anlisis del abordaje de la teora de la relatividad

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experience is the starting point for Einstein to develop his theory, contributes to generate ...... el abordaje de la Teoría de la Relatividad Especial en el Nivel Medio y ... Arruda, S. & Villani, A.: 1996, 'Sobre as Origens da Relatividade Especial: ...
PRE-PRINT VERSION Arriassecq, I. & Greca, I. M. (2007) ‘Approaches to the Teaching of Special Relativity Theory in High School and University Textbooks of Argentina’, Science & Education, Volume 16, Issue 1, pp 65-86. The final publication is available http://dx.doi.org/10.1007/s11191-005-5387-9

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Approaches to the Teaching of Special Relativity Theory in High School and University Textbooks of Argentina IRENE ARRIASSECQ 1, 2 and ILEANA MARÍA GRECA 3 1 NIECyT, Facultad de Cs. Exactas, UNCPBA, Campus Universitario, Paraje Arroyo Seco, Tandil, Pcia. de Bs. As., Argentina (e-mail: [email protected]); 2 Programa Internacional de Doctorado en Enseñanza de las Ciencias, Universidad de Burgos, España y UFRGS, Brasil; 3 In-Praxis, Comunidades en Práctica, Burgos, España (e-mail:[email protected]) Abstract. In this work, we presented an analysis of the representation of the Special Relativity Theory (SRT) in the most used texts in high school, Polimodal level1 and university level in the teaching in the Argentine Republic, from a historic, epistemological and didactic perspective. The results show that none of the analyzed texts would allow a contextualized approach on such theory.

1. Introduction In science education exists a consensus on the need for updating the Physics curricula, where in some levels of teaching, the Physics concepts approached do not overpass, in general, those at the beginning of the 20th century (Gil et al., 1987; Barojas, 1988; Aubrecht, 1989; Stannard, 1990; Kalmus, 1992; Wilson, 1992; Swinbank, 1992; F., Villani e Arruda, 1998). Some of the many reasons that are frequently present are: to trigger curiosity in the student; to show Physics as a human enterprise; to allow students the possibility to add to their scientific formation aspects of modern and contemporary Physics that have generated radical changes in science; to motivate students for scientific careers; to analyze Physics concepts that student know through the mass media but whose conceptualization is usually scientifically incorrect; to contribute for the student to build an idea of science and the characteristics of scientific work more adequate to real. From the several topics that form Modern Physics2, we think one of the most relevant is the SRT. In the particular case of Argentina, it is the most widely known by students as a reference for Physics and the one they would be most interested in learning (Capuano et. al., 1997). On the other hand, the SRT is proposed in the ministerial plans in Argentina as a topic in Physics in second year of Polimodal with Natural Sciences orientation. This topic is also recurrently pointed out in research carried out in other countries (Solbes et. al., 1987; Gil et. al., 1988; Moreira, 1990; Galetti, 1990; Farmelo, 1992; Jones, 1992; Swinbank, 1992; Barlow, 1992; Ireson, 1996; Allday, 1997; Ostermann y Moreira, 1998. Contemporary Physics Education Project, 1998; Forelimb, 1998). Furthermore, in the last years several proposals for incorporating the SRT in the high school level of teaching have appeared (for example, G.I.R.E.P., 1991, Bertali et al., Bertali et al., 1979; Solbes, 1986 and Borghi et. al. 1993 in Villani y Arruda, 1998; Fabri, 2001; Aleman Berenguer and Pérez Selles, 2000; Aleman Berenguer and Pérez Selles, 2001, Levrini, 2002), although the results of these implementations are still divergent. From the point of view of science education, the SRT is a particularly rich topic since the first contacts of students with it imply, or should imply, a real inflexion point in the knowledge of Physics, since what there can be of continuity between classic Physics and relativistic is less relevant than what makes them different. This situation sets an interesting challenge for teachers who try to approach the SRT in the polimodal level, since it is not possible to resource to intuition- developed from the experiences individuals have with basic physic systems – to understand relativistic concepts (de la Torre, 1998).

However, we think that the didactic difficulties that will come up during the trial, should not be taken as an excuse to disregard the incorporation of SRT in the Polimodal cycle. We agree with Moreira (2000) in that such arguments in which the SRT is too “abstract” or that students “are not prepared” are not valid, since it is also abstract the classic mechanic that is usually taught : years of research in students’ conceptions in themes of the classic mechanic, show that students also have difficulty in building models according to the ones scientifically correct in this theory that is more “intuitive”. In the searching on how to incorporate the SRT in the teaching at high school level (polimodal), an important aspect that so far has been hardly studied is the analysis of textbooks that are used by both teachers and students. Rodriguez and Pietrocola (1999) analyzed the results of the didactic transposition of the SRT in Physics books for high school level of teaching in Brazil, and found that in the moment of the study, only two works approached the topic. This research also shows that the textbooks’ authors seemed to took as reference for the content only articles and university textbooks. Besides, as SRT was not regarded in the official curricular contents, it is usually presented as an annex and this superficial treatment might generate in readers inadequately scientific concepts. In another research carried out in Spain by Pérez and Solbes (2003), among other matters, epistemological, historical and conceptual aspects of the SRT are analyzed referred to the SRT in teachers and teacher training college students. It was found that teachers in their everyday practice introduce SRT concepts in an acritic and little reflexive way, from distorted epistemological orientations and without taking into account the results of didactic research, a very low percentage of teachers proposes a coherent strategy with a clear conductive line for the introduction of SRT and expressions and phrases which appear reveal a profound ignorance of the central aspects of the theory. Coincidentally, the analysis of 30 textbooks of recent edition in Spain for the teaching of compulsory secondary level (ESO) and first and second year of the baccalaureate show that concepts of space and time are not properly introduced, since the SRT is not presented clearly and disregarding student’s preconceptions. On the basis of these results, we consider relevant to carry out an study on the textbooks used by teachers and students in Argentina, since the effective curricular incorporation is strongly influenced by the contents which appear in the didactic books which teachers use as reference. As it is known, teachers and also students tend to use textbooks as one of the main resources in the teaching-learning process “ the textbook reaches the practice, transmits content, organizes students’ experiences, establishes kinds of interaction, giving it an enormous legal force” (Litwin, 1997). There are many studies which analyze how the textbooks condition the learning of students (Alexander et. al., 1994; Concari et. al. 1999; Portolés, 1993; Tulip y Cook, 1991 en Concari y Giorgi, 2000) and it is known that the teacher besides choosing textbooks she/he will consult, she/he also strongly conditions those used by students. In a previous research (Arriassecq and Greca, 2002), we approached the discussion about what elements should be taken into account to present SRT from a historical and epistemologically contextualized perspective, assuming that this approach, as Hodson (1986) and Kragh (1989) argue, will allow students to understand difficulties, obstacles that needed to be overpasses and the cultural, philosophical and technological contexts different from the actual one where the scientific theories were produced; to interpret science as a human activity carried out by men who give partial contributions answering questions asked in certain periods, i.e., that there is scarcely “only one discoverer”; to understand that scientists, in every historic moment, did not think in our “actual terms” since they used the logic, methodologic and epistemologic tools and the traditions predominant in their environment and their time. On the other hand, we consider that the use of history of science as a didactic resource to structure the presentation of a complex topic, in textbooks or in class, should not derive in extreme simplifications that distort, in teaching, the sense of history of science and of science itself (Matthews, 1994, Lombardi, 1997). In the work we present here, the conceptual, epistemologic, historical, philosophical and cognitive aspects linked to the arousal and development of SRT analyzed in this research were transformed into categories for the analysis of textbooks of polimodal/high school levelmost used by teachers in Argentina, for their class preparation or the ones they recommended to students, according to a previous research. (Arriassecq and Greca, 2003).

2. Methodology For the analysis of textbooks we used “Analysis of Content” (CA) (Travers, 1973; Borg y Gall, 1983; Bardin, 1996), which allows a systematic analysis of them. To carry out the CA it is necessary to encode, consisting of a transformation process of (the) relevant characteristics of the content of a message into units, with the aim of making a precise description and analysis. To carry out the encoding, it is required to define the universe to be analyzed, the units of analysis and the categories of analysis. In this work the universe is determined by the Physics textbooks belonging to high school level of teaching which contain the SRT topic, edited before and after the implementation of the educational reform3 and the university level textbooks most used by teachers4. The units of analysis used result from the chapters of the book or parts of the chapters where the SRT topic is developed. The criteria used to pick as a unit a fragment of a text the one that expresses the same idea or topic, it may vary in extension since it depends on the way it is written and the importance that each author gives to the topic. The categories for Holsti (Simper, et. al, 1997) are the “cells or drawers” where it is possible to classify the units of analysis. For this work, the process of categorization is done beforehand, taking as reference the research works related to the learning of the SRT, the discussions posed in the scientific and epistemological environment about it and the contributions of the historians of the science. The categories were built with those aspects of the development of the topic that would be desirable to find in textbooks to make it a valid resource to give meaningful learning. The following summary of these aspects is presented (A more detailed analysis in Arriassecq y Greca, 2002).

3. A Proposal for Some Structural Axis for the Approach of the SRT in Polimodal Level

3. 1 HISTORICAL CONTEXTUALIZATION OF THE SRT A proper historical contextualization on the rise of the SRT should consider aspects such as a view on the state of Physics in the time the theory develops and the contributions of researchers who paved the way for the SRT. In this sense, the state of Physics could be discussed back to 1905. An interesting aspect in relation to this is the characterization of the Mechanics’ Newtonian Program In the last third of the XIX century, the incompatibility of the Mechanicist Newtonian Programme with the Physics of that time was manifested, particularly with the Physics related to electromagnetic phenomena. Many scientists contributed to a new vision of nature (Faraday and Maxwell, among others). Lorentz headed the trials to reform the Mechanicist Programme In the origin of the SRT it is possible to track down the most “epistemological” influence owed to Mach, through his critics to the Newtonian Mechanics.

3. 2 EPISTEMOLOGIC REFLEXION REFERRED TO THE GENESIS OF THE SRT From an epistemologic point of view, there are many aspects presented in epistemological debates nowadays which discussion can be enriching. For instance, reflexions on the genesis of a theory, its empiric contrastations , its applications, the role of the scientific community in the development of a theory and the influences of the scientific production in the society . Along with these aspects we propose the following dimensions of analysis:

3. 2. 1 The role of experimentation in the genesis of SRT

The opinion of the scientific environment not long ago was to consider the SRT as a big theoric success, the finally right answer to Michelson’s experiment and its natural continuation (Villani, 1981). This opinion, marked by the empiric vision of scientists themselves, passed on to teaching books to such a degree that even such great books as Physics of Berkely and Feynman´s Lectures on Physic scaped from this vision. In spite of this, a careful revision on the history of the rise of the SRT allows to speculate that even if Michelson’s experiment had not been performed, it would not have influenced on the rise of the SRT (Holton, 1982). Insisting on the presentations of the SRT where it is suggested that Michelson’s experience is the starting point for Einstein to develop his theory, contributes to generate in students a distorted view of the scientific activity, encouraging a radically empirist view of science, something which is not desirable, since from an epistemologic point of view there are better proposals (Matthews, 1994).

3. 2. 2 Originality of the SRT The originality of Einstein’s work has provoked a wide controversy (see a very interesting proposal in the works of Villani, 1981-1985) In fact, today there are arguemnts for the originality of his theory , as well as those who sustain that it is the logic corollary of the works of other scientists. That is, in our opinion, one more possibility to rescue in the classroom methodological aspects which discussion may influence in the vision of science that students are building along the learning process of the theory, making easier its understanding as a collective work.

3. 2. 3 Reference to experimental comprobations of the SRT In the case of the SRT, the efforts to put it under proof have not been minor and given the particularly contraintuitive aspects the theory possesses for those approaching it for first time, it should not be disregarded in textbooks and classes the mentions on the different corroborations on it. (Rossi and Hall, 1941; Friech and Smith, 1941 en Mook, D. y Vargish, T., 1998).

3. 2. 4 Reference to the applications of the SRT This aspect allows the interpretation of the SRT as a physic theory, i.e, linked to empirical matters and not as a metaphysic thesis. In this sense, it would be relevant that students could analyze and reflex that the SRT allows the interpretation and explanation of ceratin phenomena, such as the study of subatomic particles, nuclear energy sources, etc and therefore it is not restricted to just theoric matters.

3. 3 REPERCUSIONS OF THE SRT IN DIFFERENT ENVIRONMENTS The SRT, may be as a few other theories, has trascended the scientific environment to influence, sometimes strongly, other knowledge fields hard to imagine for students such as philosophy where it has generated several debates and art. As it was previously mentioned , incorporating these aspects contextualizes the scientific knowledge, showing that it is not an isolated activity and can modify unsespected aspects of reality. It is unlikely that these links can be established by students if the teacher does not encourage a reflexion in this sense.

3. 4 CONCEPTUAL DISCUSSIONS Many works indicate the difficulties students - Physics students and in some cases graduates - have to understand fundamental concepts of the SRT. For instance, they usually give explanations of purely relativistic concepts in terms of Newtonian mechanics. (Aleman Berenger, 1997); they tend to consider the “system of reference” as decorative trick, without an explicative function and, in general, they do not show to possess a metaconceptual understanding of this concept as a tool which allows a proper formulation of the physic principle of the theory of relativity (Panse et. al., 1994). The students, also, do not take into account the transformation laws of space and time given a concrete situation , handling with intuitive ideas about both concepts; they rarely use the Galilean laws of the principle of relativity though it can simplify the problem a lot and they confuse the invariant of the laws between frames of reference in relative movement with the invariance of time in a certain frame (Ramadas et al , 1996). It would seem, then, that the concepts from the SRT itself would be interpreted from conceptual basic matrix or simply by learning by heart certain definitions and formulae. The results of the research also aim to point that not only students have mistakes related to the SRT, but also the teachers. The mistakes spotted in teachers seem to be related with an inadequate formation topics such as the SRT trying to find-in the same way students do- explanations to concepts basically relativistic in terms of Newtonian mechanics (Aleman Berenger, 1997). This conceptual understanding, on the other hand, is fundamental in a contextualistic view on the teaching of Physics, since it is impossible to understand the scope and the consequences of a scientific theory without an understanding that the ideas expressed by it represent and in what way they are new and they separate from other ways of understanding the Physic phenomena. In this sense, one of the most important consequences of the SRT is the modification of the notions of space and time respect to the interpretation in the classic mechanics. However, when these concepts are intended to be described or approached in the classroom, difficulties arise and may be one of the reasons may be related to the fact that the concept of time “... reaches everything: work, economy, information, language, biology, determinel our lives which is in itself temporal.” (Loma, 1999). Despite the differences, all notions of time can be analyzed in a continuum, whose ends contain at the same time other notions such as “movement”, “change” on one side and “rest”, “continuity” or “duration” on the other. In this sense, time and change seem to be closely linked from the philosophic and scientific point of view. If we center in the scientific perspective, we find in one extreme Galileo, Leibniz, Berkeley and, lately Mach who understands time related to movement and therefore, to change. On the other extreme we find Newton with a conception of time as absolute, universal, independent from movement and with no relation to changes. This notion of time is linked with other key notions for Physics: the simultaneity and a common time to all observance with no relation at all with matter. The Newtonian concepts have been criticized along history, beginning by Berkeley and Leibniz in their own time. However, the most relevant critics to this work are the ones due to Mach in his “Historical-critical analysis the Mechanics” (1949), where he states that absolute time has neither practical nor scientific value. Mach’s idea is that a scientific notion of time is that which is objective and it is only achieved by measuring. The important thing is the instrument, that must be placed where certain event is produced. In this way the results obtained stop being universal. Poincaré, in the beginnings of the 20th century, adheres to Mach’s perspective and centers the discussion around two relevant issues for science, disregarded so far. One of them is the circularity of certain fundamental concepts for Physics and among them, space and time. Poincaré works this problem out by assuming the time as what is indicated by any instrument of measurement and that its properties are that of the clock, in the same way that the properties of space are the ones from the instruments of measurement. Although Poincaré’s idea sets an alternative to the circularity problem in the definition of concepts such as space and time, another fundamental issue for Physics comes along: the notion of simultaneity, a primary and absolute concept in the Newtonian mechanics, in the sense of being an essential property when the idea of absolute time is accepted. In Poincare´s view, it requires to be established between two events that the measure instruments (for example clocks) are found in the same place where they are produced and that those who manipulate them lately (observants) communicate with

each other and “decide” if the events were simultaneous or not. We believe that a deep discussion about the concepts of space and time and the role they perform in classic mechanics is fundamental to be lately “reinterpreted” in the framework of the SRT. Fundamentally, it is necessary that students reflect and explicit their notions of observers in the context of Physics and the classic mechanics in particular so that lately the student, with the help of the teacher, is able to differentiate the idea of observer in the SRT and that of classic mechanic. In this background, where it is accepted that the speed of light has an unlimited value, it is enough to consider that an observer is a person placed in a system of reference with a precise instrument, such as a chronometer to register time. In this way, it seems plausible what Ostermann and Ricci (2002) consider in relation to what students might link to the idea of observer with a person who “watches” giving the sense of “seeing” or “looking”. It is fundamental that the student is able to distinguish from the Physic point of view that in the context of the SRT “looking” is not the same as “measuring” and, at the same time, measuring requires to redefine the notion of observer. For this reason, in the context of the SRT, the finite value of speed of light requires “to complex” the notion of observer, which allows to get records of events occurred in distant places. Taking into account what has been previously stated, we consider that it would be important that in textbooks there were an explicit reference of the following aspects: deepening on the notion relative movement in the frame of Classic Mechanics, discussion of contraintuitive concepts (Posner, et. al. 1982; Villani y Pacca, 1987; Gil and Solbes, 1993; Arruda and Villani, 1996; Villani and Arruda, 1998), discussion on the concepts of space and time, analysis and discussion on the concepts of observer and simultaneity in the frame of SRT (Angotti et al, 1978, Aleman Berenger and Pérez Selles, 2000), and the clearing of paradoxes.

4. Indicators and Values Given to Categories In this section, values assigned to the subcategories conforming each category are assigned and exemplified (where it is possible to do so). The resultant value in a general category and the adopted indicators to give the respected values, qualitative and quantitative, are taking having as reference the development of the previous section.

4. 1 HISTORICAL CONTEXTUALIZATION OF THE SRT (HCT)

4. 1. 1 State of Physics when the SRT arises (SOP) 4. 1. 1. 1 Values: - Adequately described when the Mechanicist Program, its crisis and the Electromagnetic Program are analyzed,. - Superficially described: when the topics indicated above are (it is) simply mentioned "at the beginning of the present century, all Physics was framed into two big theories: mechanics and electromagnetism” (Text 3, high level p. 383) " By the end of the XIX century (...) the Newton laws of movement and gravity seemed to describe all the known movements about the Earth as well as the planets and celestial bodies, while Maxwell equations of electricity and magnetism could give a complete description on the electromagnetic phenomena” (Text 1, university level, p. 1100).

- It is not described: when no reference is made to the mentioned aspects.

4. 1. 2 Analysis on the concept of ether 4. 1. 2. 1 Values - Adequate: when the different conceptions of ether are presented along history up to reaching the concept of electromagnetic ether. - Superficial: when only the electromagnetic ether and its characteristics are mentioned. " The ether accepted in that time as the background of the universe was useful as a system of reference for absolute stillness, through which celestial bodies moved and as reference to measure absolute movement” (Text 4, high level, p. 168) " In other times it was though that light spreader through a medium called ether, likewise the sound waves do so in the air (...) Today it is known ether does not exist”(Text 2, university level, p. 331)

- There is no analysis: when the concept of ether does not appear to be relevant. 4. 1. 3 Values for the category HCT - Adequate: when all the categories are so (Numeric value: 2). - Superficial: when one of the subcategories is not adequate (Numeric value: 1). Non existing: when both subcategories take the last value assigned to them (Numeric value: 0).

4. 2 EPISTEMOLOGICAL REFLECTION REFERRED TO THE GENESIS OF SRT (ERT)

4. 2. 1 Role of experimentation in the genesis of the SRT (REG) 4. 2. 1. 1 Values - Vision according to the historical discussion of the role of experimentation: the different views of the historians as regard the role of Michelsons’ experiment in the SRT are discussed or mentioned. "Although the Michelson-Morley experiment was carried out before Einstein published his work about the relativity, it is not clear whether Einstein was acquainted with the details of the experiment or not” (Text 4, university level, p. 1158)

-Distorted vision on the role of experimentation: when it suggests that Michelson’s experiment was the starting point for the SRT. "The idea of Einstein was of an extreme simplicity. It consisted of considering Michelson’s results step by step ... "(Text 5, high level, p. 94)

- Neutral vision on the role of experimentation: when only the formal aspect of the SRT is presented and the Michelson experiment is mentioned/described without explicitly linking it to the SRT. "… trials were made to determine the speed of Earth through the hypothetical ether (...) The most famous of these experiments is one performed by Michelson and Morley in 1887. Only 18 years later Einstein finally explained the negative results of the experiment”(Text 6, high

level, p. 15-5).

4. 2. 2 Originality of the SRT (OTS) 4. 2. 2. 1 Values - Partially original: possible contributions are discussed. " ... Einstein, ... examined very carefully the situation of these problems, the Michelson’s experience, the theories of Physics of his time, among them Lorentz, and exposed his theory of relativity in 1905." (Text 1, high level, p. 203) " the theory of relativity... developed by Einstein and other scientists in 1905…" (Text 1, university level, 1100)

- Completely original: when all merits are attributed to Einstein and previous contributions from other scientists are not considered.

4. 2. 3 Reference to experimental comprobations of the SRT (RCE) 4. 2. 3. 1 Values - Sufficient: when the experimental corroborations are discussed in detail " A similar effect [to the time itself for the system of reference of a muon detected from the Earth] was measured by two jet planes in 1971 equipped with atomic clocks of cesium of high precision... " (Text 6, high level, p. 85)

- Scarce: when only some corroboration are mentioned. "Similar results [to the disintegration of muons] have been obtained with particles produced in the laboratory, using machines which accelerate the particles to very high speed. The observation of particules dicrease in the haz confirms the dilatation of time" (Text 3, high level, p. 414)

- Null: when no reference is made to experimental corroboration.

4. 2. 4 Reference to the applications of the SRT (ATR) 4. 2. 4. 1 Values - Diverse references: when several applications of the SRT are mentioned -Superficial references: when only some kind of application is mentioned. "Nowadays, the idea [mass increases with speed], is used with practical ends in nuclear energy plants and in the systems of propulsion for ships" (Text 2, high level, p. 138) "These theories [the relativity and the quantum mechanics] … constituted the fundamentals of new technologies which have changed the face of our civilization" (Text 1, university level, p. 1121)

- Non existing references: when applications of the SRT are not mentioned.

4. 2. 5 Values of the category RET - Profound epistemological reflection: when more than a half of the assigned values in the subcategories correspond to the first values assigned to the subcategories (Numeric value: 2). - Superficial epistemological reflection: when neither the first nor the third values are assigned to the subcategories (Numeric value: 1). - There is no epistemological reflection: when more than a half of the assigned values in the subcategories correspond to the last values assigned to the subcategories (Numeric value: 0).

4. 3. REPERCUSSIONS OF THE SRT IN DIFFERENT AREAS (RDA)

4. 3. 1 Repercussion in the scientific environment (RAC) 4. 3. 1. 1 Values - Diverse references: when the repercussions of the SRT in the scientific community are widely explained. - Scarce references: when only some fact is mentioned or a superficial comment is made. " These theories [the relativity and the quantum] revolutionized the world of science". (Text 1, university level, p. 1125)

- There is no reference: when this aspect is not considered in the development of the SRT

4. 3. 2 Repercussions in the Philosophy environment (REF) 4. 3. 2. 1 Values - Diverse references: when the repercussions of the SRT are explained in the Philosophy environment. - Scarce references: when it is only mentioned that it also influenced the Philosophy field. " The Einstein’s relativity theory has given place to many philosophical questions: what is time, exactly? ... Is there any region of the universe where time advances backwards? ... (Text 7, high level, p. 255)

- There is no reference: when this aspect is not considered in the development of the SRT.

4. 3. 3 Repercussions in the art environment (RAE) 4. 3. 3. 1 Values - Diverse references: when the repercussions of the SRT are explained in the artistic environment. - Scarce references: when it is only mentioned that the SRT also influenced the filed of Arts. " ... Time, immutable, uniform and absolute form the philosophy of Emmanuel Kant resulted relative, elastic and dependant, and it is well represented in the soft clocks by Salvador Dalí" [ there is a photo of a picture by Dalí] (Text 5, high school level, p. 95)

-There is no reference: when this aspect is disregarded in the development of the SRT.

4. 3. 4 Values of the category RTA - Diverse references: when this value is obtained in all the subcategories (Numeric value: 2). - Scarce references: when at least one of the subcategories take this value (Numeric value: 1). - There is no reference: when this value corresponds to all the subcategories (Numeric Value: 0).

4. 4 CONCEPTUAL DISCUSSIONS (CD)

4. 4. 1 Discussion on the concepts of space and time (CET) 4. 4. 1. 1 Values - It is discussed with attention: when there is a discussion of the most relevant theories that along history have developed in different knowledge environments as trials to interpret the concepts of space and time. - It is superficially analyzed-: when it is mentioned that, before the SRT appears, existed several attemps trying to interpret these concepts. " ... It was never clear whether the Universe existed in space or if space existed within the Universe. Is there space outside the Universe? Or does space only exist within the Universe? We could make the same questions about time. Does the universe exist in time or time exists only within the universe? Will there be time if the universe stops existing?" (Text 7, high school level, p. 224)

- There is no discussion: when the concepts of space and time are presented as intuitive notions that do not require a profound conceptual analysis.

4. 4. 2 Analysis of the concept of observer the SRT (ACO) 4. 4. 2. 1 Values - Adequate: when it is deeply analyzed the need to redefine the concept observer in the frame of the SRT. - Superficial: when it is mentioned that more than one instrument is necessary but there is no detailed analysis to justify the statement. " We can imagine a referential as a cubic entangled of rigid rules with a clock on each knot ... in a way that allows us to assign an event to the spacial coordinates from the vertice closer to the net and the temporal instant marked by the corresponding clock" (Text 8, high school level, p. 277) " the frame of reference used to describe an event has a net of coordinates and a set of synchronized clocks that are placed in the intersections of the net, as it is shown in the two dimension figure" (Text 4, university level, p. 1162)

- Non existing: when the role of the observer does not appear as a relevant aspect in the treatment of the SRT:

4. 4. 3 Discussion of contraintuitive concepts (DCC)

4. 4. 3. 1 Values - The analysis is emphasized: when contributions by science education researchers are considered. - It is mentioned: when some of the concepts that can turn contraintuitive are mentioned. "Relativity Theory of Einstein leads to contradictions in the common sense."(Text 5, high school level, p. 94) " ... Although it is contrary to all intuition, this statement [constancy of c] eliminates once for all the needs for ether “ (Text 5, high school level, p. 94) "If we accept Einstein SRT (...) we must modify our notion of common sense about the space and time and be prepared for some unexpected consequences". (Text 4, university level, p. 1162)

-They are not taken into account: when no reference is made to the fact some concepts of the SRT are counterintuitive.

4. 4. 4 Discussion of the simultaneity concept (DCS) 4. 4. 4. 1 Values - It is deeply discussed: when there is a special chapter for the treatment of the concept and its difficulties are specified. In the text number 6 (from polimodal level) there is a paragraph denominated “the space-time and simultaneity “ where the concept is discussed deeply. (p. 78) In the university number 2 text, p. 333 it is analyzed with the title: “The relative nature of simultaneity”

- It is mentioned: when only the concept is defined. "The invariance and finiteness of the speed of light have a demolishing consequence for the Galilean structure of space-time: the concept of simultaneity is relative. Events that occur at the same instant respect of an inertial are not necessarily simultaneous for another inertial observer who moves respect from the first (Text 8, high school level, p. 278)

- There is no discussion: when it is not presented as a relevant topic 4. 4. 5 Notion of relative movement in the frame of Classic Mechanic (NMR)

4. 4. 5. 1 Values - A profound revision is made: when the difficulties mentioned by researchers are taken into consideration. - A synthesis is presented: when a revision is made on what was studied by Classic Mechanics Text 6 (university level), p. 15-1 a 15-3.

- It is mentioned: when it is mentioned that frames of reference and relative movement will be worked, one respect to the other, taken for granted students handle the topic with no difficulties. " The idea that speed is a relative quantity is owed to Galileo, and it was well known well before Einstein’s time.”(Text 7, high school level, p. 226)

4. 4. 6 Analysis on the paradoxes of the SRT (APT) 4. 4. 6. 1 Values - They are deeply discussed: when it is analyzed what the paradox is about and it is explained how it is worked out. In the university text 1, p. 1119, with the title: " Paradox of the twins"

-

When they are mentioned: when it is mentioned that the SRT gives place to paradoxes: " ... in the case a ship was able to move at 180000 km/s in relation to the Earth, the earth clocks will be 25% faster than the ones on board. When for the astronauts four years have gone by, for the earthlings five will have gone by. (It is not easy to understand that the same argument can be used and a change in the system of reference to state exactly the opposite, this is what the relativity of time consists of, there is no absolute time)” (Text 5, high school level, p. 96)

- They are not mentioned: when no references are made to the paradoxes of the SRT.

4. 4. 7 Values of the category DCO - Profound didactic reflection in the approach to the topic: when the first assigned value predominates (Numeric Value: 2). - Scarce didactic reflection in the approach to the topic: when neither the first nor the third of the assigned values to the subcategories are predominant (Numeric value: 1). - Didactic considerations for the proposing of the topic have not been taking into consideration: when the third value assigned to the subcategories is predominant (Numeric value: 0).

5. Analysis of the Results Once the data obtained in the study of the most used textbooks of high school/polimodal level and university level in Argentina is organized, the obtained results appear in charts 1 and 2. We consider important to clear we do not pretend to make a judgement value about the analyzed textbooks, in the sense of labeling them as “good” or “bad”. Ultimately, the attributed values correspond to their adequacy or not to be used in the teaching-learning process of the SRT, from the point of view of the theoretical frame discussed at the beginning of this work and to reach the aims already commented. Table I. Summary of the analizes of high scholl and polimodal textbooks level

T1

CHT 0 1 2 •

RET 0 1 2 •

RTA 0 1 2 •

DCO 0 1 2 •

TOTAL 0 1 2 2 2 -

T2 T3 T4 T5 T6 T7 T8 T9 TOTAL



• • •

• • •

• • •

• •

3

• • 6

• • •

-

3

• •

• • •

• • • 6

-

• • 7

2

3 2 2 2 3 2 1 2

• • • •

-

• 6

3

1 2 2 2 1 2 3 2

-

-

Table II. Summary of the analizes of university textbooks level

T1 T2 T3 T4 T5 T6 TOTAL

CHT 0 1 2 • • • • • • 6 -

RET 0 1 2 • • • • • • 3 3 -

RTA 0 1 2 • • • • • • 4 2 -

DCO 0 1 2 • • • • • • 3 3 -

TOTAL 0 1 2 4 3 1 1 3 1 3 3 1 1 3 -

The first aspect derived from the charts is that textbooks, at high school, polimodal and university level, do not obtain in any of the categories analyzed the maximum value “2”. This fact seem to indicate that in the text necessary aspects to present the SRT from a historical and epistemological contextualized perspective have not been taken into account and that there are not enough conceptual discussions that contemplate the contributions of science education research such as the deepening of the notion of relative movement in the frame of Classic Mechanics, discussion of contraintuitive concepts, concepts of space and time, analysis of the concept of observer in the frame of SRT , discussion on the topic of simultaneity, and the clearing of paradoxes. These results are coincident with the ones found in Spain by Pérez and Solbes (2003). If in the charts the values are looked for each text it is observed that though some of the subcategories have the value “2”it is impossible to gather topics from different texts so as to approach the SRT from the perceptive placed here, with a proper scoring. Even in the most used textbook, according to a research carried out for both teachers and students – text 7 from annex 1 – (Arriassecq and Greca, 2003), get the value "2” in only one subcategory, being the value "0” predominant in the rest. Summarizing, the analyzed texts incorporate neither the different results of the research in science education nor the historical and epistemological discussions on the topic. Although it can be thought that the editors of books may not be worried about this aspect, it is somehow significant that the authors of textbooks, that should be aware of this necessity and incorporate issues as the ones analyzed here, do not do so. At the same time although many of the textbooks analyzed here for the teaching at polimodal level specifically discuss in separate chapters epistemological issues about science (what makes different a scientific production from another type of knowledge, how scientific knowledge is validated, which are the methodologies for work in different disciplines, etc), from visions that would be framed as non positivists, the superficial treatment, in this aspect in the case of the SRT, seem to show that like teachers, authors of textbooks repeat the old simplified university versions of the SRT. This

might confuse teachers themselves that without a proper formation on the topic – neither historical, nor epistemological or conceptual – only use for teaching modern textbooks of polimodal level that keep on approaching the SRT as a simplified version of the textbooks at university level, where the historical reference is usually non existing and when it is present usually diffused or in the worst of cases, distorted. As regards the epistemological aspect, as it was mentioned, although some authors claim to be non positivists, the selection they make on the topic and the use, in many cases inappropriate, that they make of the history of the science, favor distorted visions of the scientific work and the methods for its validation.

6. Final Comments According to the results obtained in other researchs carried out by us about the SRT (Arriassecq y Greca, 2003): • The textbooks seem to be the main resource used by teachers for the preparation of the classes, mainly in polimodal level, which are the same they recommend to students, • The way topics are approached may strongly condition the results obtained by students about the learning of it, in this case, the SRT. • Teachers who have to face the task of approaching the SRT for first time will generally resource to the textbooks for the guidance of their classes and considering that in many cases the teacher has not had the chance to reflect deeply on which are the relevant concepts to understand the theory, she/he will probably “go on” the scheme presented in the textbooks selected to prepare her/his class without a reelaboration of the material according to his own criteria. On the other hand, results presented here, which coincide with those obtained in other countries about the same topic, show the inefficiency of the didactic material available for the teachers to approach, from a contextual perspective, the introduction of the SRT in high school/polimodal cycle. Starting from this reality and from the presupposed that it is possible and necessary to introduce in high school/polimodal level, the physics contents from a contextualized view –conceptually appropriate and motivating – to give a meaningful learning to students, it seems to be necessary the elaboration of didactic material that could be used by both teachers and students. This material should present a profound discussion of the relevant conceptual aspects of the SRT from the contributions made by science education research.

ANNEXE: Analized Textbooks •

High School Level: Before Educational Reform

Text 1: MAIZTEGUI, A. y SABATO, J.1980. Introducción a la Física, Tomo I. Ed. Kapeluz: Bs. As. Text 2: STOLBERG, R. y HILL, F., 1982. Física: Fundamentos y Fronteras. Ed. Publicaciones Cultural, S. A.: México Text 3: CASTIGLIONI, R., PERAZZO, O., RELA, A.1983. Física 2. Ed. Troquel: Bs. As. Text 4: HECHT, E. 1987. Física en Perspectiva. Ed. Addison – Wesley Iberoamericana: USA.



High School and Polimodal Textbooks Level: After Educational Reform

Text 5: RELA, A. y SZTRAJMAN, J. 1998. Física I: Mecánica, ondas y calor. Ed. Aique: Bs. As. Text 6: ARISTEGUI, R. y otros. 2000. Física II. Ed. Santillana: Bs. As. Text 7: HEWITT, P. 1995. Física Conceptual. Ed. Addison – Wesley Iberoamericana: USA. Text 8: GALINDO, A. y otros. 1997. Física 2° de Bachillerato. Ed. Mc Graw Hill: Madrid. Text 9: PEÑA, A. y GARCIA, J. A. Física 2° de Bachillerato (Logse). Ed. Mc Graw Hill: Madrid, 1996.



University Texbooks Level

Text 1: TIPLER, P., 1996. Física. Ed. Reverté: Barcelona. Text 2: SEARS, F., ZEMANSKY, M. y YOUNG, H., 1981. Física. Agilar Text 3: ALONSO, M. y FINN, E., 1995. Física. Addison Wesley Iberoamericana: Text 4: SERWAY, R. 2001. Física, tomo 2. Mc Graw - Hill: México. Text 5: RESNICK, R. y HALLIDAY, D. 1981. Física, parte 1. Compañía Editorial Continental, S.A.: México. Text 6: FEYNMAN, R., LEIGTHON, R. y SANDS, M. 1971. The Feynman Lectures on Physics", Vol. 1. Fondo Educativo Interamericano, S. A.

Notes 1

Since 1992 an educational reform was implemented in the Argentine Republic, changing from a strucuture that differenciated primary level (seven years of schooling)from secondary level (five years of schooling)to another where the general basic education (EGB) is extended up to 9 years to which three more years of schooling are added, denominated polimodal, replacing the superior cycle of high school or secondary school. 2 We will denominate as Contemporary to Physics developed during the XX century, following the common use in the Philosophy of Science. In this environment, Modern Physics is applied to Physics developed during the Modern Age (XVII and XVIII centuries), although it is necessary to clarify that consent doesn't exist in this respect. Then, some authors use "Modern Science" for Physics developed in Modern Age (S. XVII), and "Modern Physics" for Quantum Mechanics, in opposition to the idea of Classic Physics. 3 Although the SRT is a topic of second year in Physics of Polimodal level, are few texts published after the educational reform that consider it but some texts previous to the reform include the SRT, so we analyzed them too. On the other hand, teachers usually consult these texts. 4 The texts of polimodal level more consulted for teachers of this country have the character of "classic" since the author is well known in national comunity of Physics teachers or for the diffusion given by the corresponding editorial. University level texts, they can also be considered classic since they are habitually used in diverse universities of the world in scientific careers that include matters of Physics (information obtained by personal communications with educational investigators of diverse countries).

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