This paper reports on five secondary school mathematics prospective teachers' conceptions of "extreme point." The analysis of the data addressed students' definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept…

This study aimed to develop a comprehensive diagnostic tool for assessing upper-secondary school students' understanding of isomers, expanding upon existing two- and three-tier conceptual diagnostic methods. By incorporating 'Confidence Rating Factor' tiers within the answer and reason sections, a four-tier test was designed and developed. This…

Teachers' knowledge of the subject matter is considered an important component of their expertise in teaching mathematics. Yet how teachers' understanding of one content area is related to other content areas has not been investigated in depth. We explored this question by investigating teachers' knowledge of two theoretically related areas: (1)…

In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students' concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition--concept image as reported by Tall and Vinner ("Educational Studies in Mathematics" 12:151-169, 1981), a…

This study used fraction number line estimation tasks to evaluate students' developmental patterns, and the relationship of such tasks with whole number bias was explored. In total, 189 fourth-grade students in a northern Taiwan elementary school were followed over 2 years. The results demonstrated that the students' fraction learning development…

The study assessed the relationship between career preparation, beliefs, attitudes, in-service training, and peer communication of primary school mathematics teachers and their knowledge of students' misconceptions. Seven hundred one Chinese teachers were selected for the test and questionnaire survey. The mathematics teacher test paper had good…

Some of the online explainer videos for physics present misconceptions as scientifically correct explanations. Even so, some of these videos achieve good ratings on online platforms. A possible reason is that explainer videos with misconceptions foster an "illusion of understanding"--the mistaken belief that a topic has been understood.…

Students expose various intuitions in probability comparison and calculation tasks. Large volumes of research looked into these intuitions by categorizing learners' strategies, but fewer studies considered how these intuitions may be associated with learners' judgments. Even fewer examined the mixed effects of multiple intuitions held by the same…

In this qualitative study, we examined how prospective mathematics teachers' instructional visions align with their instructional practices through an approximation of practice opportunity. Namely, we employed scripting tasks to understand how prospective teachers complete a scripting task and respond to students' misconceptions, and we compared…

The literature has amply shown that primary and secondary school students have difficulties in understanding rational number size. Many of these difficulties are explained by the natural number bias or the use of other incorrect reasoning such as gap thinking. However, in many studies, these types of reasoning have been inferred from comparing…

Physics teachers need diagnostic competence to effectively identify students' misconceptions, but studies have yet to sufficiently investigate how this competence can be advanced through various instructional strategies. In this study, we compared a problem-solving strategy against an example-based strategy in advancing diagnostic competence in…

This study has two aims. The first one is to reveal the science teacher candidates' misconceptions about the density by using a four-tier diagnostic test, and the second one is to determine to what extent science teacher candidates have scientific knowledge, lack of knowledge, and misconceptions about the density. In order to achieve these aims, a…

Numbers and operations is widely considered the most essential domain in elementary school grades. Nevertheless, elementary students in Indonesia have consistently performed unsatisfactorily on this domain in several international mathematics assessments. This study examined 308 Indonesian sixth grade students' current performance(s),…

In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…

One of the most important problems of today's science education is the misconceptions and lack of knowledge that arise due to the science concepts not being learned in depth and meaningfully. For this reason, in this study, misconceptions, lack of knowledge, and scientific knowledge levels of science teachers about liquid pressure, which is one of…