Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

A "Know-How vs. Know-What" Approach in the Teaching-Learning of Competences in Physical Chemistry

The methodological approach a teacher uses in the competence teaching-learning process determines the way students learn. Knowledge can be acquired from a series of perspectives, mainly: “know-what” (concept), where facts and descriptions of (natural or social) phenomena are pursued; “know-how” (procedure), where methods and procedures for their application are described; and “know-why” (competence), where general principles and laws that explain both the facts and their applications are sought. As all the three cases are interconnected, the boundaries between them are not fully clear and their application uses shared elements. In any case, the depth of student’s acquired competences will be directly affected by the teaching-learning perspective, traditionally aiming to a “know-why” approach for full competence acquisition. In this work, we discuss a suitable teaching-learning methodology for evaluating whether a “know-how”, “know-what” or combined approach seems better for enhancing competence learning in students. We exemplify the method using a selection of formative activities from the Physical Chemistry area in the Grades of Chemistry and Chemical Engineering.