Anthropological Theory Of Didactic Research Articles

Integrating the Case Studies Pedagogy and the Anthropological Theory of Didactics to Enhance the Teaching and Learning of Algebra in Undergraduate STEM Education

Methodology case studies plays a pivotal role in STEM education, especially in teaching undergraduate algebra. This article emphasizes the power of real-world scenarios and active pedagogy, a student-centered approach that makes abstract algebraic ideas tangible. The Anthropological Theory of Didactics (ATD) is spotlighted as a perspective that treats mathematical knowledge as a cultural artifact, embedding mathematics concepts deeply within cultural and historical contexts. By comparing active pedagogy with ATD, the article unveils a compelling overlap that values the significance of context in learning. Students don't just engage actively but also delve into the cultural essence of mathematical problems, gaining a profound understanding. Addressing the hurdles undergraduates face in transitioning from high school algebra to university level, the article suggests activities that merge active pedagogy and ATD. This holistic approach has the potential to transform algebra education into a more engaging, relevant, and culturally resonant experience.

Teaching correlation and regression in three European countries

In this article, we compare the presence of correlation and regression analysis in secondary education of Ireland, the Netherlands and Luxembourg, through the analysis of final-exam tasks and curricula based on the Anthropological Theory of Didactics (ATD). It points out that the same topic can appear in different ways and extent in curricula, even if the mathematics teaching goals are similar. This article is a kind of introduction to the research that explores the possibilities for the appearance of these concepts in the Hungarian mathematics education. Therefore, in the second part of the article, Hungarian curricular goals are included, and it is shown which methodology of the three studied countries has the greatest curricular basis in Hungary. Subject Classification: 97xxx

Integrating the anthropological theory of didactics in multivariate calculus education: Challenges, pedagogical shifts, and innovative activities

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and practice of mathematics in both students and teachers. This perspective is relevant for understanding the complexities of teaching multivariate calculus. Traditional approaches to this subject have been lecture-based, but with the evolution of educational paradigms, active pedagogies have emerged as vital. These include among others inquiry-based learning, collaborative learning, the flipped classroom approach, technology-enhanced active learning, and project-based learning. The challenges students face in multivariate calculus range from conceptual complexities to visualization challenges and over-reliance on memorization. In this work, we propose a holistic approach for defining class activities in multivariate calculus with emphasis in integrating visualization techniques, real-world applications, collaborative activities, and feedback mechanisms. Accordingly, four class activities, grounded in the principles of ATD and tailored to address challenges in multivariate calculus, are proposed. These activities aim to foster significant understanding, relevance, and engagement in students.

Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function

This study investigates the praxeologies teachers use about the inverse function in the teaching process when the curriculum is changed. A case study, one of the qualitative research methods, was used in the study. The participants of the study were three experienced mathematics teachers. The data were collected by recording the teaching process of the teachers with a video camera and a voice recorder. The praxeological analysis method of the Anthropological Theory of Didactics (ATD) was used in the data analysis. The findings of the study show that teachers use two different praxeologies in the inverse function. The first one is praxeology based on informal mapping with the effect of the dominant definition of the concept of function in the curriculum, and this praxeology was used to introduce the concept of inverse function. The other praxeology, which shows the monoid structure more clearly, emerged due to both a necessity and the necessity to exhibit an approach appropriate to the curriculum in more complex tasks and was shaped as a mixed praxeology. It was determined that teachers did not structure both praxeologies well and made sudden transitions from one praxeology to another.

Impact of a science and technology strategy on the learning of physics

The use of smartphones and some applications for educational purposes are valuable tools in the laboratory since they are motivating for students and the teacher can take advantage of this advantage for the teaching of physics. The experience is based on the anthropological theory of didactics and the teaching approach in science, technology, engineering, and mathematics. It is proposed to investigate a trigger question in physics. To respond, an application is used that uses the smartphone’s sensors to record the simulation data. The experience is described, and results of its implementation are presented. Methodologically, a qualitative descriptive approach was used in a group of tenth grade students taking the physics course. Finally, it is concluded that the students felt motivated since they felt they participated in the construction of their own learning, supported using technologies that facilitate the integration of knowledge in physics.

Elements of the anthropological theory of didactics in the selection of contents in a course of fluid mechanics in engineering, a case study in Spanish universities

The Anthropological Theory of Didactics has been applied to the field of didactics of mathematics with remarkable success. Fluid Mechanics is a discipline with a strong mathematical background, where mathematics is used for modeling the continuous nature. In addition, the Fluid Mechanics concepts are essential for the future engineer or scientist. For this reason, it is worth thinking whether the content that developed in engineering schools or science faculties are those demanded by the future professionals. The analysis has been done within the context of a case study framed in the Spanish noosphere, more particularly Universities and Companies. In this direction, the objective of this article is to know the institutional distance between the University and society as a demander of technologies based on Fluid Mechanics. To this end, the methodology based on the issuance of a questionnaire to experts focused on aspects such as present and emerging content associated with the Fluid Mechanics of an engineering degree is used. Note that the number of experts selected is reduced so as to consider the study as a sourcing for introducing expert thoughts on the fluid mechanics conception between university and companies. The results highlight the existence of an institutional distance between the University and the Enterprise (as a technology executor) in the conception of contents, thus establishing an area of potential improvement within the noosphere associated with fluid mechanics in Spain.HighlightsQuestionnaire to experts to understand the current institutional relations between University and Company in the Spanish system.Application of the Anthropological Theory of Didactics (ATD) techniques to Fluid Mechanics.Confirmation of an institutional distance between University and Companies in Fluid Mechanics conceptions.

Savoirs véhiculés par les manuels scolaires français et québécois à propos de l’aire. Une étude comparative

This article presents a comparative study of French and Quebec textbooks on the notion of area. Several research studies have raised students’ difficulties in understanding the concept of area, and recent work suggests studying these difficulties in connection with the learning opportunities offered by textbooks, which are a tool widely used by teachers. In order to highlight the similarities and differences in the knowledge set out in the textbooks of two territories and to interpret them according to the learning of the pupils, we have built a praxeological reference model using the Anthropological Theory of Didactics (TAD). Our results show similar limitations in French and Quebec textbooks, in particular the strong focus on the numerical dimension of the area to the detriment of the elements contributing to a conceptualization of this notion.

Co-disciplinary Physics and Mathematics Research and Study Course (RSC) within three study groups: teachers-in-training, secondary school students and researchers

This work shows the results of a research carried out in secondary school and university developing a co-disciplinary Research and Study Course (RSC) on questions connected to Physics and Mathematics in different groups. We present preliminary results of the RSC developed in three different groups: science education researchers, N=25 Mathematics teacher students (training teachers of Mathematics) at University, and N= 68 secondary school students. The development and scope of the RSC in each group is described by using the RSC components as defined by Chevallard’s Anthropological Theory of Didactics (ATD). Furthermore, a short description of the Praxeological Model of Reference is presented. This model was built by the researchers group in order to reply to the generative question, unknown in the beginning, and to anticipate and to conceive the evolution of the possible SRC in each institution. Some general results in each group are discussed and some conclusions concerning the ecology of the pedagogy of research and questioning the world at university and secondary schools are drawn.

Relações institucionais esperadas e existentes na disciplina laboratório de ensino de matemática em um curso de graduação

Este artigo apresenta os resultados de uma análise institucional, cujo objetivo foi validar a institucionalização dos conhecimentos prévios esperados das disciplinas pré-requisitos de Laboratório de Ensino de Matemática. A metodologia considerou uma análise institucional fundamentada na Teoria Antropológica do Didático (CHEVALLARD, 1992), que foi conduzida em seis fases, sob alguns princípios da Engenharia Didática Clássica (ARTIGUE, 1998). Como fio condutor dessa empreitada, buscou-se responder à seguinte questão: os conhecimentos desenvolvidos nas três disciplinas pré-requisitos de Laboratório de Ensino de Matemática estão disponíveis no repertório dos estudantes matriculados e funcionando como suporte para novos conhecimentos esperados pela disciplina em questão? Os resultados revelaram a inexistência dos conhecimentos prévios esperados como disponíveis nos alunos para o bom desempenho da disciplina em análise. Dessa forma, a pesquisa mostrou a importância de uma mudança emergente nos hábitos de ensinar e aprender noções relacionadas à formação de professores de matemática.

Noção de função quadrática na transição entre a educação básica e o ensino superior

Este artigo tem como objetivo analisar a noção de função quadrática comparando as relações institucionais, pessoais esperadas e existentes, representadas pela abordagem desenvolvida em três livros didáticos: um das séries finais do Ensino Fundamental, um do Ensino Médio e o da disciplina de Matemática Instrumental para alguns cursos de Engenharia. Além disso, são analisadas as expectativas institucionais analisadas por meio da macroavaliação Sistema de Avaliação de Rendimento Escolar dos Estudantes do Estado de São Paulo (SARESP). Trata-se de uma pesquisa qualitativa que utiliza o método documental, que se apoia na Teoria Antropológica do Didático, de Chevallard. As abordagens teóricas em termos de quadros e mudança de Douady, níveis de conceituação e de conhecimento definidos por Robert e pontos de vista segundo Rogalski complementam o referencial teórico. Desse modo, foi definida, a priori, uma grade com as categorias de análise dos tipos de tarefas sobre função quadrática que podemos encontrar na transição entre a Educação Básica e o Ensino Superior. Este estudo possibilitou identificar quais conhecimentos sobre a noção de função quadrática podem ser considerados como conhecimentos prévios mobilizáveis ou disponíveis para os estudantes que iniciam o curso de Engenharia, o que pode ajudar na proposição de novas formas de trabalho com esses estudantes.

The Introduction of Proof at the Secondary School in Cameroun: A First Approach trough the Study of Quadrilaterals and Triangles in the Textbook

The purpose of this article is to better understand how proof is introduced into the study of quadrilaterals and triangles in high school. To do this, we designed a grid to analyse mathematics textbooks in Cameroon francophone subsystems (7th Grade and 8th Grade). The Anthropological Theory of Didactics and the paradigms in geometry served as a theoretical framework for our analyses. The results of our analysis indicate that problems in the lessons section correspond to guided problems. These kinds of problems do not develop students’ spirit of research and initiative. The authors of the textbook choose to teach the functioning of deductive reasoning in the 8th Grade. They choose to introduce proof in the commented exercise section rather than lessons section. The learning problems proposed in the textbooks contain drawings wish have informative function and representative function. The preponderance of drawings with a representative function that have the same shape and name observed in textbooks can contribute to the construction of constant visual models in students’ minds. This could lead to the superficial use of drawings in proof tasks.

Formação inicial de professores que ensinam matemática e o sistema de numeração decimal

Este artigo apresenta parte de uma pesquisa doutoral em andamento que usa o suporte teórico e metodológico da Teoria Antropológica do Didático para questionar e responder se o sistema de numeração decimal é um conhecimento naturalizado no seio das práticas de um grupo de professores em formação inicial para os anos iniciais do ensino fundamental. O interesse nessa questão decorre da naturalização dos números decimais, uma vez que há dificuldade no seu ensino e aprendizagem como objetos estruturados segundo o sistema de numeração posicional. A metodologia usada, em consonância com os recursos teóricos, foi o desenvolvimento de um percurso de estudo e pesquisa, a partir de uma situação não rotineira entre as práticas docentes escolares das séries iniciais, com ajuda de um diretor de estudo tomado entre os autores dessa pesquisa. Os resultados encontrados ratificam a hipótese inicial de naturalização desse sistema de numeração pelos professores em formação inicial que demonstram e ratificam a potência da metodologia empregada nessa pesquisa como um dispositivo didático de ensino, inclusive para a formação docente.

A Theoretical Model for the Development of Mathematical Talent through Mathematical Creativity

This study was conducted from a perspective that adopts a broad vision of mathematical talent, defined as the potential that a subject manifests when confronting certain types of tasks, in a successful way, that generate creative mathematical activity. To analyse this, our study proposes a Praxeological Model of Mathematical Talent based on the Anthropological Theory of Didactics and the notion of mathematical creativity, which defines four technological functions: (1) producing new techniques; (2) optimizing those techniques (3); considering tasks from diverse angles; and (4) adapting techniques. Using this model, this study analyses the creative mathematical activity of students aged 10–12 years displayed as they sought to solve a series of infinite succession tasks proposed to encourage the construction of generalization processes. The setting is a Mathematics Club (a talent-promoting institution). The evaluation of results shows that the Praxeological Model of Mathematical Talent allows the emergence and analysis of mathematical creativity and, therefore, encourages the development of mathematical talent.

The characteristics didactic gestures of a Study and Research Path involving mathematics and physics at secondary school

This paper analyses the development of a Study and Research Path (SRP) involving mathematics and physics by means of the theoretical construct proposed by the Anthropological Theory of Didactics (ATD) called dialectics . The SRP was implemented in five secondary school math courses and 116 students participated in total. The data analysis was performed using qualitative techniques and constructing nominal variables and their modalities, which also allows the use of descriptive statistical techniques. In this work, absolute frequencies are analysed and some considerations are made - in the light of the theory - to interpret these results. Article visualizations:

A Comparative Study of Norwegian and Ethiopian Textbooks: The Case of Relations and Functions Using Anthropological Theory of Didactics (ATD)

This paper provides a comparative study of mathematics textbooks as the primary construct via the Anthropological Theory of Didactics (ATD), which was founded by Yves Chevallard. The aim is to suggest principles that can be incorporated to improve the designing of mathematics textbooks. Definitions, examples, and tasks dealing with the teaching and learning of relations and functions, as sub-construct, from several mathematics textbooks in Norway and one textbook from Ethiopia was collected and analyzed using didactical tools such as types of representations, cognitive demand levels, and response types of mathematical tasks. In the findings, similarity and differences of textbooks, both within homogeneous and heterogeneous cultures, were adequately identified and explained in a way that the results contribute to the improvement of the intended curriculum. In doing so, it shows that ATD provides an excellent tool for textbook design research in the future.

Enseignement de l’algorithmique en classe de seconde : une introduction curriculaire problématique

In 2009, the high school curricular reform introduced algorithms in mathematics teaching. This is a new hybrid object, at the crossroads of mathematics and computer science, for which most teachers are not trained. Therefore, how do teachers approach this part of the program? To answer this question, we observed a mathematics teacher in a second grade in high school, for one year school. In order to conduct an analysis, we articulate two theoretical frameworks: the anthropological theory of didactics (ATD) and the joint action theory in didactics (JATD). The ATD provides tools for analyzing the tasks proposed by the math teacher to the students against the background of the concept of mathematical praxeologies. The JATD allows to put in view the expectations of the institution with what is actually taught in the classroom over several sessions of algorithm teaching. The results show the difficulties of teaching a knowledge that has its references in two disciplines. The co-constructed knowledge developed in the class is referred either under their mathematical specificity or their computer specificity. As a result of that, students do not really learn algorithmic knowledge.

Anthropological Theory of Didactics and the Probability of the Constructivist Approach Being a Solution to the Common Mistakes Made in Mathematics Lessons

In the anthropological didactic teaching method, knowledge is passed to the students throughindividuals and institutions, which generates problems that may result in multiple misunderstandings in mathematicalteaching. These misconceptions become apparent in mathematics lessons as common mistakes. The purpose ofthis study is to identify teachers’ views regarding the common mistakes made during problem-solving in mathematicsand whether the constructivist approach is thought to be a solution. The study group consisted of 30 primaryschool teachers teaching in both state and private schools in Northern Cyprus. The data of the current study wascollected through face-to-face interviews with those teachers. All the teachers who participated in the study hadsupportive and positive answers concerning the common mistakes made during problem-solving in mathematicsand considered that the constructivist approach could be a solution.

Anthropological Theory of Didactics and the Probability of the Constructivist Approach Being a Solution to the Common Mistakes Made in Mathematics Lessons

Anthropological Theory of Didactics and the Probability of the Constructivist Approach Being a Solution to the Common Mistakes Made in Mathematics Lessons

Estudo comparado da transição entre o Ensino Médio e o Ensino Superior: análise das organizações didático-matemáticas dos documentos orientadores do Brasil e de Moçambique

Neste trabalho, discutimos a problemática da transição entre o Ensino Médio e o Superior, comparando os sistemas educativos brasileiro e moçambicano, na disciplina de Matemática, com o objetivo de mostrar como funcionam tais sistemas nessa fase e compreender as semelhanças, as diferenças e as implicações para os processos de ensino e de aprendizagem nas instituições escolares. Partimos da questão: quais as expectativas institucionais para as organizações didático-matemáticas dos sistemas educativos brasileiro e moçambicano na fase de transição do Ensino Médio para o Ensino Superior? Como metodologia, analisamos os documentos orientadores para educadores e professores para os dois países. Usamos a Teoria Antropológica do Didático de Chevallard e a técnica de pesquisa documental para identificar as relações institucionais que sobrevivem e se reconstroem nas instituições visadas. Os resultados apontam que os dois sistemas, em geral, são cronologicamente bastante próximos, mas apresentam expectativas de desenvolvimento de conteúdos muito diferentes.

Teaching of Mathematics and Physics in Secondary School through Research and Study Paths

In this paper we present a proposal for teaching based on the Research and Study Paths (RSP) involving Mathematics and Physics together at the Secondary School. We adopt the ideas of the Anthropological Theory of didactic (ATD). The Research and Study Path (RSP) and the Praxeological Model of Reference (PMR) are described and analyzed. We carried out an implementation with N=68 students of 5th year at the secondary school. Some results obtained in this experience are described.