Developing model-based reasoning in mathematics and science

It is essential to base instruction on a foundation of understanding of chi ldren's thinking, but it is equally important to adopt the longer-term view that is needed to stretch these early competencies into forms of thinking that are complex. multifaceted, and subject to development over years, rath er than weeks or months. We pursue this topic through our studies of model- based reasoning. We have identified four forms of models and related modeli ng practices that show promise for developing model-based reasoning. Models have the fortuitous feature of making forms of student reasoning public an d inspectable-not only among the community of modelers, but also to teacher s. Modeling provides feedback about student thinking that can guide teachin g decisions, an important dividend for improving professional practice.