Common Core math has gotten a bad rap. In 2007, "State chiefs discuss developing common standards during CCSSO's Annual Policy Forum in Columbus, Ohio." -Common Core Development Process
This is, let's say, the conception of the Common Core. That was 15 YEARS AGO. Common Core is 15 years old! Basically, all 50 of the United States had developed some type of learning standards by the early 2000s. After the forum in 2007, educational leaders "recommended states upgrade state standards by adopting a common core of internationally benchmarked standards in math and language arts for grades K-12 to ensure that students are equipped with the necessary knowledge and skills to be globally competitive." -Common Core Development Process
Why would educational leaders make this recommendation? Don't we want local control of our education? Well...don't we also want our country to be prosperous? Grow our economy? Continue to be a world superpower? Certain countries were starting to surpass us. What were they doing differently that we weren't doing?
In a nutshell, countries that are surpassing us have different (better) education systems than ours. These countries teach students to think instead of just regurgitate information.
If you're a 30something or older, you most likely learned the way I did: read a book, do a worksheet, take a test. Rinse and repeat. We were taught to memorize information and then spit it back out. We crammed for tests and forgot all the information afterward. Why isn't that working anymore?
1. Jobs are different now than they were. Computers and machines can do the jobs that many people used to do. Labor is cheaper in other countries so companies have transferred manufacturing there.
2. That isn't a good way to learn information for the long term or to improve skills. Many of the kinds of jobs available require skills, not the regurgitation of information. To learn many skills, you need to practice DOING things, not watching other people do them and trying to copy them. Who is going to tell you which algebra formula to use to solve a problem at your job? Your math teacher? A textbook? Nope.
3. Information is readily available everywhere. Once the internet came along, have you ever used an encyclopedia again? No, because you have one right in your hand (cell phone) or even on your wrist (smartwatch). There are even glasses you can wear to see the internet. I don't think those ever really caught on, but you get the idea.
4. Evolution. Is the human race done evolving? Are we done here, at this level? Is this as good as it gets? If we want to keep evolving, we have to expect education to change. Do we still write with slate boards? Or use feather pens? Or even on chalkboards anymore? No, because better ways have come along like paper, pencils with erasers on top, whiteboards, computers, and even electronic writing pads. Do you want to go back to those tools of the past? We have to keep moving forward. Education is the perfect avenue for making those changes. Every generation wants the next to have it easier, to be happier.
If you are still reading this, thank you. I'm going to get to the point of Common Core Homework. But I felt you needed some background information first. You've probably seen these or something like them. What do you think?
A.
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C. 
D.
A. is pretty obvious. No, it is not the way you learned it in school. See point #2 above. The way you learned it wasn't wrong. But you learned the "standard algorithm." You learned to stack numbers on top of each other and add and subtract and multiply and divide in columns. And you didn't learn these skills at the same grade level as they are being taught them now. Students as early as 1st grade are learning to add and subtract double-digit numbers. But according to the Common Core, they are not supposed to be stacking them in columns to do it. That is because students at this level have not mastered the concepts of place value (i.e. hundreds, tens, ones). They need a strong foundation in place value before they should be using the standard algorithm. Stacking numbers to add and subtract should not even be INTRODUCED until 3rd grade. I know, I was shocked by that too. But now that I'm a math interventionist and I see students in 2nd grade carrying and borrowing and doing it wrong and not understanding why it is wrong, I now get why they need to wait to use the standard algorithm.
Even though you didn't learn it that way in school, it doesn't make it wrong. The homework your child is bringing home SHOULD be something they are pretty solid with already and just need more practice on. Homework should not be the same concept they learned that day in class and are still struggling with. That is a big frustration for me. If that's happening with your own kids, I'm sorry. It is wrong and it is causing a ton of frustration for students and families.
B. This picture is just offensive. The person that made it obviously has not taken the time to read the standards or ask a well-versed educator to explain them.
The frustration that leads to a meme like this is that families are seeing their kids learn different ways to solve problems (some that the parents don't understand or really are just way too complicated) and they can't wrap their heads around a different way. Why? Because we were DRILLED on the "right way" (standard algorithm) for YEARS. We are pretty good at it and why would you want to learn a different way?
There actually are very good reasons to learn different ways to solve problems. There are innovative ways that kids can come up with to solve problems that actually can be faster than using the standard algorithm. They can and DO surprise their Common Core math teachers with them. And the way they do that is that the teachers don't just give them the answer. They give them the tools to get to the answer: manipulatives (like blocks or counting chips), paper, pencils, ten frames, base 10 blocks, 100 charts, graph paper, and many others. But the teacher introduces the problem (think story problem) and then lets the students figure out a way to solve it. Then the students can share their ways and the teacher can guide the rest of the class through the thinking by having the student draw it out or model it. The teacher can also point out problems in the child's thinking and that is how the child who made the mistake can learn from it. This makes them invested in the learning. Mistakes are expected. If you don't make mistakes, you don't learn.
Think of the teacher as a scaffold in a construction zone. The teacher shifts around the scaffold to help the student solve the problem without telling them how to get to the top.
C. Again, this is a bit offensive. For one, I can guarantee that an engineer did not make this meme. Engineers are by definition innovators. They solve real-world problems for a living. You can bet that they are coming up with their own algorithms to solve their problems, not pulling out their high school math books and finding the right formula. If my elementary-age child brought home homework that I couldn't figure out how to help them with, I would likely write a very nice note back to the teacher that my child needs more instruction on the topic before he is expected to practice it independently, again because homework should be practice on a topic they are fairly solid on. I actually have done this before. And as a teacher, I have gotten these notes, and I then took the time to go over it again with that student. Homework should not be a battle because it is too hard. If a kid just doesn't want to put in the effort, that is one thing. But if it truly is too difficult to be completed independently, it should be done at school with the teacher's scaffolding.
D. I think the point of this meme is that parents are seeing that their children are learning different ways to solve problems. Again, we all learned the standard algorithm in a much higher grade than most students are learning it in now. Our brains were more developed. We had a better understanding of place value. We also had been drilled on our math facts. There was time for that because we weren't teaching about bigger numbers in 1st and 2nd grade.
I want to tell you how wrong the Common Core was implemented. It was rushed. The US government dangled the carrot of $$$ in front of the states in the form of Race to the Top. It seemed to be well thought out but the best-laid plans...
Yes, teachers were trained in it but it hasn't been implemented the way it was intended by the many researchers and educators who were involved in its development. For example, at the beginning of the math standards, there are Standards for Mathematical Practice.
I am embarrassed to admit, but until I became a math interventionist, I didn't even know that these existed! And as my team and I have been delving deeply into the standards of all the grade levels, we became aware of their importance. As a classroom teacher, I was VERY well-versed in the first grade standards. And maybe that is why the Standards for Mathematical Practice are overlooked. Because we are so focused on ALL the grade-level standards. But these Standards for Mathematical Practice are the BONES of math instruction. All the grade-level standards should be taught using the Standards for Mathematical Practice. Here they are:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
In an early childhood classroom, this means really looking at a real-life math problem. (Not a page of math facts.) Students are trying to figure out what to do with the information given and trying different ways to get the right answer.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
In the early childhood classroom, this involves what is known as CRA. Concrete, Representational, and Abstract. Close your eyes and picture a cat. It is furry, has 4 legs and a tail, etc.
Your cat might have looked like any of these. They are all cats.
Now think of the number 4. What does it look like? To a child who can't read numbers, it might look like this.
This is concrete. The numeral 4 is not. It is our job for this standard is to help students get from the four fingers to the numeral.
Think about 36. We don't have 36 fingers. How might you show your students 36 in a concrete way?
What if you are teaching the 3rd grade standard:
3 x 12 = 36 right? Looking at these 3 cartons of eggs with a dozen eggs each makes that very concrete doesn't it? I remember having the hardest time understanding that 5 x 3 was the same as 3 x 5. If someone had shown me this (an array if you haven't heard of it)
I would have gotten it instantly. But no one did.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Were you ever allowed to show a different way to solve a math problem to your peers? Or argue why your way was right and theirs was wrong? Or even that the teacher's answer was wrong? We need to be doing this EVERY DAY.
Instead of doing a page of problems all the same way and then doing that one story problem at the end, we should be doing story problems first, letting the students try to solve them before instruction and then explaining their answers. It doesn't mean that we let them struggle to the point of frustration. But we do need to let them struggle a little bit. And we need to be ready with the scaffolds, just a little bit at a time, to get them to the correct answer.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Where are the manipulatives??? On the shelf? In a storage closet down the hall? They need to be in our classrooms every day for every lesson. The CRA model uses Concrete examples, Representational examples, and Abstract examples in every lesson. Here is a scenario:
Let's say I'm teaching double-digit addition with regrouping in second grade. This is the standard I am covering:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.I present the problem like this:
47 + 25
Students have popsicle sticks and rubber bands and together we practice counting out groups of 10 and bundling them together. This is CONCRETE. They are touching the materials. If I was the only one manipulating the materials, it would be REPRESENTATIONAL.
After we build 47 and 25, we put them together. Now we have 6 bundles and 12 singles.
I use some bundle picture cards to model what each of them has. This is the REPRESENTATIONAL part of the CRA. I could also draw the bundles and singles. With a drawing, I am representing the concrete popsicle sticks.
We practice counting the bundles: 10, 20, 30, 40, 50, 60, and then the singles: 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72.
Then the scaffold: Could there be a faster way to count to 72?
Fingers crossed, someone says: Bundle 10 of these 12.
We count them again: 10, 20, 30, 40, 50, 60, 70, 71, 72
Yes, that was faster! If I didn't get that response I might hold up one of the rubber bands as a scaffold.
The ABSTRACT is actually the original problem: 47 + 25. Remember visualizing the number 4? After this lesson, when they are visualizing 47, they hopefully will think: 4 bundles and 7 singles.
CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
We have so many math tools at our disposal these days! Like the previous standard about modeling, this involves the student choosing the correct tool themselves. Like the bundles of sticks for the problem we did. Or graph paper to make an array for figuring out 5 x 3. Or using the centimeter side of the ruler when they see cm. They can solve hard problems. We need to give them the tools and show them how to use them and then let them practice with them to solve problems without hovering over them.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
In the early childhood classroom, this standard involves learning and using correct math vocabulary. It means they understand the symbols they are using: + means to put together, - means to take apart or compare, = means the same. Showing them things like 4 = 3 + 1 and 3 x 4 = 2 x 6 can reinforce this. It also means checking their own work and being able to explain how they got their answer to others.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
In the early childhood classroom, this involves looking for patterns. 7 + 6 can be thought of as 7 + 3 + 3 which leads to 10 + 3 which the student may have memorized.
CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
In the early childhood classroom, this can be seen on a hundred chart, all the numbers under 6 also end in 6. For multiplication, students will notice that you can count by 4s to learn 4 x 1, 4 x 2, 4 x 3, etc.
Do you see how you are probably already teaching some if not all of these Mathematical Practice Standards? Are there some that you could do better with?
Something that I have been thinking about is that the story problems need to be at the center of all the lessons. The kids need to be able to see why they are adding 3 + 4.
I also need to do better at using CRA. Most teachers, me included, try to skip to the abstract too soon. Kids are at all different levels and we need to reinforce the abstract with the representational and reinforce the representational with the concrete. Someone told me to think of CRA like islands connected with bridges. Sometimes you are fine on Abstract Island. You're getting it. But then bigger numbers or fractions or decimals come along and you need to visit Representational Island or Concrete Island to get your bearings on this new concept. They need to always be there to fall back on.
Another example of how Common Core has been poorly implemented is the fault of textbook companies. Textbook companies are in the business of making money. We hope that they have best practices in mind too when writing curriculum.
When Common Core was new, textbook companies had to revamp their curriculum to make it "common core." I haven't seen or used every curriculum that is out there. There may be a Common Core Unicorn that does all these things "right." But that would probably make that curriculum an Edsel. If you are not familiar with the history of the Ford Edsel, read about it here.
A curriculum has to cover ALL the standards. The problem with that is that we teach everything but only an inch deep. We introduce lots of concepts but don't teach many to mastery. The Common Core Standards were not meant to teach everything to mastery in every grade level.
What teachers are stuck with is math curriculum that says it's "Common Core" but really isn't. Curriculum often doesn't reinforce the use of CRA. Students practice algorithms too much and too soon instead of story problems. They give us scripted lessons instead of providing teachers with scaffolding ideas or the questions to ask to elicit that problem-solving mindset. Curriculum teaches too many different ways to solve problems instead of encouraging students to be the ones who persevere in solving problems. In a nutshell, many curricula is teacher-centered instead of student-centered.
So what do we do? If you're allowed, YOU decide how to use the curriculum. Start your lesson planning with the Standards for Mathematical Practices. Which of those does the lesson you are about to teach cover? If it is none, skip it! Reorder lessons, change the problems, cross half of them out, and make your own tests! Learn about how to do number talks and how to use number strings. Add manipulatives to every lesson even if the book doesn't say to! Decide which grade-level standards need to be taught to mastery and which are introductory. Look at the standards from the grade level above to see what you have to cover to get them ready for the next grade. But if the kids aren't there yet, so be it!
Common Core isn't going to go away. It isn't a fad, it's a way of life in education. Get on board or get out of the way. I do see it getting updated in the near future. It isn't perfect nor is it realistic for every student in the whole country to have the same expectations. However, the Standards for Mathematical Practice are part of EVERY grade level's standards. Make your students THINKERS, not just memorizers.
