Common Core Miscalculation: Math Standards Don't Add Up

The Common Core State Standards (CCST) website describes the previous math curriculum as “a mile wide and an inch deep,” stating that students need to develop a deeper understanding of various strategies to solve math problems. Rote memorization is not enough, they proclaim.  Methodologies that other countries – countries with leading scores in math – won’t do either. Gone are the days that students would learn their arithmetic facts by heart, and build upon them. Now your first grader is going to be shown a variety of mental strategies to do one addition problem. Sounds great on paper…but what’s the reaction to the new math standards?

What Parents Are Seeing

One frustrated parent who likes math told me that his 2nd grader constantly felt confused.  The instruction jumps from learning one way of solving a problem to another, and the cleanest, most efficient way to the answer isn’t always considered the best.  Another parent said, “I feel like they penalize kids for things that make absolutely no sense — like which order you put your factors in a multiplication equation.  They do not for example see 3 x 5 and 5 x 3 as the same thing.” On top of that, “they don’t teach multiplication facts in order.  Children learn the 2’s and 5’s first.  Skip to 10’s, back to 3’s, go to 4’s and 6’s then leave 8,7, and 9 for last.  And they’re learning multiplication and division concurrently.”

More math mysteries abound in the new standards.  Whereas the goal is supposedly to move away from rote memorization by helping children to learn underlying concepts, the reality is that you’re going to find yourself face to face with such puzzling things like the hundred’s chart and the multiplication finger trick. The hundred’s chart, for those of you who have yet to experience something so ridiculous, is a 10 x 10 grid with ten rows of ten numbers each all the way up to 100. Your children will be learning to add and subtract double-digit numbers using this odd invention by being told to “go down one spot” to add 10, “move to the right three spaces” to add three, “go up one spot” to subtract 10, and “move to the left four spaces” to subtract four. If this is higher level thinking, we’re looking at a very sorry future for our children.  Or potentially one where people carry hundred’s charts with them in their pockets and multiply with their fingers.

Additionally, there is a lot more language skill required in a math lesson than ever before. “They want you to explain everything you do in math, using language.  There’s a lot of writing to explain the actions involved in solving an equation - and it has to be done in written paragraph form. I have a HUGE problem with this for a couple of reasons: Math is a language.  It is it’s own language. In fact, it’s the only universal language — the absolute only one that transcends borders.  When you solve a problem and show your steps, you are in fact explaining in a mathematical language what’s going on.  There is no need for an external language to describe it.  That’s like taking a French class, writing a sentence, then explaining in English why you constructed your sentence or argument in that way.”

Common Core’s Math Concepts

What’s behind these feelings of failure and frustration? The Common Core website describes the “Key Shifts in Mathematics” in the order of their importance:

1. Greater focus on fewer topics.

In grades K–2: Concepts, skills, and problem solving related to addition and subtraction

In grades 3–5: Concepts, skills, and problem solving related to multiplication and division of whole numbers and fractions

In grade 6: Ratios and proportional relationships, and early algebraic expressions and equations

In grade 7: Ratios and proportional relationships, and arithmetic of rational numbers

In grade 8: Linear algebra and linear functions

Great! So your kids will be learning fewer things in a more complicated or roundabout way!

2. Coherence: Linking topics and thinking across grades

Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. Therefore, the standards are designed around coherent progressions from grade to grade.

Strategies for solving problems are built-on in each successive grade. Coherence is also built into the standards in how they reinforce a major topic in a grade by utilizing supporting, complementary topics.

Isn’t that how math was always taught…as a coherent progression from grade to grade?  You learned the numbers first, then how to add them, subtract them, multiply, divide, and so on?  How do things like skipping around in the order that students learn multiplication facts, for instance, really support this goal?  And most importantly, are your children actually learning things more easily the higher up they go in grade-level, or have they reached a point where they feel completely and utterly lost?

3. Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity

Rigor refers to the deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades. To help students meet the standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skills and fluency, and application.

So thanks to Common Core, you have the rigor that results in such simple and useful tools as the hundred’s chart and the multiplication finger trick.  You may not be able to do mental math, because that would involve some degree of memorization – but whip out your chart and you’ll be set!

Inquiry-based Math

Many educators and math-loving parents see the introduction of conceptual understanding at too-early an age as the problem. This is known as inquiry-based math. Math teacher and author Barry Garelick describes the problem this way, “It is ironic how inquiry-based math approaches seem to spend more time showing students strategies they might discover on their own than on teaching the standard algorithms they almost certainly won’t learn on their own.”  Rather than teaching simple math facts, the Common Core committee tries to force feed children discoveries that would be more satisfying made on their own, and leaving them inept at solving easy equations.

Common Core standards include the study of “facts and procedures” in tandem with developing the ability to strategize math concepts, but that’s not the way the standards seem to be interpreted. Maybe it’s the specter of assessment and testing that hurry along the emphasis on conceptual math strategies. The two Common Core corporate testing agencies, Partnership for Assessment of Readiness for College and Careers (PARCC) and Smarter Balanced Assessment Consortium (SBAC) do assessment testing once a year but the tests are longer than the state tests given prior to Common Core. Both testing corporations produce and encourage additional interim testing two to three times a year. What teacher wouldn’t feel pressured by this?  The concepts fall by the wayside and the procedural learning wasn’t emphasized to begin with.

Is This Really Creating Better Mathematicians?

If a young student is able to demonstrate many different ways to solve an arithmetic problem, it’s assumed they understand deeper mathematical concepts. Barry Garelick comments on this idea,  “Forcing students to think of multiple ways to get the same answer, however, does not in and of itself cause understanding. It is as if the reformers are saying, ‘If we can just get them to do things that look like what we imagine a mathematician does, they will be real mathematicians.’”

The idea of teaching conceptual math thinking before plenty of practice in standard arithmetic procedure rules has gone to the extreme of warning parents not to teach math at home. Luckily, more and more parents are ignoring the warnings in favor of their own common sense.

How do you teach your children math at home…stick with Common Core or opt for common sense?