When helping your child with math homework, there’s a good chance you’ve thought something along these lines:
Doing the problem that way doesn’t make any sense!
If this resonates with you, you’re not alone. Although the Common Core Math and its new approach to math education has been in classrooms since 2010, many parents still feel overwhelmed by the difference between the math on their child’s homework and the math they’re familiar with.
Helping with math homework is a critical math moment for any parent and child, and it has the ability to build or destroy math confidence. In order to capitalize on the rich opportunities of homework time, you don’t need to be an expert in this new way of doing math. You do, however, need to understand the basics.
This post is part of a two part series that will provide you with the tools you need to successfully tackle math homework with your child. This post will take on the invigorating topic of how the standards came about and what they are trying to accomplish. If you’re not as enthusiastic about math standards as I am, bear with me – the next post will provide concrete strategies you can use to confidently approach homework with your child.
My Two Cents
People tend to have strong feelings about the Core Math standards. In case you’re wondering, here are mine:
- Are the standards perfect? No.
- Have teachers been provided with sufficient training and resources? No.
- Have parents been adequately informed and included? Absolutely not.
- Are they better than what many of us grew up with? 100%.
Before getting into the specifics of the Core Math standards, I want to provide some context as to why the standards were developed in the first place. The CCSS were developed for two main reasons:
- The United States’ sustained mediocre performance on international assessments, such as the PISA and TIMSS assessment.
- The Benchmarking for Success: Ensuring U.S. Students Receive a World-Class Education (2008) report. This report detailed the vast differences between learning expectations across states. For example, students in Tennessee were being taught content that was significantly easier than students in New York. Naturally, this puts Tennessee students at a disadvantage as they are less likely to perform well on college admissions exams as well as succeed upon entry in college.
In April 2009, work began to create a set of standards to make American students competitive with each other and with international students. This charge was led by two non-profit groups: the National Governors Association, whose members include state governors, and the Council of Chief State School Officers, whose members include the public state officials who head departments of K-12 education. The process also included input from teachers’ unions and individual math and English teachers.
In 2010, the Common Core State Standards were published. The vast majority of states have adopted the new standards, although most have done so with some slight revisions.
What on Earth does ‘Carry the One’ Mean?
The main goal of the Common Core is to push students beyond rote memorization and into the realm of conceptual understanding. Instead of simply following the procedure to complete math tasks, Core Math asks students to develop an understanding for why the procedure works.
Let’s take a look at this through the lens of the following problem: 89 + 35.
Figure A shows the standard algorithm* for adding multi-digit numbers. *The standard algorithm refers to the step-by-step procedure most of us learned for completing specific math tasks, like multiplying two-digit numbers, computing long division, and adding and subtracting large numbers. It is what that comes to mind when you hear the following terms: line up the numbers, carry the one, borrow a one, add a zero, bring down the (next number).
Figures B and C show alternative approaches that you might see on your child’s math homework. Note that with Core Math, children will learn the standard algorithm as displayed in Figure A, but this method will only be introduced to them after experiencing more conceptual methods, like those of B and C.
Why is it important for children to experience the conceptual models before the algorithm? To answer this, let’s look at the concepts that Approaches B and C build.
Approach B emphasizes the relationship between ones, tens, and hundreds. When you approach the problem in this way, you start by breaking a number down into its tens and ones. Then you create new wholes by combining ten tens to make one hundred and ten ones to make one ten. Being able to flexibly go from seeing individual units to seeing a larger whole is essential for understanding future concepts such as fractions and proportions.
Approach C highlights number flexibility, or how numbers can be broken apart in multiple ways. By breaking 35 into 1, 30 and 4, you can easily add from 89 to 124 using benchmarks, or numbers that are easy to work with. This type of thinking lays the foundation for higher level mathematics where children have to understand the relationship between equivalence and rearranging expressions.
When you look at Approach A through the lens of B and C, procedural terms like ‘carry the one‘ begin to take on mathematical meaning. Instead of just writing a little one by the next number, you are building a ten. However, if you go straight to the standard algorithm, these procedures remain nothing more than rules to follow.
The Consequences of Subtracting the Why
I have seen first hand what happens when children get to high school without an understanding of the rules and procedures they learned in elementary and middle school. First of all, students who don’t know the why behind algorithms tend to misremember the steps. This results in calculation errors that on the surface appear like careless mistakes but are actually due to a gap in understanding.
The main consequence of solely teaching the standard algorithm is that children come to believe that math is the standard algorithm. This way of viewing math leads children to struggle when confronted with a complex problem that doesn’t look exactly like the one they did as a class. Even worse, as children work diligently to memorize and replicate the procedure, many come to view math as either boring, nonsensical, or magical.
Not only do Approaches B and C build a deeper understanding of math concepts, they prove to children that math is about creativity and sense-making. While the standard algorithm might be faster in the short term, it stunts children’s mathematical understandings in the long term.
- Get excited for Homework Help Part 2 where I’ll provide concrete strategies for you to use when helping your child with math homework. If you’ve ever asked ‘What on Earth is a ten frame?’ this post is right up your alley.
- Check out some of these articles to deepen your understanding of the Common Core State Standards for Mathematics:
- The Man Behind Common Core Math: an article that shares the perspective of one of the experts who wrote the standards
- Everything you need to know about the Common Core: an article that provides a general overview of the history and purpose of the standards
- Mathematical Practices: this CCSS document is a great resource for understanding the big picture behind the Common Core’s approach to math
Social Media Plug
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Nelson, L. (2015) Everything you need to know about the Common Core. Vox. Retrieved from https://www.vox.com/2014/10/7/18088680/common-core.
Development Process. Common Core State Standards Initiative. Retrieved from http://www.corestandards.org/about-the-standards/development-process/.
National Center for Education Statistics. (2000) Highlights from the 2000 Program for International Student Assessment. Retrieved from https://nces.ed.gov/pubs2002/2002116.pdf.