Pixel International Conferences

Learning new highly formal scientific concepts such as force and energy or using mathematical concepts means, most of the time, understanding clear-cut relational concepts and/or perfectly defined algorithms. Once we understand them, no problem should arise using them. As we know, this is far from being the case. Students often fail to learn and apply scientific concepts in all the contexts, or for all the objects, they should be applied. Quite surprisingly, this is also the case for basic algorithms such as addition. We will illustrate these difficulties in these two conceptual domains. In the domain of physics, we will focus on the distinction of the notion of force and energy, describing a trajectory of developing, suggesting that what young children misunderstand can be predicted on the basis on the variables at play in a typical physical display. In fact, given the nature of the objects displayed in the problem (animate or inanimate), the location of the object, the status of the animate participant, students’ answers regarding force and energy might change. These variables will be discussed obstacles to learning arising from world knowledge. In the field of mathematics, arithmetic problem solving is often described as the selection of the relevant algorithm in order to solve the problem. Here, we will suggest that the nature of objects and more broadly the world knowledge associated to these objects influences the way participants choose an algorithm, despite the fact that these properties of objects are mathematically irrelevant and should not influence solving procedures. Math experts and math teachers are usually unaware of these influences regarding mathematical performance, that, in fact, also influence math experts in the case of simple problems, which witnesses their pervasiveness. Overall, these examples suggest that even abstract knowledge might not be completely abstract and independent of the objects they are operating on. We will argue for the necessity to include them in the teaching strategy because they are cognitive obstacles to learning.   

Keywords: abstraction, physics, mathematical knowledge, obstacles to learning, world knowledge.