Sharing Teaching Ideas: Angle Limit: A Paper Folding Investigation

In an interesting investigation in the 1997 College Preparatory Mathematics (CPM) Educational Program, students investigate the limit of angle measures formed by repeatedly folding a strip of paper. The idea originally came from Build Your Own Polyhedra (Hilton and Pederson 1994). What makes the investigation interesting is its blending of geometry, algebra, and limits. The activity works best as a discovery lesson in which students work in pairs to follow the steps, measure the angles, and make a table of their observations. They then analyze their results and try to make a conjecture as to what is happening.

Upgrading High School Mathematics Instruction: Improving Learning Opportunities for Low-Achieving, Low-Income Youth

Low-achieving, low-income students are typically tracked into dead-end math courses in high school. In this article, the authors evaluate the success of “transition” math courses in California and New York, which are designed to bridge the gap between elementary and college-preparatory mathematics and to provide access to more challenging and meaningful mathematics for students who enter high school with poor skills. The authors hypothesize that the transition courses—Math A in California and Stretch Regents and UCSMP Math in New York—allow students to keep pace with those who enter college-preparatory courses by covering rigorous mathematical content using a range of cognitive strategies. Data from 882 students in 48 math classes are analyzed using a three-level hierarchical linear model. The results show that growth in student achievement is significantly lower in general-track classes than in college-preparatory classes. Achievement in transition classes falls in between: not significantly lower than in college-preparatory classes, but not significantly greater than in general-track classes. More rigorous content coverage accounts for much of the achievement advantage of college-preparatory classes. The transition classes are judged a partial success in meeting their goal of upgrading the quality of mathematics instruction for low-achieving, low-income youth.

Implementing the Standards: Trigonometry Today

Trigonometry, either as a separate course or as part of an advanced algebra-and-precalculus course, has traditionally been an integral part of college-preparatory mathematics. As college programs evolve to encompass the full range of the mathematical sciences (Ralston and Young 1983, Ralston 1985, National Research Council 1989), preparation for college can no longer be synonymous with preparation for calculus-or at least calculus as it is often taught with the emphasis on recipes and procedural skills. This realization opens the question of the place and nature of trigonometry in contemporary high school mathematics.

The Algebra Project: Organizing in the Spirit of Ella

This article analyzes the unique impact of civil rights organizing — in the spirit of Ella Baker — on the grassroots effort of a community activist parent, Robert Moses. Moses, who is also a mathematician, argues that all children should have access to the college preparatory mathematics curriculum of the high schools, and that children without access to such programs are barred from acquiring the knowledge and skills necessary for participation in an economy driven by rapid technological change. In this article, the authors describe the interaction among parents, students, and teachers engaged in The Algebra Project, a seven-year ongoing effort to establish a pedagogy of mathematics that expects, encourages, and supports every student to study algebra at the middle-school level.

Projects

The College Readiness Program (CRP) is a project funded through the chancellor's office of the California State University (CSU) system and the state department of education in response to the underrepresentation of minority students. specifically blacks and Hispanics, in the CSU system. The goal of CRP is to give direct in· tractional assistance in mathematics and to offer a college student model to average-performance black and Hispanic students during the middle grades 6-8 to increase the percentage of these minority students who subsequently take the college-preparatory mathematics sequence in high school.

Pathfinder: A Microcomputer Experience in Interpreting Graphs

This article describes the design, implementation, and testing of a microcomputer package intended to improve students' understanding and skills in interpreting graphs of physical phenomena. In this package students interpret graphs in order to reproduce the events described by the graphs. Students may also construct events and challenge others to reproduce the events from the graphs they generate. Some previous work is described briefly to provide context for the activities. The package was used with students in grades nine through twelve. Students taking the college preparatory mathematics classes differed from those taking general mathematics in their choices of activities and in the strategies they used. There was evidence that students' strategies changed as they gained more experience.