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 (âYou must panic! The United States is falling behind!â) or the homework students bring home (âYou must panic! Second graders are using number lines!â), 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 canât 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 weekâs cold weather evidence against global warming? Should I have my child vaccinated? What does it mean for my stateâs budget if everyone buys more stuff online? To answer these questions confidently requires more comfort with numbers than you need to count change correctly â 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 âtogether totaling about 84 percent of the US population â 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, youâre scratching your head, so allow me to explain what I mean and why this book is so important.
In a Common Core classroom, studentsâ 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 theyâre 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. Studentsâ 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 wouldnât 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 â 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 didnât believe that for a moment â 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 â 2 was different from the way she was taught in school. For Lucie â and for far too many students â the methods taught in school are disconnected from the ways she thinks about numbers.
Lucieâs way of finding 1,001 â 2 wasnât 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 â 2. Similarly, it would be inefficient to use Lucieâs strategy to find 1,001 â 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 theyâre 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 â there are eight of them â and they overlap in ways that make it challenging for the average non-math teacher to tell them apart. But theyâre 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, âWhat if . . . ?â, âWhy?â and âHow do we know that?â They should also seek to answer these questions. These may not be the questions that you picture students asking in math class, but theyâre really useful questions for learning more math.
Play
When children play, they make things up and try out things. They donât 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 isnât 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 measu...
