Technological advances in high-performance computing and communications over the past decade have brought unprecedented power to the desktops of teachers and students. Within the past three years, the use of the World Wide Web-known as WWW, W3, or simply “the Web”—has increased dramatically with the advent of such software as NCSA Mosaic, Netscape, and Lynx. This software has led to an explosion of resources on the international information superhighway. These Web resources bold many possibilities for both students and teachers in secondary mathematics education by allowing new opportunities for collaboration, communication, and exploration.
Helen M. Doerr and Caroline G. Hecht
Katie Makar, Helen M. Doerr and Robert delMas
Statistical modeling allows students to construct and improve representations based on their experiences. A model development sequence is used with fifth graders to build models for comparing two distributions of the flight durations of paper helicopters. Emphasis is on the role of the teacher and using models as evidence.
Helen M. Doerr and Lyn D. English
A modeling approach to the teaching and learning of mathematics shifts the focus of the learning activity from finding a solution to a particular problem to creating a system of relationships that is generalizable and reusable. In this article, we discuss the nature of a sequence of tasks that can be used to elicit the development of such systems by middle school students. We report the results of our research with these tasks at two levels. First, we present a detailed analysis of the mathematical reasoning development of one small group of students across the sequence of tasks. Second, we provide a macrolevel analysis of the diversity of thinking patterns identified on two of the problem tasks where we incorporate data from multiple groups of students. Student reasoning about the relationships between and among quantities and their application in related situations is discussed. The results suggest that students were able to create generalizable and reusable systems or models for selecting, ranking, and weighting data. Furthermore, the extent of variations in the approaches that students took suggests that there are multiple paths for the development of ideas about ranking data for decision making.
Helen M. Doerr, Donna J. Meehan and AnnMarie H. O'Neil
Building on prior knowledge of slope, this approach helps students develop the ability to approximate and interpret rates of change and lays a conceptual foundation for calculus.
Helen M. Doerr, Cathieann Rieff and Jason Tabor
Interpreting graphs is widely recognized as being an important goal of mathematics study. Yet students face many conceptual obstacles in learning to make sense of positionversus-time graphs. A calculator-based motion lab allows students to bring these graphs to life by turning their own motion into a graph that can be analyzed, investigated, and most important, interpreted in terms of how they actually moved. The investigation of motion can become a rich site for building students' intuitions about the concept of rate of change and for developing skills in creating and interpreting graphs. The kinesthetic activity of motion becomes a powerful means for students to understand position-time graphs. The study of changes in motion need not be reserved for students in precalculus or calculus classes.
Tamara J. Moore, Helen M. Doerr, Aran W. Glancy and Forster D. Ntow
A model-eliciting activity is a useful tool that allows students' problem-solving skills and ideas to take flight.