About the course
Designed for the upper-elementary grade band, this course focuses not only on research findings about how children learn multiplication and division of whole numbers but also on the struggles students have with fraction concepts and computation. Logically extending concepts learned in whole number work to fractions can lessen the cognitive load and help students make sense of them. The course begins with a brief introduction to the Ten Principles of Thinking Mathematics instruction; using these principles leads to a better understanding of mathematics by all students. It focuses on the mathematical practices (habits of mind students develop and use as they learn math), which are now part of nearly all rigorous mathematics standards, including Common Core. Multiple representations and strategies are used to develop a deep understanding of multiplication and division. As the distributive property becomes visible, students make connections to the traditional algorithms. Participants learn ways to help students understand fractions as single numbers that can be represented on the number line. This helps them to develop a sense of fraction magnitude so they can make sense of problems and whether answers are reasonable. This course focuses not only on research findings about how children learn multiplication and division of whole numbers but also on fraction concepts and computation.
Course Objectives:
• Gain a deeper understanding of today’s rigorous content standards for intermediate students, the mathematical practices and how content and practices intertwine to create success.
• Learn the Ten Principles of math instruction drawn from research, including tapping knowledge students already have, helping them visualize and model problems, stressing both concept and procedure, encouraging multiple solution strategies, and building the expectation and ability to reason about and discuss their mathematical work.
• Discuss multiple representations and strategies that develop a deep understanding of multiplication and division prior to connecting to traditional algorithms; connect concepts and strategies to work with fractions.
• Learn how to help students understand fractions as single numbers that can be represented on the number line to make sense of fraction magnitude and whether answers are reasonable.
• Understand the importance of questioning and discussion in math class, levels of cognitive demand in tasks and what more rigorous goals for students require of teaching.