Innovation paths: Germany and the United States of America

The circulation of Johann F. Herbart’s educational ideas depended on mediators and mediation vectors (^{SIRINELLI, 1998}) in both Germany and the United States of America. He was a Fichte student (1762-1814), contemporary of Schelling (1775-1854) and Hegel (1770-1831) and developed his theories, therefore, at a time when German philosophy was quite fruitful and, in Europe, it had become synonymous with complex and rigorous systems of thought. The philosophical system proposed by Herbart encompassed Logic, Metaphysics (from which Psychology was derived), and Aesthetics (source of ethical precepts).

Rejecting the conception of the human mind as a structure composed of a set of functions (observation, comparison, classification, association) that, mediated by the senses, would lead to the formation of ideas, Herbart developed the concept of apperception. In it, the mind is conceived as a structure shaped by the individual experiences that form the perception mass that, in turn, would be in constant change due to new knowledge that would join those already existing. From this mass of apprehension, the judgments and choices of individuals would arise, and supported by this scheme of psychological functioning, education would have to interfere, through the selection of information and experiences, for the establishment of a circle of thoughts that would contribute to the shaping of character. In this mechanics, Psychology - the means - was joined by Ethics - the ends - to emphasize moral education.

Despite proposing a sequence of procedures divided into four steps (clarity in the presentation of new ideas, association with previous knowledge, formation of an integrating system of ideas and application), Herbart’s propositions did not spread at the time of their elaboration (between 1806 and 1829). ^{Dunkel (1970)} lists possible causes: it was an unclearly exposed system for which no applications were envisioned, it was not a genuinely original paper, and it lacked empirical bases.

In 1861-1862, Tuiskon Ziller took up Herbart’s ideas and created a Pedagogical Seminar, linked to the University of Leipzig, and an educational institution dedicated to teacher training; the first offered theoretical discussion and in-depth study, the second was a space for seminar participants to develop practical activities aimed at elementary education, an educational level to which Herbart had little dedication. Investing in the applicability of the general system proposed by Herbart, Ziller adopted the concept of historical stages of culture (culture epochs) and the concentration of studies to organize the curriculum of elementary education and the formal steps of instruction to guide its practice (^{DE GARMO, 2001}) to enrich the circle of thoughts and shape the childlike character. Another important initiative was the foundation, in 1868, of a Society for the scientific study of education, which quickly became a source of publications and brought together students and teachers, contributing to the dissemination of the work of the Seminar.

In addition to Tuiskon Ziller, two other German educators were relevant for disseminating of Herbart’s thought or for the constitution of what came to be called Herbartianism. One of them, Karl Volkmar Stoy, a former student of Herbart, also created a Pedagogical Seminar and a Practical School linked to the University of Jena (1874), without introducing significant changes in the theories of the master. The other was William Rein, a former student of Ziller. He succeeded Stoy in the direction of the Seminar (1885) and established the five formal steps of the teaching method that were identified in this regard - preparation, presentation, association, generalization, and application - explaining them in language purified of academicism. In addition, he devised detailed teaching programs in which formal steps were exemplified. Rein’s seminar was attended by many international students who created Herbartian societies outside Germany, widening their repercussions radius.

The interpretation of Johann F. Herbart’s propositions produced by his successors, mainly at the Jena Seminar, reached the United States of America. Among the many students who took part in their training in Germany were Charles de Garmo and the brothers Charles and Frank McMurry who, upon returning, translated papers linked to the Seminar, produced bibliography aimed at teachers and created the Herbart Club, becoming the prominent North American leaders of Herbartianism (^{KLIEBARD, 2004}; ^{DUNKEL, 1970}; ^{HARPER, 1970}, RANDELS, s / d; ^{CRUIKSHANK, 1998}).

In this trio, Charles Alexander McMurry (1857-1929) was the most prolific author⁵, and through his production (or part of it) one can analyze the diffusion cycle of the Herbartian educational conception and monitor its modulations. In addition to bibliographic production, he worked at different levels in the school system, which allowed him to address a large audience of readers. He attended Illinois State Normal University and the University of Michigan; in Germany, he studied at the University of Halle and, in a second visit, obtained his Doctorate (1887) and joined his brother, Frank McMurry, at the Pedagogical Seminary of the University of Jena. He was a teacher, director, and superintendent on primary schools and courses for teacher training in different North American states. He was one of the founders, in 1892, of the National Herbart Club, which became (1895) the National Herbart Society, acting as its secretary. In 1899 he implemented, at the Northern Illinois State Normal School, in DeKalb, a program based on Herbart’s ideas; between 1906 and 1907, he was director of California State Normal School (Pennsylvania), returned to DeKalb as superintendent in 1911 and developed a teacher training program integrated with municipal schools; in 1915 he became a professor at Peabody College of Education at Vanderbilt University.

Charles McMurry’s study trips and the production of pedagogical bibliography were integrated, in the late decades of the 19th century, to the set of demands for a rapidly expanding educational system. Between 1870 and 1898, the general North American population doubled quantitatively, mainly in urban areas, as well as the school population. To serve it, an educational structure was created in each state composed of different degrees and modalities of instruction. Railroads, press, and industries that then spread contributed to creating the greatest good achieved by the public education system in the United States: a population that reads newspapers and books, has general knowledge, and is interested in national and international issues, vital to a nation governed primarily by public opinion, as Commissioner General of Education William T. Harris proudly described (HARRIS, 1900).

The official report pointed out that in 1895-6, there were 130,366 teachers and 269,959 teachers working at that moment: 362 Normal Schools in operation, with 67,380 students and 7,184 public libraries with 34,596,258 volumes (^{DRAPER, 1900}, p. 30). Such data were related to the improvement in educational literature, including official statistical reports and results of studies on different problems, such as educational theory, teaching procedures, child development, and hygiene (^{BUTLER, 1900}).

These indicators outline an environment conducive to questioning the teaching methods and the curricular organization then in force. The Pestalozzian conception, widely disseminated among teachers and school superintendents (^{HARPER, 1970}), came to be criticized for the insufficiency of scientific foundations that, in the period, began to be identified with knowledge about the psychological processes of learning. Despite their contributions, such as fixing the importance of the senses and the concrete facts for the acquisition of knowledge, it was pointed out its transformation into formal training of the intellect for emphasizing the process more than the content to be taught. In the 1890s, the Herbartian propositions seemed to offer a systematic, erudite pedagogy with academic status⁶; the guidelines for school practice, something that his successors gave him, secured his renewing potential, and introduced a new pedagogical vocabulary in the Normal Schools (^{HARPER, 1970}). Charles McMurry’s handbook played a strategic role in this process.

In the Preface to the book The elements of general method based on the principles of Herbart, Charles ^{McMurry (1893)} clarifies his intention to explain the Herbart pedagogical theory developed and practiced at Jena Seminary. This explanation consists of a set of mutually related principles from which practical guidelines are derived that can be adopted in the North American school system.

The book has about 200 pages, and it is organized into eight chapters that deal with the purposes of education, the educational values on different fields of knowledge, and the principles that underlie the concept of learning, namely, the interest, the concentration of studies, the induction and perception that, together, would enable the formation of character, a primary objective to be achieved with schooling. According to the author, the last chapter included a commented bibliography that will expand the understanding of this educational theory.⁷

After a brief examination of different pedagogical systems, the author states that the main objective of education, pursued by society in general and by parents, must be character formation. This moral element must be subordinated to all schools’ actions develop. The book then presents an organizational proposal for primary education with a description of the means to carry it out.

Among these means would be the selection of knowledge and, inquiring about the intrinsic values at each school content, McMurry replies that the most valuable is History, followed by Natural Sciences and formal studies - Grammar, Writing, Arithmetic, and the symbols used in reading.

According to the author, History should be the most valued knowledge. After all, it is directly related to moral formation given that its content reveals human action. Through the careful choice of simple and clear episodes, it would be possible to show people acting in a noble or less virtuous way and understand all the social and individual motivations that shaped their conduct. Such knowledge would serve the purpose of evidencing the empirical basis of moral judgments that, through repetition, could become convictions.

The Natural Sciences derive their value from the fact that they contribute avoiding the solidly rooted tendency to substitute words for ideas, as they are the raw material for the exercise of inductive thinking. For the author, they constitute a field for observation and human needs development, materializing work and creative skills, bringing information, utility, training of the senses, and the capacity for judgment to school. In this perspective, they should not be taught only for their intrinsic usefulness. However, for the contributions they bring to the development of the scientific spirit and the multifaceted achievement, interdependent and transversal culture, characteristics that some well-chosen themes could typify.

In this classification, formal studies occupy third place and should be at the service of actual studies and not just memorization, therefore, ceasing to occupy the center of school programs. To emphasize his argument, the author describes how the curriculum, then in force, made formal use of literary works (reading, writing, fluency, and expression of rhetoric) and proposes that its educational purpose be expanded so that students could appreciate it. They can encourage habits and bring values to moral and artistic culture. Biographies, masterpieces, and poems, among other literary genres, express human thoughts, habits, dispositions, and institutions and, therefore, should be seen as contributions to the teaching of History and not just as languages.⁸

The following chapters of the manual address the conceptual framework on which the school organization content was structured. Interest, defined by Herbart as the natural inclination of the mind to find satisfaction in a subject, would act as a learning engine. Since it can be speculative, empirical, or aesthetic, it can be fueled by History and Natural Sciences and is more easily captured by specific people and objects than by general propositions, laws, or classifications. Provided that they are properly presented in school activities, these fields and their themes would keep the students’ mental action in operation, as they relate to human actions and, thus, would promote the necessary energy for character development.

According to the author, the organizational principle, according to the author, most conducive to the development of interest is the concentration of studies. Its adoption aims to establish relationships between the fields of knowledge to generate unity in the child’s mind, without dispensing with the variety (culture of multiple interests), since no matter can be well understood in itself, but in the relationship with other fields and with the experience. A study plan organized according to the principle of concentration is based on the selection of the best (morally educational) themes and materials that would function as centers in different school grades, from which multiple relationships could be established. This organization is supported by the conviction that only thoughts resulting from a strong idea and that are connected to others remain in mind. The final test of the concentration value of studies is the ability to readily use them in everyday experience, which is also constituted as a network of connections.

The cultural stages (culture epochs) would be the key to objectify the concentration of the studies, affirms McMurry supported by the German Herbartian. Such a proposition advocates the existence of similarity between the development of the human species and child development: “The child began where primitive man began, feels as he felt, and advances as he advanced, only with more rapid strides; that as his physique is the hereditary outcome of thousands of years of history (MCMURRY, 1893, p. 111). According to this proposition, it would be possible to find, in the different historical periods, intellectual and moral material to understand the stage in which society was.

To adapt cultural internships to the North American school program, McMurry suggests four main periods - for pioneers, navigators, and explorers; the agreements of colonial history and the struggles with the Indians; from the revolution under the confederates to the adoption of the constitution and self-government and the federalist idea -, accompanied by an excellent bibliography, both biographical and literary. With these periods as axes, the various types of knowledge would be articulated to them for the effectiveness of the concentration of studies. The selection criterion would be the organic harmony between the knowledge, the connection between the themes, and the mutual clarifications they can provide.

This organizational form of instruction adopts induction, which is the mind’s tendency to progress from observing specific objects to abstract concepts. According to McMurry, it consists of a solid path to gradually transform the unconscious inductive tendency into careful scrutiny, an essential quality for intellectual and moral formation. By characterizing the inductive process, the author seeks to expand the scope and meaning that the lessons of things conferred on him, a teaching method of Pestalozzian orientation in use in primary education:

By object lessons is usually meant things in nature perceived through the senses. But it is necessary to extend the idea of object lessons beyond the objects and phenomena of the physical world, to which it has been usually limited’ (^{MCMURRY, 1893}, p. 143).

That extension must cover the direct exercise of the senses in the acquisition of experiences of all kinds, including objects, people, and everyday events, on which it would be possible to anchor the progress of knowledge and reflection. Therefore, it would be lessons in extensive and systematic things applied also to moral education. This cognitive process would be facilitated by adopting cultural periods as content and concentration as a strategy. The described mental processes would lead to perception, defined as “the process of acquiring new ideas by the aid of old ideas already in the mind” (^{MCMURRY, 1893}, p.157, emphasis added), the most complex stage of the learning process.

In conclusion, the author states that the exposed principles serve the purpose of showing the mutual and dependent relationship between objectives, theoretical conception, and teaching method, all aimed at character formation.

Thus, it was under the sign of renewal that J. Herbart’s ideas were put into circulation in the United States of America, with the support of foreign authors and institutions. Both the papers’ translation and production were aimed at a large contingent of readers - professionals who needed to be trained to work in an expanding school system - and in them, as exemplified by Charles McMurry’s handbook, practical procedures and theoretical justifications were intertwined giving them cohesion and depth. In this arrangement, which transformed examples into arguments, the author defended innovations with other intellectuals interested in educational change and approached teachers through detailed prescriptions supported by his professional experience.

Adaptations of Herbartianism

The lengthy editorial cycle of the manual The elements of general method based on the principles of Herbart allows accompanying the clash with other conceptions that came into circulation. In successive editions, the changes are indications of intellectual conflicts and fights between the intellectuals, as well as the meanings the author gave to the flow of innovations.

On the 5th. edition, published in 1907⁹, it is possible to identify revisions and deletions, through which the author shows himself to be an unorthodox Herbartian. Compared to the 1893 version, already analyzed, it is possible to observe changes at the first-page layout: larger letters highlight the expression Elements of general method and smaller letters subtitle the Herbart principles on which it is based. The authors referenced in the body of the text corroborate this inflection: Herbart’s citations decrease, mentions to Tuiskon Ziller, Karl Volkmar Stoy, and Wilhelm Rein almost disappear, and references to works by William James and John Dewey predominate. There was, therefore, a shift from the German conceptual pole to the North American pole.

The main education goal, that is, the formation of character, and the relative value of the different fields of study, remained unchanged. However, the understanding of two central principles to the Herbartian theoretical framework - interest and concentration - has been modified.

McMurry explains that John Dewey, based on research developed at the University of Chicago Laboratory School, classified children’s interest into four types: communication, research, constructive activities, and artistic expression, emphasizing the child’s relationship with the natural world and with society, which allowed industrial activities to be incorporated into the school program. This classification seemed to the author more comprehensive than that proposed by Herbart (empirical, speculative and aesthetic), which attached little importance to out-of-school relationships and the child’s physical and motor development and gave centrality to attention in the learning process. The two conceptions of interest would have in common that they were against the conviction that the syntheses of culture that made up school content would be enough to develop intellectual capacities.

The other significant change concerns the organizational principle of the curriculum. McMurry says that several terms were being used to name the need to establish a relationship between its components - coordination, concentration, and correlation - which would translate the importance of different aspects attached to the theme. In the 1893 edition, the chapter of the book and the process described therein were called concentration, but in the 1907 edition, they were named as correlation, with the following explanation: coordination would mean giving equal importance to the different branches of study present in the school curriculum; concentration concerned the connections and dependence between these branches and correlation would express the purpose of connecting the studies, but also to the child’s experience, as demanded by the new definition of interest.

Programs based on Cultural Internships have been removed from this edition, along with indications of materials related to them. In its place, other examples were developed whose methodological treatment was intended to operationalize the connection between the different fields of knowledge, the mutual dependence between them, and the incorporation of facts from life outside of school to increase the practical power of knowledge.

^{Kliebard (2004)} describes the dispute over the meaning at the studies concentration as one of the elements of the clash between renovators and the traditional school curriculum defenders. William T. Harris, who held the highest rank in the educational hierarchy (Commissioner of Education), appropriated the central term to Herbartianism to emphasize traditional school content, precisely the point at which Herbartians proposed the most radical changes. Giving up the term concentration, McMurry made moves to distance himself from the conservative group and remain with others who also sought to renew the curriculum.

However, the most incisive criticisms seem to have come precisely from the space created for the diffusion of Herbartian ideas, the National Herbart Society, an evolution of the Herbart Club, which brought together intellectuals without requiring theoretical affiliation.¹⁰ The Society demanded preparatory texts on specific topics to be discussed at its annual meetings that took place during the National Education Association Congresses and published, under the coordination of McMurry, both texts and debates, in the respective YearBooks.¹¹ The first two, referring to 1895 and 1896, focused on the concentration of studies and the theory of Cultural Internships. The relationship between interest and character formation, published as a Supplement, was redefined by John Dewey¹²; the relations between citizenship and education were discussed in 1896 and 1897, which implied reexamining the educational purposes proposed by Herbart. The shift from the focus of the individual character of education to its relationship with society was further deepened in the 1898 edition through discussions on knowledge and conduct. The 1899 edition (the last) witnessed a reduction in the initial ambitions of Herbartianism: the volume presents contributions on specific topics, namely, methodology and curricular organization for the teaching of History and Geography.

The Cultural Stages theory was the first to fall into the debates of the Herbart Society, which may explain its elimination from the McMurry manual; new understandings of interest and child psychology made their prescription for school practice theoretically unsustainable. Other conceptual changes, such as the incorporation of the studies of William James and John Dewey into the learning processes, were covered up by the maintenance of the same title in the manual and by the absence of demarcation of the differences between Herbart’s idealism and pragmatism, a theory about knowledge. that was beginning to gain strength in the educational field.

Externally, other factors tensioned the Herbartian conceptions. The psychology that integrated his philosophical scheme was criticized and contested, even in Germany, for the work of Wilhelm Wundt, in whose experimental laboratory a generation of American students was formed who, upon returning, began to work in different universities, as shown in the analyzes of Mirian ^{Warde (2018)}. The new explanations about the functioning of the mind led to questioning the speculative framework of Herbart’s conception and revealed that much of what was reputed to him was the creation of his successors, whose focus was the teaching method.

Institutional changes also marked the decade that separates the two editions of the manual compared here. The training of teachers and educational leaders was not restricted to the Normal Schools, locus of irradiation of Herbartianism, and began to integrate the higher level of instruction with the creation of departments, schools, or faculties of education in large universities (^{FRASER, 2007}; ^{RIBEIRO, 2016}). The introduction of educational studies in these institutions took place by fulfillment of academic standards that began to model the pedagogical field; the development of research and the production of knowledge has transformed them into teaching and experimentation centers (^{VALDEMARIN, 2016}). It can be said that the conception of science had changed and that Herbartianism no longer fulfilled the requirements to be identified with it.

The residual permanence of Herbartianism

The adaptations mentioned did not negatively impact the circulation of the manual The elements of general method based on the principles of Herbart, as it was published until at least 1915 without further changes. At the same time, the author participated in forms aimed at guiding teaching practices and methods without explicit theoretical affiliation.

A set of volumes called Public School Methods¹³ circulated in the 1910s and 1920s, in the United States of America and Canada, containing Teaching Plans for elementary instruction - what to teach, how to teach. School grades organized the volumes, and the plans were written by teachers, supervisors, and school principals who worked in different North American states, providing technical support and, probably, repercussions to their prescriptions. Charles McMurry participated in these publications, which intended to offer readers a “Normal School in the form of a book”, as the author of Type Studies on Reading, Geography, History, and Elementary Agriculture. When these volumes were published in Canada in 1913, he was presented in the preface as the greatest American authority in the elaboration of Type Studies and, devoid of the laudatory connotation, this methodological contribution is also recognized by analysts (^{FUJIMOTO, 2014}; ^{AKENSON and LERICHE, 1997}).

Despite the new name, it is possible to detect residual traces¹⁴ of Herbartianism in these prescriptions for teaching practice, as the expression Type Studies were used in previous works to explain the operationalization of the principle of correlation and the process of induction. In the 1893 edition of the manual already analyzed, McMurry stated that in order to operate with the principle of concentration, it was necessary to select themes that could illustrate similar cases: “If the concrete object or individual is carefully selected it will be a type, that is, it illustrates a whole class of similar objects” (MCMURRY, 1893, p. 73, emphasis added). Another record can be found in the Geography teaching program, published in the latest supplement by the National Herbart Society: “The central topics for discussions throughout the grades should be types. Other more general exercises are necessary to supplement the type-studies” (^{MCMURRY, 1899}, p. 121). In the book The Method of recitation (1903), the types are considered the strategy to operationalize the inductive movement to combine the factual data with general truths, as the scientists do. The teaching plans called Type Studies correlated objects, facts, and information to develop different themes, such as the British colonies, Lake Michigan, the Panama Canal, and a steamship trip from New York to Hamburg.

This detachment is an indication that the practical prescriptions acquired a certain autonomy concerning to the conceptions to which they were initially linked, and probably survived, due to the contributions they offered to the demands of the teaching activity, whose pace is different from that which moves the conceptual and academic debate.

The correlation principle also proved its versatility in another theoretical context (^{NULL and RAVITCH, 2006}). In 1920, Charles McMurry published the Teaching by projects manual. A basis for purposeful study (^{MCMURRY, 1920}), an impressive volume of 257 pages, divided into 13 chapters containing detailed plans to guide the teaching work in the development of projects.

The conceptual vocabulary that characterizes Progressive Education, from the title, permeates the discourse of the manual. The author states that the organization of teaching through projects would lead to the achievement of intentionally defined objectives and supported by the premise that knowledge is not formal and static but progressive. The projects would have the merit of providing self-directed organization of the students’ physical and mental resources and given their practical bases and their relationship with experience, they would stimulate reflective thinking to obtain good results. To develop good projects, says McMurry, the teacher must study children’s tendencies, characteristics, the world, and the activities developed to direct educational practices to the real problems of education. The term project, borrowed from the language of business and industry, would remind the school of its links with the outside world, suggesting a return to applied science, everyday daily obligations, and operational forces in the real world, and in these respects, their merits would reside.

The analysis of Teaching by Projects allows us to state that regardless of the denomination received - concentration of studies, standard studies, or projects - the teaching plans proposed by McMurry operationalize the principle of correlation. They involve different fields of knowledge around a theme that, in turn, consists of a demonstration on a scale (local, national, or worldwide) of industrial processes or linked to everyday life. They may turn to simple themes (such as creating a vegetable garden) or more complex ones, such as those dealing with the construction of bridges, railways and power plants, the channeling of rivers, the study of biographies, works of literature, or historical events.

In the author’s explanations, this permanence takes on an evolutionary meaning. Standing between conservatives, who defend maintaining the old programs and methods, and progressivists, who intend to introduce new content, McMurry inserts the project method in a continuous process of improving school practices. He says that reading the projects contained in the manual would reveal that his themes were already present in some schoolbooks but that they received a more in-depth treatment:

They are not new, and yet one thing in them is strangely new. They are dressed up in their proper clothing. We do not recognize them at first because we never before saw them in full equipment and with an adequate setting (^{MCMURRY, 1920}, p. 15).

This justification supports McMurry establishing an equivalence between expressions and, simultaneously, resilience to the practice prescriptions. First presented in this paper as teaching projects, the plans are integrated into the new pedagogical concept, but throughout the text, they are also designated as large units of study, as large projects, as standard studies or as lessons in expanded things. The intended reversibility of the expressions indicates the end of the Herbartian conception circulation cycle; in the dynamics of pedagogical innovation, it also reveals the consolidation of the progressive or deweyana conception of education before which capitulation took place.

Final considerations

The time the sources analyzed here remained in circulation, around three decades, was a condition for the perception that the dynamics for the diffusion of Herbartian ideas, objectified in different forms addressed to teachers, was composed by many cycles.

Under the indication of renewal, this conception was introduced in the United States of America and, in this first movement, foreign academic prestige, and the intellectuals exchange played a significant role. Through bibliographic production with clear institutional identification – the Normal State University and Herbart Society - the Herbartian conceptual structure was explained and, occupying the foreground, gave cohesion and depth to the proposal for a new curricular ordering whose viability was demonstrated by the detailed exemplification of the school procedures and routines articulated to it, thus configuring a repertoire of new knowledge.

However, the clash with other theoretical currents changed the cohesion of this pedagogical discourse. The author’s professional experience, his position in the educational field (increased, including, with publications) and the readers reception seem to have marked this movement. The meaning of the conception was strongly determined through its practical elements and adapted to the new and varied theoretical context. The correlation of studies remained the organizational principle of examples and lessons plans but under the denomination of type-studies that camouflaged their originals links and replaced its vector with investment in practical continuities.

The final step for the Herbartian movement, identified in the production of Charles McMurry, consisted of an attempt to maintain its relevance in a theoretical context that was adverse to it and became hegemonic - progressive education. The author dressed up the new concepts with old clothes by incorporating the new theory’s key terms, reversing the pedagogical lexicon¹⁵, and making small reformulations in the methodological prescriptions for teaching. Thus, he conferred resilience to the correlation of studies and minimized the impact of innovation, giving it a sense of continuity. He was not successful (^{NULL; RAVITCH, 2006}).

The cycle of diffusion of Herbatian ideas here analyzed in different movements is not exclusive of this pedagogical conception and can be identified - with particularities - in the spread of other strands or contexts. The innovation is presented as a system, followed by the critique of theoretical and practical problems that it intends to overcome. The adaptation or remaining residual cycles acquires the connotation of a possible version of emerging conceptions.

As other studies have indicated (^{VALDEMARIN, 2010}; ^{SILVA, 2007}), textbooks played a central role in this strategy. Sometimes, they introduced practicable innovations; sometimes, they distance themselves from ruptures through insertion into a general code of pre-existing meanings.