The Degree that Nature of Scientific Knowledge Aspects are Included in the Science Classes of Greek High Schools

The present study examines the integration level of the Nature of Scientific Knowledge in secondary school science classes in Greece. The research was designed and organized on the basis of the Cultural-Historical Activity Theory. The activity system of the researchers, who use the proper tools each time, are in network relations with the activity system of Science Education. Major components of the educational system are studied (the curriculum, textbooks, teachers’ know-how and teaching methods, school inspectors’ viewpoints, students’ knowledge) in relation to the nature of scientific knowledge, to ensure valid results. The curriculum and textbook content is decoded, the knowledge of teachers and students is assessed with the use of an internationally validated questionnaire, and interview protocols are analyzed. Research results reveal that the nature of scientific knowledge is included in a small degree in the curriculum and textbooks, teachers refer intuitively to some of these aspects, without assessing the knowledge of students, and, finally, the majority of high-school graduate students have naïve views regarding the nature of scientific knowledge.

The Problem
This study presents the results of the research that took place in Greece aiming to examine the integration level of the Nature of Scientific Knowledge (NOSK) in science classes in the secondary education system (grades 7-12, students aged 12-18). It is part of a wider project which started with the Need Analysis, as presented here, and was later followed by the design and implementation of a professional development (PD) program for science teachers, regarding NOSK teaching (see paragraph 4).
An initial research (Koumara & Plakitsi, 2017) revealed that NOSK teaching in Greece is problematic. The present study aims to expand the research in the entire secondary education system (the former study focused on Lower Secondary School, grades 7-9), using more tools, statistical analysis and interviews conducted both with teachers and students. Another goal is to study the cultural characteristics of teachers, their historicity and the activity system of science classes, and analyze them based on the Cultural-Historical Activity Theory (CHAT) in order to facilitate the design of a PD-program for science teachers in the future (Roth & Lee, 2007). CHAT serves to the multi-faceted depiction of the problem.
The views of students and pre-service and in-service teachers regarding NOSK (e.g. Akerson & Abd-El-Khalick, 2005;Lederman, Abd-El-Khalick, Bell & Schwartz, 2002;Schwartz & Lederman, 2008;Stefanidou & Skoroulis, 2018) have been recorded and researched since the early days of this field (Lederman, 1992) and their analysis continues until today (e.g. El-Takach and Yakoubian, 2020). There are many assessment tools specifically designed to achieve valid results (Abd-El-Khalick, 2014). The initial studies were conducted in North America but have now expanded to the rest of the world, e.g. BouJaoude and Santourian (2012) in Lebanon, Dogan and Abd-El-Khalick (2008) in Turkey, Leden, Hansson, Redfors and Ideland (2015) in Sweden, Thye and Kwen (2004) in Singapore. Especially in Turkey, this study is part of a wider government-funded project, named BIDOMEG, the initials of

The Nature of Scientific Knowledge and Why its Teaching is Important in Compulsory Education
For the past 100 years, the definition of Nature of Science (NOS) and its aspects has been a matter of constant debate between philosophers/historians/sociologists of science and educators. Until today, there is no consensus on its definition and its aspects (Lederman, Antink & Bartos, 2014;Piliouras & Plakitsi, 2015;Lederman, 2019;McComas, 2017;Clough, 2007;Allchin, 2011;Matthews, 2012;Erduran & Dagher, 2014;Van Dijk, 2011). However, all of them acknowledge the importance of NOS aspects in Science teaching. They argue that NOS a) provides a better understanding of the limitations of science, b) increases interest in classroom, c) achieves better understanding of scientific knowledge, and d) achieves scientific literacy (Matthews, 1997;Lederman, 2019). Especially, scientific literacy is widely recognized and incorporated in the global science curricula (Allchin, Andersen & Nielsen, 2014. They also agree that teaching needs to be carried out in an explicit and reflective manner. In the present study, we prefer to use the term "Nature of Scientific Knowledge" (NOSK) to refer to the characteristics of scientific knowledge that are inherently derived from the manner in which it is produced (Scientific Inquiry). In this context, we accept the framework proposed by Lederman , Lederman 2019. The main reasons for this decision is a) the great volume of implementation studies in various countries and populations (students, pre-service teachers, in-service teachers) and the extensive availability of highly validated and reliable assessment tools (VNOS questionnaires). This allows us to compare our results with other studies and facilitates b) the design and implementation of a PD-program for science teachers with NOSK aspects for the continuation of the project. The Lederman group was chosen because their thirty-year research experience makes them probably the most cited and influential researchers in this field (Matthews, 2012). According to our estimations, their suggestions are the easiest to adopt in Greece, in comparison to other frameworks.
The NOSK aspects are :

(A1) Scientific knowledge is empirical
Scientific knowledge is based on /derives from empirical data.
(A2) Observations and inferences are different "Observations" are descriptions of natural phenomena that are directly accessible to the senses, or expansion of them. They are subject to limitations of existing equipment and the dominant theory, but observers usually reach consensus on what they see, hear, feel, etc. "Inferences" are the explanation of observations and the same observations could lead to different inferences, according to the background of researchers.

(A3) Scientific knowledge is creative
Scientific research -contrary to common belief -is not a rational and orderly process. Creativity and imagination is required in every part of the research: in design, data collection and creation of interpretations; it is similar to the creative process of an artistic work.

(A4) Even though objectivity is the goal, subjectivity within scientists is unavoidable
All scientists are susceptible at every stage -interpretation of results, observations and research design -to their own personal beliefs, prior knowledge, training, expectations, etc. Therefore, even though objectivity has always been the goal in Science (through the use of standard scales and precision in measurement), subjectivity is unavoidable. Also, Science is a social activity. Scientists are interacting with each other through scientific publications; their reviews and the continuous testing are meant to enhance the objectivity of their methods. Scientific knowledge is reliable and durable, albeit relative and uncertain. It is subject to change every time new evidence comes to light due to the evolution of technology or new interpretations of older evidence.

(A6) Socio-cultural embeddedness of Science
Science is a human endeavor that affects and is affected by all societal, cultural, philosophical, religious, political and economic factors.

(A7) Scientific Laws and Theories are different types of knowledge
Laws are generalized descriptions of relationships among observable phenomena and are based on many observations. They describe what happens in the (usually idealized) natural world, but never explain why. Those inferred explanations are provided by Theories.

CHAT Framework
Cultural-Historical Activity Theory (CHAT) is a "cross-disciplinary framework to study how humans purposefully transform natural and social reality, including themselves, as an ongoing culturally and historically situated process (Roth et al, 2012). Vygotsky introduced CHAT and Leontiev (1978) expanded on it, with his perception on a collective system of human activity. Engeström (1987) presented Leontiev's views using the triangle for human activity systems (see Figure 1).

Figure 1. The Structure of a Human Activity System
The relations between the Subject (usually people, lately they are also corporations, moving towards a desired goal) and the Object (the activity goals) are mediated through tools, the community, the rules and division of labor. Tools/artefacts are culturally-produced means that subjects use to perform the activity. They may be material, like a magnet, a telescope, or mental, like language. Community refers to all the participants who share the same object that shapes and directs individual actions to the collective activity. Division of labor refers to the way subjects, as members of the community, divide their responsibilities during an activity. The triangle of the activity system refers both to the horizontal actions and interrelations between the members of the community and the vertical distribution of power, resources and relative societal/professional status. The nodes of an activity system are not static and isolated to each other, but they are dynamically connected; the system is regarded as a unity (Hasan & Kazlauskas, 2014;Kolokouri & Plakitsi, 2016;Barma, 2011;Plakitsi, 2013;Kornelaki & Plakitsi, 2018;Igira & Gregory, 2009).
In the present study, we use Engeström's model because it fits to the needs of our research, indicating the factors that need to be studied in order to answer our research question. The results of the educational activity system are more complex due to its interaction with other activity systems (Engeström, 2001, Engeström, 2009Kornelaki & Plakitsi, 2018;Plakitsi, 2013). The entire CHAT framework is presented in another paper (Koumara & Plakitsi, 2019) and will be applied for the continuation of this project.

Method
Education, in general, and more specifically in Science, is a complex activity system with various parameters. Its complexity could be illustrated using CHAT (Kolokouri & Plakitsi, 2016), as shown in Figure 2. In order to evaluate the level of integration of NOSK aspects in the teaching of Greek secondary school science classes, all components of the educational system recorded in Figure 2 are studied, apart from the educational policy makers and textbook authors. The research focuses on science classes from 7 th Grade until 11 th Grade. 12 th Grade is not included in our research, because it is a preparatory year for university entrace exams and students specialize in particular subjects; as a result, not all students follow Science courses. For the purposes of this research, we examine what all students are taught in Secondary Education.

Figure 2. Activity System of Science Education in Secondary Schools in Greece
The researcher, the Subject in their own activity system (see Figure 3), in order to assess: 1. Whether the teaching of NOSK aspects was suggested in science curricula and included in textbooks (tools in Figure 2), studied 1) the science curricula, and 2a) all subject textbooks, and also studied and classified 2b) the recommended textbook exercises. Figure 2) were aware of NOSK aspects, 1) asked 50 science teachers from Thessaloniki, Greece to complete the VNOS-D+ questionnaire (Lederman et al. 2002) and 2) interviewed 10 of them. Figure 2) NOSK aspects in the final exams, the researcher analyzed the final exam content. Figure 2) knew if NOSK aspects were taught in science classes, they interviewed 7 School Inspectors from all regions of Greece.

Whether school inspectors (members of the community in
5. Whether high-school graduates 1 (subjects in Figure 2) were taught and were aware of NOSK aspects, the researcher 1) asked 149 students to complete the VNOS-D+ questionnaire (Lederman et al. 2002) and 2) interviewed 30 of them.

Curriculum
Curricula for all Science subjects in Lower Secondary School, apart from 7 th Grade Physics, were published in 2003 and used in the school year 2007-08. Regarding 7 th Grade Physics, the curriculum was published in 2013 and used in the school year 2013-14, when the subject was introduced for the first time.
The general part of all curricula is oriented towards scientific literacy, but neither the NOSK term (or any similar one), nor any of its aspects are mentioned.
The special part of curricula includes primarily cognitive goals and secondarily goals for inquiry skills. NOSK is not mentioned explicitly. However, if teachers are aware of NOSK aspects and wish to integrate them in their lessons, the curriculum allows them to do so. It is noted that a new Physics curriculum (Plakitsi et al., 2011) included NOSK, but, even though it was successfully piloted in 100 schools, it was not generally applied and did not lead to the writing of new textbooks.
Regarding Higher Secondary Education, the textbook content was based on the Science Curricula published in 1999. In recent years, there have been many changes, mainly the removal of specific chapters and rearrangements in the curriculum, i.e. some chapters that were originally written for one grade are taught in another. In other words, new curricula have been published, as modified versions of the 1999 ones, and no new books have been written.
In Science Curricula of Higher Secondary Education, no NOSK aspects are included, nor the term itself. However, there are objectives upon inquiry and references to everyday life which allow science teachers to include NOSK aspects in their lessons, if they are aware of them and they wish to do so.

Content of Textbooks
It is internationally recorded that Curricula are regularly substituted by textbooks, which control what is taking place inside the classroom (Abd-El-Khalick et al, 2017). Teachers usually rely on textbooks for daily instructions and use of their recommended student exercises, either for use in the classroom (75-90% of teachers) or for homework (90% of teachers). This happens either due to lack of time, or due to lack of knowledge 2 , or because there is only one official textbook (DiGiuseppe, 2014; McDonald & Abd-El-Khalick, 2017a).
Greece has only one official textbook for each subject, which is compulsory in all private and public schools in each grade. Teachers traditionally work with the textbook and not the curriculum. The content of textbooks and their proposed exercises play an important role in the teaching of science and consequently in learning, since they are extensively used in the daily teaching process determining to a great extent the final learning outcome (Anagnostopoulou, 2015, p.175).
In order to assess the reference of NOSK aspects in textbooks, a rubric, adjusted from Abd-El-Khalick et al (2017), is used. The scoring of each NOSK aspect is based on the criteria described in Table 1: An initial study on textbooks, prior to scoring with the use of the rubric, indicated that the reference of NOSK aspects is limited. Phrases like "nature of scientific knowledge" and "this is how scientists think/work", and other similar ones, were missing from textbooks. Direct references on NOSK aspects were few. Therefore, the explicit representation score would be near 0 for all textbooks. However, this will not allow us to identify the actual differences between textbooks, for example, the significant differences between 8 th Grade Chemistry and Biology.
We considered the possibility of reaching conclusions regarding the reference of some NOSK aspects examining the vocabulary used in textbooks, for instance, the use of verbs such as "observe", "conclude", etc. Consequently, we decided to be more lenient regarding the explicit/implicit representation of these aspects. Therefore: • The representation of a NOSK aspect was categorized as Explicit/Implicit; this was determined by the content of written information that teachers would receive and whether this allowed them to make reference to these aspects or not.
• The representation of a NOSK aspect was categorized as Informed/Partially Informed/Naï ve based on its reference in school textbooks. If an aspect was addressed correctly it was categorized as "informed"; if it was addressed to the correct direction but its formulation was problematic, it was categorized as "partially informed"; and, if it was addressed incorrectly and was misleading, it was deemed as "naïve". The "correct" and "incorrect" directions are defined by the international literature on NOSK aspects.
• The content was assessed based on the consistency of the representation of each NOSK aspect in the entire textbook.
The rubric is limited since scoring does not include the position of each recorded aspect. For example, introductions and appendixes are not usually read by students, contrary to the main body of the text.
Results of the study are summarized in Table 2: The conclusions from Table 2 are: 1) Apart from Biology textbooks, the rest of them provide the opportunity to teachers to refer to NOSK aspects, if they are aware of them and should they wish to do so.
2) The empirical aspect in Lower and Higher Secondary School textbooks, the difference between observations and inferences in the Lower Secondary School textbooks and the tentative aspect in Higher Secondary School textbooks have the highest scores. The lowest scores are on the creative thinking aspect both in Lower and Higher Secondary School, the social and cultural embeddedness for Higher Secondary School, while the difference between theories and laws receives negative scores.
3) Regarding Biology, our results are in agreement with Kampourakis (2017), who claims that both textbooks and the Curriculum provide opportunities -some very implicitly though -for integration in teaching to those who are aware of NOSK aspects. Kampourakis raises the question which will also preoccupy us later, whether teachers are actually aware of NOSK aspects.
However, despite their scores, the total absence of the term "nature of scientific knowledge" is highlighted in textbooks, whereas when NOSK aspects are mentioned, these appear exclusively in chapter introductions or appendixes, which are not usually assessed. As a result, it is highly likely that these parts are not being taught.

Student Exercises in Textbooks
Most of the suggested exercises for students in textbooks test cognitive knowledge and almost none of them is related to NOSK aspects. Specifically, only 15 out of 2261 (0.7%) questions/exercises were related to aspect A2 (observations and inferences) but the difference between observations and inferences was not clear. Regarding the suggested projects, which could also be used for assessment, around half of them in each subject could be related to NOSK aspects. However, their formulation is very generic, and they could incorporate NOSK aspects only if the teacher wishes to provide that direction in their lessons. Another study concluded that the recommended exercises in Lower Secondary School textbooks test cognitive knowledge by 92.7% and only a 7.3% assesses the knowledge of science, part of which is related to NOSK (Anagnostopoulou, 2015, p.270).

VNOS-D+ Questionnaire
Apart from the Curricula and the textbook content, teachers can interpret instructions as they wish. Therefore, an interesting question is whether teachers are aware of NOSK aspects . To study the above question, in April 2018, 50 science teachers were asked to complete the internationally validated VNOS-D+ questionnaire (Lederman et al, 2002).
VNOS-D+ questionnaire is an acronym for "Views of Nature of Science" and consists of 10 open-ended questions, which target directly or indirectly the knowledge of one or more NOSK aspects. "Directly" means that the answer on a question is linked to an aspect, whereas "indirectly" means that the answer on a question may or may not be linked to that aspect . Question 4 has four sub-questions.
According to the guidelines provided by the creators of the questionnaire 3 , NOSK aspects are detected from the questions as presented in Table 3: The sample consists of 50 science teachers in public and private schools in the region of Thessaloniki, Greece, of whom 18 were men and 32 women; there were 32 physicists, 3 geologists, 6 biologists and 9 chemists. All but one had permanent placements, and were aged between 35 and 60, with an average around 50. Since their placement in Thessaloniki was permanent, they had either many years of teaching experience or high academic qualifications (Master's or PhD degrees). Science teachers would participate voluntarily in a PD-program on NOSK taking evening classes (see paragraph 4) and their answers were the pre-test. Teachers who traditionally attend those PD-programs are motivated to learn and improve their teaching, as they do not receive certificates of attendance [which would otherwise be useful for promotions or similar use].
Questionnaires were scored twice within four months by the first author, after being trained by the creators of the questionnaire. At the same time, she trained two other researchers enabling them also to score. The three researchers attributed the final scores in unison, reaching consensus of agreement at 91%.
Each question was scored in 4 categories: • Ν-Naï ve: when the answer indicated that the teacher had a misrepresented view on the specific NOSK aspect • Μ-Mixed: when the answer indicated that the teacher knew some elements on the specific NOSK aspect, but not sufficiently • Ι-Informed: when the answer indicated that the teacher had an informed (correct) view about the specific NOSK aspect • Ι + -Super Informed: when the given answer was well-documented, well-formulated and could be given as an excellent correct example for the specific NOSK aspect in question • U-Unanswered: for questions that teachers did not answer The difference between informed (I) and super-informed (I+) responses is defined by the vocabulary used (for example, the use of certain keywords), whether an example is mentioned or if there is a more analytical description in I+ responses in comparison to I. Both categories include correct responses.
To score the responses, it was important to create the "profile" of each participant for every NOSK aspect. To enhance their "profile", the first author interviewed 20% of the participants, as instructed by the creators of the questionnaire. Interviews took place after the researcher scored the questionnaires for the first time. At each interview, the interviewee answered each question of the VNOS-D+ orally. If the researcher discovered a mismatch between what they meant and what they had written (or between what the researcher thought they meant) she changed her score and noted it down for the other researchers.
The overall results are presented in Figure 4 and Table 4:  For our statistical estimations, we used confidence intervals to ensure, at a percentage defined at the beginning, that we have an interval within the range of the real value of the parameter we are interested in. The 95% confidence interval of the real range of teachers who give super informed and informed answers is provided by the relation (Kounias, Kolyva, Bagiatis & Bora, 2009, p. 141-142): where p = Number of people from the sample who give the desired answer number of people from the sample , n is the number of people from the sample the desired confidence interval is (95%), Z(a/2) = 1,96.
The sample results are presented in Table 5:

) O B S E R V A T I O N -I N F E R E N C E S A 3 ) C R E A T I V E A 4 ) S U B J E C T I V E -O B J E C T I V E A 5 ) T E N T A T I V E A 6 ) C U L T U R A L E M B E D D E D N E S S A 7 ) T H E O R Y -LAW
unanswered naïve mixed informed informed+ difference between theories and laws 28 ± 12,4 (15,6 -40,4 Table 5 reveals three groups: the first group contains aspects 1, 2 and 5 and the second contains aspects 3 and 7. These two groups are statistically different -there is no overlap between them. The third group contains aspects 4 and 6 and there is a small overlap with the first and the second group.
• Almost half of the teachers are well aware of the subjective aspect (22/50) and the aspect about social and cultural embeddedness (28/50). Teachers' mixed views are higher for these aspects (21/50 and 17/50 respectively).
• The biggest issues seem to be a) on the difference between theories and laws, where only 14/50 are aware of it and 30/50 teachers have naï ve views, the most common being that Law is superior to Theory, something like a proven theory and b) that scientific knowledge is a product of creative thinking, since only 10/50 know of it. More than half (27/50) have mixed views.
It is noted that teachers who completed the questionnaire are superior to the average Greek science teacher, and consequently the results cannot be generalized for the whole population. However, they are still important, since they clearly demonstrate that even if those teachers who care to improve their teaching performance find difficulty in answering this questionnaire, then average teachers, with traditionally basic lessons, would provide worse responses (this is an inductive conclusion, there is no data from random sample).

Interviews with Teachers
Semi-constructed interviews took place with ten of the above teachers. The topics for discussion were the questions of the VNOS-D+ questionnaire, which NOSK aspects they were aware of and which they used in their lessons, each subject's relative chapters and some general school life questions. The interviews took place in May 2018 and additionally in October/November 2018.
Six out of ten teachers claimed that they had never heard of NOSK aspects before and had not thought of what these might be -or they might have heard the term but did not remember it. Four teachers who claimed to have previously heard of it, had either completed a PhD in Science Education (2 teachers) or attended PD-programs and conferences (2 teachers). They had no recollection of having been taught about it during their studies, definitely not explicitly.
Even though they did not know the collected NOSK aspects, they claimed that they teach intuitively some of them: all of them teach that scientific knowledge is empirically-based, through which scientists come to inferences, but they do not stress the difference between observations and inferences. They also teach the tentativeness of scientific knowledge. Two teachers claimed that they partially teach the subjectivity and creativity in scientific knowledge. Three teachers claimed that they teach the interactions between science and society. Regarding the difference between theories and laws, only one teacher knew of it and claimed to teach it. They all answered that they do not teach NOSK aspects explicitly and reflectively and they never assess students' knowledge on them.
All teachers claimed that the educational system does not incorporate NOSK in its lessons, but some of its elements may be included, although not taught, in textbooks, mostly in introductions and appendixes, which students traditionally do not read.
Their biggest teaching anxiety was to complete the curriculum in time and prepare their students for the exams, while avoid having problems with principals and parents. As they mentioned, "success in teaching is defined by how well you have prepared your students for exams and how successful they were."

Students' Assessment by Teachers in Relation to NOSK Aspects
Students' studying (and, in general, trainees of every age) is mainly determined by the assessment type and the characteristics of the exams they take. What they will finally learn is not determined as much by the content of textbooks but by the exam type. The evaluation requirements affect students' studying strategies (Anagnostopoulou, 2015, p.177-178;Green & Oates, 2009;Arons, 1990, p.365-366). To study whether students are assessed in their NOSK knowledge, we analyzed the topics of final exams.
For Lower Secondary School, Anagnostopoulou (2015) concluded that 4233 out of 4288 exam topics (1476 Physics, 1413 Chemistry, 1359 Biology), at a percentage of 99.6%, assessed the body of knowledge. Only 15 exam topics, a percentage of 0.4%, assess the knowledge "of science", where scientific research is included, part of which might be the knowledge of NOSK (p. 284). As for Higher Secondary School, almost no topic was related to NOSK -apart from 3 out of 1630 -as included in the Test Bank created by the Ministry of Education.

Interviews with School Inspectors
Seven Science School Inspectors from all regions of Greece were interviewed during January -June 2017 either face-to-face or via telephone. Four of them held a PhD in Science Education and one was a member of the authors' team for a textbook. The interview was a semi-constructed discussion on NOSK aspects and school life in the Secondary Education. Their responses did not differ significantly from teachers' opinions (see paragraph 3.2.2); however they emphasized the limited time for teaching and preparation for National Exams (which students take to enter university), a restriction that forces most teachers to prioritize solving complex mathematical exercises. School Inspectors claimed that only 15% of teachers use inquiry-based learning and around 2-5% of them teach most NOSK aspects regularly and explicitly 4 . They estimated that in most cases teaching contains the empirical and the tentative aspects, the latter as a path towards the truth.
In conclusion, School Inspectors argued that NOSK is not an objective in Science Education and it is not included in everyday teaching. They also claimed that most teachers are not aware of NOSK and are not being taught how to integrate it into their lessons.

Students
The final recipients of all the above are the students. Consequently, what graduates know about NOSK is another source of information, whether NOSK is being taught -and, most importantly, if it is being learnedin Secondary School. Our research continues with the VNOS-D+ questionnaires and the interviews with graduate students.

VNOS-D+ Questionnaire
The sample consists of 149 first-year students in the School of Education of the Aristotle University of Thessaloniki. University students were chosen, instead of 12th Grade students, as a means to obtain more objective results for the total student population. Specifically, university students in a big city come from all over Greece, from urban, rural and island areas, they have attended schools with different science teachers, and they potentially have received different stimuli. Furthermore, we considered that first-year graduates who attended university for only one month are not adjusted to university life yet and, as a result, they maintain the same mindset and have similar characteristics with high-school students. We conducted 30 interviews (20% of the sample), where we discussed the VNOS questionnaire and other general questions. The research took place in November 2017.   Table 7 results from the data of Table 6. On its second column there is the number of students that give informed and super informed answers and on the third column is the 95% confidence interval (Kounias et el, 2009, p.141-142) where the value of the wider population of Greek graduate students can be found. The conclusions which arise from Table 7 are: • Students' knowledge on the empirical aspect is statistically distinguished, since 30-40% of students seem to be aware of it.
• Students' knowledge on the tentative and subjective aspects, the aspect about creative thinking and the social and cultural embeddedness do not differ significantly. Students' knowledge on all these aspects is around 10-20%.
• The difference between observations and inferences and between Theories and Laws seem not to be understood by students, even though the former is included in textbooks and teachers seem to be aware of it. This will be further

Interviews with Students
After having scored the answers on VNOS-D+ questionnaires for the first time, we interviewed 30 students (20% of the total sample, as guided by the creators of the questionnaire), during December 2017 -January 2018. Each interview consisted of three parts: a) every student was asked to answer again all the VNOS questions orally and explain what they wrote. The results of this part of the interviews formed the final scoring of the questionnaire. b) Students were asked to answer whether they were taught about NOSK during their school years and whether they were assessed on that. They were also asked to comment on c) various general matters about their school life and education, which were used in a different research stage.
All students claimed that they had never heard the term "nature of scientific knowledge" before, or at least they did not remember it. When asked whether their daily lessons included NOSK aspects (in order to understand the question, they were given a sheet of paper with the NOSK aspects and discussed them briefly with the researcher), 10 students answered that they had never referred to any of them in any subject, whereas 15 students remembered having heard that knowledge is empirically-based (the empirical aspect) and has an inferential character, but they were not aware of the difference between observations and inferences. Three students claimed that in their Physics classes there were extensive references on the evolution of scientific ideas. They discussed that scientific knowledge is subject to change over time (the tentative aspect), but it seemed as if they only referred to the past. Also, students had the impression that these references were only for their own information and were not part of the actual lesson. Finally, one student participated in an eTwinning program regarding "how science works", where most NOSK aspects were presented, although not in an organized and explicit manner.
To sum up, the questionnaires and interviews with students indicated that students were not taught about the NOSK aspects in an organized manner and any knowledge originates from implicit teaching.

Discussion
In conclusion, the Greek educational system is not oriented towards the integration of NOSK aspects in science teaching. The curriculum objectives do not contain it and textbooks, which tend to follow the curriculum, include only a few aspects, mainly the empirical and, at a smaller degree, the tentative one, but without referring to them by their names. Also, the term "nature of scientific knowledge" or any similar term is not used. Teachers usually follow the textbooks and do not mention NOSK in their lessons. However, even when they do, they do not assess them. School inspectors, with a wider understanding of what is happening in schools, regard that NOSK is not a goal for Science Education and, generally, it is not included in daily lesson planning. This is consistent with the observation that most students have naï ve views on NOSK aspects. Regarding the difference between observations and inferences, interestingly, even though it is clearly mentioned in textbooks, teachers are the only ones who are aware of it. This indicates that probably teaching is not explicit and reflective, as suggested in the literature , and students are not becoming aware of it.
Schematically, all of the above are illustrated in Figure 6, using the sub-triangles of CHAT (Plakitsi, 2013): Figure 6. A typical Science Class Activity System in Greek Secondary Education, as Resulting from Our Research Contradictions arisen from students, parents and principals who insist that teaching should lead to success in all National exams. However, at the same time, students feel that what they are being taught does not reflect their interests.
In relation to the embeddedness of NOSK aspects, the sub-triangle of production is interesting, since teachers who wish to integrate NOSK in their teaching must design new lesson plans that demand extra time and effort. The sub-triangle of consumption is also interesting, since the same teachers need to persuade the community (parents, students, principals and peer teachers) that NOSK teaching is in favor of the evolutionary learning route of students, in order to be accepted.
Other studies from Greece (e.g. Kampourakis, 2017) and abroad, draw similar conclusions, validating our research. For instance, in Lebanon (El-Takach & Yakoubian, 2020) NOSK is not included in the curriculum and teachers have no formal pedagogical training. Regarding books, Abd-El-Khalick et al (2017) claim that NOSK aspects are included in the introduction chapters of most books.  in their review article, claim that a plethora of studies conclude that both teachers and students have naï ve views on most NOSK aspects and that NOSK teaching, when it takes place, is not explicit and reflective. The case of Greece is not disheartening; on the contrary, it has many similarities with other countries.

Conclusion
In this study it was presented the multi-faceted method that we used to study all the components of the Greek Secondary Education system in relation to NOSK. The fact that all tools gave the same results and agreed with each other, is a factor that validates our research. Other factors are the agreement with other Greek studies, that examine specific components of the Greek Secondary Education, plus the consistency with international studies.
Furthermore, the particularities of the Greek educational system were brought out, which are useful for the whole project. Following up in the wider project, a PD-program for science teachers can be organized which would take into consideration: i) the results of the present research, ii) the literature of NOSK and iii) the CHAT framework. The objective of the program would be the training of teachers on a) NOSK aspects, b) possible teaching approaches and on c) ways of being incorporated in the present curriculum, through the design of competent lesson plans.
In the future, we consider that the Greek government could organize a wider project, similar to the Turkish BIDOMEG one (see Introduction). The project could start with a quantitative record, similar to the one presented here, for a wider and more representative number of teachers and students. The method of the present study could be used as a model.

1.
First-year students in their first month of university were regarded as graduate students, because they come from all regions of Greece and have followed all specializations.
2. In some countries, teachers have no subject-specific university degrees and may feel unfamiliar with the subject they are teaching (McDonald & Abd-El-Khalick, 2017a). This is not the case with Greece.
3. https://www.physport.org/assessments/assessment.cfm?A=VNOS 4. School inspectors mean that this is the rate of teachers nationally that are aware of NOSK aspects and teach them.
5. The relation that gives the confidence interval is valid if ≥ 5, so it is not valid on this case. But, if 5 students gave this answer instead of 4, then ≥ 5, it would be valid and the respective interval would be 3.4±2,9, which means 0.5 -6.3. So, in our case it is a bit smaller, which is obvious enough.


IMPROVING READING SKILL OF PROCEDURE TEXT TROUGH PICTURE WALK

This study has a purpose at improving the reading skill in the topic “Procedure Text” of the students through Picture Walk. This research was a classroom action research conducted in two cycles, consisting of plan, implementation, observation or evaluation and reflection. The subjects of this study were 30 students of class VII A SMP Putra Juang Cianjur. There were 14 boys and 16 girls. The result of data analysis of the mean score of the first cycle was 67. Meanwhile, the mean score of the second cycle was 94.3. From the data, it can be said that the result of learning reading skill in the material “Procedure text using picture walk” in cycle I to cycle II has improved by 27.3. Based on the results of data analysis and discussion it can be concluded that the result of learning Reading Skill in the material “Procedure Text using Picture Walk” can be improving Reading Skill on the students of class VII A SMP Putra Juang. It is recommended for English teachers to apply Reading skill using Picture Walk because it can improve the students’ achievement on Reading skill.

INTRODUCTION
In our lives, language is the most significant communication tool in communication. Communication can be done by speaking, writing and so on. The field of language study is a very important field of study. In line with the development of human science and technology, it is demanded to have good language skills, a person who has good language skills will more easily absorb and convey information both orally and in writing (Rediasih, 2017).
Language as a medium of information is imperative to master. One of the languages we must quasi is English. English has been introduced at playgroups, elementary school, junior high school, as of education in Indonesia that use in the workplace. Widely used for many people around the world to communicate with each other. English has a big contribution in accommodating many people to enrich their knowledge and skills in various fields, such as education, tourism, religion, technology, and the global economy. In Indonesia English is used as a foreign language. Most of the countries are including English as a compulsory lesson in the school. Harmer in (2001: 3) states that the reasons that many countries take English as a compulsory lesson are because of some factors like economics, travel, information exchange, and popular culture English as an international language, which is often used in the world as a means of communication. In addition, English language skills are very important possessed by children who live in areas that have tourist attractions. Because, the English language skills of regional children are expected to introduce regional wealth to foreign tourists (Sutarsyah, 2017). The purpose of learning English in schools is to develop language skills both verbally and in writing.
The intended English language skills are listening, speaking, reading, and writing skills. The four language skills are a unity that cannot be separated from one another but can only be distinguished. Reading is an activity informed by the apprehension of images, shapes, patterns, and rhythms, which come to be recognized through repeated encounters and remembered forms; the meanings that are made in reading are in excess of the meanings that arise from the interpretation of written language (Lorange, 2014: 30) as cited in Parmawati (2018). However reading as an interactive process. (Lems, Kristin., Leah D Miller., 2010) believe that reading is an activity involves an interactive process that connects the reader's background knowledge and their processing strategies to the text they read. Other experts as Celce-Murcia, Brinton, & Snow, (2014) argues, "reading is an interactive sociocognitive process, involving a text, a reader, and a social context within which the reading activity takes place." Thus, many people consider reading is just like other activities. People interpret reading from what they see through their eyes (Subekti, 2018). Some other people define reading as an interactive and sociocognitive process which relate the reader to the interactive and social context. According to Alderson (2000: 1) cited in Apsari & Yana (2015), reading is to process text meaning through some process of interaction with print. When some peoples define reading as articulating words and as an interactive process, some experts also enrich reading the definition as an active and involved process. Reading is an active process what is proposed by (Stanovich, 1982) who state "reading is an active cognitive process that does indeed require using graphic (letter) and phonics (sounds) information, but for fluent readers particularly, the language-based cues-semantic (meaning) and semantic (grammar) seem far away more important than graphics and phonic cues". Besides, Grellet (2010) adds that reading is an active skill. Reading involves some strategies such as guessing, predicting, checking, and asking oneself questions. As a result, without these strategies, reading becomes very hard to do.
In reading, English learners in their school often learn some kinds of English texts graphics, namely narrative, recount, report, and procedure. Sometimes procedure text as one of the texts could be found by students outside the classroom. They can find procedure text when using a new gadget, sign up to social media, and even when making a cup of coffee. As (Knees & Miller, 2006) define that procedure text is a piece of text type to explain how something can be done. Derewianka (2004) argues that procedure text is a kind of text designed to describe how something is achieved through a sequence of actions or steps. From the two statements above, the writer infers that procedure text is a kind of text that gives us instructions to do something through a sequence of actions or steps. Realizing the importance of procedure text, Indonesia government states the teaching of procedure text in some school levels such as junior high school. (Nasional, 2007) Some of the junior high school students, however, have not reached the functional level well. They still have difficulties in the reading lesson. When the English teacher asked them to read a procedure text, only a few of them understood it. The result of their assignment of procedure text is not satisfactory. Some of them still have difficulties in knowing the idea of a process sequence. Use the medium or another strategy in teaching reading may be an alternative to make the student more understand the procedure text Some of the junior high school students, however, have not reached the functional level well. They still have difficulties in the reading lesson. When the English teacher asked them to read a procedure text, only a few of them understood it. The result of their assignment of procedure text is not satisfactory. Some of them still have difficulties in knowing the idea of a process sequence. Use the medium or another strategy in teaching reading may be an alternative to make the student more understand the procedure text.

METHOD
This research was conducted at Putra Juang Middle School at Jl. Cipetir, Sukatani, Kec. Haurwangi, Kab. Cianjur, West Java. This class action research was conducted in the even semester of class VII A of Putra Juang Middle School in the 2018/2019 school year. This research was conducted in two cycles, each of which was only 1 meeting. Cycle I was held on Thursday 10 January 2019, while cycle II was on Thursday 17 January 2019. The subjects in this study were students of class VII A, amounting to 30 people. This class was chosen as the subject of research based on the results of preliminary observations, which showed that student reading was still low.
In implementing this class action the variables investigated are as follows: a) Input variables: Grade VII A students of Putra Juang Junior High School totaling 30 people, b) Process variables: Using Picture work strategies, c) Output variables: Increasing students' reading comprehension. This study uses a class action research design. Classroom action research is research conducted by a teacher in the classroom by performing specific actions the problemsolving. The problem that is being faced by the teacher in learning. There are three words in CAR, classroom, action, and research.
Research is an activity to investigate an object using certain methodology to gain data or information which is beneficial to improve the quality of anything, interested by researchers and important. Action is a planned activity to gain certain goal. Classroom defined as a group of students at certain time and certain teaching from similar teacher. Classroom here defined not only room space but defined as a group of students in the learning process (Arikunto & Jabar, 2004) in journal (Mahmudi, 2011). This research is called classroom action research because this type of research offers a way and procedure to improve and improve the quality of learning in the classroom. In this study, researchers offer the application of Picture work to improve students' mastery of Reading.  (McTAGGART, 1994) and in journal (Widayati, 2014). In Indonesian case,generally use Kemmis & Taggart model, as it is the development from the basic concept of Action Research introduced by Kurt Lewin. Kemmis and Taggart's model is a string of integrated four components: plan, action, observe, and reflection which is united in one cycle. 2) The test is used to measure the increase in students' ability in reading skill. This research uses pre-test and post-test. The pre-test is given at the pre-cycle stage before the strategy is applied and post-test is given at the end of each cycle. 3) Giving questionnaires, the purpose of giving questionnaires conducted in this study is to determine student responses regarding learning using the strategies implemented. 4) The purpose of the interview conducted in this study was to determine the observer's response regarding learning using the strategies implemented, where the input from the observer will be used as teacher reflection material.
The instruments used included observation sheets, questionnaire guidelines, and evaluation sheets. Observations were made by the teacher and observer, which aims to determine the habits and activities of students during the learning and teaching process. Questionnaires are used to determine students' responses to the actions given. Evaluation sheets are given after the strategy is applied. Evaluation is carried out to find out the development of students' reading mastery ability with the strategies implemented. Evaluation form sheets provided are in the form of reading tests. Analysis of the data used in this research is descriptive qualitative analysis and quantitative descriptive.

Results
This research was carried out on Thursday 10 January 2019 at 10.00-11.20 West Indonesia Time and Tuesday 17 January 2019 at 07.00-08.20 West Indonesia Time, in class VII A of Putra Juang Middle School in 2018/2019, amounting to 30 students, 14 sons, and 16 daughters. a.

Preliminary Observation Research Results
Student pretest scores at the pre-cycle stage are shown in the following Based on Table 4.1 it can be explained that out of 30 Class VII A3 students who completed or reached KKM as many as 12 students or only 40%, while those who had not reached KKM were 18 students or 60%. At this stage, the highest score obtained by the participant is 90, and the lowest score is 15. Thus it can be concluded that student learning outcomes in understanding the topic of Procedure text are still shallow.
Based on the above data it can be concluded that the average value of student learning outcomes in mastery of reading on material Procedure text classically has not yet reached graduation. Teachers still apply conventional models in the learning process, where most are still focused on the teacher or what is often called the Teacher Learning Center. This, of course, makes student involvement in the learning process low which results in student inactivity in the teaching and learning process. Teachers need to increase student activity in the learning process by using more innovative learning models. For this reason, in this study, the authors used Reading Picture Work in Procedure text to increase reading interest. b.

Cycle I Research Results
Based on the analysis of learning outcomes data in cycle I of the Procedure text material, the data obtained are as in Table 2 Based on the table above seen an increase in learning outcomes, for the average value increased from 46.6 in pre-cycle to 67 with 60% completeness learning increased from pre-cycle 40%. In this cycle, the highest value obtained by participants is 100, and the lowest value is 30.
Based on these results, it can be seen that the mastery of students' reading has increased in the number of students who have completed under the KKM score ≥70 and the average value classically. However, in this cycle, the level of completeness of students has not met the standard completeness criteria. For this reason, the next step is summarized in cycle II.

c. Cycle II Research Results
Based on the analysis of learning outcomes data in cycle II with Procedure Text material, it can be grouped into the completeness category of student learning outcomes as in Table 3. The table above shows the average value of the class rose 94.3 from the first cycle 67, and mastery learning from 60% in the first cycle increased by 96.8% in the second cycle. In this cycle, the highest value obtained by participants is 100, and the lowest value is 60. Based on the above data it can be concluded that the average learning outcomes in students' mastery of reading is 94.3 and has reached the graduation criteria classically that is an average value of ≥ 70 following KKM scores and in this cycle students who complete by KKM scores have reached 96.8%.

Discussion
Overall, research on the application of contextual teaching and learning picture walk models in teaching reading comprehension of seventh-grade students of SMP 165 Putra Juang provides positive results in the form of an increase in students' ability to read comprehension. This is based on the results obtained from two cycles of action implementation. The implementation of several cycles is a certain stage by implementing a learning plan that has been compiled based on the picture walk model.
In the implementation of this cycle II action, students preview the images or graphic features in fiction or nonfiction texts to make predictions, and activate background or prior knowledge to enhance comprehension, so as to stimulate and inspire students' potential optimally in determining the main points of thought in reading that ultimately can improve students' ability to read comprehension. With the inclusion of images that are in accordance with the text, learning feels more varied so that it is not boring for students and students to become more interested in learning, but also to overcome verbalism in relation to the content of the discourse so that it can increase students' insight, especially for other subjects. Based on the test results in this second cycle, most students have been able tofind the main points of thought in the reading. Based on the test results in the second cycle there is a significant increase in value so that the author is considered enough of this research until the second cycle. The Student responses to the application of Reading Picture walk to improve students' mastery of reading showed a positive response with the acquisition of an average student response of 27.6. It means that students agree with the application of the Reading Picture Walk that can improve the reading comprehension of Grade VII A students at Putra Juang Middle School.

CONCLUSION
The results of the study prove that students' ability to read comprehension after the learning is carried out by applying the picture walk model has a significant improvement. Based on the results of pretest the highest score obtained by the participant is 90, and the lowest score is 15. Thus it can be concluded that student learning outcomes in understanding the text are still shallow. In this cycle I, the highest value obtained by participants is 100, and the lowest value is 30. Based on these results, it can be seen that the mastery of students' reading has increased. In cycle II the highest value obtained by participants is 100, and the lowest value is 60. Based on the results of the data analysis and discussion above it can be concluded that the mastery of reading in VII A grade students at Putra Juang Middle School increased by using the Reading Picture Walk.


extfieldsofstudy: Psychology Medicine

text:
Editorial: Interactions Between Education, Practice of Physical Activity and Psychological Well-Being

During the elaboration of this Research Topic, our dear
colleague Valerii Malkin from the Federal University of the
Urals (Russia) passed away. We hope that this work constitutes
some kind of homage to his person and academic figure, very
relevant in the complex effort to make visible the Russian
Psychology of Sport, of such a long and fruitful tradition
in past years. AM-M was a recipient of a Jose Castillejo
Fellowship from the Spanish Ministry of Science, Innovation, and
Universities (CAS19/00265).

Interactions Between Education, Practice of Physical Activity and Psychological Well-Being
Physical activity is scientifically recognized as a modifiable habit lifestyle with a wide array of benefits for a human being. Thus, there is strong evidence that performing human movement has a positive impact on the lives of people. Traditionally, these implications have been associated only on a physical dimension, but in recent times there is much evidence on mental or brain level, specifically on certain aspects of human behavior and personality traits. Additionally, the interest between this modifiable factor (physical activity) and the educational field is being the target of recent investigations. This Research Topic aims to update the scientific knowledge within this triangle built up around physical activity, psychological well-being, and education. Specifically, it yielded 16 articles, which are the result of a process of free sending, peer reviewing and modification of the manuscripts, embedded in three strands of research. Firstly, three articles focused on the role of physical activity in different population contexts. Secondly, six articles examined the effects of physical activity, sport, and exercise on psychological variables. Thirdly, seven articles examined the implications of physical activity in a variety of educational contexts. These three research strands are presented below.
Worldwide insufficient physical activity is worrisome (Guthold et al., 2018). In this scenario, the use of electronic media has been noted as an important risk factor for a sedentary lifestyle. Zagalaz-Sánchez et al. analyze the possible relation between the misuse of smartphones and the reduction in the practice of physical activity. Although they found scarce scientific evidence, it seems that improper use of this technology might be linked with lower levels of physical activity. In addition to these intriguing facts, the situation is even more alarming in the female gender, being much less physically active (Serra et al., 2018). Thus, Serra et al. focused the research on determining factors affecting interest in pursuing a degree in Physical Activity and Sport Science (PASS) among teenage students. They found a lack of interest by young women in studying a degree in PASS in comparison with boys, which was partially explained by perceived social supports and positive conceptions of outcome expectations. Likewise, physical activity could also play an important role from an early age, thereby, Palou et al. suggested that parent's reports of their children's physical activity levels were associated with relevant health markers (physical fitness and body composition indicators) in preschool children.
The second strand of our Research Topic has attempted to advance knowledge in sports psychology by investigating relationships across some psychological factors in a diverse context. Sports performance is a subsequent result of multiples factors, among them psychological variables play an important role, such as competitive anxiety or flow disposition (Swann et al., 2018;Rice et al., 2019). Thus, as far as we know, Ponseti et al. have been the first ones in demonstrating by means of a Bayesian network two probability trees that have extrinsic motivation and motivation at the top, while the anxiety/activation due to worries about the performance was found clearly at the bottom of the probabilities. In addition, Fernando Garcia et al. found a positive link between dispositional flow and performance in ironman athletes and Ribeiro Contreira et al. demonstrated that young athletes' and coaches' sport satisfaction is strongly influenced by the satisfaction of their basic psychological needs. Our Research Topic also explores some psychological variables in relation to physical activity and exercise in a non-sport population. For instance, Castro-Sánchez et al. developed an explicative model suggesting that practicing physical activity in a natural environment is a key to acquire healthy patterns and diminish the consumption of harmful substances. However, as evidenced by Chacón-Cuberos et al. the practice of physical activity seems to be not only beneficial for a physical health dimension, as well as, for its role to develop a better resilience capacity, tolerance to adversity and the positive acceptance of changes. In a further step, Aguirre-Loaiza et al. have demonstrated the effects on executive functions, and mainly, in the emotional contextual recognition with a single bout of moderate-high intensity exercise.
Within the scope of this Research Topic, the third strand was centered in an education context. A group of researchers examined theoretical approaches to understand the relation of self-concept and physical activity on students. Fernández-Bustos et al. observed that physical activity had a positive and indirect effect on self-concept and direct effects on body dissatisfaction and physical self-concept. Onetti-Onetti et al. confirmed this positive relationship between physical activity self-concept, however, they also found a negative relationship between the self-concept dimensions and the amount of time the adolescent spends sitting. These results reflect the usefulness of promoting physical activity to achieve a positive self-concept and promote psychological well-being in both adolescents and university students.
An innovative methodological approach was conducted by Florese et al. whose results showed that the majority of scientific interest in Sport and Exercise Psychology is developed by Exercise and Sport Science programs rather than Psychology in Brazil universities, data that perhaps may drive us to have some reflection about the strength and power of the paradigm in which we are currently working. In this field, and for the first time in the scientific literature, Gavala-González et al. described the perception of the dual career in both professional and semi-professional under-23 canoeists. They encountered that athletes have specific problems that make it difficult to efficiently combine their athletic and academic careers. Certainly, both studies might serve as a precedent to intervene in the university to counteract the limitations of this field.
In a school context, one of the most intriguing debate is around the most suitable pedagogical model for a successful in physical education (Casey and MacPhail, 2018;González-Víllora et al., 2019). This issue is also addressed in this topic, specifically, Sierra-Díaz et al. tried in their systematic review to find implications of a model-based practice or instructional models on student's self-determined motivation and basic psychological needs. They concluded that modelbased practice is an ideal pedagogical framework to produce significant increases in sport competence and self-determined motivation. More specifically, Gil-Madrona et al. studied the effects of an intervention based on a personal and social responsibility model. In brief, the intervention was effective to generate positive changes in children's attitudes and social skills. Lastly, Malkin et al. corroborate the importance of the physical activity to interfere in psychological factors, such as hardiness. These researchers found higher levels of hardiness in those students who engaged regularly in sports activities in comparison with those who did not. These studies enrich our understanding of physical activity and education binomial and offer new insights for developing interventions in physical education classes.
Collectively, this Research Topic has embraced a large spectrum of scientific concerns. Mostly, the publications of this Research Topic cover how psychological factors are influenced by physical activity, exercise and/or sport through a compendium of cross-sectional and systematic reviews studies. These works contributed toward the understanding of the impact of human movement on the physiological well-being, and also may show how the different fields placed under the umbrella of Sport Sciences interacted among them to produce and disseminate new knowledge both in theoretical and applied ways.

AUTHOR CONTRIBUTIONS
AM-M wrote the initial draft. AM-M, PP, PA, and AG-M review critically the final version of the manuscript.

ACKNOWLEDGMENTS
Finally, during the elaboration of this Research Topic, our dear colleague Valerii Malkin from the Federal University of the Urals (Russia) passed away. We hope that this work constitutes some kind of homage to his person and academic figure, very relevant in the complex effort to make visible the Russian Psychology of Sport, of such a long and fruitful tradition in past years. AM-M was a recipient of a José Castillejo Fellowship from the Spanish Ministry of Science, Innovation, and Universities (CAS19/00265).


extfieldsofstudy: Physics Economics

text:
A paradox of tournament seeding

We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might potentially punish a team for its better results by having to face stronger opponents on average in the next stage. Major football competitions are revealed to suffer from this weakness. Incentive compatibility can be guaranteed by providing each qualified team with the highest coefficient of all teams that are ranked lower in its qualifying tournament for seeding purposes. Our proposal is illustrated by the 2020/21 UEFA Champions League.

Introduction
Every sports tournament has to provide appropriate incentives for the contestants to exert effort (Szymanski, 2003). In particular, the ranking method should not reward teams for poor performance (Vaziri et al., 2018). But the rules are complex in practice and sometimes lead to unforeseen consequences such as a situation when a team is worse off by winning (Kendall and Lenten, 2017).
Unsurprisingly, various theoretical models of sports contests have been considered in view of incentive compatibility. Pauly (2014) derives an impossibility theorem for championships consisting of two qualifying tournaments with disjoint sets of participants. Vong (2017) proves that, if more than one contestants advances to the next round, some players can benefit from shirking to qualify with a lower rank. Dagaev and Sonin (2018) investigate tournament systems, composed of multiple round-robin and knockout tournaments with the same set of participants when the sets of winners of noncumulative prizes have a nonempty intersection. Csató (2020a) considers group-based qualification systems where teams from different groups are compared, which can create incentives for both teams to play a draw instead of winning (Csató, 2020c). Csató (2021) and Csató (2022c) present how neglecting these theoretical findings has led to problems in European football. Krumer et al. (2020) show that strategic considerations may motivate a contestant to lose in a round-robin tournament because this can result in a higher expected payoff. Last but not least, Lenten and Kendall (2021) collect similar compelling ideas within the academic literature that could yet be considered and adopted by sports administrators.
Although the round-robin format in which each team meets all the others is one of the most common sports tournaments, it requires a lot of time to organise. On the other hand, if the competitors can play only against a limited number of opponents, the set of matches should be chosen carefully. This can be achieved through seeding, by ordering the entrants based on playing history and/or the judgement of experts to pair them according to their ranks. The problem of seeding in knockout tournaments has been thoroughly explored in the literature, see e.g. Hwang (1982); Horen and Riezman (1985); Schwenk (2000); Groh et al. (2012); Dagaev and Suzdaltsev (2018); Arlegi and Dimitrov (2020);Della Croce et al. (2022). The seeding rules of the most prominent football competition, the FIFA World Cup have also got serious attention (Scarf and Yusof, 2011;Guyon, 2015b;Laliena and López, 2019;Cea et al., 2020;Csató, 2022a). Similarly, several statistical papers have analysed the effect of seeding on tournament outcome (Monks and Husch, 2009;Corona et al., 2019;Dagaev and Rudyak, 2019;Engist et al., 2021).
However, no academic work has addressed the incentive compatibility of the seeding rules except for Csató (2020b), a paper revealing a unique shortcoming in the UEFA Champions League group stage draw that emerged from the 2015/16 season due to a misaligned way of filling vacant slots. Our main result is more universal: traditional seeding systems based on exogenous measures of teams' strengths are generically incentive incompatible-but they can be made strategyproof in a straightforward way.
Admittedly, these potentially unfair seeding rules rarely create incentives to lose ex ante. Analogously to the previous literature (Csató, 2019(Csató, , 2020aDagaev and Sonin, 2018), we can only provide hypothetical examples when a team is better off by losing. This is not surprising since these regimes are widely used in practice, thus, they probably would have been changed long ago if the probability of a tanking opportunity would be substantially higher. Nonetheless, we think that (a) even the punishment for better results can be detrimental to the business model of the sports industry if the stakeholders realise this unfairness at the end of a competition; and (b) the academic community can make an important service to the decision-makers and the society by highlighting every issue of potential problems around incentives.
Consequently, the current paper makes a contribution by calling attention to a shortcoming of standard seeding systems that are extensively used in major sports competitions. Therefore, the regulatory bodies will have an opportunity to consider the seriousness of this weakness, and to adopt our proposal for an incentive compatible seeding rule, or to take other measures to prevent tanking, for instance, by choosing a schedule that maximises competitiveness.
Our roadmap is as follows. Section 2 presents two real-world cases to highlight the issue. A mathematical model is given in Section 3. We provide a strategyproof seeding mechanism and summarise policy implications in Section 4. Finally, Section 5 concludes. • The first leg of Sweden vs. Italy was 1-1 (instead of 1-0) on 10 November 2017 in the UEFA Second Round, hence Italy qualified for the World Cup.
In the draw for the 2018 FIFA World Cup, the composition of the pots depended on the October 2017 FIFA World Ranking. The only exception was the automatic assignment of the host-Russia-to Pot 1 besides the seven highest-ranked qualified teams. Hence Uruguay (17th in the relevant FIFA ranking) would have been drawn from Pot 3 as among the best 16 teams, only Chile would have not qualified in the above scenario (Wales was the 14th and Italy was the 15th in the FIFA World Ranking of October 2017). The allocation of the teams in the above scenario is given in Table 1. Consider what would have happened if the result of the match Paraguay (34) vs. Uruguay, played on 5 September 2017 in the South American qualifiers, would have been 2-1 instead of 1-2. Then Uruguay would have remained second and Paraguay would have been fifth in this qualifying competition. Paraguay would have played against New Zealand (122) in the OFC-CONMEBOL qualification play-off, thus Peru (10) could not have qualified for the World Cup. Therefore, Uruguay would have been drawn from the stronger Pot 2 instead of Pot 3 merely due to its loss against Paraguay. It probably means a substantial advantage: in the 2018 FIFA World Cup, seven and two teams advanced to the knockout stage from Pots 2 and 3, respectively.  (2) Switzerland (11) Costa Rica (22) Australia (43) Portugal (3) England (12) Sweden (25) Japan (44) Argentina (4) Colombia (13) Tunisia (28) Morocco (48) Belgium (5) Wales (14) Egypt (30) Panama (49) Poland (6) Italy (15) Senegal (32) South Korea (62) France (7) Mexico (16) Iran (34) Saudi Arabia (63) The pots are determined by the FIFA World Ranking of October 2017, see the numbers in parenthesis.
Russia is the top seed as host.
Teams written in italics qualified only in the hypothetical but feasible scenario of Example 1.
Uruguay (17) Example 1 contains a small sloppiness since we have not checked whether the October 2017 FIFA World Ranking would have been changed. However, this issue does not affect the potential case of incentive incompatibility.
Example 2. In the draw for the 2020/21 UEFA Europa League group stage, the composition of the pots was determined by the 2020 UEFA club coefficients, available at https://kassiesa.net/uefa/data/method5/trank2020.html. Assume the following hypothetical modifications to real-world results in the play-off round of the qualifying phase, with the first favourite team advancing to the group stage in place of the second unseeded underdog (the UEFA club coefficients are given in parenthesis): There were 48 teams in the group stage. Leicester City (22.0) was ranked 20th because Rapid Wien (22.0) had the same 2020 UEFA club coefficient but the tie-breaking criterion-coefficient in the next most recent season in which they are not equal (UEFA, 2020b, Annex D.8)-preferred the latter club. Due to the above changes, five teams with a higher coefficient than Leicester City would have qualified instead of five teams with a lower coefficient. Hence, Leicester City would have been only the 25th highest-ranked, namely, the best club in Pot 3 as each of the four pot consists of 12 clubs. In addition, suppose that Leicester defeated Norwich City at home by 2-1 (instead of 0-0) in the 2019/20 English Premier League. Then Leicester City would have remained fifth at the end of the season with 64 points. The allocation of the clubs in the above scenario is presented in Table 2. Consider what would have happened if the outcome of the match Wolverhampton Wanderers (18.092) vs. Leicester City, played on 14 February 2020 in the 2019/20 Premier League, would have been 1-0 instead of 0-0. Leicester would have remained fifth with 62 points, while Wolverhampton would have been sixth with 61 points rather than Tottenham Hotspur (85.0), which scored 59 points. Consequently, Wolverhampton would have entered the Europa League qualification in the second qualifying round, and it could have qualified for the group stage in the place of Tottenham. Then Leicester would have been drawn from the stronger Pot 2 merely due to its loss against Wolverhampton. This probably means an advantage, although in the 2020/21 Europa League, six teams advanced to the knockout stage from both Pots 2 and 3, respectively.
Examples 1 and 2 uncover that a team can be worse off by winning in the South American qualifiers of the FIFA World Cup and the English Premier League, respectively. By changing the schedule of these round-robin tournaments such that the sensitive games (Paraguay vs. Uruguay and Wolverhampton Wanderers vs. Leicester City, respectively) are played in the last round, losing can be made beneficial for a team because its final ranking is not affected but the modified set of the teams qualifying (Paraguay instead of Peru and Wolverhampton Wanderers instead of Tottenham Hotspur, respectively) allows to be placed with a higher probability in a higher-ranked seeding pot, independently of the outcome of the matches to be played later. For instance, note that Leicester City always prefers to qualify together with Wolverhampton Wanderers instead of Tottenham Hotspur as the former scenario results in gaining one position in the ranking used for seeding compared to the latter scenario, which might lead to being in a better seeding pot with a positive probability.

Theoretical background
Consider a round-robin qualifying tournament with a set of teams T , where each team t ∈ T has a coefficient ξ t . The teams ranked between the pth and qth (p ≤ q) positions qualify for the second stage. There, a qualified team t has a seeding value Ψ t , which is usually (but not necessarily) its coefficient ξ t as we have seen in Examples 1 and 2.
Any team prefers if more teams play in the second round with a lower coefficient. In other words, it is a common belief that these measures positively correlate with true abilities. All coefficients used in practice are constructed along this line. For instance, the FIFA World Ranking and the UEFA coefficients for national teams, countries, and clubs alike award more points for wins (draws) than for draws (losses), thus better achievements in the past translate into a higher value.
Therefore, the first goal for every team is to qualify and the second goal is to qualify together with teams having a lower coefficient. Any team t ∈ T may lose a match to improve the second objective without deteriorating the first. Denote the (strict) rankings of the qualifying tournament by ≻ and ≻ ′ , the ranks of team s ∈ T by #(s) and # ′ (s), as well as the sets of teams qualified by Q = {s ∈ T : p ≤ #(s) ≤ r} and Q ′ = {s ∈ T : p ≤ # ′ (s) ≤ r} before and after the manipulation, respectively. Definition 1. Incentive compatibility with respect to seeding: A round-robin qualifying tournament is said to be incentive compatible with respect to seeding if no team t ∈ T ever has a manipulation strategy such that: • team t qualifies for the second stage both before and after the manipulation, that is, t ∈ Q and t ∈ Q ′ ; • team t has a better seeding position after the manipulation than before, namely, |s ∈ Q ′ : Ψ s > Ψ t | < |s ∈ Q : Ψ s > Ψ t |.
Otherwise, the qualifying tournament is called incentive incompatible with respect to seeding.
As it has been revealed in Section 2, a qualifying tournament is incentive incompatible if Ψ t = ξ t for all t ∈ Q and 2 ≤ |Q| < |T |. In particular, a situation may exist where team i has already secured qualification, while teams j and k compete for another slot such that ξ k > ξ i > ξ j . Then team i may consider losing against team j in order to push it to the next stage at the expense of team k as team i can get a better seeding pot by taking team j to the second round instead of team k.
The result below provides sufficient conditions to prevent a strategic manipulation of this type. For the sake of simplicity, we assume that ties in the seeding values of qualified teams are broken in favour of the team ranked higher in the qualifying tournament.

Proposition 1. A round-robin qualifying tournament is incentive compatible with respect to seeding if at least one of the following conditions hold:
• Only one team is allowed to qualify: p = q; • All teams qualify: p = 1 and q = |T |; • The seeding value of each qualified team t ∈ Q in the second stage is equal to the maximal coefficient of the teams that are ranked lower than team t in the qualifying round-robin tournament: Ψ t = max{ξ s : t ≻ s} for all t ∈ Q.
Proof. If p = q, then t ∈ Q leads to |s ∈ Q : Ψ s > Ψ t | = 0. Consequently, no manipulation strategy can be found according to Definition 1. p = 1 and q = |T | result in Q = T , thus |s ∈ Q ′ : Ψ s > Ψ t | = |s ∈ Q : Ψ s > Ψ t |, which excludes the existence of a manipulation strategy as required by Definition 1. Ψ t = max{ξ s : t ≻ s} for all t ∈ Q implies that s ∈ Q and Ψ s > Ψ t ⇐⇒ s ∈ Q and s ≻ t.
Since team t cannot be ranked higher in the round-robin qualifying tournament after the manipulation, holds. Hence, the qualifying tournament is incentive compatible with respect to seeding.
In the previous literature on the incentive compatibility of sports tournaments, only two papers consider multistage competitions. Csató (2022b) discusses the case when the subsequent phases are related such that the results of some matches played in the previous stage(s) are carried over. Vong (2017) analyses a general model with an arbitrary design but, crucially, the allocation of the teams into groups is assumed to be fixed a priori. Therefore, in the proof of his main theorem, a team is interested in manipulation because it knows that if it achieves a higher rank in the qualifying tournament, then it will play in a group where elimination is guaranteed. On the other hand, our model contains more uncertainty regarding the opponents in the next stage. Hence, losing is beneficial only if it leads to a better seeding position, which is impossible under the conditions of Proposition 1.

Discussion
Now a general procedure is presented to guarantee our requirement, incentive compatibility with respect to seeding, on the basis of the theoretical model. Some alternative ideas are also outlined shortly.
According to Proposition 1, there are three ways to achieve strategyproofness in a round-robin qualifying tournament. However, the first two conditions-when exactly one team qualifies or all teams qualify for the next round-could not offer a universal rule. Nonetheless, they can be exploited in certain cases, for example, only one team advanced from the Oceanian (OFC) section of the 2022 FIFA World Cup qualification. Fortunately, there is a third opportunity, that is, to calculate the seeding value of any qualified team t ∈ Q as Ψ t = max{ξ s : t ≻ s}. In other words, team t is seeded in the second stage based on the maximum of coefficients ξ s of all teams s ranked lower than team t in its round-robin qualifying competition. This is a reasonable rule: if team i finishes ahead of team j in a league, why is it judged worse for the draw in the next round? Our proposal is called strategyproof seeding. Table 3 applies strategyproof seeding for the 2020/21 Champions League group stage. Even though the seeding values of 15 teams, including the 11 lowest-ranked, are increased, it has only a moderated effect on the composition of pots as one German and two French teams benefit at the expense of four teams from the Netherlands, Austria, Greece, and Russia. That amendment usually favours the highest-ranked associations, where some clubs emerging without a robust European record (recall the unlikely triumph of Leicester City in the 2015/16 English Premier League (BBC, 2016)) can "obtain" the performances of clubs with considerable achievements at the international level. Thus, strategyproof seeding contributes to the success of underdogs in the European cups, which may be advantageous for the long-run competitive balance in the top leagues. In addition, it probably better reflects the true abilities of the teams since playing more matches reduces the role of luck in sports tournaments (McGarry and Schutz, 1997;Scarf et al., 2009;Lasek and Gagolewski, 2018;Sziklai et al., 2022). Consequently, it is more difficult to perform better in a round-robin league than in the Champions League or Europa League.
From the 2018/19 season onwards, UEFA club coefficients are determined either as the sum of all points won in the previous five years or as the association coefficient over the same period, whichever is the higher (Kassies, 2022;UEFA, 2018). This rule was effective in the 2020/21 Champions League, the lower bound applied in the case of some Spanish, German, and French teams in the 2020/21 Europa League. A somewhat similar policy is used in the UEFA Champions League and Europa League qualification, too, if a later round is drawn before the identity of the teams is known (Csató, 2022d): "If, for any reason, any of the participants in such rounds are not known at the time of the draw, the coefficient of the club with the higher coefficient of the two clubs involved in an undecided tie is used for the purposes of the draw." Therefore, the principle of strategyproof seeding is not unknown in UEFA club competitions, which can support its implementation. Table 3 reinforces that the strategyproof seeding system may result in more ties than the current definition. If some teams inherit their seeding values from the same lowerranked team, then these remain identical, and the tie should be broken by drawing of lots (UEFA, 2020a, Annex D.8). Although tie-breaking does not affect incentive compatibility, it is reasonable to prefer the teams ranked higher in the domestic league. If clubs from other associations also have the same seeding value (which has a much lower probability), they can be assigned arbitrarily in this equivalence class. Alternatively, the original club coefficients can be used for tie-breaking. In Table 3, two French teams at the boundary of Pots 2 and 3, Marseille and Rennes, inherit the same seeding value from Lyon. However, Marseille finished ahead of Rennes and has a higher coefficient, hence it is placed in Pot 2.
Our incentive compatible mechanism has further favourable implications. UEFA has modified the pot allocation policy in the Champions League from the 2015/16 season, probably inspired by the previous year when Manchester City, the English champion, was drawn from the second pot but Arsenal, the fourth-placed team in England, was drawn from the first pot. This decision-intended to strengthen the position of domestic titleholders (UEFA, 2015)-has considerable sporting effects (Corona et al., 2019;Dagaev and Rudyak, 2019), especially since the poor way of filling vacancies leads to incentive incompatibility (Csató, 2020b). On the other hand, the proposed seeding rule guarantees that a national champion has at least the same seeding value as any team ranked lower in its domestic league.
Naturally, other strategyproof seeding policies can be devised. One example is the system of the 2020 UEFA European Championship: the ranking of all entrants on the basis of their results in the qualification. However, that principle is not appropriate if the achievements in the qualifying tournament(s) cannot be compared. Another solution might be to associate seeding positions not with the coefficients but with the path of qualification. For instance, a club can be identified in the UEFA Champions League as the Spanish runner-up rather than by its name. The results of these "labels" can be measured by the achievements of the corresponding teams (Guyon, 2015a).
To conclude, the recommended strategyproof seeding mechanism provides incentive compatibility in any setting. While other rules are also able to eliminate perverse incentives, they are unlikely to be independent of the particular characteristics of the tournament.

Conclusions
The present work has analysed a mathematical model of seeding for sports tournaments where the teams qualify from round-robin competitions. Several contests are designed this way, including the most prestigious football tournaments (FIFA World Cup, UEFA European Championship, UEFA Champions League). The necessary conditions of incentive incompatibility have turned out to be quite restrictive: if each competitor is considered with its own coefficient (usually a measure of its past performance), only one or all of them should qualify from every round-robin contest.
Similar to the main findings of Vong (2017) and Krumer et al. (2020), our result has the flavour of an impossibility theorem at first glance. However, here we can achieve strategyproofness by giving to each qualified competitor the highest coefficient of all competitors that are ranked lower in its round-robin qualifying tournament for seeding purposes.
The central message of this paper for decision makers is consonant with the conclusion of Haugen and Krumer (2021), that is, tournament design should be included into the family of traditional topics discussed by sports management. In particular, administrators are strongly encouraged to follow our recommendation in order to prevent the occurrence of costly scandals in the future.