A r c h i v e d  I n f o r m a t i o n

River City High School (RCHS), a traditional public high school, is one of several state sites for the implementation of ideas from a National Science Foundation (NSF) State Systemic Initiative Program in mathematics, encompassing the mathematical and pedagogical tenets of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989). Specifically, this project espoused combining traditional (algebra, geometry, trigonometry, and calculus) and non-traditional (probability and statistics) mathematics topics with the use of technology (graphing calculators and computers) and multiple teaching techniques in a constructivist mode to solve mathematical problems based on applied contexts. Corresponding curriculum materials were written by a variety of people, most of whom are secondary school mathematics or science teachers, under the guidance of university professors and college educators, to replace traditional mathematics courses at the high school level. This restructuring of mathematics is designed to make mathematics more accessible and more widely used by students.

This case is not a study of this state-wide program but a study of one school that chose to use its ideas and materials in mathematics. To date, RCHS offers its students a choice between the new and traditional mathematics for their first two mathematics courses to meet state graduation requirements and begin college preparation.

RCHS mathematics teachers have a demonstrated culture of sharing their time, energy, material resources and enjoyment of mathematics with each other and seek opportunities to expand their pedagogical and mathematical knowledge. It has resulted in success in training students for academic mathematics experiences. The prevailing ethos in the department is one of caring about teaching the students and the mathematics. They see the new approach as an attempt to expose more students to mathematics and to assist these students in gaining more mathematics skill and knowledge. Some of these teachers were among the first trained in the new approach, having the most classroom experience with the curriculum, while others are just now coming on board. RCHS teachers make use of both the initial inservice training as well as the ongoing training that is available.

The teachers of the new classes also teach some traditional mathematics classes. For their new classes the teachers share two especially equipped rooms which are outfitted with eight long tables having seating for eight students per table and one computer per table. They also share the class set of graphing calculators and manipulatives.

Several elements of the new approach are problematic for the teachers. These elements include the small group, cooperative learning techniques, the reduced emphasis on drill, limited experience and/or poor directions for the use of the integrated technologies, presentation of non-mathematical skills and knowledge necessary to present the context of the real-world problems, and new methods of assessment. Despite these difficulties, which in general the teachers solve through collegial interactions, teachers carry some of the new techniques, especially the questioning techniques, into their regular math classes. Beyond the classroom concerns, these teachers have questions about the cost/benefit relationship of the resource intensive new classes to the traditional math classes, the amount of mathematics content taught in the new classes, and a need to be more directive in their teaching to make certain that their students know the basics.

The student body at RCHS is mostly white, with the largest minority being American Indian. The students who enroll in the new courses come overwhelmingly from the lower-economic status feeder school. A third of these students come from homes whose parents are employed in a business that requires frequent relocation. While taking the new classes for a variety of reasons, a quarter of them said that they now are a better mathematics student than they have been in the past, or than they think they would be in a regular mathematics class, and most believe it is more appropriate for them than a traditional mathematics class.

The students categorize their new classes as easier than a traditional class, meaning that the mathematics is less complicated, less number oriented, less repetitive and easier to understand, but not less or easier in the scope of the work. The students cite interpersonal dynamics (both teacher-student and student-student), use of technology, and formats for material presentation as key elements of the difference.

Student responsibility in the new classes is greater, as are the consequences for not participating. Students are responsible not only for their homework but also for participation in their cooperative group, by explaining concepts to other group members, by not "sliding" by or relying heavily on other group members, and by being pro-active in seeking the help of their group when they need it. Assignments are less frequent, less repetitive, more explanatory, and more thoughtful, thus not completing homework assignments for these classes students can affect both their individual progress, and the progress of their small group and/or whole class.

Change here necessitates continuation and clarification of several aspects of the new approaches. One point of growth and struggle at RCHS is the need for teachers and students to continue their participation in new experiences and acquisition of new skills and knowledge. The process of developing consensus must continue, especially while clarity about the role of the new classes within the culture of the mathematics department is being considered. An environment for continued teacher learning is needed for the areas of the new curriculum (e.g. the group work, the technology, the assessments) which still present challenges to both teachers and students. If these new classes are to succeed, their goals must be made clear not only about which students they serve but also about the alignment of the knowledge generated in these classes with college course knowledge. More administrative involvement is necessary. A presence in new curriculum classrooms as well as a sensitivity to resource needs, primarily staff development are critical.

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