Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Domino games are used to illustrate problem-solving techniques in a college principles-of-mathematics course. Students develop tables and use Pascal's triangle to find the total number of pips and the sum of numbers on the pieces. (DC)

Presents the template method developed by Galileo for calculating areas of geometric shapes constructed of uniform density and thickness. The method compares the weight of a shape of known area to the weight of a shape of unknown area. Applies this hands-on method to problems involving calculus, Pythagorean's theorem, and cycloids. (MDH)

Presents activities to create designs with different arrangements of square tiles, which gives students an opportunity to make conjectures about perimeter and to make convincing arguments to justify those conjectures. Includes worksheets. (MKR)

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…