The teaching of monetary concepts and processes is necessary to prepare young children for experiences that they are probably already facing in the real world. Because coins are nonproportionate models in terms of the value they represent, they are abstract models for teaching purposes. To offer concrete experiences, teachers must use proportionate models that can be associated with each coin. The models and processes illustrated in this article prescribe concrete instruction that can be translated into meaningful abstract processes like those used in the real world.

Mathematics teachers face daily challenges in using scarce resources to address the needs of students, particularly those who are disadvantaged. Federal education resources can be used to support your efforts to improve learning. This article explains how Title I of the Elementary and Secondary Education Act (ESEA), which at over $7 billion is the largest federal investment in K–12 education, can support your work. We hope that you will read this article and begin a discussion with principals and administrators about how Title I resources can be used to improve mathematics teaching and learning in your school and district.

In the conversations described in this article, positioning the students so that they could see one another encouraged richer conversations among them and increased the likelihood that the teacher could become a member, rather than leader, of the mathematical community. Students of that community began to form a collegial relationship in which they challenged, modeled, and reconstructed one another's ideas.