Teaching Math The Right Way – Part 2: Focus On Content Emphases…What Is Essential In Each Grade Level?

This video is Part 2 in a video series I’m doing all about a question I get asked a lot, “Am I teaching math right?” I’m Christina Tondevold, the Recovering Traditionalist. Today we’re going to delve into the content emphases, in order to help us answer the question, “Am I teaching math right?”

Watch the video or read the transcript below.

Now if you missed it, Part 1 of this video series was all about trying to figure out should we be teaching math conceptually or should we be teaching math procedurally? So if you missed that, click the link below this video to find out.

What Are The Content Emphases

Okay, so let’s first start off with, what are the content emphases? Some of you may know them as the major work. When Common Core State Standards came out, it was just a list of standards. Now, whether or not you use the Common Core State Standards, I’m going to use a document that is geared towards it, but the idea is something that you should be doing no matter what standards you are using.

So these content emphases documents were put out to help us really understand which standards play a larger role in helping to develop our students understanding. Let’s face it, not all the standards carry the same weight; not all of them should be getting basically the same “play time” inside of your classroom. Each standard is not just a list of things to go through and make sure that you cover. Instead, there are certain standards that we should be taking time to delve deeper into. So these content emphases documents are broken down into the clusters of standards. Each cluster is highlighted with a certain color. The document below shows there are green clusters, there are blue clusters, and there are yellow clusters.

The document displays Kindergarten through 8th grade. This example is showing Kindergarten. As you can see, next to each cluster, there’s a green rectangle, a yellow circle or the blue outline of a rectangle.

• The green ones dictate the major clusters. These are the things that are the huge, really big deals at that grade level.
• The yellow ones are the ones that are kind of additional. They are things that aren’t really tied to other things. We have to find a way to bring them into another area.
• The blue ones tied to the green ones. They’re known as supporting standards. They aren’t stand alone, big ideas, but they are mathematical concepts that will help our children better understand that major work.

Let’s review 5th grade, to get another view (shown above). Look closely at the blue, specifically at 5.MD.A. It says, “Convert like measurement units within a given measurement system.” This is not necessarily a lone skill that we need to teach to kids. Instead, it is a mathematical concept (this idea of converting measurements) that we can use to help our kids better understand some of the related green clusters. Could we use conversion to help our kids be able to perform operations with multi-digit whole numbers and with decimals to the hundredths? You bet! Could we use conversions to help our kids better understand our place value system? You bet! So those blue clusters are things that we should be doing to help support the green clusters. They aren’t standalone standards. That’s what’s difficult with our standards; everything is just kind of in this big list. However, 1) We don’t know which ones play a bigger role; and 2) We don’t know in what order to teach them. That information is coming up in Part 3 of the series, so stay tuned!

Why Are These Helpful

Right now we’re going to build on that idea of which standards we should really be focusing on. That’s what this document really helps us do. It’s through https://achievethecore.org/ and when they first put them out they were known as the “content emphases”. What are the things that should be emphasized at certain grade levels?

Now, one of the things I want to draw your attention to is the very tiny print at the bottom of the document (shown below). The small-print line talks about the percentage of time in the classroom that we should be spending on this major work, and it’s a little eye-opening. It states that “at least 65% and up to approximately 85% of the class,” time should be devoted to the major work of your grade level.

That is huge. To get an idea of what this means for your class time, you may want to calculate how many days of school you have. When calculating, be honest with yourself:

• How many actual teaching days do you have (ex. you get interrupted for assemblies, the first few days before holiday breaks are pretty much a wash, etc.)?
• Keep in mind all of those things that come into play when you’re not really focused on a lesson per day.

Break down into how many days you actually have to teach the blue and the yellow clusters; and how many days should be devoted to the green clusters? At this point, you’ll likely want to reflect a little bit about how much time you have spent on the other things.

 How Should You Use This Document

Now here’s the deal: These documents can seem a little overwhelming when you start looking at those numbers, but I want you to really reflect, okay? Because I know you’re already strapped for time. Your textbook already has more than you can teach and you’re trying to do the best you can with the information you have. With this video series, I don’t want you to watch this and think, “I’m not doing it right.” This series is encouragement for you to reflect and feel like you’re okay. To think, “Where am I right now and what can I do to make it a little bit better?” And, as we learn more, we get better and better at our teaching.

We don’t do it right the first time. None of us do. So use this information in a way that makes you feel like, “Okay. I’m doing just a little bit better here, and a little bit better here.” Reflect on whether or not you’re going deep enough into those green standards.

I’m going to stop for a moment and play a little clip of Phil Darro talking about this whole idea of breadth: the width or breadth versus the depth. And why it’s so important that we really focus on going deep for our kids and not just trying to cover it all.

“…So mile wide, inch deep, we didn’t want be a part of that problem. Our goal is to attain for focus and coherence. The Singapore website’s banner says, “Teach Less, Learn More.” The results, the only one we have for this 4th grade that I know about, in the TIMMS (the international comparison), the test has more than any country teaches because if kids learn stuff they wanted the nation to get credit.

Singapore taught 45% of the topics on the TIMMS test, less than half. They were the number one performing. Now this is Hong Kong. The U.S. taught 80% of the topics. They were among the lowest performing. So covering does not translate into test performance. The Hong Kong students got more depth on less topics and did better on this test than the U.S. students who got superficial knowledge. And we know in mathematics, that it’s not until your understanding reaches a certain depth, which is deeper than we teach to, that it transfers. It drives us crazy as teachers. They learn it in this context. The next day you give them a different context. It’s like they didn’t learn a thing. That means their learning was superficial. Transfer is a task. I’m not pretending it’s not. If they can get deeper, it transfers more readily.”

Now, I have to say, I really hate it when I see international comparisons, but that’s the world we live in. We are being compared to other countries and how they perform no matter what. It’s a thing that we have to deal with. However, the piece that I hope you really take away is that we can’t teach it all. When we try to teach it all, all we’re doing is giving just a surface view of the mathematics, and kids aren’t really getting a true understanding of the math in a way that allows them to apply it.

You don’t have the time to teach everything to your students and in every possible way that they might see it on a test. We have to teach a concept deeply so that no matter how they see it, how it’s presented to them, they have a true understanding of the concept and can make sense no matter how it’s presented. So, I want you to really use this document to help you remember what is truly important. What is it that, if my students leave with nothing else this year except for this, then that’s great! And hopefully it’s not just this one thing, right? But there are a few things that each grade level that kids should really, really go deep into. What is that? Have that conversation.

The last thing I really want to leave you with is how to use this document. Don’t keep it to yourself. This is not just for you and your grade level. The most powerful way I’ve seen this used, and the way I’ve used it in PD with schools I work with, is doing it throughout all the grade levels. I’ve done it K5 and I’ve done it K12 with districts. Where we look at what is truly important at each grade level. These are the things this grade level is responsible for. Every group of kids is different so I hate using that “you’re responsible for this” terminology, but these are the big things, at this grade level, that we’re trying to get them to understand. This grade level is doing these pieces. It’s helpful when you have that conversation with the whole span of grades, to determine what’s happening with each grade level. It allows a little bit more freedom because you know what the focus is for each grade level. I’m going to use a non-math example, here, but if you’re a 5th grade teacher and have to get kids ready for the science test, and you’re the only teacher, that’s a heavy weight to bear. So, we have to view this as a long distance run. Teaching kids mathematics is a long distance marathon. It is not just for the short-term, it’s thinking long-term about everything that they’re going to be learning through their mathematical journey and how it all fits together. So, sometimes we have to be okay with letting things go so we can focus on the pieces that really matter. And I really love the quote Phil Darro talks about, “Teach Less, Learn More.” We have to be able to focus in on what’s important and teach that deeply so that our kids can really understand more. The more that we can give kids the time to go deep and learn about connections between things, the more that they will really understand about mathematics.

I hope this document helps you out! Helps your whole school out! Helps your whole district out! Take it, use it, and talk about it throughout all the grade levels. Really have a deep conversation about what’s important through each grade level, and be okay with sometimes letting things go, so that you can slow down and focus on things that are truly important. I hope this helps you build your math mind, so you can build those math minds of your students.