Bøger af Pamela Weber Harris

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.

"I continue to be amazed at the power we can harness in our secondary students by teaching ourselves and our students real numeracy." Pamela Harris As secondary math teachers, we're often frustrated by the lack of true number sense in our students. Solid research at the elementary level shows how to help all students become mathematically proficient by redefining what it means to compute with number sense. Pam Harris has spent the past ten years scrutinizing the research and using the resulting reform materials with teachers and students, seeing what works and what doesn't work, always with an eye to success in higher math. This book brings these insights to the secondary world, with an emphasis on one powerful goal: building numeracy. Developing numeracy in today's middle and high school students is reflective of the Common Core State Standards mission to build "the skills that our young people need for success in college and careers." (CCSS 2010) Numeracy is more than the ability to do basic arithmetic. At its heart, numeracy is the ability to use mathematical relationships to reason with numbers and numerical concepts, to think through the math logically, to have a repertoire of strategies to solve problems, and to be able to apply the logic outside of classrooms. How can we build powerful numeracy in middle and secondary students? Harris's approach emphasizes two big ideas: Teach the importance of representation. The representation of student strategies on models such as the open number line, the open array, and the ratio table promote discussion on relationships rather than procedures Teach with problem strings. Introduced by Catherine Twomey Fosnot and her colleagues in the Young Mathematicians at Work series, problem strings are purposefully designed sequences of related problems that help students construct numerical relationships. They encourage students to look to the numbers first before choosing a strategy, nudging them toward efficient, sophisticated strategies for computation. Understanding numerical relationships gives students the freedom to choose a strategy, rather than being stuck with only one way to solve a problem. Using the strings and activities in this book can empower your students to reason through problems and seek to find clever solutions. They'll become more naturally inclined to use the strategies that make sense to them. Students become engaged, willing to think, and more confident in their justifications. When we give secondary students this numerical power, we also help them learn higher mathematics with more confidence and more success.