A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…

Although the scientific inadequacy of Le Chatelier's principle has long been documented in the literature, the principle is still treated as a central concept of chemical equilibrium by textbook writers and teachers in many countries. In the past, researchers' interest has focused on student misconceptions about chemical equilibrium and has…

Often students' inquiry can be a great teachable moment as well as a "researchable moment." Today, even though much has been written about culturally responsive teaching, the author is often surprised to find that the notion of culturally responsive teaching does not resonate with urban teachers and when it does, they do not know how to teach…

Energy is a critical concept in physics problem-solving but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. The first article in this series discussed student confusion generated by traditional treatments of work. In any discussion of work, it is important to state…

The present study is concerned with assessing Logo programming experiences among seventh grade students. A formal multiple-choice test and five performance tasks were used to collect data. The results provided that students' performance was better than the expected score by the probabilistic laws, and a very low correlation between their Logo…

In this article, we provide a discussion on our revision method (termed "prescriptive tutoring") aimed at revealing students' misconceptions and misunderstandings by getting them to solve physics problems with an anonymous partner via the computer. It is currently being implemented and evaluated in a public secondary school in Singapore,…

Energy is a critical concept that is used in analyzing physical phenomena and is often an essential starting point in physics problem-solving. It is a global concept that appears throughout the physics curriculum in mechanics, thermodynamics, electromagnetism, and modern physics. Energy is also at the heart of descriptions of processes in biology,…

Object-oriented analysis and design (OOAD) is not an easy subject to learn. There are many challenges confronting students when studying OOAD. Students have particular difficulty abstracting real-world problems within the context of OOAD. They are unable to effectively build object-oriented (OO) models from the problem domain because they…

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their…

Secondary school chemistry teachers' understanding of chemical equilibrium was investigated through interviews using the think-aloud technique. The interviews were conducted with twelve volunteer chemistry teachers in Hong Kong. Their teaching experience ranged from 3 to 18 years. They were asked to predict what would happen to the equilibrium…

This study explored the differences between eight-year elementary school pupils (before the curriculum reform) and nine-year elementary school pupils (soon after the curriculum reform) in Slovenia, as regards specific chemistry knowledge and motivation to learn chemistry. Altogether, 191 elementary school pupils participated in the study. The…

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. Confusion can be caused by the careless use of language in energy discussions. Students consciously or unconsciously imitate a teacher in their use of…

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. In the first three articles in this series we discussed several issues related to the teaching of energy concepts. We have saved a major single issue for this…