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…

Presents a framework to guide teaching and assessment procedures with particular emphasis on the importance of communication in learning mathematics. The Lesh translation model contains five modes of mathematical representation: manipulatives, real-life contexts, written symbols, verbal symbols, and pictures. Describes teaching scenarios. (MKR)

This study investigated the effects of various levels of secondary school calculus experience on performance in first-year college calculus, with focus on student performance on conceptual and procedural exam items. Students who had a year of secondary school calculus differed significantly in performance from those who had either no experience or…

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

Described is an activity that uses the techniques of integral calculus to determine the volume of a bundt cake. The cake is used as an example of a solid of revolution. Included are the procedures and assumptions used by students to solve this problem. (KR)

The absolute-value scale, a manipulative that students can construct from a sheet of ruled notebook paper, helps to promote conceptual connections between the number line and the notion of absolute value as distance. This manipulative technique is particularly suited to students who are struggling with transitional abstract cognitive development.…