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What You Should Know About Common Core Math


If you’re a parent of a school-aged child in the United States, you’ve no doubt heard of the Common Core standards. To date, 43 states have adopted these standards, which aim to better prepare students from kindergarten through 12th grade for higher education and career success.

As a lead writer of the Mathematics Common Core standards, I hear a lot of talk about Common Core. And based on that talk, it seems that people think everything is new about these standards. The truth is, while some aspects are new, many are not.

So let’s start with what is NOT new about Common Core:

children in elementary school still have to learn to add, subtract, multiply and divide, the same way their parents did;
children in middle school still have to learn about ratios, rates, and proportional relationships;
children in high school still have to learn to solve equations.
Indeed, there is a greater focus on these core topics than was typical of state standards before the Common Core.

This brings us to what IS new. To put it simply: the standards expect students to understand what they are doing so they are able to use and apply mathematics when they leave the classroom.

Who doesn’t want their children to think about what they are doing? Teachers and parents have been aiming for this for years. We tell them, “Think about what you’re doing!” in other situations all the time: as they’re crossing the street, as they’re learning to play an instrument, as they’re making an important decision. Now teachers and parents are supported by standards that lay out clear and coherent trajectories toward building a better understanding of mathematics, so children are less likely to lose their skills after graduation.

For example, many of today’s parents learned to add whole numbers by using the so-called standard algorithm: lining numbers up vertically and adding each column, carrying when necessary. This traditional method is still required by Common Core. But how many of today’s parents understand why it works? If you learned this way, it’s likely that the “how” of doing the calculation has been drilled into your head, but the “why” has been lost. Knowledge not supported by understanding is fragile.

Today, through the standards, kids learn mental strategies for addition and subtraction that help them use the standard algorithm with common sense about how those operations work. For example, it wouldn’t make sense to use the standard algorithm to subtract 998 from 1001, when you can see that 1001 is 3 more than 998, so 1001 – 998 = 3. Mental strategies based on understanding make procedural knowledge flexible, applicable to other disciplines and situations.

Teaching at the university level, I see the consequences of learning mathematics without understanding all the time. Students whose knowledge of algebra is based on a million meaningless mnemonics often crumble when faced with problems posed in an unconventional way or using unconventional notation, as they inevitably will be in their classes in a wide variety of subjects.

The students who do well understand that the letters in their equations are just numbers, and that the things they can do with equations follow the same arithmetical properties they learned in elementary school. The Common Core standards explicitly focus on those properties in order to prepare students for success in college. And as a result of the math standards, you can expect to see your child learn a better balance between procedural fluency (the “how”) and conceptual understanding (the “why”), so that she will develop the ability to apply mathematics in solving all kinds of problems. And that’s a skill that will serve your child for the rest of her life.

So, what do you as a parent need to know about the Common Core? Here are three things to remember:

1)  The Common Core standards are not curriculum.
Curriculum is what teachers actually follow, or do, in the classroom, and what students do at home. Standards simply say what we want students to learn. Common Core establishes a set of goals for learning. But without good curriculum, the standards are just that: goals.
 
2) Through the standards, your child will be able to explain the math, not just “do the math.”
For example, through the standards, students will now understand how our number system is based on ten, with the digits in a two-digit number telling you the number of tens and the number of ones. This goes well beyond being able to simply read and say the number out loud, or to point to the “tens digit.” It means being able to break the number up in ways that are fruitful for addition or for other operations. You can also expect your child to be able to explain how she knows what she knows, show how she thought about an answer, and choose different strategies for different problems.
 
3) The math problems that you remember are still important.
Chances are, you’ll recognize these problems as similar to the ones you completed as a child. If none of the homework problems your child brings home seems familiar to you, try asking her teacher about what’s happening in the classroom, or check out the resources below.
The Common Core standards are both old and new. As a parent, you should expect many things from these standards, but above all you should expect your child to reap the benefits of what’s new.

For more information about the Common Core standards, visit CoreStandards.org. And check out these links for additional information:

About Bill McCallum

Bill McCallum is University Distinguished Professor of Mathematics and a member of the Department of Mathematics at the University of Arizona. He is also participating in the National Math Festival on April 18, 2015. The National Math Festival is sponsored by the Mathematical Sciences Research Institute (MSRI) and the Institute for Advanced Study (IAS)in cooperation with the Smithsonian Institution(For more information, visit MathFest.org.)