Conceptual and procedural knowledge in mathematics: their development after decades of research

Research on conceptual and procedural knowledge in mathematics has been an object of interest and focus of debate throughout the years. In the literature it is possible to find discussions that address topics ranging from which should be further developed in school -the skills or the procedures-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 characterisations 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, it contributes a summary-table of the most significant studies in the literature of each type of knowledge focusing on the mathematical domain to which they belong. The papers consulted suggest that early studies about conceptual and procedural knowledge focused on children, while later they spread to adolescents, young adults and pre-service teachers. Initially, research on types of knowledge mainly focused on the counting domains, single-and multi-digit addition, fractions and proportional reasoning; trying, in most cases, to 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 spread 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.