Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

"Transcendentalism" refers to philosophical, religious, and literary beliefs held by Ralph Waldo Emerson, Henry David Thoreau, Margaret Fuller, Amos Bronson Alcott, and other writers in New England during the 1830s and 1840s. Emerson believed in the significance of one's intuition and individuality. He expresses these beliefs in his…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

Describes a classroom activity featuring a simple stay-switch probability game. Contends that the exercise helps students see the importance of empirically validating beliefs. Includes full instructions for conducting and discussing the exercise. (CFR)

Presents a technique for introducing analysis of variance (ANOVA) at the concrete level of operational thought, enabling students in introductory statistics courses to understand the complex correlations and interactions between variables. Helps students develop an intuitive understanding of the concepts of between- and within-groups variance and…

This article examines ways in which intuitive understandings may help teachers in developing the thinking of pupils with autism. The article suggests that, by working toward students' development of an autobiographical memory, it may be possible for them to establish an awareness of their own role as a problem solver. (JDD)

This article describes a process for increasing the quality of students' thinking through alternating from a quiet intuitive state to rational logical processing. The article provides specific teaching suggestions using guided imagery for students in grades K-2, grades 3-4, and grades 5 through college. (DB)

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

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)