Didactic Contract Research Articles

Exploring the Primary School Teachers’ Reasoning and Individuals with Limited Education When Solving False Proportionality Problems

In this study employing a qualitative approach, we explore and compare the mathematical reasoning of active primary school teachers and individuals with limited education when tackling problems involving false proportionality and lack of authenticity. The research is justified by the importance of understanding how these issues are addressed in various educational groups and how teaching strategies in this area can be enhanced. An individual questionnaire containing five problems was administered to five participants in each group. The results indicate that teachers tend to more frequently succumb to the illusion of linearity, incorrectly applying linear relationships to non-proportional problems compared to individuals with lower educational attainment. This suggests a greater influence of algorithmic approaches and clauses of the didactic contract on their mathematical reasoning. This tendency could be attributed to a greater exposure to algorithmic approaches during the formative stages, as well as certain clauses in the experimental contract. Conversely, individuals with limited education approached problems with greater flexibility, linking their responses to everyday experiences. The study concludes that it is imperative to implement educational strategies aimed at overcoming limitations such as the illusion of linearity and fostering meaningful problem-solving skills from the early stages. It is recommended to developteacher training programs that promote a more contextualized and flexible approach to mathematics teaching, as well as the include contextualized and meaningful problems in the school curriculum.

The Didactic Contract in Hybrid Education: A Prospective Analysis

Following the COVID-19 epidemic in March 2020, Algerian universities were forced to implement remote teaching across the country. Nonetheless, the major players in this context have not been pre-implemented. We are therefore interested in the difficulties encountered in this new context, mainly in the didactic relationship. Having made this preliminary statement regarding distance teaching, we should now ask what the nature of the problems is that flow from these breaches of the didactic contract and what their consequences are for both the introduction of teaching content and for the assessment methods. To answer these questions, a questionnaire was addressed to both teachers and students of the faculty of letters at Hassiba Benbouali University, in the French department, to detect the nature of the obstacles encountered. In other words, the data analysis aims to solve the various problems presented by these new hybrid teaching situations within Algerian university settings. The findings provide valuable insights into preparing for and addressing the challenges of hybrid and remote teaching. Thus, it is crucial to proactively develop actionable strategies to elevate the overall quality of education in this ever evolving academic prospect.

Strongly didactic contracts and mathematical work

Strongly didactic contracts and mathematical work

Strategy for Teaching Numerical Expressions through the Wordwall Platform for EJA Students

This work is a pedagogical practice with students of Youth and Adult Education of a public school in Brazil with insertion of the basic operations of mathematics and numerical expressions. The objective of this research was to analyze the contributions of Gamification in meaningful learning based on the Theory of Didactic Situations with the contents of basic operations and numerical expressions with EJA high school students. The methodology at work is the qualitative approach with descriptive-exploratory objectives, applied to twenty-three EJA students, is composed of dynamic parts that occur simultaneously, following the stages of concept, structuring, application, development, resolution and conclusion of each student from the Didactic Contract and Didactic Transposition inserted in the concept of arithmetic and numerical expressions. Results show that gamification plays an important role in teaching mathematics learning inserted in the EJA high school class, which can be demonstrated at the time of the calculations described in the proposed activity. Finally, it is observed that the study carried out with Gamification and the students' discourse had a positive impact on the learning of all students, especially with regard to basic operations and numerical expressions.

Didactic transposition in music education: Exploring didactical suitability in three Navarrese schools

Didactic transposition occurs when scholarly knowledge is transformed into knowledge to be taught in order to reach didactical suitability. In this study, we explore didactic transposition implemented in music lessons from the perspective of didactical suitability. Utilising Design-Based Research, the current study collected qualitative and quantitative data from three urban schools in the Chartered Community of Navarre, Spain. Findings reveal that didactic transposition depends on the teacher’s beliefs because, while one-to-one teaching and academicism are preferred by educators who prioritise music theory, collective teaching and creativity are promoted by teachers who favour holistic development. In conclusion, didactic transposition enables the aspiration to didactical suitability, explaining the characteristics of didactic contracts. Lastly, some pedagogical implications are provided.

Pedagogical touch: exploring the micro-realities of coach–athlete sensory interactions in high-performance sports

ABSTRACT Background Touch has emerged as a social taboo rather than as an educational tool among sport pedagogues, especially in the #MeToo era. Believing that minimising physical contact will protect themselves from sexual allegations, instructors (coaches and PE teachers) are increasingly opting for hands-off practices, which transforms sport into a no-touch zone. Although extant sport literature has focused on the potential risks and controversial issues of intergenerational touch, academic endeavours exploring its pedagogical value in sensory interaction are limited. Purpose This study emphasises the fundamental necessity of pedagogical touch (PT) in high-performance sports. Drawing on Merleau-Ponty’s (1968) ‘flesh’ as an elemental tissue knitting the inter-world by entangling (subjectively sensing and objectively being sensed) the existences of oneself, others, and the world, we examine the micro-realities of PT occurring in coach–athlete interactions. As one of the few empirical investigations using video analysis, this study is expected to complement the current understanding of coach–athlete tactile communication by linking it with Merleau-Ponty’s phenomenological concepts. Methods Sensory ethnography was employed to comprehend the nuances and dynamics of PT in coach–athlete relationships. Sixteen participants, comprising eight coaches and eight adolescent athletes across four high-performance sports (golf, taekwondo, wrestling, and handball), were selected. Empirical data were gathered through observations using body-mounted camcorders (GoPro7), stimulated recall interviews, and semi-structured interviews. The data were analysed by alternating between inductive fieldwork and deductive framework. Results and discussion Our empirical investigation revealed three key findings. First, PT aims to transfer each sport’s normative body schema of postures, muscles, and senses. Second, the overlapping zone of tactile, visual, and auditory sensations—synaesthesia—enables coaches to explore athletes’ inner sensory conditions appropriately for individualised prescriptions of PT. Third, coaches utilise objects as extended bodies to touch opposite-sex athletes without skin-to-skin contact. Reflecting on the results, we discuss conducive considerations for coaches to maintain the pedagogical benefits of touch: (a) educational persuasion regarding the discomfort caused when athletes’ body schema is de/reconstructed by PT; (b) appropriate questions to understand athletes’ internal sensations; and (c) inclusive application of object-mediated touch to ensure the safety of PT by avoiding direct contact with athletes’ sensitive body parts, irrespective of sex or gender. Conclusion Based on the findings, the authors suggest that sporting agencies broaden their attention towards supporting coaches to be professionally prepared for potential touch-related problems. This can be achieved by offering coaches opportunities to cultivate their ethical and pedagogical sensibilities about intergenerational touch through education on actual un/professional PT cases, instead of continuing with the current no-touch discourses (less touch, less problem). Thereby, coaches, who face dilemmas regarding tactile communication without alternative pedagogies, can reflect on their own practice compared to others’ PT cases while building didactic contracts with their athletes and handling problematic circumstances.

Le contrat didactique différentiel et le positionnement de genre épistémique : concepts pour éclairer la fluidité du genre au cœur du processus d’enseignement-apprentissage

Cet article s’appuie sur une étude en didactique de l’EPS au cœur de laquelle nous avons croisé deux cadres théoriques : le modèle de l’action conjointe en didactique et les Études de genre. Plus spécifiquement, nous leur avons emprunté deux concepts : le contrat didactique différentiel et le positionnement de genre épistémique tout en nous inscrivant dans une réflexion de nature épistémologique, avec pour horizon des perspectives pour l’intervention. Nous montrons comment, loin d’être passif·ves, les filles et les garçons peuvent être acteurs·tricesi de leur positionnement de genre et de leurs apprentissages, même si des arrière-plans éducationnels, sociaux représentent un frein à une émancipation possible. Ces freins existent également du côté des enseignant·es qui eux-mêmes sont installés dans des assujettissements prégnants.

THE USE OF PERSONAL RESPONSE SYSTEMS TO RENEGOTIATE THE DIDACTICAL CONTRACT IN TERTIARY MATHEMATICS EDUCATION

Challenges experienced by first-year students transitioning from secondary to tertiary mathematics education are examined through the lens of the didactical contract. The didactical contract describes the expectations of both lecturer and students about their mutual obligations towards teaching and learning. First-year students’ beliefs about the nature of mathematics and mathematics teaching/learning need to be challenged to renegotiate the didactical contract at tertiary level. The study focuses on how to elicit and confront transitioning students’ beliefs in order to support their learning and influence a shift in the didactical contract. A Likert scale questionnaire was deployed at the beginning of students’ first year to gauge their beliefs about mathematics and mathematics teaching/learning and redeployed near the end of the first semester (or term) to observe possible changes in their beliefs and hence the didactical contract. The intervention consisted of personal response system (PRS) sessions regularly incorporated into the traditional transmission mode lecture to flip the classroom and create a student-centred learning environment, aimed at influencing students’ beliefs in order to make them aware of their own learning and their responsibility for learning. Questionnaire data were quantified and compared for the before and after surveys. There is evidence of a shift towards students taking ownership of their learning and a renegotiation of the didactical contract. Qualitative data generated by focus group interviews confirm the role of the PRS sessions in influencing student beliefs and the didactical contract.

Semiosis and joint student–teacher action. Contract-milieu dialectics in a case study of two subsequent primary school earth science sessions

ABSTRACT This paper addresses the subject of the semiosis process in the transactions between teachers and students about the knowledge at stake in science education. We present a conceptualisation of these transactions as a joint action between students and teachers. This conceptualisation enables us to understand the semiosis process as it unfolds during teaching–learning situations as the semiosis of both the didactic contract and the didactic milieu. We analyse this semiosis in a case study of earth science education at 5th grade, which comprised two subsequent teaching sessions delivered by the same teacher. Our results give an account of the contract–milieu semiosis under the description of different semiotic modes (speech, gestures, stance, gaze, writings, modellings and proxemics). We also define the generic and specific dimensions of semiosis in relation to the knowledge at stake. Finally, we evaluate the relevance of the teaching practice we observed in terms of its staging of a relationship between the semiosis of didactic contracts and didactic milieus.

Design of 3D Metric Geometry Study and Research Activities within a BIM Framework

This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices and is framed in the Didactic Situations Theory and in the Anthropological Theory of the Didactic. Although the mentioned theories, which the French school has developed since the seventies, are widely known and studied by secondary school mathematics teachers during their training in pedagogy, especially in Spanish- and French-speaking countries, their innovative approach has not been fully implemented in the field of algebraic geometry. Mathematics textbooks follow the traditional approach in which the teacher simply provides the contents and instructs the student, who captures these concepts and reproduces them as they have been supplied. In the presented didactic proposal, the approach proposed by Brousseau is followed, in which three fundamental elements take part: student, teacher, and the didactic environment. The teacher is the one who facilitates the environment in which the student builds his knowledge. In the proposal the didactic contract is stablished, the didactic situations are designed, and the means and didactic variables for the study of 3D metric geometry are chosen. The methodology followed in this study consisted of identifying educational problems; describing the theoretical framework; developing the didactic proposal; and analysis, reflection, and criticism of this training product. The contextualization of the geometry workshop in the field of the construction of structures and the use of deductive reasoning techniques that are applied in synthetic geometry and also in the building information modeling (BIM) methodology may be a way of showing the use of analytical geometry in the industries of engineering and architecture; they also serve as an opportunity for students to better understand this mathematical work.

Breaches of the didactic contract as a driving force behind learning and non-learning: a story of flaws and wants

AbstractIn agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians’ mathematics (‘scholarly mathematics’). One main result is that the mathematics taught, too often taken for granted by curriculum developers and teachers, is in fact problematic not only to students but also to teachers and curriculum developers and is sometimes a challenge even to current scholarly mathematics. The mathematics taught during a given historical period within a given institution contains flaws that, when they cease to go unnoticed, generate crises, in the form of breaches of the prevailing didactic contract. The resolution of these crises allows the institution and its actors—in particular students and teachers—to learn new contents and often also leads to the more or less damaging unlearning of old contents. This key phenomenon is illustrated, at the triple level of the classroom, the curriculum and scholarly mathematics, with regard to elementary algebra and mathematical analysis, most importantly in the case of maxima and minima problems.

Understanding Prospective Teachers’ Task Design Considerations through the Lens of the Theory of Didactical Situations

Task design, in general, and task design in a technological environment, is attracting the attention of educational researchers. The present research investigates task design of prospective teachers in the Scratch programming environment. A total of twenty-three female prospective teachers participated in a professional development program. They were in their third academic year majoring in teaching mathematics and computer science in the middle school. The prospective teachers attempted to design mathematics-based programming problems. The present research utilizes the theory of didactical situations in mathematics, specifically the situation types, the paradoxes of the didactical contract and the situation components, to study the task design of the prospective teachers. It does that by focusing on one group of prospective teachers. The research results indicated that the prospective teachers were concerned mainly with the situation of information, situation of reference and situation of action. Doing so, they were concerned with the paradox of the said and the unsaid, the paradox of uncertainty, and the paradox of devolution. In addition, they took care of both algorithmic and creative reasoning. They also took care of students’ devolution, where this devolution was conditioned with following an institutionalization. They were also concerned with giving students autonomy and encouraging decision making regarding the solution of the problem. Furthermore, they planned to enable students’ control over their learning.

Didactical Engineering in the Conception of a Teaching Situation Originated from Brazil´s SPAECE Assessment with the Support of the GEOGEBRA Software

"Abstract: This work presents a discussion about the Didactic Training Engineering (EDF) methodology, of French origin, emphasizing the role of the teacher, during his initial or continuous training, through the conception and structuring of a didactic situation, organized by such methodology and based on the Theory of Didactic Situations (TSD). Therefore, the objective of this work is to present a didactic situation, based on the research methodology of (EDF) and focused on the analysis of the teacher's role, through the application of the dialectical phases (action, formulation, validation and institutionalization) provided by the TSD. The mathematical problem chosen to compose such a situation, through preliminary and a priori analyzes by EDF, will be focused on Flat Geometry directed to the Permanent Evaluation System of Basic Education in Ceará (SPAECE). SPAECE (Brazil) is a large-scale assessment, held annually in the state of Ceará, Brazil, involving all elementary and high school students in public schools. In addition, the use of the GeoGebra software as a technological resource for carrying out a didactic transposition of the content covered in the proposed didactic situation stands out. For a better conduct of this teaching and learning process, it is suggested the adoption of a didactic contract between the characters involved and the consideration of possible epistemological obstacles and obstacles that may arise during this process."

Theory Of Didactical Situation (TDS), Kajian Karakteristik dan Penerapannya dalam Pembelajaran Matematika

This study aims to describe the characteristics of the Theory of Didactical Situation (TDS), especially in mathematics as an alternative information for educators to design learning according to the characteristics and needs of students and the learning objectives to be achieved. This study uses a literature review to explain the characteristics of TSD obtained from scientific papers and articles, relevant books, research reports, and other scientific sources. Based on the literature review, there are three characteristics of TDS, namely TDS' special attention to mathematics and its epistemology, epistemological characteristics, and students' cognitive dimensions. These three things are interrelated and support each other. This article also discusses the concept of adaptation through understanding adidactical situations and milieu and acculturation through understanding didactic situations and didactic contracts. In conclusion, through didactic situations that are built during learning and facilitated by the teacher, it is expected to be able to develop the potential of students, namely students can build their own knowledge to be achieved.
 Keywords: Theory of Didactical Situation, epistemological barriers, milieu, didactic contract, didactic situation

How students use the ‘see similar example’ feature in online mathematics homework

Homework is one of students’ opportunities to learn mathematics, but we know little about what students learn from homework. This study employs the instructional triangle and didactic contract to explore how students used the ‘see similar example’ feature in an online homework platform and how that use reflected their learning goals. Findings indicate students used similar examples to troubleshoot, to check if they were on the right track, and to see the form of the answer. Students also sought to unpack the reasoning in solution steps, used solutions as templates for solving their own problems, and sometimes copied answers. One student did a ‘see similar example’ problem for more practice. Students’ goals included completing the homework, maximizing their score, and understanding the content. This research lays groundwork for future work characterizing what students learn from homework and how features that provide students with similar examples help or hinder their learning.

Identifying Student Responsibilities While Watching Mathematics Instructional Videos

This study investigated the ways in which college algebra students watch mathematics instructional videos about completing the square with the goal of identifying student responsibilities within a particular video and across different videos. Guided by the theory of didactic situations that have defined implicit teacher and student responsibilities within the context of the face-to-face mathematics classroom, participants watched three different videos about completing the square and answered interview questions. Using categories previously identified by the didactic contract for the face-to-face classroom, this study expanded the types of student responsibilities identified specifically for video watching and found that participants, regardless of overall prior knowledge but who had prior knowledge of completing the square, held a responsibility to use the specific set of steps they were taught by their teacher to solve problems. Findings may be useful to both mathematics teachers and video creators.

Using Primary Sources to Improve Classroom Climate and Promote Shared Responsibility

ABSTRACT To address a deteriorating classroom climate at the midpoint of a two-semester course sequence, we employed a novel intervention: reading a research manuscript together with students as an invitation to legitimate peripheral participation in scholarly reflection on teaching and learning. This intervention resolved many student complaints about the structure and level of the course, and the manuscript’s discussion of the didactical contract helped students claim their share of responsibility for their own learning. We propose that reading research literature with students can be an effective tool for addressing classroom challenges, and recommend the didactical contract for promoting shared responsibility.

The Didactic Contract in Times of Accreditation

The Didactic Contract in Times of Accreditation

The Properties of Powers: Didactic Contract and Gender Gap

National and international large-scale assessments of mathematics show that, in most nations, males achieve better results than females and Italy is one of the countries with a greater gap. Many research studies in mathematics education have analysed this issue, using both quantitative and qualitative methods to understand the sources and characteristics of this gap. This study focuses on a specific Grade 10 task that requires algebraic manipulations of powers with the same base. Item-level analysis enables the study of gender differences on specific content, before using the lenses of mathematics education theories to interpret macro-phenomena emergeing from standardized assessment results. The quantitative analysis, carried out using the Rasch statistical model, highlights a gender gap in favour of males in this task and, furthermore, a variance in choices of incorrect options between males and females; the interviews conducted provide a key to understanding this phenomenon in terms of didactic contract.

Physical contact in physical education – immigrant students’ perspectives

ABSTRACT Physical contact is common in physical education (PE) and is often also perceived as necessary in the subject. At the same time, no-touch discourses in sport and PE affect both teachers and students in many western countries. Teachers in the subject have for example become increasingly reluctant to touch their students due to risks of allegations. In addition, many European countries have recently experienced a great influx of immigrants from non-western countries, which has resulted in more multicultural classrooms across Europe. This can be problematic in PE due to cultural differences regarding physical contact, especially with the opposite sex. The purpose of this study is to investigate physical contact between teachers and students in PE from an immigrant student perspective. This is understood through the didactic contract. For this purpose, interviews using photo elicitation have been conducted with immigrant upper secondary school students in Sweden. The major findings suggest that the following negotiation aspects determine whether physical contact can be regarded as legitimate by the students: the professionalism of the teacher, the teacher-student relationship, teachers’ instructive skills, the emotionally engaged teacher, opposite sex issues and teachers and students with similar immigrant backgrounds. These aspects are also part of the process of developing a didactic contract regarding physical contact between teachers and students. In conclusion, it is clear that some of the aspects legitimise physical contact and build trust between the teachers and the students, while others challenge this legitimisation and trust.