Every Math Learner, Grades K-5

A Doable Approach to Teaching With Learning Differences in Mind

Nanci N. Smith

• Publisher: Corwin
• Year: 2017
• Print ISBN: 9781506340739
• eBook ISBN: 9781506390307
• Edition: 1
• Topic: Education
• Subtopic: Education Theory & Practice

As an elementary teacher, you know that students are different and learn differently. And yet, when students enter your classroom, you somehow must teach these unique individuals deep mathematics content using rigorous standards. Is differentiation really the answer? How can it be done well and in less time? 

Nationally recognized math differentiation expert Nanci Smith debunks the myths, revealing what differentiation is and isn't. In this engaging book Smith reveals a practical approach to teaching for real learning differences. You'll gain insights into an achievable, daily differentiation process for ALL students in the K-5 classroom.

Theory-lite and practice-heavy, this book shows how to maintain order and sanity while helping your students know, understand, and even enjoy doing mathematics. Classroom videos, teacher vignettes, ready-to-go lesson ideas, and rich K-5 mathematics examples help you build a manageable framework of engaging, sense-making math. 

Busy K-5 mathematics teachers, coaches, and teacher teams will learn to

• Provide practical structures for assessing how each of your students learns and processes mathematical concepts
• Design, implement, manage, and formatively assess and respond to learning in a differentiated classroom
• Plan specific, standards-aligned differentiated lessons, activities, and assessments
• Adjust current instructional materials and program resources to better meet students? needs

This book includes classroom videos, in-depth student work samples, student surveys, templates, before-and-after lesson demonstrations, examples of 5-day sequenced lessons, and a robust companion website with downloadables of all the tools in the books plus other resources for further planning. Every Math Learner, Grades K-5 will help you know and understand your students as learners in order to provide daily differentiation that accelerates their mathematics comprehension.

"Every Math Learner is a powerful tool for educators serious about meeting the needs of all learners in their mathematics classrooms. Nanci Smith balances philosophy with practicality while providing a glimpse into real classrooms with real students. Teachers will ultimately learn how to lift students up to their greatest potential in learning."
—Eileen Hogan, District Mathematics Facilitator, Winnetka District #36

Chapter One Start Up Why Knowing and Addressing Students’ Learning Differences Is Critical

I always hear from teachers that differentiation seems too hard because they don’t even know where to start. This chapter will focus on the fundamentals to get you going with differentiation. In this chapter, you will find:

• Introduction
• What Differentiation Is and Is Not
• A Glance at a Differentiated Classroom
• Frequently Asked Questions
• Keepsakes and Plans

Introduction

Welcome to school! There is something so very exciting about a new class of students, a new year of potential, and the fulfillment of touching the future. As teachers, we love getting to know our students. We love thinking about how much they will grow this year. We are excited to share activities that we love to do, and we hope our students will not only love to do them too but more importantly also will learn from them.

And very quickly, as we get to know our students, we recognize who each student is as an individual human being and as an individual learner. We come to understand that Maddi already knows much of what is in our grade-level content and that what she doesn’t already know, she will learn in less than half the time it takes the rest of the class. There is outgoing Elena who prefers to learn with others, asks for help freely, and offers help equally as freely. Judah is a constant bundle of energy and desires to follow directions, even if he usually forgets what the directions were. There is Izzi who prefers to draw and think in color and pictures, and there is Landon who is shyly constant in his learning. There is also Alexia who reads voraciously and above grade level, but she is less inclined to enjoy mathematics. Sophia is extremely shy, bright, and capable but doesn’t want to show it and does not like to do anything in front of the class. And then there is Justin, who you didn’t even realize was a special education student with an Individualized Education Plan (IEP) until the IEP showed up in your mailbox. Aamino just moved to this country from Somalia and hasn’t been in a formal school before, and he does not speak English. Nick is very bright but is slowly losing interest in school because he is tired from taking care of his little brother and sister after school, even though he really needs to be taken care of himself. And that is just a few of the students in your class. When we consider all of the students, and the overwhelming amount there is to learn this year, we don’t lose our love for students and enthusiasm, but we begin to wonder just how to pull all of this off!

Let’s face it. We didn’t go into teaching for the prestige or money. We care about students. We care about the quiet and shy, the rowdy and rambunctious, the leaders and followers, the musicians, artists, athletes, cheerleaders, scholars, strugglers, and everyone in between. And in most classrooms, I have just described your student population! Our kids come to us from a wide range of backgrounds and families, experiences, and mastery levels. And we need to reach and teach them all: to have high expectations for each student and help each one fulfill his or her potential and beyond. And that is where differentiation comes in.

Watch It!

As you watch Video 1.1, Getting Started With Differentiation, consider the following questions:

1. How is differentiation not considered individualization, yet still about the individual?
2. What descriptions confirm your understanding of what differentiation is and is not?
3. What is new or surprises you in the descriptions?
4. Why a three-legged stool? Why balance the three “legs” of differentiation?

Video 1.1 Getting Started With Differentiation

What Differentiation Is and Is Not

If you ask a group of educators what is differentiation, you will undoubtedly hear it is about helping every student succeed to the best of his or her ability. That is true. Nevertheless, if you dig deeper for details, explanations can vary drastically and have changed in emphasis over the years. I have heard everything from “it’s just the old individualized instruction back again with a new name.” Or, “this is just about multiple intelligences,” or even, “all you have to do is give choices.” Today, largely because of a common description of Tier 1 of the Response to Intervention (RTI) as quality core instruction for all students that is differentiated, most educators equate differentiation with interventions for struggling learners. Just like the story of the blind men describing an elephant based on the part of the elephant they can feel, all of these explanations give a small sliver of the bigger picture of differentiation. Far too often a person’s sliver of differentiation is taken as the whole and applied in ways that are neither appropriate nor purposeful, and the conclusion is that differentiation just does not work.

According to Carol Ann Tomlinson (2014, p. 4), “Teachers in differentiated classrooms begin with a clear and solid sense of what constitutes powerful curriculum and engaging instruction. Then they ask what it will take to modify that curriculum and instruction so that each learner comes away with knowledge, understanding, and skills necessary to take on the next important phase of learning.” In essence, differentiation is a teacher’s decisions about instructional and assessment design to best equip his or her students for learning.

Sounds simple, and in some ways, it is. In some ways, though, it absolutely is not! The decisions teachers make need to be based on the foundation of explicitly clear standards and learning goals, knowledge of their students as learners, effective pedagogical strategies and task choices, and assessment data. When thinking about students as learners, there are three areas as defined by Tomlinson (2001) that provide a structure for decision-making: Readiness, Interest, and Learning Profile. These three characteristics of learners will be the basis on which we discuss and develop how we can embrace and address the differences in our learners. What follows is a brief introduction to each characteristic that will be developed in detail with lesson examples in the following chapters.

Readiness

“This is easy.” “This is too hard. I can’t do this.” Neither of these reactions from students is what we want to hear. If those are honest reactions from the students, then we have not addressed their readiness. In some ways, readiness differentiation is like the Three Little Bears of Education: We want “just right.” The problem is that it is usually impossible to find just one “just right” for an entire class (Hattie, 2013).

Readiness differentiation begins with determining the entry point for each student on the learning trajectory for the activity, lesson, or unit. We tend to link readiness with “ability grouping.” Yet there are significant differences in what we commonly think of with readiness grouping and ability grouping, no matter how flexible the ability grouping may be designed to be. Many areas impact readiness, including but not limited to life experiences, prior knowledge, ability to abstract and generalize, and home support.

We have all experienced the wide range of learners in our classrooms that can be based on a wide variety of factors. Certainly, a student’s prior knowledge plays a major role in whether the student is perceived as advanced, typical, or struggling. Additionally, there are factors that have equally (or perhaps have greater) impact on a student’s alacrity with learning mathematics, such as the speed at which students process and learn new information, the help and attitudes about education students experience at home, and past experiences in school. Add to this those students who are from other countries, learning English as a second language, or are identified as gifted or with a form of learning disability, and the range of learners can seem overwhelming. To teach all students with the same strategies, at the same pace, with the same expectations does not make sense. This is the essence of readiness differentiation.

Please notice that readiness does not imply ability! In fact, we now know without a doubt that ability is based on effort and is not a fixed commodity. According to Carol Dweck (n.d., 2006), “No matter what your current ability is, effort is what ignites that ability and turns it into accomplishment.”

Readiness addresses that range of challenge where learning can happen for the student, being neither too easy nor too hard. One problem with considering readiness is that when looking at the student’s actions, it is easy to associate readiness with what students can and can’t do . . . especially with what they can’t do.

I remember reading an article several years ago about the new superintendent my district had just hired. In it she stated that we would be committed to finding all of the holes and gaps our students had and to filling them. At first this might sound noble and like an appropriate endeavor. But think about it. The implication is that our education was to work from a deficit model—find what is wrong and fix it! Working from this negative frame of mind leaks out in our attitudes and speech too often, leaving students to feel unsuccessful, unable to learn, and at worst, dumb.

Read...

Table of contents

• Cover
• Acknowledgements
• Half Title
• Acknowledgements
• Title Page
• Copyright Page
• Contents
• Video Clips by Chapter
• Foreword
• Preface
• Acknowledgments
• About the Author
• Chapter One Start Up Why Knowing and Addressing Students’ Learning Differences Is Critical
• Chapter Two Find Out Strategies for Determining Who Each of Your Students Is as a Mathematics Learner
• Chapter Three Teach Up Making Sense of Rigorous Mathematical Content
• Chapter Four Step Up How to Make Proactive Planning Decisions That Deepen Thinking
• Chapter Five Set It Up Establishing the Right Tone to Make Differentiation Doable
• Chapter Six Power On Mastering and Modeling Daily Routines for Achievement All Year
• Chapter Seven Step Back Tools for Assessing and Evaluating in a Differentiated Classroom
• Chapter Eight Close Up A Week in the Life of a Differentiated Mathematics Class
• Appendix A Further Reading on the Topic of English language Learners
• Appendix B Further Reading on the Topic of Special Education
• Appendix C Further Reading on the Topic of Rich Problems and Mathematical Discourse
• References
• Index
• Publisher Note