The proof that the area of a quadrilateral is one-ninth the area of another quadrilateral is presented. The proof is designed to give geometry students insight into techniques that can be used in other problems. (FL)

A mathematical misteak" is an incorrect operation that leads to a correct result. An introduction to the use of the misteak" to emphasize the mathematical operations being taught. Examples and brief explanations of several types of misteaks" are given. (FL)

Focused on cardinality acquisition (thought to be crucial to correct counting) and on the relation between cardinality and counting. Gathered data with three groups of children three to five years old on four kinds of tasks. Found no empirical evidence for considering counting as a single prerequisite to cardinality. Suggests new approach to…

Describes a classroom activity based on the practice of fishermen tying knots in boat anchor ropes to determine river or lake depth. Knot-tying provides a simple hands-on context for students modeling in algebra. Students were actively involved in measuring, collecting data, fitting a line to data, finding an equation for a line, and checking a…

Attempts to reveal students' (N=800) misconceptions regarding quadratic functions, and identifies conceptual obstacles that may impede students' understanding. Findings indicate that the conceptual obstacles identified were fairly pervasive. Discusses the educational implications of the findings. Contains 34 references. (JRH)

Reports on a project that highlights the difficulties encountered when considering randomness. Findings indicate that the concept of randomness tends to make very subtle intellectual demands when considering it. Presents a game that may be helpful in developing understanding of two-dimensional random differences. (JRH)