Spontaneous Concepts Research Articles

Decentralising mathematics: Mutual development of spontaneous and mathematical concepts via informal reasoning

AbstractThis paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton’s distinction between reasoning and argument, and Ernest’s concept of intrapersonal dialogue, we propose two theoretical perspectives for understanding the roles of informal reasoning in argumentation: the semi-formal, and the negotiation perspectives. From the latter perspective, we can say that informal reasoning involves creating alternatives, eschewing the relatively unpromising ones, and choosing the most promising one. To illustrate the advantage of the negotiation perspective over the semi-formal perspective, we present two examples of students’ statistical written reports from a previous study. These examples illustrate that spontaneous concepts influenced the students’ creation of multiple alternatives, and choice of the most promising one, in informal reasoning. Therefore, to better understand the development of mathematical concepts, we need to recognise the role of spontaneous concepts through decentralising mathematics. Finally, we introduce inferentialism as an additional theoretical perspective for investigating both the mathematical development of spontaneous concepts, and the spontaneous development of mathematical concepts. The inferentialist idea of the game of giving and asking for reasons indicates how to empirically investigate the mutual development of spontaneous and mathematical concepts.

Sketching Versus Digital Design Tools in Architectural Design

Sketching is a design tool that can be assumed to be ill-structured, does not offer exact solutions, is intuitive, and is open-ended in the initial stages of architectural design. Sketching creates an opportunity for architects to release their creativity and intuition, giving rise to spontaneous ideas and concepts in an organic and natural way. During the initial design phases, like in the conceptual stage of the design, designers receive aid from conventional sketching as their concepts and ideas can easily transform into tangible, real-world forms. With the development of digital design methods like CAD (computer-aided design) in pursuit of AI (artificial intelligence), it has been accepted that manual sketches are no longer the only method used in the design process, and the trend toward using new methods has begun. The diversity and evolution of tools used in architectural design, together with the integration of CAD, AI, and traditional sketching techniques, have contributed to the development of architectural design and facilitated enhanced collaboration, visualization, and efficiency across the design process. As a result, it has evolved to embrace the use of CAD, which was the first method adopted from these developments, as a basic skill in the field of architectural design education. This shift places a strong emphasis on the professional field of architectural design while also encouraging students to explore the innovative potential of CAD for design purposes. CAD presents architects with a robust platform that facilitates the creation of intricate designs and precise measurements during the initial stages of the design process. Following CAD, the development of AI-driven design tools motivates architecture students and designers to transform their concepts into concrete designs. Although it is known that each method mentioned has its own positive or negative aspects, it is not possible to say that any of them is used alone in architectural design processes. At this point, combining the design process with CAD and AI-supported design tools, as well as traditional manual sketching in architecture, helps develop a diverse and adaptable skill set in design. Integrating digital design tools into the architectural field emphasizes the enduring importance of traditional sketches, especially in terms of inspiration and conceptualization in architectural design, while also updating the design process. This document aims to explore the progression of employing diverse design tools, namely manual sketching, CAD, and AI-driven design tools, throughout the architectural design process. This paper undertakes a comparative analysis of using computational design tools instead of traditional sketching with pen and pencil, aiming to juxtapose their respective benefits and drawbacks. In conclusion, although it is not yet possible to assert the superiority of one method over the other, it is evident that traditional sketching continues to hold significant relevance and effectiveness in the design process despite its long-term use.

Od slike do misli preko geometrije i stripa - ikonička sredstva u nastavi filozofije - teorijski okvir, mogućnosti primene, primeri

How to bring abstract philosophical concepts and their relations in proximity with everyday, concrete pupils' experience and spontaneous concepts? What factors can effectively and meaningfully mediate between usual perception and experience and abstract philosophical concepts, especially in the initial stages of teaching and learning, when pupils are introduced to philosophical problems? In accordance with these questions, the paper examines the meaning and possibilities of applying iconic tools or visual and graphic representations in the teaching of philosophy as intermediate elements that can connect complex, abstract philosophical concepts and theories with everyday experience and with the domain of phenomena and objects given in the immediate perception. First, the general theoretical foundations are explored, then possible directions of application, then a characteristic and valuable example already designed and adopted in teaching practice, and finally concluding considerations and proposals are made. The paper focuses on two specific groups of iconic tools: geometric (and geometrized) visuals and graphics and comics as a visual-graphic representation: we explore the foundations of their value in teaching and learning. Our conclusion is that iconic tools in teaching philosophy, if they are applied in a pedagogically and psychologically justified manner, if meaningful, relevant and aligned with the objectives of philosophy teaching and curriculum, have a great potential as an important intermediate factor for the gradual movement towards higher levels of abstraction, while preserving the transfer between philosophy and other subjects, as well as between philosophy and pupils' life experiences. In addition, their application can deepen crosscurricular connections, as well as a more intensive integration of teaching philosophy with key competencies and cross-curricular competencies.

SHILPA GUPTA: AN ARTIST CONCEPTUALIZING WITH TECHNOLOGY

India follows the catchy, trendy, uncertain, and spontaneous concepts of new media art for the last few decades. New media practice in India has dealt with issues of identity, critiques of violence, narrative, and performance, and other subjects that come under the umbrella of new issues. New media art began to appear in India since the inception of the 21st century, but it showed in the works of artists like Vivan Sundaram, Nalini Malam, Ved Nayar, Rummana Hussain in the 1990s. New media ideologically mixed art with scientific craft, which resulted in an amplified narrative of our country and world that is a union of different creative languages. New media create a futuristic ethos in the art that is developing every second. It is a medium that symbolizes freedom of mediums, as it is spontaneous and enough. In all this, Shilpa Gupta came as a ‘blind star and star blind’.Shilpa Gupta is one of the leading contemporary, influential, and critically acclaimed new media artists of India’s new generation of international artists. A transcultural artist even when influenced with regional specificity. She considers new media art (a web of technology) as a key part of today’s existence, and, ensuing, prefers various forms of cutting-edge technology as the vehicle for her interactions with the viewer. Although Gupta’s works are developed largely through technological means their significance lies in their candid communication, the various issues that shape contemporary life, particularly the lives of young and adults. Her work is often coded with meanings that are not always instantly available but require the efforts of the viewer. Uniquely and humorously, Gupta reminds us of the danger of taking for granted – that it is indeed technology that connects us to the world. She is an artist who deals with her viewers, her audience is 70 percent part of her artwork. She brings reality from a new perspective.

A APRESENTAÇÃO DE CONCEITOS EM UM LIVRO DE DIVULGAÇÃO CIENTÍFICA INFANTIL: O CASO ISAAC NO MUNDO DAS PARTÍCULAS

ABSTRACT: This work aims to analyze the scientific ideas and concepts present in the science communication book aimed at the child’s public “Isaac in the World of Particles”, written by Elika Takimoto. We start from the contributions of historical-cultural psychology on the potential, spontaneous and scientific concepts, seeking to understand the relations and forms of meaning of the scientific ideas presented by the work. Excerpts from the book in which scientific concepts or key ideas were present were selected and analyzed. The unit of analysis was the word. The results indicated that the book mobilizes several meanings and logical-abstract (conceptual) structures to formalize complex elaborations and scientific concepts. The analysis of the concepts: atom, particle and vacuum, indicated strategies for the meaning production, which contemplated: argumentative disputes, contextualization, curiosity, history of science, spontaneous concepts etc.

Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis

This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.

How scientific concept develops: Languaging in collaborative writing tasks

This qualitative case study explored the extent to which learners' L2 writing concepts changed across different collaborative writing tasks, and how languaging helped learners make meaning between scientific and spontaneous concepts. Four first-year MA students from a Chinese university formed a study group and engaged in collaborative writing tasks as required by an Academic English Reading and Writing course. Multiple sources of data were collected, including audio-taped group discussions, group writings, individual reflections, and course-related documents. Data analysis demonstrated the microgenetic evolving trajectories of the rhetorical modes of “maintaining the flow of information”. The participants progressed from spontaneous knowledge of those concepts to a scientific system through languaging about a text containing these conceptual features. Learners' conscious usage of scientific terms, constant revisiting to their prior knowledge, and critical reading of the academic text highlight the mediating role of languaging in empowering the dynamic interaction between scientific reasoning and spontaneous thinking. This study suggests that the integration of stylistic analysis tasks, peer collaboration, and rhetorical concepts may facilitate the transformation of students’ thinking patterns as well as the development of their L2 academic literacies.

Investigating the Double-Move in Pedagogy in a Grade 4 Namibian Science Classroom: A Cultural Historical Analysis

This paper investigates how a teacher in a rural school in Namibia teaches science. Of interest to us is the nature of the classroom discourse in constructing scientific knowledge that is meaningful to students. We draw on the work of Vygotsky (1978) in order to understand teaching/learning as dialectically entailed and to understand the notion of scientific and spontaneous concepts as distinct from science concepts, and operationalise his pedagogical theory utilising Hedegaard’s (1998) notion of the double-move in pedagogy as fundamental to meaningful engagement. Through a detailed analysis of one teacher’s pedagogical discourse we show how the linking of scientific and spontaneous concepts can either facilitate or hinder learning. Our analysis points to the importance of co-constructing meaning in the class, between teacher and taught and illustrates how analogies and metaphors can fail to create meaning in a classroom if the teacher does not recruit the learners’ own everyday concepts.

Os processos criativos na práxis musical: uma análise a partir do enfoque histórico-cultural

A finalidade da pesquisa é compreender a influência da apropriação dos conceitos científicos e espontâneos nos processos criativos a partir de intervenções pedagógicas de cunho experimental no ensino da música. O objetivo da pesquisa é analisar as manifestações criativas dos participantes no processo do ensino e aprendizagem do violão em práticas coletivas. A fundamentação teórico-metodológica é o enfoque histórico-cultural de raiz materialista, histórica e dialética. Constata-se que o ato de criar vincula-se às vivências dos sujeitos e às apropriações de conceitos de diversos matizes, objetivando-se em qualidades distintas nas manifestações criativas.

A FUNÇÃO DO PROBLEMA: APROXIMAÇÕES ENTRE VYGOTSKY E FREIRE PARA A EDUCAÇÃO EM CIÊNCIAS

Alguns estudos na área de Educação em Ciências têm-se apoiado no pensamento de Lev S. Vygotsky para discutir aspectos que envolvem a linguagem, a Zona de Desenvolvimento Proximal (ZDP) e o processo de formação de conceitos científicos em de sala de aula, em diferentes níveis de ensino. Além disso, há pesquisadores que compartilham da concepção de que a perspectiva marxista fundamenta tanto as ideias de Vygotsky quanto as de Freire, no que concerne ao processo de humanização, e buscam estabelecer relações entre esses autores. Com o intuito de aprofundar essas relações, objetiva-se investigar articulações teóricas entre as ideias de Freire e Vygotsky que possam contribuir na elaboração e desenvolvimento de programas curriculares na Educação em Ciências. Para tal, realizou-se um estudo das principais obras de Vygotsky e Freire utilizadas no ensino de ciências brasileiro por meio da Análise Textual Discursiva. Dentre os resultados, destacam-se as relações teóricas estabelecidas entre Freire e Vygotsky, quais sejam: i) conceitos espontâneos e codificação; ii) conceitos científicos e descodificação e ii) problematização e ZDP. Essas relações se constituem em parâmetros analíticos a serem considerados no planejamento e desenvolvimento de atividades de sala de aula, bem como na organização de programas escolares, em que o ponto de partida sejam situações da vivência dos sujeitos, marcadas por contradições sociais e/ou demandas sociais, e as estruturas conceituais subordinadas à essas situações.

Generalizations, concepts, and pseudoconcepts: The subjective content of epistemic violence

Barbara Held’s article (2020) challenges the “for/about prepositional divide” (p. 349), which is presumed by critical and Indigenous psychologies, at two empirical and epistemological levels. I argue that Held’s critique can be further strengthened empirically, with reference to Lev Vygotsky’s analysis of the relation between spontaneous and scientific concepts, and epistemologically, with reference to Evald Ilyenkov’s treatment of concepts in contrast to mere notions.

Зона ближайшего развития, скаффолдинг и деятельность учителя

The construction of the zone of proximal development (ZPD) in the context of teaching activity is discussed in the paper.ZPD is compared and contrasted with the concept of scaffolding as introduced by Jerome Bruner. In the context of its potential for operationalisation in the form of teacher activities, the author examines key ZPD content given by Lev Vygotsky in terms of the complex interaction of spontaneous (everyday) concepts formed prior to the beginning of school education with scientific (theoretical) concepts formed during schooling. Vygotsky’s main idea about the leading role of scientific concepts in the restructuring of previously formed spontaneous concepts, as well as in the development of the child’s holistic thinking, leads to the conclusion that it is possible also to directly influence the spontaneous formation concepts change through the organisation of collectively distributed forms of educational activity and in a polylogue based the Socratic method. The leading psychological processes, which ensure the development of spontaneous concepts through their greater generalisation and awareness, comprise the processes of exteriorisation of spontaneous concepts, reflection and subsequent interiorisation of a collectively constructed concept. Therefore, the activities of teaching in constructing a ZPD include providing conditions for the distribution of individual operations in the course of a joint learning action and facilitating a polylogue to ensure the effective functioning of these psychological processes in the course of specifically organised learning activities.

Understanding and Prediction of the Clouding Phenomenon by Spontaneous and Effective Packing Concepts

AbstractIn this work, we show by which mechanism branching of the hydrocarbon chains influences the cloud point of nonionic, ethoxylated surfactants. The temperature‐induced separation into a dilute and a concentrated liquid phase is of liquid–gas type and can be explained by the relative probability of endcaps and branching points of the cylindrical micelles in both phases. The influence of branches on the hydrocarbon chains can be easily understood by means of spontaneous and effective packing concepts, while quantification via hydrophilic/lipophilic balance (HLB), hydrophilic‐lipophilic difference (HLD), and HLD‐Net Average Curvature requires parametrization. The phase equilibrium above the cloud point phenomenon is equivalent to the Winsor I type phase equilibrium, one of the five known phase equilibria in ternary systems.

A Case Study of an Early Childhood Teacher Introducing Scientific Concepts, Aiming to Challenge the Practical Side of Concept-Based Pedagogies

이 사례연구는 개념중심교수방법(concept-based pedagogies)을 바탕으로 유아교육현장에서 유아교 사가 유아들에게 과학적 개념(scientific concepts)을 효과적으로 전달할 수 있는 방법을 모색해 보고자 하였다. 이 연구는 Vygotsky의 핵심이론 근접발달영역(ZPD) 및 역동적 평가(dynamic assessment), Gal’perin의 추상화 네 단계를 이론적 분석틀로 하여 연구에 참여한 유아교사가 학습자의 과학적 개념 획득수준을 어떻게 인지하고 교수에 적용할 수 있는지를 연구문제로 설정하였다. 학급 참여관찰과 반구조화된 인터뷰를 통해 드러난 이 연구의 결과는 다음과 같다. 참여교사는 역동적 평가의 기본원칙에 입각한 암시적인 중재와 명시적인 중재를 적절히 구사할 수 있었고 특정 과학적 개념을 전달하기 위해 형체화 자료를 효과적으로 사용할 수 있는 역량을 보여 주었으나 개별유아의 과학적 개념 획득 및 내면화 정도를 정확히 이해하는 데 다음과 같은 한계를 드러냈다. 첫째, 참여교사에게는 유아가 외형화 된 매개(mediation)의 도움을 필요로 하는지에 따라 유아가 도달한 추상화단계를 보다 정확히 파악할 것이 요구되었다. 둘째, 참여교사는 근접발달영역 및 특정 과학적 개념 획득의 수준을 개별유아에 따라 파악하는 것뿐만 아니라 과학적 개념별로도 세분화하여 파악할 것이 요구 되었다. 셋째, 유아의 임의적 개념을 바탕으로 과학적 개념 획득을 도모하기 위해 특정 과제와 결합된 개별유아의 흥미를 정확히 파악할 것이 요구되었다. 홀리스틱 교육철학을 지향하는 개념중심교 수방법의 보다 효과적인 실천을 위해 유아교사에게는 유아에게 전달하고자 하는 과학적 개념 자체와 유아의 획득수준을 정교하게 인식하고 형체화 자료 및 과제와 결합된 개별유아의 흥미를 적절히 활용할 것이 요구된다.This instrumental case study explored how an early childhood teacher could help children understand scientific concepts by implementing the practices within concept-based pedagogies. Gal’perin’s theories about mental actions as well as Vygotsky’s signature concepts (i.e., the zone of proximal development and dynamic assessment) offered theoretical frameworks and provided the analytic tools for answering the following research question: How can an early childhood teacher assess the learners’ acquisition levels of scientific concepts and respond to them accordingly? Classroom observations followed by a semi-structured interview yielded the following results: (1) The teacher was able to provide both implicit and explicit mediation on the principle of dynamic assessment and offer physical objects or their representations, if necessary. (2) The teacher had to assess the abstraction levels of her students more accurately by seeing how much their thoughts were externalized. (3) The teacher needed to consider each case of scientific concepts separately since each one creates separate zones of proximal development within an individual child. (4) In order to maximize the use of the learners’ spontaneous concepts, the teacher had to accurately detect what was the particular interest of the child being added to the subject being explored. Well understanding the concepts being taught, knowing how and how much each child is grasping them, materializing teaching aids, and reorganizing the tasks as the child maintains his or her interest in them seem to be necessary prerequisites for an early childhood teacher to put concept-based pedagogies in practice from a holistic perspective.

Qualitative Research to Explore the Patient Experience of X-Linked Hypophosphatemia and Evaluate the Suitability of the BPI-SF and WOMAC® as Clinical Trial End Points

BackgroundX-linked hypophosphatemia (XLH) is a rare genetic disorder characterized by renal phosphate wasting and defective bone mineralization. Symptoms include bone pain, joint pain, stiffness, and fatigue. Published evidence regarding the patient experience of XLH is sparse and no XLH-specific outcome measures have been validated. ObjectivesTo understand the symptoms, impacts, and patient experience of XLH and to evaluate the face and content validity of the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC®) and the Brief Pain Inventory Short Form (BPI-SF) for use as end points in XLH clinical trials. MethodsFace-to-face, qualitative, semistructured interviews were conducted with 18 adults with XLH in the United States using concept elicitation and cognitive debriefing techniques. Open-ended questioning elicited spontaneous concepts focusing on XLH-associated symptoms and functional limitations. Cognitive debriefing of the WOMAC® and BPI-SF assessed the relevance and patient understanding of item wording, recall period, and response options. ResultsVarious distinct symptom concepts were elicited including pain symptoms, dental symptoms, sensory symptoms, tiredness/fatigue symptoms, and musculoskeletal symptoms. Participants reported experiencing significant bone and joint pain, stiffness, mobility limitations, and an impact on their ability to work. Cognitive interviewing found both instruments to be relevant and well understood by most patients. ConclusionsThe interviews generated rich, qualitative insights into the patient experience of XLH. Cognitive debriefing of the BPI-SF and WOMAC® supported their value as XLH clinical trial end points. Future research will assess the psychometric properties of these instruments for use in the XLH population.

A significação do conceito função quadrática por estudantes do 1º ano do ensino médio: uma abordagem histórico-cultural

O presente estudo objetiva ampliar entendimentos acerca da significação do conceito função quadrática por estudantes de uma turma do 1º ano do ensino médio, considerando ideias e conceitos da abordagem histórico-cultural. Os dados empíricos foram produzidos a partir de aulas de matemática ministradas por uma acadêmica do curso de matemática ao cursar a disciplina Estágio Curricular Supervisionado: Matemática no Ensino Médio. Como dados empíricos considera-se: registro das aulas apresentados em um relatório analítico-reflexivo que se constitui como diário de campo; recortes dos planejamentos desenvolvidos. Elementos como conceitos científicos e espontâneos, relações conceituais e zona de desenvolvimento proximal (ZDP) estruturam o texto em unidade e subunidades de análise. Caraça (1998) e Vygotsky (1991), entre outros, ampliam as condições de análises propostas. Dentre as considerações finais apresentadas destaca-se a ideia de que os conceitos podem ser elevados a um nível maior de significação pelos estudantes, por meio do estabelecimento de relações conceituais, e que o professor interfere no plano interpsicológico da formação dos conceitos.

Vygotsky: Une Alternative Psychope dagogique

In this essay, the author attempts to underscore some of the most important theoretical positions held by Vygotsky, a Russian psychologist and educator. After briefly sketching the philosophical foundations that inspired most of Vygotsky 's works, the author discusses some of the major psychological theories of Vygotsky that seem to have relevance to many of today 's educational questions. The theoretical formulations presented in this essay concerned the following: cognitive development, development of scientific and spontaneous concepts, the zone of proximal development and the relationship between language and thought. When appropriate, comparisons with Piaget were made and educational implications were underlined.

O estudo da Óptica na modalidade de Educação para Jovens e Adultos (EJA) por meio de uma sequência didática diversificada

Neste artigo discutimos a aplicação de uma sequência didática para ensinar Óptica para alunos da Educação de Jovens e Adultos (EJA). A sequência de atividades, composta por estratégias como exibição de vídeos, leitura de artigos de divulgação científica, reconstrução e demonstração de experimentos, e discussões em grupo, foi elaborada tendo por base um ensino de física contextualizado visando uma formação caracterizada pela autonomia intelectual e pensamento crítico. O referencial teórico baseia-se na abordagem histórico-cultural de Vygotsky, que inter-relaciona o aprendizado e o desenvolvimento do indivíduo com a interação deste com o meio social. Na aplicação da sequência de atividades, duas etapas foram essenciais: o pré-teste, no qual foram identificadas as necessidades de aprendizagem dos alunos, bem como seus conhecimentos prévios sobre fenômenos da Óptica; e o pós-teste, que permitiu identificar o desenvolvimento da aprendizagem na maioria dos alunos, indicando o início de uma construção de conceitos científicos a partir dos conceitos espontâneos previamente identificados.

02. Emergent science in preschool: The case of floating and sinking

This article studies an activity in a Swedish preschool setting where children’s elaborations and understandings of floating and sinking are central. In a Swedish preschool context, it is advocated by the National Agency for Education (2016) that different forms of knowledge and ways of learning are used within the institutions to form a coherent whole. Based on a cultural-historical framework (Fleer, 2010; Hedegaard, 2012; Vygotsky, 1978, 1987), it is argued that if children are supported by a teacher, who mediates a cultural and historical, as well as institutional, perspective of knowledge, children may enhance their knowledge of science. Data was collected using a video-based technique called shadowing (Czarniawska 2007), and the overall study was framed within a case-study methodology. The analyzed activity show four children collaborating and exploring a range of aspects related to floating and sinking together with one teacher, acted out in a playful but focused manner. The results show that aspects such as the item, the fluid, and the way children handled the items to remove or add weight, were found important by the children. They used everyday language to talk about size, holes, weight, amount of water, and what changing preconditions would mean when different objects were placed in water. Their vocabularies were enhanced during the activity and seemed to foster emergent notions of density and Archimedes’ principle, indicating that the language used has the potential to mediate the progress of both spontaneous and scientific concepts, where scientific concepts are understood as emergent.International Research in Early Childhood Education, vol. 7, no. 3, pp. 16–32

A apropriação de conceitos científicos no contexto escolar e as pedagogias do aprender a aprender

Resumo O artigo objetiva discutir teoricamente como a escola atua na apropriação de conceitos científicos e como essa atuação pode se alienar. Justifica-se este estudo por trazer acréscimos à Psicologia e à Educação, evidenciando o pensamento por conceitos como elemento cognitivo essencial do processo de elaboração do conhecimento. A partir da Psicologia Histórico-Cultural evidencia-se o papel da escola na mediação do desenvolvimento dos conceitos espontâneos e científicos no sistema interfuncional da consciência. Além disso, como este papel mediador e este desenvolvimento podem se alienar por conta das tendências pedagógicas atuais, como as Pedagogias do Aprender a Aprender, consideradas a expressão ideológica da materialidade da sociedade de classes contemporânea. Por último, defende que a escola deve se ater ao conhecimento sistematizado e não ao conhecimento espontâneo; ao conhecimento fruto da prática e da teorização histórico-social humana e não ao conhecimento pragmático e construído individualmente; ao saber totalizante e não ao saber fragmentado.