Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)

Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…

Explores alternative strategies to solve algebraic equations that do not lend themselves to traditional methods. Examines one nontraditional equation by a graphical approach using a graphing utility and by a numerical approach using spreadsheets. Discusses new basic skills for algebra utilizing technology. Provides a computer program to solve…

Describes a laboratory-type activity, liquid assets, used to illustrate, develop, or reinforce central concepts in first-year algebra. These include linear function, slope, intercept, and dependent and independent variables. Presents a group activity for collecting data, transition from group to individual activity in plotting data points, and…

Presents the hierarchical structure of quadrilaterals as an illustration of learning a geometric concept by moving from the levels of visualization and analysis to the level of formal deduction. The development discusses the classification of quadrilaterals, the inheritance of properties within the hierarchy, connections between algebra and…

Describes how the use of journal prompts is closely aligned with the use of student discourse and open-ended, open-response test items. Students can use their responses to assess their own growth, whereas teachers can use them to detect trends across and within classes regarding the progression of understanding of specific topics, concepts,…

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…

Presents activities that use toy balloons to offer students interesting opportunities to connect algebra and geometry. Involves students measuring the speed of a released balloon and investigating the subtle relationship between the volume of a sphere and its surface area. Prompts a rich and revealing discussion about why the experimental results…

Describes computer or calculator-graphing technology to develop parametric representations which help students connect mathematical topics from algebra and trigonometry through algebraic, graphical, and numerical representations. Computer or calculator graphing utilities instantly transform algebraic expressions into visual and numerical displays…

Reports part of the results of the Design, Development, and Assessment in Mathematics Education Project that tested the booklet on descriptive statistics called "Data Visualization" in six experimental algebra classes in Whitnall, Wisconsin. Describes examples of problems presented, use of cooperative learning during instruction, and…

Reviewed are 13 computer software packages including "Algebra I Second Semester"; "The Algebraic Proposer"; "SVE AutoGraph"; "Geometry: Concepts and Proofs"; "Geometry 1&2"; "Graphics Calculator"; "Interactive Physics"; "Learning Data Analysis with Data Desk";…

Describes a method for teaching Euler's line, the co-linearity of the circumcenter, centroid, and orthocenter of a triangle. Discusses teaching results. (KHR)

The question "What shape will have the largest area for a given perimeter?" identifies an important relationship between area and perimeter that has long been intuitively realized in many cultures. Historically, numerous cultures have made use of this relationship between area and perimeter when struggling to build dwellings with shapes…

Uses a graphing calculator to demonstrate that dividing by a fraction is the same as multiplying by the reciprocal. Students graph a division problem and an equivalent problem, multiplying by the reciprocal. They find that the graphs are the same. (SKS)

Describes an approach to the initial teaching of composite functions that relies primarily on mapping representations. (MKR)