The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying algebraic equations and inequalities, and the extent to which teachers are aware of these mistakes and how they assess them. The study was conducted among 50 ninth grade students and 63 practicing teachers of mathematics. The data…

Research indicates that troubleshooting activities that require students to reflect on pre-prepared erroneous examples, i.e. erroneous solutions to problems that correspond to common naïve ideas, impact their learning positively. These include asking students to diagnose erroneous examples; in other words, detect the conceptual errors and then…

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

Success in Algebra I often predicts whether or not a student will pursue higher levels of mathematics and science. However, many students enter algebra holding persistent misconceptions that are difficult to eliminate, thus, hindering their ability to succeed in algebra. One way to address these misconceptions is to implement worked-examples and…

Computational thinking (CT) is a way of making sense of the natural world and problem solving with computer science concepts and skills. Although CT and science integrations have been called for in the literature, empirical investigations of such integrations are lacking. Prior work in natural selection education indicates students struggle to…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

Computational Thinking (CT) is an increasingly relevant concept that researchers are promoting in formal learning contexts. In their mission to prepare teachers to integrate CT into K-12 schooling, teacher educators would benefit from understanding the different kinds of preconceptions of CT that their students bring to the classroom in order to…

Event-related potentials are used to test the hypothesis that an intuitive misconception persists in the mind even after the acquisition of scientific knowledge. We investigated the temporal dynamics of neural mechanisms in solving a scientific problem involving a common misconception. It showed that the increased P2 component was elicited by the…

Anthropomorphisms are widespread at all levels of the educational system even among science experts. This has led to a shift in how anthropomorphisms are viewed in science education, from a discussion of whether they should be allowed or avoided towards an interest in their role in supporting students' understanding of science. In this study we…

Ratio-proportion is one of the topics that middle school students have difficulty in comprehending. This study aims to determine the learning difficulties that seventh-grade students face while learning about ratio-proportion. Three commonly used strategies to solve ratio-proportion problems are buildup, unit ratio and cross-multiplication. The…

Students' difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing, we applied previously developed frames to seek an underlying structure to the long lists of published…

This study examined the pedagogical content knowledge of pre-service preschool teachers on quantity concepts in terms of children's mistakes. A total of 94 pre-service teachers who were attending a teacher training program at a state university, in Turkey, participated this study. 52 of them were second-year, and 42 of them were third-year…

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…

Confusion is an important epistemic emotion because it can help students focus their attention and effort when solving complex learning tasks. However, unresolved confusion can be detrimental because it may result in students' disengagement. This is especially concerning in simulation environments using discovery-based learning, which puts more of…

We examined the type of errors on multiplication and division computation problems of 326 rising fifth graders enrolled in four elementary schools in Northern Portugal. We further examined whether there was a difference in the number of errors across age and whether there was an association between students' performance on number knowledge and…