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…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

In this study, preservice preschool teachers' pedagogical content knowledge about geometric shapes was examined in the context of children's mistakes. A total of 84 preservice teachers, who were studying in preschool teacher education program at a state university in Turkey, participated in this study. Of the preservice teachers, 34 were sophomore…

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs' faulty reasoning displayed in errors they make.…

Many pre-service mathematics teachers in South Africa are apprehensive about the content of Euclidean geometry, because they did not study Euclidean geometry in high school but will be expected to teach the content when they start their teaching career. This article reports on a study that explored the role of semiotic representations in…

In this study, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music. The case study, one of the qualitative research designs, was used in the study. Study group of the research consisted of 113 pre-school…

Units of measure are critical in many scientific fields. While instructors often note that students struggle with units, little research has been conducted about the nature and extent of these difficulties or why they exist. We investigated calculus students' unit use in area and volume computations. Seventy-three percent of students gave…

In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. First, we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. This study is based on the results of several test administrations of open-ended…

This article details the results of a written test designed to reveal how education majors construct and evaluate histograms and frequency polygons. Included is a description of the mistakes made by the students which shows how they tend to confuse histograms with bar diagrams, incorrectly assign data along the Cartesian axes and experience…

The transformation of a solid to its net is based on something quite different from simple perceptual impression. It is a mental operation performed by manipulating mental images. The aim of this study was to observe pre-service and in-service teachers' ability to visualize the transformation of a curved solid to its net and vice versa, and to try…

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…