On Common Core Mathematics

what I tell the parents who email me for help

My Common Core Story

The pandemic has changed many things about our lives. Many of us spend time now doing things we never imagined would be part of our lives in the halcyon days of 2019—washing cloth masks, going to multiple grocery stores. Of all the tasks that the pandemic has made part of my life, answering questions about the Common Core mathematics is probably the most unusual.

Early in the pandemic, millions of parents became homeschoolers overnight, with minimal warning and zero preparation. I was already advertising mathematics tutoring services on Twitter, so the amount of email my public address receives was, for a time, quite extensive.

Here are my thoughts on Common Core, based on my research and tutoring experience.

What Is Common Core?

Common Core is a set of standards laid out in an Obama-era education initiative. The mathematics standards were written in response to the criticism that mathematics was taught in America in a way that was “a mile wide and an inch deep.” The idea was to cause students to learn some of the deeper whys of mathematics, to develop a type of mathematical fluency that goes beyond proficiency in the basic algorithms of addition, subtraction, multiplication, division, and everything that flows from those operations. The standards themselves are not objectionable, in my view. Here are three of the Common Core mathematics standards for fifth graders:

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Perform operations with multi-digit whole numbers and with decimals to hundredths.

CCSS.Math.Content.5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.

CCSS.Math.Content.5.NBT.B.6
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

CCSS.Math.Content.5.NBT.B.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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The first standard is to get kids to the point where they are able to use the normal mathematical algorithm to do multiplication. What the other two standards say in English is basically “teach students how to do long division of both whole numbers and decimals, using drawings, models, and mental shortcuts based on the way place values connect to mathematical properties; also, require them to be able to explain these methods and why they work in writing.”

The first standard here is the most important, in my view: fluently use the standard algorithm to multiply whole numbers. If American public schools could improve to the point where we were actually doing that on any consistent basis, it would represent both a dramatic change and an almost inestimably enormous victory.

American public schools continue to fail miserably at this standard, and Common Core requires teachers to introduce other standards and other methods. In that sense, Common Core represents something truly asinine, something along the lines of “Kids suck at reading and writing English, so let’s require them to take classes in Latin so they can better understand the mechanics of how languages work, which will in turn improve their English skills.”

I mean…yeah, that’s probably true. Requiring all students to take Latin from an early age probably would improve their English skills eventually, over time—provided they had these four conditions in place: appropriate learning environments at school; skilled teachers; support at home from parents who could answer their questions; and a high level of internal motivation to learn.

American public schools can’t provide the first two with any consistency, and the home lives of many students neither provide the third nor create a fertile ground for the growth of the fourth.

What the Common Core Standards Aim To Do

I understand what they’re trying to do. The Common Core standards aim to give students fluency in mathematics.

Here’s an example of something Common Core parents frequently ask me to explain. This is the “box method” of multiplication, compared to the normal algorithm, and then an example of the box method standing alone.

Comparing 23 x 7 in the normal algorithm vs the Common Core Box Method.

958 x 46 in the Box Method of Common Core

The box method is exactly how I, and other people I know who have a high level of mathematical fluency, multiply numbers in our heads. It’s fun, and useful, and certainly promotes mental acuity and confidence.

But is it important? I don’t think so. I would teach it to a really advanced mathematics tutoring student for fun, or if I sensed they were the kind of kid to whom being able to “wow” their parents might be the most motivating thing of all. I would never teach it in place of the standard algorithm, or short-shrift the necessary time to gain proficiency in the standard algorithm, by teaching this instead.

Likewise, the Common Core emphasis on number line methods aims to teach students the mental fluency to appreciate that addition and subtraction are not the wholly separate operations we think of them as being. 13 - 5 and 13 + (-5) produce the same answer. Adding the negative version of a number (technical term: additive inverse) produces the same answer as subtracting that number, and this in turn helps to promote a flexibility in mathematical thinking. But this is a fairly abstract idea, one that I doubt many children are ready for—and one that can only be really imparted to children by a skilled and enthusiastic teacher (more on teaching in a moment).

Write A Paragraph on How Addition Works?

Explaining mathematical methods and mathematical thinking in writing is a strategy that helped me enormously as a mathematics major in college, and I’m sure it has some value for advanced elementary students. For average or below-average readers, however, I cannot imagine anything worse. Students who “catch on” to mathematics easier than they do to correct spelling or otherwise producing writing that comes back without a teacher’s red pen having bled all over it, for example, now have to face their deficits in other areas hurting them in mathematics.

For some, this robs them on an arena that might otherwise produce confidence and make part of school enjoyable. Additionally, writing and spelling call on different skill sets than mathematical operations, which is why it was helpful to me as a mathematics major: it brought in a skill set I find much more easy and natural to help me with one that required a metric ton of work and effort. If writing were not easy for me, it would not have been helpful. Many little kids (perhaps most, in our poverty-stricken urban schools, especially) are in situations where nothing academic is easy. I have enormous sympathy for kids who understand just fine how and why 2 + 3 = 5 works, and why it produces the same answer as 3 + 2, but can’t just move on to the next problem and instead must worry and sweat over whether addition has two d’s and one t, or vice versa. This cannot help but interrupt their thinking flow and make it harder to return to the next problem, if/when they eventually can.

Isn’t It The Curriculum?

Some of my tweeps have pointed out to me that the standards are fine; it’s the curriculum, they say, that causes problems. That is mostly true, but I don’t think it matters much. Time, money, and resources are being spent on curricula to learn the box method and other procedures that help students meet the Common Core standards only because those standards are how teachers, schools, and school systems are evaluated.

No. It’s the Teachers.

Here’s the truth as I understand it: Common Core was written by mathematicians with the best of intentions. They are people with high levels of mathematical fluency who love and understand mathematics. With the benefit of the hindsight that a successful adult career can produce in an expert, they sat down and wrote standards that would’ve gotten them to their level of expertise and fluency faster and more easily.

What they either didn’t understand or didn’t consider is the reality of teaching. Elementary school is taught by people who majored in education. Very few—I would venture to guess, almost none—of these people deeply love and understand mathematics. I tutored many education majors, and they only had to go through Calculus 1. That was it. Some teachers I’ve talked to tell me that they only had to go through pre-calculus, or even college algebra.

None of them had to take proof writing, logic, or other mathematics courses that inculcate a deeply mathematical method of thinking in the precisely logical way that high level mathematics requires.

In high school, if a student is very lucky, he or she might have one teacher who deeply loves mathematics, understands it at a high level, and chooses to teach it to share their passion. Many students will not have even one. Many middle and high schools, due to staffing shortages, union rules, or other factors, are run on seniority—so the teachers with the most seniority choose what they want to teach. In these situations, the least experienced teachers often get “stuck” with mathematics, as mathematics is often the least favorite subject.

What Should Parents Do?

The public schools are so abominably bad now that I think even mediocre homeschooling is going to get a kid miles farther than public school would, and I strongly advocate homeschooling to everyone. I will do free consulting to help you plan your mathematics curriculum—email me.

But if I had a kid in public school and homeschooling wasn’t a choice for some reason, this is what I would do: find out the mathematics plan for the year and get them ahead of it. On the day that the box method of multiplication was introduced, my kid would already know how to use the standard algorithm and have done plenty of practice with it at home. That doesn’t mean that they’ll be able to not be confused by the high-level abstract thinking that Common Core attempts to introduce in various ways. Kids develop at different rates, and it has absolutely nothing to do with their future potential in mathematics. I could not have done the kind of abstract thinking that some of the Common Core standards attempt to introduce when I was in third, fourth, or fifth grade. I am not and never have been a “natural math person” for whom any of this came easily, but I earned a degree in mathematics and have a tech job using mathematics every day.

Will Common Core Last?

I don’t know. If we could get American schools to a point where just the “master the standard algorithm” bit was consistently achieved, it would be nearly miraculous. American schools are in such dire straits now that if we could just manage to not shut down for a whole year it would feel like a triumph. (My best guess is that post-COVID, teacher unions will demand—and get—schools shutting down every year for some portion. If COVID is ever considered to be in the past, it’ll be a demand based on flu or other wintertime illnesses.)

The standards are fine goals in and of themselves, but the school systems of whom my tutoring has made me aware seem to constantly emphasize the implementation of the standards that require less of both students and teachers—that offer shortcuts, like the box method, or simply take less time and practice than really mastering long division or multiplying 3 digit numbers using the normal algorithm. This is not going to help our kids in the long run.

Mathematics, it turns out, is like almost everything else in life that’s truly worthwhile: it’s not easy, and really getting good at it takes time, energy, and practice—things that look an awful lot like work.