Teleological structure of scientific and mathematical education

One of the main educational objectives in the current Spanish curricula is to develop mathematical and scientific competences, understood as the set of skills and abilities needed to apply Mathematics and Science in situations where are required. This is therefore closely related, on one hand, to the functionality of the knowledge, in the sense of its usefulness in problem solving and in mathematical and science modeling problems. And, on the other hand, is related to the understanding of disciplinary knowledge, a cognitive phenomenon that enables and gives competence to the individual to elaborate contextualized and accurate answers. These answers involve the use of mathematical and scientific knowledge in some of the categories of their phenomenological and epistemological dimensions. For this reason, in this work we carry out a theoretical and reflexive analysis that tries to determine which aspects of the Mathematics and Science Education should be promoted in order to optimize the formative dimension of an individual in these disciplines. This dimension, frequently forgotten in learning and teaching processes, turns out to be, in conjunction with the functional and instrumental dimensions, necessary to acquire the appropriate knowledge in Mathematics and Science that will enable future citizens to permanently adapt to the environment and eventually transform it positively. The results of the analysis show the components of this dimension that should be prioritized in the Science and Mathematics Education: the intellectual autonomy, understood as the ability to think for ourselves and to put in use our abilities and skills to generate information to solve real life problems and to make the right decisions; the moral autonomy, defined as the capacity to face with real life problems with ethical implications; and the social autonomy, understood as the aptitude to make decisions using social abilities and skills.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.“Criterios e instrumentos de evaluación de unidades de enseñanza y aprendizaje” (PPIT.UMA.B1.2017/16) financiado por la Universidad de Málaga en la convocatoria de 2017-2018

Some Thoughts on the Teaching of Mathematics -- ten years later

I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete mathematics.Comment: 10 pages, to appear in Notices of the AM

An Illustration of Students’ Engagement with Mathematical Software using Remote Observation

Students using three types of spreadsheet calculators for understanding expected value were observed remotely. This remote observation involves the use of webcams and application sharing for observing students learning mathematics. The study illustrates how remote observation can be used for collecting mathematical education data and raises questions about the extent to which such a method can be used in future experiments