Math is not rote-memorizable. Math is not random-guessable. Math is figure-out-able.

Author Pam Harris argues that teaching real math--math that is free of distortions-will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do.

Memorization tricks and algorithms meant to make math easier are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they've learned more and more math, but in reality their brains never get any stronger.

Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. The mountain of trivia piles up until students hit a breaking point. Humanity′s most powerful system of understanding, organizing, and making an impact on the world becomes a soul-draining exercise in confusion, chaos, and lost opportunities.

Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. 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

This book is a valuable resource for educators looking to reach more students by building a strong foundation of mathematical thinking in their students. By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math.

Building Powerful Numeracy for Middle and High School Students brought the world of research on numeracy at the elementary level to the secondary level, helping teachers build numeracy in their students and showing how that work supports students in understanding higher math. Now, Pam Harris continues her work by offering lessons and activities that promote her strategies for teaching as much mathematics as possible with as little memorization as possible.

Two types of activities for building numeracy are included in this workbook:

Student Workouts include reproducible worksheets that students can work on independently or in pairs, followed by robust class discussion to promote understanding of the ideas.

Teacher Directed Activities are whole-class mini-lessons designed to help students construct numerical relationships as they work with the teacher.

While the student workouts provide starting points for students to build important numerical relationships and choose effective strategies, the teacher directed activities provide opportunities for discussing, comparing, modeling, verbalizing strategies, finding and describing patterns, and making generalizations. Together they help develop the mathematical habits of mind that students need for higher math.