Conocimiento conceptual y procedimental en matemáticas: Su evolución tras décadas de investigación

Investigations related to the conceptual and procedural knowledge in mathematics have been an object of interest and focus of debate throughout the years. In the literature is possible to find discussions that address from which should be further developed in school, if the skills or procedures; up to proposals about how to study interactions between both types of knowledge. This paper analyses the current situation in the field by reviewing the most relevant characterizations in the literature for both types of knowledge, the reasons that led to changes in research focus, the current problems and the open lines of research. In turn, contributes with a summary table of the most significant studies in the literature of each type of knowledge on focus on the mathematical domain to which they belong. The consulted research suggests that initially the studies about conceptual and procedural knowledge focused on children, and being later extended on adolescents, young adults and pre-service teachers. Initially, research on types of knowledge mainly focused on the counting domains, single-digit addition, multi-digit addition, fractions and proportional reasoning; trying in most cases, determine the acquisition order of the concepts versus skills. Over the years the interest in these two types of knowledge has increased, and its study has been extended to other mathematical domains, such as equations, principles of addition and subtraction, multiplication and division. Nevertheless, it is observed in this work that after decades of research there is no consensus about how to define and measure the conceptual and procedural knowledge with an adequate validity level.