the EP and results indicated after teaching in Greek schools.

EP concepts
Einstein theorized that space and time unite, creating a four-dimensional manifold called spacetime.In 1916 he published a paper about general relativity theory proposing a new theory of gravity that applies to accelerated systems (Cherepashchuk and Chernin 2008, Kersting and Steier 2018, Kersting et al 2020).According to Einstein, gravity has a geometric approximation since it is the curvature of the four-dimensional manifold of spacetime due to the presence of masses in the universe.The existence of black holes, the Big Bang theory, the expansion of the universe et al can be explained by EP (Cherepashchuk andChernin 2008, Postiglione andAngelis 2021).
Additionally, Einstein has made a scientific breakthrough by claiming that light does not only travel as waves, as Hertz had already confirmed, but also consists of a finite number of 'packets' of energy, well-known as photons (Stuewer 2005, Klassen 2011, Hentschel 2018, Rablau et al 2019, Spagnolo et al 2020, Passon 2022).
Einstein's revolutionary idea about the particle nature of light interpreted an experiment for which the scientific community has disputed for decades, the so-called photoelectric effect.According to this experiment, electrons ejected from the surface of a metal when ultraviolet light shined on it (Rablau et al 2019).The theoretical explanation of this experiment came along with Einstein's introduction of the dual nature of light, considering that light has both wave and particle nature (Stuewer 2005).Explaining the nature of light constituted a solid foundation for the development of Quantum Physics.

Educational aspect
Physics laws and mathematics are presented as self-evident truths in schools.Indeed, it is quite challenging to understand new ideas, i.e., the curvature of space-time or the dual nature of light (Bandyopadhyay and Kumar 2010, Pablico 2010, Levrini 2014, Kersting and Steier 2018, Choudhary et al 2020).Regarding the nature of light, children learn from an early age that the concepts of wave and particle are diametrically opposite.Therefore, teaching becomes difficult because it comes to overturn perceptions that students formed through the same educational system, which later attempts to undo them (Bandyopadhyay and Kumar 2010, Pablico 2010, Pitts et al 2014, Kaur et al 2020).
One of the aims of science educators is to determine the way as well as the best student age in which modern physics can be understood (Alstein et al., 2020, Kaur et al 2020, Postiglione and Angelis 2021).For example, Kavanagh and Sneider (2006) mentioned the National Science Education Standards and Benchmarks for Science Literacy guidelines that gravitational phenomena should not be taught to primary school students because they are too abstract.She and Liao's (2010) research provides proof of the significance of students' capacity for scientific reasoning when learning about abstract scientific ideas.In case students' reason is well justified, they could learn about abstract scientific concepts at a younger age.In later research by Foppoli et al (2019), the authors reported that many of the teachers involved in their research considered that modern physics could be taught from year 5 (8-9 years old) and on.
Generally speaking, most studies focus on introducing EP to 16-18 years old students or undergraduate students.There are only four studies available, according to the current information, that investigates students' understanding of EP in primary and middle education (9-15 years old) (Haddad and Pella 1972, Baldy 2007, Pitts et al 2014, Kaur et al 2017c).Within the context of constructivist epistemology, the pedagogical tool that teachers often use is the activity-based learning.Choudhary et al (2020) and Kaur et al (2017a) emphasized the importance of using models and analogies in teaching EP.

Models and analogies in teaching EP
Models and analogies activate the participation of students and improve their cognitive level since the visualization of an image tends to be easily retained in mind (Passmore et al 2014, Kersting and Steier 2018, Dua et al 2020).Furthermore, they form a short link between everyday life and the scientific world, thus providing a way of understanding the scientific processes and goals (Gilbert 1999, Passmore et al 2014).
Models that represent a physical system aiming to explain the universe are an idealization of reality because they include certain parameters and reject others.Therefore, each model must be evaluated to identify its limitations (Gilbert 1999).Moreover, analogies can lead to misapprehension by students as they involve limitations.A typical example is the rubber sheet analogue used to teach Einstein's gravity.In this analogue, constraints, such as frictions from the material, may confuse students (Baldy 2007, Choudhary et al 2020).Therefore, it is important to emphasize the differences between the analogous system and the real world (Kaur et al 2017a).

Research objectives
The purposes of the current research are as follows: (a) Assess a teaching intervention concerning the teaching of EP concepts, (b) Compare students' level of understanding between primary education (grade 6), lower secondary education (grade 9), and upper secondary education (grade 11), (c) Investigate whether the intervention could change students' attitudes towards science.
The research questions (RQ) are the following: (1) Does EP intervention change students' conceptual ideas about gravity and light?(2) Is there any difference in students understanding of EP in terms of their school level?(3) At which educational level should EP be introduced to be more intelligible?(4) Does the EP intervention impact students' attitudinal change?

The sample
The research was conducted among primary and secondary students in Ioannina, Greece.The sample consisted of 325 students (178 boys and 147 girls) coming from 8 different school units.The participating students were as follows; 83 students from the primary education of 6th grade (11-12 years old), 126 students were from the lower secondary education at 9th grade (14-15 years old), and 116 students were from the upper secondary education at 11th grade (16-17 years old).The choice of targeting 6th-grade students was based on the fact that this is the last grade before transitioning from primary to lower secondary education.By this age, Greek students have been introduced to various physics concepts and should have acquired a general knowledge of science.Additionally, the selection of 9th-grade students was made because this grade is the final compulsory year before attending upper secondary education.Concerning the 11th-grade group, we considered that students in the 12th grade in Greece have already chosen an orientation group (either humanitarian or scientific), which means they attend only subject-related lessons.Therefore, selecting students from the immediately prior grade was necessary as it might be their last opportunity to learn about EP.Most students had no access to the teaching of modern physics, observing that any information available, pre-teaching, was likely grasped by their social environment.

The study
The study was based on a face-to-face teaching intervention during which students were taught about two basic EP concepts: gravitational gravity and the dual nature of light.The EP concepts were found in the study of Choundary et al (2020:308), considered necessary to teach only some of them due to the limited time available.The chosen concepts were related to the Greek curriculum.Each school unit attended 3 lessons of 1 h duration each.The teaching process included PowerPoint presentations, videos, questionnaires, and activities.The learning strategy that was implemented was activity-based learning (Kavanagh and Sneider 2006).The program was delivered by a science educator-physicist who is the first author of this paper.Before the intervention, the instructor underwent training in teaching EP for a semester under the guidance of professors who specialize in this subject.For this study, two pairs of questionnaires have been used; students filled them in before (pre-test) and after the teaching intervention (post-test).Post-test questionnaires were precisely the same as pretest questionnaires.All students responded to all parts included; no blank responses needed to be categorized.

Conceptual questionnaire
The conceptual questionnaire consisted of 15 questions-5 open-ended and 10 closed-ended questions (see appendix).This mixed method for data collection is considered optimal for drawing safer conclusions (Clark and Creswell 2008, Mertens 2014).The questionnaire was designed to explore various conceptual issues related to gravity, spacetime, light, and the photoelectric effect.The composition of the above-mentioned questionnaire was derived from similar questionnaires that have been implemented and identified in the international literature (Pablico 2010, Özcan 2015, Taslidere 2016, Choudhary et al 2020, Postiglione and Angelis 2021).In openended questions, the kids were encouraged to explain their answers.Students' answers to this questionnaire were judged as correct or incorrect depending on whether they agreed with EP.Also, to consider an answer as correct in open-ended questions, this had to include a correct justification.In this regard, the answers that described gravity as the curvature of spacetime due to any mass and light as a beam of photons with both a particle and a wave nature were perceived as correct (Foppoli et al 2019).

Attitudinal questionnaire
The attitudinal questionnaire that we used in this research was found in the study of Choudhary et al (2020).The questions were 11 on the 5point Likert scale with the following options: 1 = strongly disagree; 2 = disagree; 3 = neutraluncertain; 4 = agree; 5 = strongly agree.Some of the questions needed to be reversed.The only modification made to the original questionnaire was splitting the first question into two sub-questions for gravity and light to be studied separately.

Questionnaires validity
The questions were validated based on the following points: (a) The conceptual questionnaire concluded only content-related items.A pilot survey has been conducted to detect the difficulties encountered by participants before using the questionnaire of the current study.(b) The attitudinal questions were selected from the literature (Choudhary et al 2020).(c) A panel of 3 science educators and physicists validated the questions to make it comprehensible at the right level.

About the teaching intervention
The 3 lessons program we applied was based on using models and analogies.Overall, lessons had been structured according to the following format (Kaur et al 2020): ( Quantum physics and the concept of light were only explored superficially in this program.The main aim for students was to understand 'what light is' through their acquaintance with the photoelectric effect (Foppoli et al 2019).We used  the photon analogue by which Nerf toy weapons shoot small projectiles (Kaur et al 2017b).In the context of this research, the materials used for this experiment are Nerf guns, small-diameter bullets, identical ping pong balls, and bowls of various depths (figure 2).It should be recalled that according to the photoelectric effect, electrons are ejected from the surface of a metal when light falls on it.The ping pong balls represent electrons on the metal surface, which are thought to be the bowls.The activity occurs when students shoot the ping pong balls with Nerf, observing if the latter will be fired from the bowls.

Data analysis procedure
The data were processed by SPSS and the Excel software.For each student individually, we calculated the score that he achieved in the conceptual questionnaire as long as his score in the attitudinal questionnaire.Regarding conceptual score, correct answers in the conceptual questionnaire scored with 1 point and incorrect answers scored with 0 points.The existence or not of differences in the median of the score between pre-and postmeasurement was tested.To analyse attitudinal pre-/post-questionnaires, data combined for positive responses according to the Likert scale given above.In general, the Kolmogorov-Smirnov test, the Wilcoxon signed ranks test and the Kruskal-Wallis test, were used for comparing the performance and attitudes of students in the three different school levels.The statistical significance value was of p = .05.In each case, the values of every test obtained to be less than .05.

Reliability
For the two questionnaires, we used internal consistency as a measure of reliability.Therefore, we used Cronbach's alpha.The values of Cronbach's alpha are given in table 1 below.

Results
In order to answer RQ1, we compared the conceptual scores (table 2) and to answer RQ2, we analysed the percentage mean scores for every school level, before and after the intervention.RQ3 answered after the previous results.Similarly, for RQ4, attitudinal scores have compared before and after the intervention, as well as based on students' school level.

Analysis of conceptual questionnaire
The percentage of students who provided an Einsteinian explanation to questions before and after the course was analysed.Table 2 shows students' results of understanding EP concepts.As shown, results from pre-tests were generally low, but after the course they significantly increased.After the teaching, most students provided an Einsteinian explanation for open ended question 1-5.For example, before the intervention, the majority of students in 6th grade (73.5%) and in 9th grade (62.7%) were not able to describe gravity based on any scientific theory, while in 11th grade, the percentage is almost equal (50.0%) between Newtonian mechanics and not being aware of the concept of gravity.However, results following the intervention improved, as students in 6th grade answered anew based on Newton's theory on a percentage of 13.3%.The equivalent percentage reached 37.3% and 36.2% for students in 9th and 11th grade, respectively.
Table 3 summarises the overall mean score about students' conceptual performance for the three school levels based upon pre-test and posttest results.To observe whether the intervention improved conceptual scores, we used the non-parametric Wilcoxon signed rank test.The test indicated that in primary education, posttest ranks were statistically significantly higher than pre-test ranks, Z = −7.817,p = .000.Moreover, the results indicate a statistically significant improvement in student learning for lower secondary education, Z = −9.451,p = .000,and upper secondary education, Z = −9.281,p = .000,respectively.
It appears quite important to consider the validity of comparing the mean scores between the three school levels.To compare so, we used Kruskal-Wallis test.Pre intervention, the test indicated that there was statistically significant difference between students' performance, χ 2 = 6.012, p = .049.Specifically, the statistically significant difference was only between the mean performance of primary education students and upper secondary education students.After the intervention, the Kruskal-Wallis test indicated that there is also a statistically significant difference in the mean scores between school levels, χ 2 = 15 294, p = .000.In particular, the performances that differ from each other are of upper secondary education students with both those of lower secondary education and primary education students.The performances of primary and lower secondary students, respectively, do not actually show a statistically significant difference (p > .05).

Analysis of attitudinal questionnaire
The calculation of students mean score for statement in attitudinal questionnaire is of outmost importance.Table 4 shows the calculated results before and after the intervention.The evaluation of the results is based on the literature (Sözen and Güven 2019) in which the mean score between 1-1.80 refers to 'strongly disagree', mean score between 1.81-2.60refers to 'disagree', the mean score between 2.61-3.40refers to 'neutral', the mean score between 3.41-4.20refers to 'agree' and the mean score between 4.21-5.00refers to 'strongly agree'.
To observe if the intervention improved attitudinal scores (table 5), the non-parametric Wilcoxon signed rank test applied.The test indicated that in primary education, post-test ranks were statistically significantly higher than pre-test ranks, Z = −2.790,p = .025.In lower secondary a Scores of S6, S8, S9, S10, S11 (which were designed for negative response in the Likert scale) were inverted for analysis.education the results do not indicate a statistically significant improvement, Z = −1.585,p = .056,and in upper secondary education, Z = −2.776,p = .003,there was an improvement.Also, the Kruskal-Wallis test conducted for determining if there was any difference between attitudinal scores in terms of students school level.Before the intervention the test indicated no statistically significant difference, χ 2 = 5.196, p = .074.After the intervention, the test indicated that there was statistically significant difference, χ 2 = 10.371,p = .006,specifically only between primary and lower secondary students' attitudes towards science.

Discussion
The majority of students who participated in this study appear to have had from low to zero levels of knowledge of modern physics prior to the teaching intervention.This fact complies with the results of the study of Kaur et al (2017c).As illustrated above, most of the students have shown inability to describe the concepts of gravity and light in a scientific way or turned to classical physics and Newtonian mechanics.The results of the answers to the conceptual questionnaire before the intervention are considered to be partially expected because students are not taught modern physics.
On the other hand, after teaching, it was found that students understood the theories of Modern Physics to a satisfactory degree, as was found in similar research by Baldy (2007), Kaur et al (2017c), Kaur et al (2020) and Pitts et al (2014).More precisely, the comparison of the students' performance before and after the teaching intervention in each school level, resulted in a statistically significant difference, with the exception of question 9 from conceptual questionnaire, for primary students.The aforementioned question indicated low improvement because kids believe that there is absolutely no gravity in space; a belief that cannot be easily changed.Overall, the teaching intervention resulted in conceptual change and is perceived as successful.
Additionally, a comparison of the students' performance between the school levels implemented.This showed that after the teaching intervention, conceptual scores in primary and lower secondary students did not differ significantly.In contrast, scores between primary-upper secondary students and primary-lower secondary students had a statistically significant difference, with upper secondary students scoring higher.It is thus suggested that the in-depth teaching of Einstein's physics concepts would be more beneficial to apply to upper secondary students.However, the results in the scores of younger students indicated that some basic ideas might be introduced at an earlier stage in order for children to gain an insight into modern physics.At the same time, the foundation of a modern conceptual background enables students to understand easier modern concepts, in the future.The latter view is also in line with Choudhary et al (2020).
Teaching abstract concepts such as EP in 6th grade might appear challenging, but as it turns out, students at this age possess a great curiosity about the world and can easily absorb new information.Furthermore, it may be difficult for young children to understand the concept of gravity as a force, making the choice of the models and analogies mentioned above, the ideal way to introduce modern physics to this target group.On the other hand, 11th grade students have already a specific point of view about physics concepts and as a result the introduction of EP is treated with distrust.Nevertheless, it is worth noting that upper secondary students are generally more capable of understanding and applying new concepts more quickly than primary students.
As far as students' attitudes towards scientific issues are concerned, in this survey, the findings indicated that the majority had a positive attitude, pre intervention, as mentioned in Choudhary et al (2020).In each school level, the average score had classified in the category 'agree'.After the intervention, a statistically significant improvement in the attitudes of primary and upper secondary students established.Positive attitudes recorded as well in the study of Pitts et al (2014) for primary students.The scores recorded before the intervention taken as quite high, and the reason is because children seem to recognize by themselves the value of EP (Kaur et al 2020).
A drop in attitudes was noticed in question 5 and 8, as primary students attitudes appear to be reduced after the intervention.This might be explained by the fact that Greek students in primary education are not very familiar with science experiments.Consequently, introducing modern physics to them using a new experimental setup compelled them to rely on educator's guidance during this process.Furthermore, in question 9, there is a noticeable decline in students' attitudes of all targeting ages likely due to the fact that concepts as the curvature of spacetime or the photoelectric effect are not commonly encountered in their daily experiences.

Conclusion
The current paper presents outcomes of the questionnaires which provided to 325 students in 6th, 9th and 11th grade, in schools of Ioannina, Greece.The main purpose of this study is to investigate the optimum educational stage for introducing EP concepts and induce a positive attitudinal change.To achieve this goal, an attempt has been made to adapt the new theories of gravity and light into pedagogical tools.
Our results indicate that modern concepts can be understood by students at all school levels.Each class that attended the program demonstrated a considerable improvement in conceptual comprehension of EP.The greatest improvement occurred in the 11th grade students, with the average class scores increasing from 22.5% to 69.8%.In addition, teaching EP improved most students' attitudes towards learning this subject.To conclude, the research proposes that introducing modern physics into the school curriculum is deemed necessary, as far as data of the concrete grades are concerned; and in line with other researchers teaching modern physics (Kersting and Steier 2018, Choudhary et al 2020, Dua et al 2020, Kaur et al 2020, Adams et al 2021).In general, we expect that students who were exposed to Einsteinian science at a young age, will accept modern scientific ideas as common sense.Most importantly, by visualizing things, all students' attitudes towards science should be improved if taught using the above-mentioned methods.Furthermore, our study adds to a growing body of research that aims to introduce modern physics in school curriculum, broadly.
In the near future, shall be planned to continue testing the current proposal, analysing data based on the gender of students and researching students' inherent interest about physics.This would also have the added advantages of a better understanding as well as quantify the effect of introducing the EP in the Greek educational system.

Limitations-further research
The methodology applied in this research had some inherent limitations, fully listed hereby in order to be addressed by the readers with a view to the possible skepticism of outcomes.The student sample selected, based on the possibility of collaboration and not on the exact randomness that distinguishes the research process of sampling.The fact that all students attended schools located in Ioannina, Greece, remains an issue of concern regarding the effectiveness, or even the comparison of the final results.Moreover, the models and analogies that used contained some assumptions that might have caused confusion in students' understanding of the concepts (Kaur et al 2017a).Last but not least, the research has found no evidence that contradicts the findings presented above, although there may be papers in the international bibliography that deriving in contradiction with the above-mentioned results which remains to be seen.
It is suggested that the upcoming studies should try to eliminate at least some of the above restrictions It would be beneficial if the teaching intervention was also applied to other school grades for more complete comparisons between school levels.The teaching time is proposed to be increased, in order for students to have time to assimilate knowledge and evaluate modern physics.Also, it would be challenging to introduce to students, mathematical terms and equations of modern physics.
1) The first 15 min of each lesson was dedicated to presenting material for the lesson, (2) The next 20 min devoted to group activity, (3) The last 10 min allocated for class discussion.The model of the space-time stimulator was applied to study the concepts of gravity and curved space-time (Kaur et al 2017a, Kersting and Steier 2018, Foppoli et al 2019).Model's experimental layout (figure 1) usually consists of an elastic fabric-membrane, which represents the spacetime, and balls of various masses, to represent the movements of objects in it (Kaur et al 2017a, Kersting and Steier 2018, Foppoli et al 2019, Dua et al 2020, Kersting et al 2020).In the centre of the sheet, a body with a large mass is placed to cause distortion in the membrane and affect the movements of the balls on it (Foppoli et al 2019, Kersting 2019).In this way, there is no need to introduce the concept of force acting remotely and usually confuses students (Kersting and Steier 2018).

Figure 1 .
Figure 1.The structure of the spacetime simulator we built.

Figure 2 .
Figure 2. The photon analogue used by a student.
at picture 2. If someone falls from an aeroplane, is there any gravity?a) Yes, about the same as on the ground, b) Yes, but much less than on the ground, c) Yes, but much more than on the ground, d) No, there is no gravity, e) I do not know Picture 2. Falling from an aeroplane 8) Look at picture 3.If someone is standing on the moon, is there any gravity?a) Yes, but much more than on earth, b) Yes, about the same as on earth, c) Yes, but much less than on earth, d) No, there is no gravity, e) I do not know Picture 3. Standing on the moon 9) Look at picture 4. The satellite is going around the earth.Is there any gravity up where the spaceman is? a) Yes b) No c) I do not know Picture 4. Spaceman near a satellite 10) Look at picture 5. Is there any gravity when the person is swimming under water?a) Yes b) No c) Depends on whether the person is going up or down d) I do not know Picture 5. Swimming underwater 11) What is the spacetime?a) It is the union of space and time, who together form a 4-dimensional entity, b) It is the union of space and time, who together form a 2-dimensional entity, c) It is the fourth dimension, d) It is the velocity, e) I do not know 12) What do you think can deform the spacetime?a) Any mass, b) Only a very big mass, c) A force that points downward, d) A force that points upward, e) None of the previous answers, f) I do not know 13) Which of the following expression explains in the best way the behaviour of light in one experiment?a) Light behaves both like particle and wave at the same time b) Light behaves only like a particle c) Light behaves either like wave or particle d) Light behaves only like wave e) Light behaves neither like wave nor particle 14) Look at picture 6.How would you describe the photoelectric effect?a) The ejection of electrons from the photosensitive metal surface by the battery b) The production of photoelectric current as a result of reflection of light from one plate to another c) The ejection of electrons from the photosensitive metal surface by the light shining on it Picture 6. Experimental layout of the photoelectric effect.15) Which one of the following is the reason for your answer to the previous question?a) The battery provides a potential difference between the two metal surfaces and the electrons are liberated by the current flow, b) The photons are absorbed by the electrons, c) The reflection of the photons from one metal surface to the other produces a photoelectric current and the electrons are ejected from the flow of this current

Table 1 .
Cronbach's alpha for the questionnaires used in this study.

Table 2 .
Percentage of students who learned the Einsteinian concepts.

Table 3 .
A comparison between conceptual scores at the three school levels.

Table 4 .
Analysis of students' attitudinal scores.

Table 5 .
A comparison between attitudinal scores at the three school levels.