This study investigates the challenges faced by second-year undergraduate engineering students in understanding Stokes' theorem in vector calculus, focusing on the misconceptions found in interconnected concepts that form its foundation. Stokes' theorem involves the application of line integrals, surface integrals, the curl of a vector field, and…

This study examined the types of mathematical connections established by four secondary school students while constructing concept maps on transformations of the parabola. The use of concepts maps revealed students' understandings--including some misconceptions--of transformations of the parabola and confirmed the usefulness of a model for…

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students' common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students' understanding of the wrong…

This study was conducted to reveal potential sources of students' difficulty and misconceptions about geometrical concepts with the help of eye tracking. In this study, the students' geometrical misconceptions were explored by answering the questions on the geometry test prepared based on the literature and test-taking processes and represented…

This study aims to determine students' difficulties in understanding the concept of polygons in elementary schools. This research is qualitative research with a case study method. The subjects of this study were 30 grade 5 elementary school students from two different schools in the city of Bandung. The instruments used are test and non-test. The…

This study explores how hard of hearing students decided whether the shape was a polygon and which semiotic sources were used when the students engaged in explaining geometrical concepts. It was defined how the students interacted with geometric shapes using semiotic sources and examined how such multimodal interactions with geometric figures…

Research suggests that teachers struggle to find effective ways to introduce proof. In 1940, in an article in this journal, Roland Smith argued that being aware of student misconceptions in geometry is the first step in preparing to address the fundamental challenges of learning to prove. Through careful study, he identified and analyzed…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

Teachers are often perplexed realizing students ending up with different understandings of the same lesson after attending the same class. This study investigates the use of Variation Theory as a pedagogical design tool in improving students' problem-solving skills in trigonometry. This action research utilizing the 'Learning Study' approach was…

To shed light on the value of the area model as a tool to elicit pre-service teachers' (PSTs') understanding of fractions and area, we explored their understanding of the fractional knowledge and geometric measurement knowledge incorporated in the area model by providing PSTs area models in an "atypical" way. We administered a written…

One pedagogical approach to challenge a persistent misconception is to get students to test a conjecture whereby they are confronted with the misconception. A common misconception about a 'direct linear relationship' between area and perimeter is well-documented. In this study, Year 4-6 students were presented with a conjecture that a rectangle…

The 21st-century mathematics classrooms should equip learners with well-grounded knowledge and thinking skills pertaining to geometry. However, Euclidean geometry remains one of the challenging, if not the most difficult topic for many learners. As a result, the purpose of this article is to interpret Grade 12 learners' learning difficulties in…

Many students share a certain amount of discomfort when encountering proofs in geometry class for the first time. The logic and reasoning process behind proof writing, however, is a vital foundation for mathematical understanding that should not be overlooked. A clearly developed argument helps students organize their thoughts and make…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

This article describes several ways to connect probability to other topics within mathematics, over a range of year levels, and across the curriculum. It includes a description of common issues and misconceptions, and practical learning activities to address them.