Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Latent growth curve modeling provides a powerful and flexible tool for researchers to study individual differences in change as well as the correlates and predictors of change. Recent developments in estimation and hypothesis testing procedures are largely based on confirmatory structural equation approaches. In this article, an alternative…

Past research demonstrates that the estimated size of the federal government earnings differential shrinks substantially with the addition of detailed occupational controls. Possible explanations for this reduction are: controlling for the differing sectoral distributions of common occupations, and controlling for detailed occupations unique to…

Officials at the Carnegie Foundation for the Advancement of Teaching changed the system that had been used to classify institutions of higher education in 2000. Part of the redesign was a change in the criteria for placement of doctoral degree granting institutions. Especially noteworthy was the removal of specific levels of research funding as a…

This article presents an historical overview of pedagogical orientations of school leadership in the United States, and then considers issues facing contemporary educational leaders in this context. Our survey begins with a consideration of the early influence of Frederick Taylor and ends in the present day, a time when the fields of practice and…

Auditory pattern recognition skills in children with reading disorders were investigated using perceptual tests involving discrimination of frequency and duration tonal patterns. A behavioral test battery involving recognition of the pattern of presentation of tone triads was used in which individual components differed in either frequency or…

Alecia Ford, co-author of this article, had a problem that teachers everywhere face more and more frequently with the predominance of standardized testing--too much world history to teach in too little time. Her problem relates to how she can help her sixth-grade students develop an in-depth understanding of the Enlightenment, a period in history…

A sequential-touching task was used to investigate whether 14-month-old infants can rapidly change how they categorize a set of objects, recognizing new groupings of objects they had previously categorized in a different way. When presented with a collection of objects that could be categorized by shape (balls vs. blocks) or material (soft vs.…

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…

Several math activities designed to teach patterns which can be found in arrays of 16 squares organized into a four-by-four pattern are presented in this issue of "Student Math Notes." The activities include: (1) determining how many squares and rectangles are contained in a four-by-four array; (2) figuring out the least number of lines…

Upper-level secondary students investigated square and triangular numbers and Pythagorean triples using computers. (SD)

When primary children were interviewed to determine their perceptions of embedded triangles, they failed to observe overlapping triangles. Possible explanations for this and other response patterns are discussed, and implications for schooling are explored. (SD)

Students, using the materials provided, can determine the number of diagonals, number of triangles formed by the diagonals, and degree measures of interior and exterior angles of regular polygons. The activity is designed to lead them to general formulae for polygons with n sides. (SD)