Este trabalho tem como objetivo discutir a importância do uso dos canais auditivo e visual no contexto da elaboração de materiais didáticos e atividades para sala de aula, voltados à alfabetização matemática. A metodologia consistiu na revisão de literatura de diversos trabalhos relacionados à Teoria Cognitiva da Aprendizagem Multimídia, visando destacar a aplicação dos princípios dessa teoria na apresentação de atividades de alfabetização matemática comumente usadas em sala de aula.Palavras-chave: Alfabetização Matemática, Aprendizagem Multimídia, Princípios da Teoria Cognitiva de Aprendizagem Multimídia.In this article, we aim to discuss the importance of the use of auditory and visual channels in the context of the elaboration of didactic materials and activities for students in classroom, focusing on mathematical literacy. The methodology used by us consisted of a literature review of several works related to the Cognitive Theory of Multimedia Learning, highlighting the application of the principles of this theory in the presentation of mathematical literacy activities commonly used in classrooms.
Keller's article entitled "Good-bye teacher. . . " [J. Appl. Behav. Anal. 1, 79-89 (1968)] was fundamental for the development and dissemination of Keller's Personalized System of Instruction (PSI), which was one of the central issues in the discussions on psychology and education in the 1970s and 1980s, and nowadays has attracted attention in the context of the increasing use of online education. Belonging to a class of approaches usually named as mastery learning, PSI and modified PSI courses (Keller-type courses) present several interesting results, such as final grade distributions where the majority of students achieve the highest grades. Here, we present a simple mathematical model underlying Keller-type individualized teaching methods, describing, in terms of average characteristic parameters, the time evolution of the distribution of students per unit of content, and that most students achieve the highest grades at the end of the course. By applying this model to a real case of an introductory electromagnetism Keller-type course, we obtained its characteristic parameters with which we showed good agreement between the predictions and observations. The model presented here results in a simple formula, which is very accessible for use by a wide audience interested in planning or investigating Keller-type or other mastering learning methods.
Courses based on the Keller method (also named Personalized System of Instruction -PSI) present several interesting features and results, such as final grade distributions which are upside down (the majority of students achieving the highest grades) and a workload for the elaboration and implementation considerably greater than that involved in traditional courses. In the present paper, we propose a mathematical model to describe the scheme of a course implemented according to the Keller plan. This model predicts the time evolution of the distribution of students per unit of content, predicts the upside down effect in the final grades and establishes conditions under which this effect can be observed. The model also provides a quantification of the workload spent in implementing assessments, so it can be an useful tool for those planning or interested in further investigations on Keller courses.
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