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.

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.

Didactic Contract from the Perspective of the Theory of Didactical Situations

The phenomena related to the mathematical teaching and learning process have a significant and direct influence on the construction of knowledge and studying these issues is of interest to the theory developed by Guy Brousseau, called Theory of Didactical Situations. When dealing with the relations established between student, knowledge and teacher, Brousseau presents those that are specific, explicitly and implicitly, of the relationship between teacher and students, as well as their influences on the teaching and learning process, defining, for this, the Didactic Contract, which consists of the set of behaviors that the teacher expects from the student and the student from the teacher. With this, the following question arose for this work: What is the relevance of the Didactic Contract when designing teaching sequences with input in the Theory of Didactical Situations? The objective was, then, to carry out an integrative review in order to systematize information present in scientific articles about the Didactic Contract in the perspective of the Theory of Didactical Situations. A search for works was carried out in the databases Scielo, Google Scholar and Portal de Periódicos CAPES/MEC through the descriptors "Didactic Contract" and "Theory of Didactical Situations", with the following exclusion criteria: works not related to the theme and book, theses, dissertations and monographs. That is, only papers of the scientific article type were chosen. A total of one hundred and seventy-seven works were obtained as an initial result, of which thirteen were repeated. After reading the abstracts and adopting the exclusion criteria, sixteen articles remained, of which nine responded to the elaborated question. With the research, it was found, in the period consulted, a limitation of publications that deal specifically with the Didactic Contract and, in spite of that, it was concluded that the Didactic Contract is a very important element in a teaching and learning situation, because it can favor or cause an obstacle in the acquisition of new knowledge by the student.

Relações entre o Livro Didático e o Contrato Didático: a proposição do Contrato Didático Potencial (CDP)Relationships between the Didactic Book and the Didactic Contract: the proposition of the Potential Didactic Contract

Este trabalho tem como objetivo tecer discussões a respeito do Contrato Didático Potencial (CDP), o qual se refere especificamente ao Contrato Didático presente na abordagem do livro didático. Este contrato não se encontra originalmente definido na literatura, sendo sua definição uma contribuição desse estudo. Consideramos que o livro didático é escrito em função de professor e alunos hipotéticos possuindo intenções sobre como o saber deve ser negociado em sala de aula, partindo disso propomos a definição dos elementos contratuais já discutidos na literatura sob a ótica do Livro Didático, isto é, expectativas, regras de contrato potencial, indícios de rupturas e indícios de efeitos de contrato. O Contrato Didático Potencial apresenta um campo frutífero para a investigação do livro didático sob a ótica do Contrato Didático.