Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

Fostering students' computer programming skills has become an important educational issue in the globe. However, it remains a challenge for students to understand those abstract concepts when learning computer programming, implying the need to provide instant learning diagnosis and feedback in computer programming activities. In this study, a…

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

The purpose of this study was to 1) help novice students scaffold problem-solving and engage safely in the deliberate practice of diagnostic reasoning and medical decision-making in real time; 2) assess how accurately students gather and apply data in medical reasoning and treatment during high-fidelity patient simulations (HFPSs); 3) identify…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

In this article we study the conceptions of an American and a French group of undergraduate pre-service teachers regarding the concept of independent events. Specifically, we study the role that intuition plays in their answers, ascertain the presence of probabilistic biases, and compare the findings with previous results collected on a different…

We sought to test a hypothesis that systemic blind spots in active learning are a barrier both for instructors--who cannot see what every student is actually thinking on each concept in each class--and for students--who often cannot tell precisely whether their thinking is right or wrong, let alone exactly how to fix it. We tested a strategy for…

When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN ? QUAL) was used to examine students' reasoning processes when solving…

The contribution investigates opportunities that an educational tool called Concept Cartoons can offer in future teachers' education, namely in comparison with word problems in standard written tests. The referred empirical study was conducted in two separated consecutive stages, with two groups of future primary school teachers (the first one…

Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

In-class example problems that students work out on their own using active problem-solving are typically well received and help the students better learn the material; however, they are difficult to enact in large classes with limited resources due to the number of questions received and the speed at which different students work through the…

This study compared students' learning in troubleshooting and problem solving activities. The troubleshooting activities provided students with solutions to conceptual problems in the form of refutation texts; namely, solutions that portray common misconceptions, refute them, and then present the accepted scientific ideas. They required students…

The present study investigated the differences of strategy use between low-, average-, and high-achieving students when solving different multiplication problems. Nineteen high-, 48 average-, and 17 low-achieving students participated in this study. All participants were asked to complete three different multiplication tests and to explain how…

Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…