Explore the foundational principles of our base-ten number system to deepen your understanding of place value, number composition and decomposition, and efficient strategies for whole number and decimal computation. Through hands-on mathematical tasks designed for adult learners, you will refine your reasoning and broaden your understanding of how the structures and patterns that underpin our number system can be leveraged to develop fluency in addition, subtraction, multiplication, and division. You will also analyze student thinking across multiple grade levels to better support the diverse needs of your own students.This course is a reimagined and refreshed version of the Developing Mathematical Ideas (DMI) module Building a System of Tens and is designed for educators looking to deepen their content and pedagogical knowledge while enhancing their instructional practices. Whether taken independently, with colleagues, or as part of a larger professional learning network, this course offers practical strategies to help you guide students in building a strong conceptual foundation for computation—one that will serve as a cornerstone for future mathematical learning.

Learning Objectives:

As a result of this course, participants will be able to:

1. Appreciate the power and complexity of students’ mathematical thinking.
   
2. Ask questions of students that will deepen their mathematical understanding.
   
3. Connect their experiences in the course to research results.
   
4. Explain how key mathematical ideas in the context of the study of the base ten structure of our number system are interconnected.
   
5. Recognize key mathematical ideas in the context of the study of contextual problems with whole numbers and operations of fractions.
   
6. Reflect on experiences and practices that affect students’ developing math identity, explore ways they can support the development of positive math identities within their students, and examine how their mathematical identities impact the decisions they make.