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- Herausgeber: John Wiley & Sons
- Kategorie: Bildung
- Sprache: Englisch
Help your child succeed with a better understanding of Common Core Math Common Core Math For Parents For Dummies is packed with tools and information to help you promote your child's success in math. The grade-by-grade walk-through brings you up to speed on what your child is learning, and the sample problems and video lessons help you become more involved as you study together. You'll learn how to effectively collaborate with teachers and keep tabs on your child's progress, so minor missteps can be corrected quickly, before your child falls behind. The Common Core was designed to improve college- and career-readiness, and to prepare U.S. students to be more competitive on an international stage when it's time to enter the workforce. This guide shows you how the standards were created, and how they've evolved over time to help ensure your child's future success. The Common Core Math Standards prepare students to do real math in the real world. Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math. * Understand the key concepts being taught in your child's grade * Utilize the homework tools that help you help your child * Communicate more effectively with your child's teacher * Guide your child through sample problems to foster understanding The Common Core was designed to ensure that every student, regardless of location or background, receives the education they need. Math skills are critical to real-world success, and the new standards reflect that reality in scope and rigorousness. Common Core Math For Parents For Dummies helps you help your child succeed.
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Veröffentlichungsjahr: 2015
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Common Core Math For Parents For Dummies®
Published byJohn Wiley & Sons, Inc.111 River Street, Hoboken, NJ 07030-5774,www.wiley.com
Copyright © 2015 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Control Number: 2014954677
ISBN: 978-1-119-01393-8 ISBN 978-1-119-01393-8 (pbk); ISBN 978-1-119-02112-4 (ebk); ISBN 978-1-119-02111-7 (ebk)
Common Core Math For Parents For Dummies®
Visit www.dummies.com/cheatsheet/commoncoremathforparents to view this book's cheat sheet.
Table of Contents
Cover
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part I: Getting Started with Common Core Math Standards
Chapter 1: The Lowdown on Common Core Math, Just the Basics
Understanding What Common Core Math Is
Examining the Standards for Mathematical Practice
Looking at the Standards inthe Different Grades
Helping Your Child with Homework
Chapter 2: Looking at Math Teaching Then and Now
Setting Goals for the 1900s
Competing Globally with Advanced Math and Science
Returning to Basics
Teaching Math in the Info Age
Holding Teachers Accountable
Agreeing on the Common Core
Chapter 3: Exploring the Standards for Mathematical Practice
Focusing on Asking Questions
Playing with Math
Arguing Is a Ton of Fun
Connecting Ideas
Chapter 4: Understanding Homework Assignments
Getting the Inside Scoop: Teachers’ Views on Homework
Examining the Homework Assignments on Social Media
Becoming Unstuck: What to Do
Helping Your Child without Doing the Work Yourself
Part II: Focusing on Elementary Math: Kindergarten through Fifth Grade
Chapter 5: Beginning with Kindergarten Math
Counting by Ones and Tens
Focusing on Operations and Algebraic Thinking
Noticing Ten: Place Value
Comparing and Classifying: Foundations of Measurement
Getting Started with Geometry
Chapter 6: Solving Problems in First-Grade Math
Digging in to Addition and Subtraction
Focusing on the Decimal Number System: Place Value Begins
Working with All Sorts of Measurements
Delving into Basic Geometry
Chapter 7: Prioritizing Place Value in Second Grade
Adding, Subtracting, and Looking for Groups
Focusing on Place Value
Going Deeper with Measurement
Identifying and Building Shapes
Chapter 8: Finding Fractions in Third-Grade Math
Studying Multiplication and Division
Mastering Addition and Subtraction
Exploring Fractions
Putting fractions on number lines
Categorizing Shapes
Chapter 9: Mastering Multiplication in Fourth-Grade Math
Focusing on Multiplication: Factors and Multiples
Calculating with Place Value
Forming Fractions
Eyeing Units and Angles
Addressing Lines and Angles
Chapter 10: Anticipating Algebra in Fifth-Grade Math
Expressing Relationships: Early Algebra Ideas
Extending Place Value and Algorithms
Operating on Fractions
Measuring Volume and Graphing Data
Concentrating on Properties of Shapes
Part III: Moving Up to Middle and High School Math: Sixth through Twelfth Grade
Chapter 11: Relating to Ratios in Sixth-Grade Math
Understanding Ratios
Examining Multiplication
Extending from Arithmetic to Algebra
Measuring Area and Volume
Measuring Datasets
Chapter 12: Pursuing Proportions in Seventh-Grade Math
Examining Ratios and Proportional Relationships
Working with Negative Numbers
Describing Things with Algebra
Delving Deeper into Geometry
Studying Data and Chance
Chapter 13: Arriving at Algebra in Eighth-Grade Math
Tackling Irrational Numbers
Using Exponents Equations
Delving into Functions
Doing the Ancient Greeks Proud
Addressing Bivariate Data
Chapter 14: Looking at Advanced Math: High School and Beyond
Knowing What College Ready Means
Advancing an Algebraic Agenda
Getting Formal with Geometry
Understanding the World, Statistically Speaking
Part IV: The Part of Tens
Chapter 15: Ten Awesome Resources for Parents
Talking Math with Your Kids
Moebius Noodles
Estimation 180
Visual Patterns
Math Educators Stack Exchange
Math Forum
YouCubed
Your Public Library
Math Munch
Common Core State Standards Initiative
Chapter 16: Ten (or So) Proven Ways to Support Math at Home
Talking about Math Together
Perusing Your Child’s Notebook
Explaining a Solved Problem
Playing a Board Game
Having Number Talks
Grocery Shopping Together
Arguing about Words
Building Things
Asking “What If?”
About the Author
Cheat Sheet
Connect with Dummies
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
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Introduction
Math shouldn’t be scary. This idea is at the heart of this book. The big reason that many people find math scary (and I know you’re out there — you confess it to me when we meet for the first time and I tell you that I teach math) is that math has always felt like one big club with a bunch of rules that make no sense, but that absolutely must be followed.
This book presents a very different vision of math — one that should be empowering rather than frightening. A major goal of the Common Core State Standards is raising the mathematics achievement of large populations of students to whom quality mathematics instruction has previously been denied. Part of this effort involves bringing children’s ways of thinking into the classroom and developing these ways of thinking into powerful, useful, and efficient strategies. I wrote Common Core Math For Parents For Dummies to help parents like you understand this development.
I have been writing about students’ math learning at all levels for many years now, with an audience of both parents and teachers. With this book, I want to bring together many of these ideas into a coherent and comprehensive guide to classroom math learning. Common Core Math For Parents For Dummies is that book. So go ahead and join in — the mathematical welcome mat has been laid out for you.
About This Book
This book is your guide to math class in the 21st century. Education policy can be highly political and contentious, so this book cuts through it all and tells you what you need to know about what and how your child is likely to be learning math in the era of Common Core.
In place of inflated claims about the perfect world that will supposedly result from adopting these standards, you can find honest information about the goals and intent of these standards. Instead of scary tales of data mining and big government, you can find reasonable, measured, and careful descriptions of what the standards actually are.
If you’re a parent or guardian, you can find suggestions for helping your children learn the math appropriate to their grade level. This information may take the form of written tips for working example problems or video explanations of important ideas. Furthermore, this book shows you how ideas you learned in school are likely to appear in your children’s math class. Despite what you may have heard, the standards don’t have any New Math in them. Children are being asked to think, and this thinking can look unfamiliar to their parents on the surface. But underneath, many of these ways of thinking are old and familiar. Many times people who identify themselves as “not a math person” will say something such as, “That’s how I always thought about it, but I didn’t know it was okay to do it that way!” This book can help you connect your child’s ways of thinking with your own.
If you’re a teacher, you can find a most welcome big picture. You can see connections between the math that you teach at your grade level (which you probably know quite well) and the math that is taught at adjacent and distant grade levels (which you probably haven’t had time to study).
This book is organized as a reference that you can spend as little or as much time with as you want. You can read the grade level that matters to you without worrying about what came before and what comes after. All in all, I wrote this book with a busy person in mind. I have organized things so you can find what you need and move on.
Foolish Assumptions
As I wrote this book, I made some assumptions about you. I’m sure I didn’t get them all right, but at least one of these categories describes you:
You have a K–12th grade student in your life
. You may be a parent, guardian, grandparent, neighbor, or tutor to a child you care about very much, and you want to help him (or her) be successful in math in school.
You don’t really know what Common Core Math means.
You have probably heard of the Common Core State Standards, but you probably haven’t read them.
You have seen something unfamiliar in your child’s homework.
Seeing something that you thought you knew well (for example, multiplication) but realizing that you have no idea what the questions are asking for can be frustrating.
You are a teacher looking to know the standards better.
Understanding the standards beyond the grade level you teach is extremely helpful for day-to-day classroom teaching. (How did they learn this last year? How will this get used in high school?) It’s also helpful in supporting parents when they have questions. Either way, you need information quickly.
I understand that your life is busy. I wrote this book in a way that makes the phrase Common Core Math concrete. The goal is to bring you up to speed quickly on what Common Core means for your child’s math class.
Icons Used in This Book
Throughout this book, I include icons in the margins. You can use these icons to navigate this book.
A tip is intended to make your life easier. A tip can give you suggestions of what to look for in the standards or in your child’s work.
This icon helps you find summaries of the most important ideas in a section. This icon points to something that you won’t want to forget.
This icon lets you know when you can do something with your child in order to understand the content and help your child. You can do some of them on your own as you read; others suggest things to do together with your child.
Technical stuff gives you the real deal, mathematically speaking. Most of the time, you and your child don’t really need to know the things that go with this icon, but sometimes you want to know the full story.
Beyond the Book
In addition to the content of this book, you can access some related material online. A series of videos that cover some techniques and big ideas from the book is available at www.dummies.com/go/commoncoremathvids.
Check out the related videos for additional help:
Chapter 5: Making tens
Chapter 6: Decomposing numbers
Chapter 7: Eyeing adding and subtracting strategies
Chapter 8: Using addition algorithms
Chapter 9: Comparing fractions
Chapter 10: Tackling multiplication algorithms
You can access a free Cheat Sheet at www.dummies.com/cheatsheet/commoncoremathforparents that contains additional information about the standards. You can also access some additional helpful bits of information at www.dummies.com/extras/commoncoremathforparents.
Where to Go from Here
Feel free to start reading from Chapter 1 to get an overview of what the book has to offer. You also can turn to the grade that interests you most, which may be the grade one of your children is in right now or (if you’re a teacher) it may be the grade you teach. That grade most likely refers to another grade for more information. You can follow the references that interest you and skip the ones that don’t. If you’ve been frustrated by a strange-looking homework assignment, get yourself to Chapter 4 to get an overview of the nature and purpose of homework in Common Core classrooms. Or you can flip through the table of contents or index to search for any topic that interests you.
Part I
Getting Started with Common Core Math Standards
Go to www.dummies.com/cheatsheet/commoncoremathforparents for a Cheat Sheet that gives you some easy-to-refer-to tips that can help you when trying to familiarize yourself with the Common Core State Standards for math.
In this part …
Understand how the Common Core State Standards fit in the history of math teaching in the United States and how math education has evolved during the last century.
Look at the different ways that students are doing math in Common Core classrooms so that you know what to expect when your child enters a certain grade.
Get tips about your child’s homework so that you’re better prepared to help and can reduce any related stress.
Comprehend the purpose of some nontraditional homework assignments that you may have seen on social media (or in your own child’s backpack!) to avoid frustration on your part or your child’s.
Chapter 1
The Lowdown on Common Core Math, Just the Basics
In This Chapter
Knowing what Common Core Math means
Getting tips on helping with homework
Developing math from kindergarten through high school
In recent years, news outlets have regularly covered stories on the math that students are learning in school. Whether the story is about international comparisons of student learning (“You must panic! The United States is falling behind!”) or the homework students bring home (“You must panic! Second graders are using number lines!”), these news stories have an element of urgency to them.
This urgency is understandable. Parents want their children to have the best possible opportunities in life and career. In a modern, technology-dependent society, a solid math background is an important part of creating those opportunities. People who struggle to work with numbers, spatial relationships, and algebra can’t find employment in sectors that rely on technology and science, and more industries than ever do rely on technology and science.
You can think beyond the employment picture and still be concerned with how your child learns math. Everyday life requires more thinking about quantities than in the past. Is this week’s cold weather evidence against global warming? Should I have my child vaccinated? What does it mean for my state’s budget if everyone buys more stuff online? To answer these questions confidently requires more comfort with numbers than you need to count change correctly — which may have been a primary concern for citizens 100 years ago. You still need to count change correctly (or risk getting swindled on a daily basis!), but you need so much more than that to participate fully in the modern-day United States.
As of this writing, in 44 states and the District of Columbia —together totaling about 84 percent of the US population — have enacted the Common Core State Standards. Just like your child will need more math for career and citizenship than your grandparents needed, you need a bit more math than your grandparents did to understand what your child is doing in school. This chapter serves as your jumping-off point into the world of Common Core Math.
Understanding What Common Core Math Is
There really is no such thing as Common Core Math. Okay, you’re scratching your head, so allow me to explain what I mean and why this book is so important.
In a Common Core classroom, students’ ideas are center stage with the focus not on Common Core Math, but on student thinking. Teachers work every day to help students improve their thinking and to provide students with new ideas when they need them and when they’re ready for them.
The Common Core Standards still require students to memorize addition and multiplication facts. They still require students to learn the standard algorithms and the Pythagorean theorem. None of those things have disappeared from the math curriculum. Instead, the role of student thinking has changed. Students’ ideas are an important beginning place for math learning rather than being seen as an irrelevant distraction.
Many people in this country have experiences with school math that can be summarized as rules without reasons. They were told to do this in situation A, but do that in situation B. They never understood why and they struggled to remember whether to do this or that in situation A. And they struggled to tell situation A from situation B so they just applied what they hoped was the right rule in the right situation and prayed that they could earn enough partial credit to pass the test.
A quick story helps to illustrate. My mother-in-law, Lucie, is a fabulous woman. She wouldn’t describe herself as a math person. While talking to her about math teaching (no one escapes that fate in my personal life), I asked her to calculate 1,001 – 2. She thought for a moment and said 999. I asked her how she knew, and she said that she had learned it in school. I didn’t believe that for a moment — there is no way this particular fact was one that she had to memorize in second grade, plus I could see that she thought for a moment before responding. When I pressed, she finally was able to say that she knew 1,000 was one less than 1,001, and so 999 was two less than 1,001.
We talked about her solution, and she noticed that she had done something different in her head than she would have done on paper. The way she solved 1,001 – 2 was different from the way she was taught in school. For Lucie — and for far too many students — the methods taught in school are disconnected from the ways she thinks about numbers.
Lucie’s way of finding 1,001 – 2 wasn’t Common Core Math. It was just good mathematical thinking. The standard algorithm (see Chapter 10) is a correct but seriously inefficient way of finding 1,001 – 2. Similarly, it would be inefficient to use Lucie’s strategy to find 1,001 – 999 (you would have to count backwards from 1,001 until you got to 2).
Examining the Standards for Mathematical Practice
One unique aspect of the Common Core State Standards is that their focus goes beyond the familiar content of numbers, geometry, algebra, and statistics. They also include a set of Standards for Mathematical Practice that describe how people work when they’re doing math. These standards apply across all grade levels, with kindergarteners operating at a level of sophistication appropriate to them and high school students working at a much more sophisticated level.
The list of Standards for Mathematical Practice is fairly long — there are eight of them — and they overlap in ways that make it challenging for the average non-math teacher to tell them apart. But they’re important aspects of the work that children do in Common Core classrooms, so in this book, I have boiled the Standards for Mathematical Practice down to four simple statements about what students at all grade levels should be doing in math class. In Chapter 3, I describe these four statements in detail and relate them to the eight standards from the Common Core.
Ask questions
Students should ask questions such as, “What if . . . ?”, “Why?” and “How do we know that?” They should also seek to answer these questions. These may not be the questions that you picture students asking in math class, but they’re really useful questions for learning more math.
Play
When children play, they make things up and try out things. They don’t worry about getting everything perfect. They repeat the same scenario many times, changing it a little bit each time to see what happens. They challenge themselves. They laugh.
All of this can happen in the math classroom, too. Math is challenging, but so are handstands, video games, and soccer. All of these activities involve risk-taking and exploration. Math should too. Often, the line between play and work is drawn with consequences. If an activity has high stakes, it isn’t so much fun and turns into work. A Common Core classroom has many opportunities for students to play with math: to try something new, to create challenges for themselves and others, and to get things wrong and try again.
Math has right answers, just as football has touchdowns. But not every game is for the championship, and not every math activity needs to be high stakes.
Argue
Arguing is a highly mathematical activity. A good argument has some agreed-upon starting point, has some rules for moving forward, and seeks to uncover the truth. In a Common Core classroom, students have to figure some things out for themselves, which means that they need to formulate an argument to support their thinking. The sophistication of these arguments increases as students age and as they gain more practice.
For example, in second grade, a student might need to convince someone else that 14 is an even number. In high school, a student might need to write a proof that the sum of the angle measures of any quadrilateral is 360°. Both of these activities count as arguing.
Connect
Math is often taught as a long list of disconnected facts, but it shouldn’t be. Mathematical ideas are connected to each other, and they’re easier to use and to remember when students see connections among them.
Even memorizing multiplication facts — an activity that should be rich with connections — sometimes boils down to a conditioned response activity where each fact is different from each one. Math isn’t memorizing. To be sure, being able to quickly remember multiplication and addition facts is useful, but an overemphasis on memorization can keep many students from developing the even more useful skill of thinking through things they don’t know right away.
In a Common Core classroom, students spend time noticing how new ideas relate to old ones, how solutions to certain kinds of problems are just like solutions to others that seem unrelated, and so on. Looking for and talking about connections is an important part of doing math.
Helping Your Child with Homework
Whatever the standards may be — Common Core or anything else — most children will be frustrated with a homework assignment from time to time. The advice to you, the parent, doesn’t change just because your home state has adopted the Common Core.
What may change is the ways children are expected to work on their homework (refer to the earlier section, “Examining the Standards for Mathematical Practice” in this chapter for more details). Teachers may ask their students to practice something they worked on in class, but it may look unfamiliar to you. Productive ways of helping children with their homework are the same, though.
Don’t do the homework for your child. Help your child clarify her thinking and identify what she knows and doesn’t know. Monitor the difficulty level to make sure your child has interesting and challenging work, but not work that is far beyond her present abilities. Keep in touch with her teacher if things are out of balance so that you can work together for your child’s benefit.
In the heat of the moment, though, you can easily lose sight of the big picture. So here are three simple tips for productive involvement with math homework. See Chapter 4 for more tips as well as some information about specific homework assignments that have become famous on social media:
Ask “How do you know?
” This question forces students to think about their own thinking, which is an important part of making that thinking better.
Wait for a response.
Ten or 15 seconds seems like a long time to sit silently when
you
know the answer, but it’s not long at all to the person trying to figure the answer out.
Share a strategy.
After your child explains her thinking, talk about your own. If you want your child to engage with math homework, you can model it by talking about how
you
think about these problems.
