When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

This study diagnoses and explores year eight students' misconceptions and mistakes in algebra. An in-depth exploration of students' misconceptions were carried out by conducting interviews based on the students' work as outlined in a cognitive map. Based on the cognitive maps, it can be seen that the students emphasize procedural knowledge rather…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was…

The ability to offer constructive feedback to students concerning their errors is an indispensable requirement for mathematics teachers, for the purpose of providing cognitively challenging learning opportunities. However, if they are to react adequately, teachers need to identify student errors immediately. The fast perception of student errors…

Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to…

The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…

In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students' answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master's Degree in Mathematics. In order…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

This pilot study explores the effectiveness of a strategy for overcoming post-primary students' misconceptions within the topic of algebra. Although central to the study of mathematics, algebra can be an area of difficulty for many students. A misconception is typically classified as flawed understanding of a concept causing repeated errors, and…

The article analyses the test results evaluating the knowledge of students of basic mathematics courses at the University of Economics in Prague and at the University of Finance and Administration in Prague. The relationships between the study of the theory, the ability to formulate definitions and to solve exercises are analysed based on the…