Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

This article explores relationships between designing and making in the work of children within the age range 5-11 when engaged in practical modelling tasks. The notion of the model is explored from the perspective of concrete representations. It is suggested that concrete models may be used as hypotheses from which to test ideas about the nature…

This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

Presents a discussion on the significance of questioning techniques in the development of critical thinking skills. Stresses that teachers can increase a student's mental engagement by using appropriate wait time, increasing nonevaluative responses, avoiding rephrasing a question, and avoiding questions requiring a yes or no response. (RT)

Discusses a study that examined the role of four cognitive factors (formal reasoning ability, prior knowledge, field dependence/independence, and memory capacity) on achievement in chemistry as measured by tests of lab application, chemical calculations, and content knowledge. Reports the significance of prior knowledge and formal reasoning…

This paper has two purposes: (1) to explain briefly in terms of Piaget's theory why relationships are fundamental for constructivist teachers; and (2) to show how constructivist teachers can think about relationships in classroom activities. In a nutshell, the message is that the process by which children are constructing their intelligence,…

Describes a study which was designed to determine the effect of a 25-hour introductory qualitative analysis course on high school students' understanding of formal concepts related to electrolytes. Suggests that introductory concrete experiences better prepare students to deal with more formal abstract concepts. (TW)

Higher order cognitive development and success in the study of high school mathematics and science require an understanding of rational number concepts and facility with proportional reasoning and computation. Proportional reasoning is an essential schema for developing formal operational thought. This study involving 16 ninth-grade students was…