*Powerful Problem Solving: Activities for Sense Making with Mathematical Practices*. 2013: Heinemann, Portsmouth, NH. pages 192

ISBN-13: 078-0325-05090-4

This book is an excellent source of information for teachers to learn or review how to facilitate student's mathematical problem solving. The authors apply George Polya's problem solving suggestions, in his book* How to Solve It,* and the ideas of the NCTM Process Standards: problem solving, representations, connections, communication, and proof and reasoning, to the eight categories of the Common Core Standards for Mathematical Practice. It is an excellent source of detailed how to information with specific problem solving activities and suggestions to help teachers faciliate the development of not only problem solving, but students' practices of mathematics.

*Mathematics a Good Beginning*. 7^{th } edition 2013: Medrith Learning LLC. pages 572

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.

The author has kept the price down by not selling the text through a large publishing company and not including color images or text. The format is mostly two columns of text with a nice sized font making it easier and quicker to read and turn a page. The information is focused on the content with only a few tangential activities or related ideas. However, there is suffiient activities and ideas to support a teacher so she or he would be able to facilitate students' development of mathematical literacy conceptually while also providing paths for students to be able to proceduralize their understanding to be able to solve problems efficiently.

Chapter Titles:

- Teaching in a Changing World
- Designing Mathematics Instruction
- Pathways to Thinking and Problem Solving
- Getting Ready for a Good Beginning
- 100s, 10s, 1s, ... Our Base Ten System of Numeration
- Addition and Subtraction Meaning
- Addition and Subtraction Algorithms
- Multiplication and Division, Whole Numbers
- Multiplication and Division Algorithms
- Some Theory about Numbers
- Not All Numbers are Whole Numbers: Representing, Adding, and Subtracting Rationale Numbers
- Security Is Knowing Why: Multiplying and Dividing Rationale Numbers
- Seeing is Believing: Constructing Geometry Ideas
- The Magic of Children?
- Sizing It Up: The Attributes of Measurement, The Measurement of Attributes
- Making Numbers Count: Collecting and Represent, Interpret and Predict. (Data analysis and probability)

*Mathematicians at Work: Constructing Algebra. * 2001: Heinemann, Portsmouth, NH. pages 192

ISBN-13: 978-0-325-02841-5.

Excellent information of how mathematical understanding can be facilitated in children with a specific focus on mathematical instruction for constructing mathematical ideas (sign-posts) conceptually for learning algegra.

*Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. * 2001: Heinemann, Portsmouth, NH. pages 182

ISBN-13: 0-325-00353-x.

Excellent information of how mathematical understanding can be facilitated in children with a specific focus on mathematical instruction for constructing mathematical ideas (sign-posts) conceptually for learning about number value, addition, and subtraction.

Chapter Titles:

- "Mathematics" or "Mathematizing"?
- The Landscape of Learning
- Number Sense on the Horizon
- Place Value on the Horizon
- Developing Mathematical Models
- Addition and Subtraction Facts on the Horizon
- Algorithms Versus Number Sense
- Developing Efficient Computation with Minilessons
- Assessment
- Teachers as Mathematicians

*Mathematicians at Work: Constructing Multiplication and Division. * 2001: Heinemann, Portsmouth, NH. pages 159

ISBN-13: 0-325-00354-8.

Excellent information of how mathematical understanding can be facilitated in children with a specific focus on mathematical instruction for constructing mathematical ideas (sign-posts) conceptually for learning about multiplication and division.

Chapter Titles

- Mathematizing - describes and illustrates what it means to do and learn mathematics
- The landscape of learning - provides strategies to help teachers turn their classrooms into math workshops that encourage and reflect mathematizing
- 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
- Connection division to multiplication - takes a close look at the strategies and big ideas related to division
- Multiplication strategies - defines modeling and provides examples of how learners construct models with a discussion of the importance of context
- 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
- Developing Efficient Computation with Minilessons
- Assessment - describes how to strengthen performance and portfolio assessment
- Landmark ideas, strategies, models - emphasizes teachers as learners by encouraging them to see themselves as mathematicians.

*Mathematicians at Work: Constructing Fractions, Decimals, and Percents. * 2002: Heinemann, Portsmouth, NH. pages 159

ISBN-10: 0-325-00353-x.

Excellent information of how mathematical understanding can be facilitated in children with a specific focus on mathematical instruction for constructing mathematical ideas (sign-posts) conceptually for learning about fractions, decimals, and percents.

Chapter Titles

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

*Elementary and Middle School Mathematics: Teaching Developmentally.* 8^{th} edition. 2013: Pearson. pages 487

ISBN-13: 978-0-13-261226-5.

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.

The text is about $150 new. It is pubished through Pearson and uses color images or text. The format is two columns of text with a smallish sized font and small margins filling each page with information. The information is focused on the content with many tangential activities or related ideas included as Pause and Reflect, Problems, Investigations, Resources, Reflection ideas, MyEducationLab, Field Experience Guide, . However, for those that what to differentiate for your individual needs there is able information for a solid core and resources for individuals to branch in a variety of different ways. There is an amble supply of activities and ideas to support a teacher so she or he would be able to facilitate students' development of mathematical literacy conceptually while also providing paths for students to be able to proceduralize their understanding to be able to solve problems efficiently.

Chapter Titles:

- Teacing in the 21
^{st}Century - Exploring What It Means to Know and Do Mathemtics
- Teaching Through Problem Solving
- Planning in the Problem-Based Classroom
- Building Assessment into Instruction
- Teaching Mathematics Equitably to All Children
- Using Technology Tools to Teach Mathematics
- Developing Early Number Sense
- Developing Meanings for the Operations
- Helping Students Master the Basic Facts
- Developing Whole-Number Place-Value Concepts
- Developing Strategies for Addition and Subtraction Computation
- Developing Strategies for Multiplication and Division Computation
- Algebraic Thinking: Generalizations, Patterns, and Functions
- Developing Fraction Concepts
- Developing Strategies for Fraction Computation
- Developing Concepts of Decimals and Percents
- Proportional Reasoning
- Developing Measurement Concepts
- Geometric Thinking and Geometric Concepts
- Developing Concepts of Data Analysis
- Developing Concepts of Probability
- Developing Concepts of Exponents, Integers, and Real Numbers

*Letters to a Young Mathematician. * 2006: Joat Enterprises, Portsmouth, NH. pages 203

ISBN-13: 978-0-465-08231-5.

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 one or two as read alouds in math classes fifth grade and above.

*Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School Outline of Content. * 2003: Heinemann, Portsmouth, NH. pages 137

ISBN-10: 0-325-00565-6.

Excellent information of how mathematical understanding can be facilitated in elementary students with a specific examples of mathematical instruction of teacher and student interactions for constructing arithmetic and algebra ideas conceptually.

Includes a CD of interviews with children.

Outline and annotations of video clips

Chapter Titles -

- Developing Mathematical Thinking
- Equality
- Developing and Using Relational Thinking
- Making Conjectures About Mathematics
- Equations with Multiple Variables and Repeated Variables
- Representing Conjectures Symbolically
- Justification and Proof
- Ordering Multiple Operations
- "If… Then…" Statements: Relations Involving Addition, Subtraction, Multiplication, Division, and Equality
- Answers for Selected Challenges

*Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10. * 1999: Heinemann, Portsmouth, NH. pages 164

ISBN-10: 0-325-00154-5

Great ideas for middle school teachers and above to implement as well as important information that al teachers should know about algebraic thinking so preschool and early elementary teachers understand the importance of providing students in the early grades opportunities to explore and play with mathematical ideas concretely so students will begin to connect a variety of external events to mathematical ideas so they will have a solid background of representations to use to construct understanding in algebra in their later grade experiences.

*The Roles of Representation in School Mathematics: 2001 Yearbook. * 2001: NCTM. pages 282

ISBN-13: 978-0873534956.

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

*Teacing and Learning Proof Across the Grades: A K-16 Perspective. * 2009: Routledge. pages 408

ISBN-13: 978-0415887311.

Great ideas about the importance of teaching proof, different types of proofs, and how to implement them to facilitate students learning them K-16.

*Knowing and Teaching Elementary Mathematics. * 2010: , . pages 192

ISBN-13: 978-0805829099.

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.

Also a newer version: *Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series).* 2012

ISBN-13: 978-0415873840

232 pages

*Children's Mathematics: Cognitively Guided Instrution (CGI). * 1999: Heinemann, Portsmouth, NH. pages 110

ISBN-13: 978-0325001371.

*The Simpsons and their Mathematical Secrets *- 2014,* Bloomsberry: New York*. pages 213 ages 12+.

ISBN-13: 978-1-62040-277-1.

Excellent story for anyone that is a fan of the Simpsons, interested in mathematical ideas, trivia nut, *Futurama* fan, or people that are interested in stories behind the scene stories.