Excellent overview of information students learn in mathematics from preschool through the middle grades. Includes developmentally appropriate ideas on how children can and can't think in mathematical ways along with many activities that can be used to implement the ideas presented.

Excellent information of how mathematics can be facilitated in children.

Chapter Titles

1. "Mathematics" or "Mathematizing"?
2. The Landscape of Learning
3. Number Sense on the Horizon
4. Place Value on the Horizon
5. Developing Mathematical Models
6. Addition and Subtraction Facts on the Horizon
7. Algorithms Versus Number Sense
8. Developing Efficient Computation with Minilessons
9. Assessment
10. Teachers as Mathematicians

Excellent information of how mathematics can be facilitated in children.

Chapter Titles

1. Mathematizing  - describes and illustrates what it means to do and learn mathematics
2. The landscape of learning - provides strategies to help teachers turn their classrooms into math workshops that encourage and reflect mathematizing
3. Developing multiplication strategies and big ideas - examines several ways to engage and support children as they construct important strategies and big ideas related to multiplication
4. Connection division to multiplication - takes a close look at the strategies and big ideas related to division
5. Multiplication strategies - defines modeling and provides examples of how learners construct models with a discussion of the importance of context
6. Algorithms versus number sense - discusses what it means to calculate using number sense and whether or not algorithms should still be the goal of computation instruction
7. Developing Efficient Computation with Minilessons
8. Assessment  - describes how to strengthen performance and portfolio assessment
9. Landmark ideas, strategies, models - emphasizes teachers as learners by encouraging them to see themselves as mathematicians.

Excellent information of how mathematics can be facilitated in children.

Chapter Titles

1. Mathematizing - describes and illustrates what it means to do and learn mathematics.
2. The landscape of learning - contrasts word problems with true problematic situations which support and enhance investigation and inquiry.
3. Equivalence on the Horizon - provides strategies to help teachers turn their classrooms into math workshops.
4. Developing big ideas and strategies - explores the cultural and historical development of fractions, decimals, and their equivalents and the ways in which children develop similar ideas and strategies.
5. Developing mathematical models  - defines and gives examples of modeling, noting the importance of context.
6. Algorithms vs. number sense  - discusses calculation using number sense and the role of algorithms in computation instruction.
7. Developing efficient computation with minilessons 
8. Assessment  - describes how to strengthen performance and portfolio assessment.
9. Landmark ideas, strategies, models - focuses on teachers as learners by encouraging them to see themselves as mathematicians.

Excellent information of how mathematics can be facilitated in children. See table of contents and additional information.

A collection of letters written by mathematicians about what it is like being a mathematician. Each can be read alone or as a series. Great reading for anyone interested in math and would be great to read as read alouds in math classes from fifth up.

Includes a CD of interviews with children.
Outline and annotations of video clips

Chapter Titles -

1. Developing Mathematical Thinking
2. Equality
3. Developing and Using Relational Thinking
4. Making Conjectures About Mathematics
5. Equations with Multiple Variables and Repeated Variables
6. Representing Conjectures Symbolically
7. Justification and Proof
8. Ordering Multiple Operations
9. "If… Then…" Statements: Relations Involving Addition, Subtraction, Multiplication, Division, and Equality
10. Answers for Selected Challenges

See also Great ideas about algebraic thinking that need to be known by all teachers. Preschool and early elementary teachers need to know how what they do relates to later algebraic ideas that students will learn later, but play activities in these lower grades will provide important background experiences. Great ideas for middle school teachers and above to implement.

Want to know more about representation in mathematics K-12. This is a very good source.

Great ideas about the importance of proof, different types, and how to implement those ideas K-16.

Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)

Rules or theory - both.

See also Chasing Vermeer - A new character, Tommy, joins Petra and Calder. Pentominoes go 3-D, many math themes, great read for intermediate, middle school, and others.

See also Chasing Vermeer - A new character, Tommy, joins Petra and Calder for three adventures in urban Chicago. Includes logic, mystery, and Pentominoes go 3-D, many math themes, great read for intermediate, middle school, and others.