We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers. One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners' solution strategies and cognitive…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

Students in first-year physics courses generally focus on hunting for suitable equations and formulas when tackling a variety of physical situations and physics problems. There is a need for a framework that can guide them to disciplinary ways of thinking and help them begin to think like physicists. To serve this end, in this study, a framework…

The need for some form of explicit grammar instruction is recognised in most current approaches to second language teaching. Since the usefulness of explicit instruction is at least to some extent dependent on the difficulty of the rules that are taught, an important question for teachers is whether their judgements of rule difficulty are…