The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

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…

In Sri Lankan advanced level mathematics curriculum, teachers are required only to provide the intuitive idea of the concept of limit. The purpose of this study is to explore the strategies used by mathematics teachers to achieve this. Twelve in-service secondary mathematics teachers working in government and private schools participated in the…

Research in genetics and genomics is advancing at a fast pace, and thus keeping up with the most recent findings and conclusions can be very challenging. At the same time these recent findings and conclusions have made necessary a reconceptualization of genes and heredity, both in science and in science education, beyond the mostly gene-centred…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

Electricity is regarded as one of the most challenging topics for students of all ages. Several researchers have suggested that naive misconceptions about electricity stem from a deep incommensurability (Slotta and Chi 2006; Chi 2005) or incompatibility (Chi et al. 1994) between naive and expert knowledge structures. In this paper we argue that…

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…

This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations (algebraic, tabular, and graphical). The nature of learning is analyzed in terms of intuitions and misconceptions. (TJH)

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)