In this paper, we describe student understanding of the "force concept" (basic concepts of Newtonian mechanics) by representing it as a vector-valued quantity, which we refer to as the "score-state vector," in a (30-dimensional) Force Concept Inventory (FCI) score space. We use a large ensemble of FCI results collected…

Cognitive diagnostic assessment based on Bayesian networks (BN) is developed in this paper to evaluate student understanding of the physical concept of buoyancy. we propose a three-order granular-hierarchy BN model which accounts for both fine-grained attributes and high-level proficiencies. Conditional independence in the BN structure is tested…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts,…