- Subjects:Curriculum Development, Logic and Problem Solving, Math Fluency and Intervention, Real-World Math, Educational Policy, Educational Standards, New Teacher Resources, School Reform

# Common Core: Key Shifts in Mathematics

- Grades: PreK–K, 1–2, 3–5, 6–8, 9–12

**“I can, you know, do math and stuff,”** says Harry Potter defensively in *Harry Potter and the* *Sorcerer’s Stone. *Math and stuff. I'm sure Professor McGonagall would shudder to hear that. The key shifts in Common Core math are leading students to a deeper understanding of why they do math and what the numbers mean. The thought is that students will be able to apply this deeper understanding to any problem they come across, not just explicitly taught problems, and be better mathematicians in the long run. In the short run it may have you beating your head against the wall! Here are the key shifts in mathematics and a few baby steps towards achieving them.

## Key Shift #1

### Focus strongly where the standards focus

It used to be that a student would study place value at the start of the year. They might learn ones and tens in kindergarten, review and add on in 1st grade, bust into the thousands place in 2nd grade, and by the time I saw them in 4th grade, we’d glide into the millions. And then the next month? Done. Finished. See you next year. We had fifty million standards to skedaddle across and no time to stop and dally on any one item. What the math standards do is take a deep, not wide approach. For example, instead of teaching thirty different objectives in a year, you might teach three. The difference is that you will teach those three inside, outside, and upside down so that each child fully understands and masters the concept. **Focus** on going **deep** for **mastery** and **transferring **those skills.

### Baby steps towards focus

First things first: find out what your grade level is supposed to focus on exactly. AchievetheCore.org offers an easily read document that shows the grade band priorities and more specific priorities at each grade level. The problem for teachers wanting to align to Common Core is the gap in what has been taught and where the standards are now. This can be overwhelming, so think about prioritizing the way you would with any large task. Creating your own pacing guide is a good way to dig in and get familiar with the standards, while making a feasible plan.

- Get a list of your standards, and be sure to check if your district or state is requiring anything additional.
- Take your available resources and go through the standards one by one, marking what aligns and what you need to supplement. If the standard looks as though it is written in Greek, use a site like IXL to see sample problems with each standard.
- Get a calendar. If you have required pacing, fill that in first. Then break up what needs to be taught over how long you have to teach it.
- Constantly assess how your plan is going. Each week assess whether or not you gave yourself enough time and adjust as necessary. You’ll notice patterns and be in great shape with a solid plan for the next go-round.

## Key Shift #2

### Coherence: Think across grades, and link to major topics within grades

When I teach fractions, I need to know that my students saw parts of a whole last year. I need to know that next year their understanding of decimals will relate to percentages. Coherence means that students are not learning entirely new skills in isolation, but building on previously learned material. I think the best example of coherence I’ve heard deals with money. Young students are being taught to understand ones, fives, and tens. They can count forward and backward by 10, 25, or 100. They truly know what it means and how 100 is created. By the time a 2nd grade teacher shows them a nickel or dime, the learning isn’t totally new. They just have to take what they know and attach the picture of a coin to it. Bam! That’s coherence!

### Baby steps towards coherence

Grab the doorknob, stick your head in the hallway, and talk to those people you work with. Coherence cannot be done in isolation. Grab a person from the grade below you and ask about their standards. Ask your co-worker in a higher grade what foundations you need to lay for them. Our Professional Learning Team meets monthly with a representative from each grade level and we discuss the learning going on in our classrooms. When we implemented the standards, we took all the old standards, cut them apart, and put them where they now fall in the Common Core. You can’t just know what is happening in your room. You need to understand where your kids have been, and where they need to go, to ensure that they are making connections throughout their learning. The Publishers’ Criteria for Common Core has a table that shows the kindergarten through 8th grade skill coherence moving towards algebra. It is a great visual for getting started thinking across grade bands.

## Key Shift #3

### Rigor: In major topics, pursue conceptual understanding, procedural skills and fluency, and application with equal intensity

Do you ever feel as though the creators of Common Core just like big words? Some places, such as EngageNY.org, break this shift into three smaller parts. The keys here are conceptual understanding, procedural skill and fluency, and application. What does that all mean? Conceptual understanding means that you don’t just know it’s the hundreds place, you understand that hundreds are ten times the tens place and one-tenth of the thousands place. Conceptual understanding will help students apply what they know to problems they have never seen. Procedural skill and fluency is what you know as good ol' “skill and drill.” Kids have to be able to perform computation with speed and accuracy to ever be able to apply functions to complex problems. Application is taking math into the real world and connecting it to life outside the math textbook. Rigor? I think of it as mental toughness. We want our kids to have that!

### Baby steps towards rigor

Rigor is not just harder. That’s missing the point. Rigor is all about truly understanding the meaning behind the numbers, getting those facts down pat, and then applying all that knowledge to the real world. Conceptual understanding is aided with the use of manipulatives. Give students the hands-on, concrete experiences they need with numbers before making them use paper. Take away the algorithms and see what purposeful questioning can help students derive on their own. Make sure they “get it” from every angle you can throw it. The lower grades in particular are charged with getting those basic facts rolling off the tongue. Programs like FastMath help get the fluency rolling after the conceptual groundwork has been laid. Then take those lessons out of math class. Science is a great fit for real life measurement, graphing, and probability. Figure out the ratios used in art. Use reading strategies to decipher mathematical text. Apply knowledge across subjects to make sure they have sunk in and aren’t going to leak out anytime soon!

## So What . . . ?

### Math matters.

Why? Check out these statistics from the National Math and Science Institute:

- Only 55 percent of high school graduates are ready for college-level math.
- Out of 31 countries, the United States ranked 25th in math proficiency.
- Without quality education, the U.S. might lack a necessary three million high-skilled workers by 2018.

The key shifts in mathematics don’t stand alone. They are used with the mathematical practice standards and integrated throughout lessons and curriculum. Alone they are meaningless, but together — wow. What if Harry didn’t just mix potions? What if he could create his mixtures by applying his knowledge? Snape wouldn’t know what hit him!

Have you started on Common Core math? What has been challenging for you?

## Comments (5)

>It used to be that a student would study place value at the start of the year. They might learn ones and tens in kindergarten, review and add on in 1st grade, bust into the thousands place in 2nd grade, and by the time I saw them in 4th grade, we’d glide into the millions.

But that's exactly what Common Core does.

http://ccssimath.blogspot.com/2012/05/wholesale-whole-number-murder-and.html

It does, to a certain extend. The hope is that they have such a strong foundation in each skill, they are ready to build on it at the next level. We had place value trouble with our kids doing it at the beginning of a year, but not touching it again. It wasn't incorporated and mastered the way it should have been, which created problems when we got to harder topics (like long division) and the didn't know what each place actually meant. I hope Common Core is a good fix for that! (Or at least a starting point!)

I'm not sure that I agree with fluency as a result of "drill and kill", or sorry, "drill and skill". My idea of fluency is being able to attack the problem from so many different angles that you are sure you have the right answer. For example, when my youngest son approaches the problem 4x7=? He doesn't automatically say 28. Instead he thinks to himself out loud of course, "well I know 7+7=14 and 14+ 14 =28 so 4 7's must be 28. To me that is fluency, not just memorizing facts and procedures in a certain amount of time but reasoning to prove that your answer is correct. I cringe when teachers give students timed tests for fluency, it's about the practices that make kids fluent. I hope I don't have the wrong idea about fluency, but with all the training I have received about Common Core, I think I am on the right track.

I see what you are saying, but I think by skill and drill I was thinking more automaticity. Not that they don't know the meaning behind it, but that they can arrive at that meaning quickly. So your child, who can think through how to get to the correct answer, is still showing fluency with those addition skills to get to the answer. It is fine to arrive at "28" the way he thinks through it, but the idea with fluency would be that he can think through and arrive at that answer in a quick and easy enough way to be useful to him in harder problems. If he didn't have the fluency (automaticity) with those addition problems, he'd be sunk. In my grade, I hope they kid has the understanding to back it up, but they also have to know it quickly and easily enough for it to be useful and applicable to the problem 439 x 28. See what I mean? I think what Common Core is getting at is not to drill the child to death, but to have enough exposure and repeated reasoning that they can apply it to harder problems as they go.