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Developing Mathematical Reasoning: Avoiding the Trap of Algorithms

by Pamela Weber Harris

 

This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning.

Everyone is capable of understanding and doing real math. This book:

  •  Highlights the important mathematical relationships, strategies, and models for students to develop
  •  Offers personal stories, reflection sections, and extensive practical exercises for easy implementation
  •  Includes real math—a lot of it—to provide teachers with examples they can put to use in their classrooms immediately

$39.95

Table of Contents

 

Preface

Chapter 1: Math is Figure-out-able

Chapter 2: Developing Mathematical Reasoning

Chapter 3: The Trap of Addition and Subtraction Algorithms

Chapter 4: The Trap of Multiplication and Division Algorithms

Chapter 5: The Trap of Fraction- and Proportion-Solving Algorithms

Chapter 6: Lost in Functional Reasoning

Chapter 7: If Not Algorithms, Then What?

Conclusion

Discussion Questions

#MathStratChat - An Example of Problem Talks and Problem Strings

References

Index

"I have seen a lot of things come and go through my classroom over the years. Problem Strings are not a passing fad—they are the real deal! When you start to use Problem Strings, you will never go back to the 'old ways'. You will never need to keep searching for the next fad."

Maureen Ryan-Dobbin, Teacher

"As an intervention teacher, the Problem Strings books have been a reliable source of powerful lessons at my finger tips. I no longer have to spend hours either searching or writing lessons. The books not only provide my students with lessons that help them understand numbers, but I am also learning something new each time I plan; useful lessons and PD all rolled into one! "

Julia Quinto, Math Intervention Teacher

"As a coach, I now have a resource to give to teachers who are ready to dive into listening to students' thinking and reasoning. This resource is a great way for us to have conversations that are centered around students and how to continue to help them learn and grow. "

Lauren Gangel, K-12 Instructional Coach

Table of Contents

Chapter 1 Teaching with Problem Strings

Developing Mathematical Reasoning
Algorithms versus Strategies
Strategies and Models
About Problem Strings
About the Lessons
Facilitating Problem Strings
Planning for Using Problem Strings

Chapter 2 Additive Reasoning

Counting Strategies
What is Additive Reasoning?
The Major Models for Addition and Subtraction
The Major Strategies for Addition
The Major Strategies for Subtraction

Chapter 3 Addition Lessons
Chapter 4 Subtraction Lessons
Chapter 5 Multiplicative Reasoning

Solving Multiplication Problems Using Additive Reasoning
What is Multiplicative Reasoning?
The Major Models for Multiplication and Division
The Major Strategies for Single-digit Multiplication
The Major Strategies for Multi-digit Multiplication
The Major Strategies for Division

Chapter 6 Single-digit Multiplication Lessons
Chapter 7 Multiplication Lessons
Chapter 8 Division Lessons

"If you are looking for a comprehensive and engaging math resource for your students, this Problem String book is an outstanding choice. This book masterfully combines clarity, depth and enthusiasm, making it a perfect companion for both struggling and advanced students. One of the most remarkable aspects of this book is its accessibility. The explanations are clear and concise, breaking down complex concepts into manageable steps. Additionally, the book is well organized and thoughtfully designed. It has plenty of visuals, diagrams and key points. Overall, the Numeracy Problem Strings: Third Grade book is an exceptional resource that I highly recommend for any math classroom. If you want to help your students develop mathematical reasoning and build their numeracy, this book is a must have."

Velvet Sloan, 3rd Grade Math and Science Teacher

"As a coach, this gives me more resources to share with my teachers. I appreciate the layout of the lessons and how there are several strings provided to support growth with each strategy. There are even extension strings! This book is a comprehensive tool to utilize when implementing Problem Strings."

Cheryl Berkuta, K-5 Elementary Math Coach

"As a leader in math for my district, I can now give my teachers a resource to help them build numeracy and mathematical connections for themselves and their students. The Numeracy Problem Strings book series is going to help change the way we teach in our district. "

Beth Roberts, K-12 District Math Coordinator