Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)

Uses the process of normalization in the Cartesian coordinate system which entails radial projection onto a transect to compare different compositions of minerals. Warns that the ternary diagram should not be used as a framework for calculations. (MVL)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Describes a model for teaching early algebraic concepts using manipulative materials for elementary school students. Presents a rationale for the model. Provides activities for solving algebraic equations using envelopes and counters. (YP)

Summarizes some student misconceptions concerning the concept of equality. Provides several ways to modify present instruction. Describes a way to model the relational view of equals using balances. (YP)

Presented are three cases for intuitive understanding in secondary and college level geometry. Four ways to develop the intuition (physical experience, mutable manipulatives, visualization, and looking back) step are discussed. (YP)

Offers three practical tips for teaching of topics in the secondary school curriculum: (1) methods for identifying problem areas; (2) a device for teaching slopes; and (3) methods for teaching the property of collinearity in geometry. (YP)

This article discusses two data analysis methods: (1) Box plot; and (2) Outlier. Described are the procedures for drawing the two diagrams, wing median, quartiles, and highest and lowest values. (YP)

Reports a study which identified different problem-solving strategies among Hong Kong high school chemistry students. Finds that student experts employed a recognition plus a working forwards strategy, whereas student novices attempted a means-end analysis to create a solution procedure. Comparisons were made with problem-solving in physics. (GG)

Explored relations between measuring procedures and reasoning about amount on the part of 36 children of 3-8 years in 2 studies. Transformation on a relevant measurement procedure predicted difficulty of transformation for a domain. (RJC)

Hierarchical concept maps can be used to preview or review a topic, serve as a means of formal or informal assessment, promote classroom discourse, and provide a visual representation of mathematical connections. (MKR)

Discusses the teaching of vectors and the inadequate and inappropriate examples given in many textbooks. Suggests using the motion of a sailboat or the motion of a car moving on the Earth's surface as possible examples. Details a proper vector teaching example. (MVL)

Two studies (n=228 and n=175) showed that college students more readily solve proportion problems if the items in the problem are relatively distinct from one another. Translation of units of one item into units of another is easier if the items are substantially different. (MDH)

Presents four investigations involving geometric sequences and series: folding a sheet of paper in half 8 times, stacking pieces of paper cut in half 50 times, snapping your fingers at intervals doubled in length for 1 year, and summing time intervals continuously cut in half. (MDH)

Studied the influence of school- and age-related variables on tasks involving quantitative skills. On conservation of number, performance improved as a function of age but not schooling. On mental arithmetic, accuracy improved with schooling rather than age. Results support the utility of the cut-off design for investigating instructional and…