Sixth Grade Math Makes No Sense

But it's not the math that's the problem.

What, exactly, is “sixth grade” math?

Practically speaking, this is an easy question to answer. Sixth grade math includes ratios, fraction operations, one-variable equations and inequalities, surface area and volume, and statistical reasoning. There are detailed standards on everything sixth graders should learn, and any number of high-quality curricula designed to help sixth graders learn it.¹ This content, as opposed to nearly everything taught in high school, is the kind of math that people will actually use. It’s valuable stuff, and young people should learn it.

So I ask this question more philosophically. “Sixth grade” is, in most cases, an age category: students in sixth grade are typically 10–12 years old. Some of these students have demonstrated grade-level math proficiency in previous years, but the majority — at least judging by the fact that only 36% of America’s fourth-graders earned proficient scores on the most recent National Assessment for Educational Progress² — have not. And while it depends on the state and each child’s attendance, sixth grade typically lasts for around 180 school days.

So my question is, basically:

Why do we expect all 10–12 year-old students in America, regardless of prior understanding, to learn the exact same amount of math in the exact same amount of time?

This question, as opposed to the one I started with, is not just philosophical. It has real implications for millions of 10-12 year-olds, who are expected to learn what we consider “sixth grade” math, and for the thousands of educators who are expected to teach it.

In fact, I have been one of those educators. I spent most of my teaching career teaching high school, but I spent my first year as a classroom aide in a middle school. In one class, I distinctly remember three students:

• Jamal loved math, and his mother was an engineer at Boeing. She was teaching him trigonometry at home.

• Luisa had recently arrived in the United States. She spoke little English, and it was not clear how much prior schooling she’d obtained.

• Marcus took care of his grandmother and younger siblings. He was often absent, and when he was in school, often seemed distracted.

Their teacher, Ms. Duncan, was everything you’d want a teacher to be: energetic, thoughtful, and committed to helping all of her students - regardless of their needs - learn. Ms. Duncan worked very hard to teach the curriculum she had been given. 

But no matter what Ms. Duncan did, many students didn’t learn.

Why not? 

• Jamal already knew most of the syllabus’s content. You can’t really learn things you already understand.

• Luisa wasn’t prepared to understand. She couldn’t read in English, and Ms. Duncan didn’t speak any other languages.

• Marcus’s attendance was too sporadic for him to understand much. Class on Wednesday didn’t make sense if he hadn’t been there on Monday or Tuesday.

Were these young people capable of learning about ratios, fraction operations, one-variable equations and inequalities, surface area and volume, and statistical reasoning? Of course! Jamal already had, and I’m confident that Luisa and Marcus could have too. But sitting through lessons they weren’t prepared to understand wasn’t helping.

So despite the fact that these young people were all of “sixth grade” age, learning “sixth grade” math together didn’t make much sense.

A Better Approach

When I tell people about Jamal, Luisa, and Mario, they usually understand why our age-based system of education fails to meet many learners’ needs. But they often ask a reasonable question:

“What’s the alternative?”

As a society, we’re so used to this model of education that it’s hard to envision anything else. But I think we have a few models we can use to envision alternatives.

1. The one-room schoolhouse. In the old days - and in some rural communities even today - students of different ages learned together in the same rooms. Teachers had to deliver different levels of instruction to different-aged students, all within the same room.

2. Graduate school. When I went to graduate school after a few years of teaching, I had classmates in their 40s and classmates straight out of college. It didn’t matter. We all followed the same course of study and we all had to pass the same exams.

3. Swim lessons. It would be dangerous to group kids at a swimming pool based on age. A teenager who had never swum before would be out of his depth - literally - in an advanced class, while a five-year-old who already knew how to swim would have little to learn in a class for beginners. This would also drive the swim teachers crazy. We can keep kids in groups that are generally age-bound - to keep older beginners together, for instance - but it’s ultimately skill level, not age that should determine what kids learn.

I don’t know if any of these is a perfect comparable for a math class. But they do illustrate that age-based education isn’t inevitable. And I think that Jamal, Luisa, and Marcus would all benefit from a system that took into account their needs, not just their age.

Equity, Equality, and Efficiency

If age-based education fails same-age learners with different needs, and alternatives exist, why don’t we use them?

I think there are two main reasons:

1. Efficiency. We see the age-based system as efficient. It’s predictable for students, teachers, and families; it ensures a steady labor supply of 18-year-old high-school graduates; and it generally preserves the status quo.³

2. Equality. It seems fair to give all students the same chances to learn the same content. It might not feel fair to give Jamal trigonometry while Luisa focuses on building her English-language skills instead.

Personally, I question whether age-based education is either efficient or equal: it’s a waste of learners’ time to receive instruction they already understand or aren’t prepared to grasp, and Mario can’t receive the same instruction as his peers if he isn’t in class. But I think that’s open to debate.

It’s clear to me, on the other hand, that age-based education is not equitable.

Equity, as I understand it, requires that individuals receive support based on what these individuals actually need. So, in an equitable classroom:

• Jamal would be challenged to extend what he already knows, with challenging activities that go beyond the scope of the “sixth grade” curriculum.
  

• Luisa would receive the support she needs to build her knowledge from the ground up, whether that’s more instruction in English and/or math.⁴ 
  

• Marcus would be able to pick up wherever he last left off, as soon as he returns to class.

That kind of class wouldn’t just be equitable. It would actually help each of these young people learn.

An Interim Solution

If you agree that we can do better than age-based education, you might ask another good question:

“What do we do about it?”

This is also a good question, because our education system is both deeply entrenched and fquite complex. Replacing age-based instruction with skill-based instruction, at scale, would be such a big shift that I’m not even sure where it would begin.

But if you think about it, what we call our “education system” is really just a bunch of classrooms. And there are things you can do, at an individual classroom level, to make the instruction students receive more responsive to the level of challenge and support those students need. For instance, you can:

• Digitize direct instruction. If you explain content to your students live, it’s inevitable that Jamal will be bored, Luisa will be lost, and Marcus might miss out together. But if you use short videos - either ones you record or ones you find online - to explain your content, then students can watch (and re-watch) any time, anywhere, at their own paces. They can ask you questions one-on-one, rather than needing to interrupt the class. And you can spend your time in class working closely with your students.
  

• Help learners set the pace. Students inevitably need different amounts of time to learn new things. If you can develop systems that give learners the time they need - a clearly organized LMS, consistent routines, and progress trackers for both you and your students - then you can keep every learner appropriately challenge and supported every day. You can also let learners like Jamal fly.

• Require mastery. It’s great for students to take ownership of their learning, but only if they truly understand. So make sure they do! Give your students Mastery Checks at the end of each lesson, and don’t let them move on until they have proven they are ready.

Classrooms like these are still age-based: you’ll still have Jamal, Luisa, and Marcus in one class, and you’ll still see gaps between these learners at the end of the year. But within them, you can actually provide the things these diverse learners need. Thousands of educators worldwide already are, and they are seeing the benefits of this approach.

So “sixth grade” math may not make a lot of sense. But Modern Classrooms do. 

I hope you’ll start one soon.

1. There are 47 distinct Common Core State Standards for sixth grade math, starting with “Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities,” and ending with “Summarize numerical data sets in relation to their context.”

2. See the Nation’s Report Card.

3. While this system guarantees a predictable supply of 18-year-old high-school graduates, it also essentially guarantees that most of these graduates will not be ready for college. In 2022, for instance, only 22% of graduates met all four college-readiness benchmarks on the ACT test. I’m not sure whom this benefits, but it doesn’t serve most young people.

4. I’m not an expert in supporting English learners. But it seems to me that a student like Luisa, who struggles in math classes conducted in English might (a) have strong enough math skills but not be able to understand instruction in English, (b) have strong enough English skills but weak math skills, or (c) have weak skills in both math and English. Whatever the case may be, Luisa needs someone who can diagnose her skills and provide next steps accordingly.