This report serves as a timely, up-to-date resource for all who teach mathematics to teachers-mathematicians, statisticians, and mathematics educators-and all who are responsible for the mathematical education of teachers-department chairs, educational administrators, and policymakers. Organized into three grade bands, this book covers the preparation of prospective and current teachers of mathematics in Pre-K-12 classrooms. Each chapter includes specific ""Calls to Action"" designed to mobilize the diverse audiences involved in the mathematical education of teachers. To set the stage, the book explores cross-cutting themes that impact the mathematics teaching community across all grade levels. Topics include teacher certification policies, equity and access issues, STEM pathways, integrating new technology (including artificial intelligence) into mathematical knowledge for teaching, and the recruitment and retention of a diverse pool of mathematics teachers. These themes are expanded during the following grade-band chapters. Each of them can be referenced separately and include guidelines for the mathematical needs of teachers and students in that band. This overview is deepened via numerous vignettes and classroom activities for teachers to draw on in their own classrooms. Taken together, the grade-band chapters provide a bird's-eye view of the knowledge that teachers need to support students through their mathematical education. The report is sponsored by CBMS. Each of the writers is a mathematician, statistician, or mathematics educator with substantial expertise and experience in mathematics education. In the rapidly changing landscape of twenty-first century education, The Mathematical Education of Teachers III is an update that builds on the tradition of the first two reports. It serves as a call to action and an invaluable resource for mathematics teacher educators and anyone involved in the teacher education process.