No abstract

No abstract

This article presents a new paradigm for the study of Math and Sciences curriculum during primary and secondary education. A workshop for Education undergraduates at four different campuses (n=242) was designed to introduce participants to the new paradigm. In order to make a qualitative analysis of the current school methodologies in mathematics, participants were introduced to a taxonomic tool for the description of K-12 Math problems. The tool allows the identification, decomposition and description of Type-A problems, the characteristic ones in the traditional curriculum, and of Type-B problems in the new paradigm. The workshops culminated with a set of surveys where participants were asked to assess both the current and the new proposed paradigms. The surveys in this study revealed that according to the majority of participants: (i) The K-12 Mathematics curricula are designed to teach students exclusively the resolution of Type-A problems; (ii) real life Math problems respond to a paradigm of Type-B problems; and (iii) the current Math curriculum should be modified to include this new paradigm.

A critical set of advances in the world of cognitive sciences during the last two decades is redefining the directions of research of cognitive processes. A set of obsolete cognitive principles has been identified and new methods and objectives have been set for the study of complex problems. We investigate in this paper one such problem in an experiment with students (n=192) from four universities in Spain. The experiment reveals that (i) students easily and reliably acquire (appropriately designed) complex algorithms and (ii) students learn and apply these algorithms in an affective state of ease. These students systematically outperformed published results in an isomorphic task (inheritance genetics). These results indicate that appropriate data encoding, explicit algorithmic definition, and the activation of human cognitive primitives is sufficient to accomplish the task.

The field of research in educational methodologies has been offering during the last decade a series of innovative and promising new initiatives. These initiatives have tried to apply to the educational environment the fruits of current psychology research. Ideas such as student motivation, gaming, multiple intelligences, project-based learning, flipping the classroom, makerspaces, and others, abound in the field of educational methodologies. These new initiatives are evaluated with traditional procedures grouped under the umbrella of the scientific method. This paper first discusses the limitations of these evaluations. Second, it describes learning and teaching as a computational process. Finally, it proposes the use of principles of Information Theory as the foundation for the design of modern educational methodologies.