"Where do content and pedagogy meet? They converge in these beautifully crafted cases of teaching-richly detailed, deeply interpreted, sensitively glossed, moving effortlessly between written and visual media. Jo Boaler and Cathy Humphreys model the exquisite collaboration between a scholar of practice and a scholarly practitioner." -Lee S. Shulman, President, The Carnegie Foundation for the Advancement of Teaching
In math, like any subject, real learning takes place when students can connect what they already know to new ideas. In Connecting Mathematical Ideas, Jo Boaler and Cathy Humphreys offer a comprehensive way to improve your ability to help students in the middle grades link different mathematical ideas, representations, and strategies.
Video case studies from Humphrey's own classroom are included in the online resources. You'll see students bridging complex mathematical concepts with their prior knowledge, engaging in math talk, and investigating topics like representation, reasonableness, and proof. The online resources also include complete transcripts and study questions to stimulate professional learning. The accompanying book guides you through the online videos with in-depth commentary from Jo and Cathy that breaks down and analyzes the lesson footage from both a theoretical and a practical standpoint.
In addition to addressing the key content areas of middle school mathematics, Connecting Mathematical Ideas covers a broad range of frequently asked questions, such as:
- How can I organize productive class discussions?
- How do I ask questions that stimulate discussion and thought among my students?
- What's the most effective way to encourage reticent class members to speak up?
- What role should student errors play in my teaching?
Go inside real classrooms to solve your toughest teaching questions. Use the case studies and the wealth of professional support within Connecting Mathematical Ideas and find new ways to help your students connect with math. Discover more resources for developing mathematical thinking at Heinemann.com/Math
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About the Author
Jo Boaler is associate professor of Mathematics Education at Stanford University, where she researches the impact of different teaching approaches on learning, identity, and equity. She is a former president of the International Association of Women and Mathematics. Her Ph.D. and first book - Experiencing School Mathematics (2002)-won national awards in England. She lives with her husband and daughter in California.
Cathy Humphreys, teacher and Noyce Mathematics coach in California's Silicon Valley, has taught middle-school math for more than twenty years. She has been an instructor for Marilyn Burns Education Associates, a lecturer for preservice mathematics teachers at Stanford University, and is an instructor for the Mathematics Education Collaborative. Her current teaching and coaching focus is on helping low-attaining students build mathematical proficiency.
Table of ContentsOpening the Door to My Classroom, Cathy Humphreys Building on Student Ideas: The Border Problem Part 1 Building Understanding of Algebraic Representation: The Border Problem Part 2 Defending Reasonableness: Division of Fractions Introducing the Notion of Proof Continuing Our Discussion of Proof: Convincing Others Class Participation: Through the Eyes of Students Volume: Extending Prior Knowledge Surface Area: Generating Geometric Formulas