So, the title should hopefully alert you to the fact that this blog is going to MOSTLY be a POSITIVE view of Common Core (which I will refer to as “CC” in many cases for the purpose of saving bytes). I think I should quickly alert you to a few other things before you read on though:
- I have NOT done extensive research into Common Core. This blog is not intended to be a the world’s definitive source for information on Common Core. This is simply my opinion based on the information I have from my kid’s homework, my educational background (bachelor’s degree in Mechanical Engineering), the few videos I have watched, the ACTUAL common core standards that I have reviewed, and the articles I have read. I have done some research and have formed an opinion. That is all. You are welcome to disagree (see item 3 though).
- I am going to focus ONLY on the math side of CC because it is what I see the most controversy over and it’s what interests me most and it’s what got me fired up to write this blog.
- I have been and plan to continue to be both HONEST and GRACIOUS in my writing about this subject. I would ask that you are the same in any comments you may make. Attacks on character, conspiracy theories, and rude comments are not appreciated. As I write this, I just watched the new Cinderella movie with my girls and so I would ask you to “have courage and be kind“.
- I already mentioned conspiracy theories in the last point, but just to make it even more clear…this blog does NOT deal with the motives behind CC, who came up with it, Bill Gates funding of the standards, or any other conspiracy-like theory. I have heard everything from “this is intended to dumb our children down and make them into submissive worker bees” to “this is intended to provide a new billion dollar market for services to aid teachers and schools in teaching common core”. I don’t know anything about any of that.
OK…so let’s dive in.
What is Common Core?
I think it is important to make a point right from the start here:
- Common Core is NOT a curriculum or a methodology. It is a standard. It does not tell teachers how to teach math to students. It does not make up math problems for students to solve daily in the class room. It simply provides a standard set of things that students should know at the end of each grade.
With that said, curricula have been and are being developed to teach to the standard. So, I won’t say that all the arguments of “common core math is stupid” are irrelevant but I think it is important to note that the CC is not a curriculum that teaches weird math. The weird math is taught to help students understand the concepts needed to meet the standard.
My kids are in Kindergarten. Here is one of the Common Core math standards for their grade level under the “Operations and Algebraic Thinking” Section:
[important]CCSS.MATH.CONTENT.K.OA.A.3
Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).[/important]
The problems that come home from the curriculum that our school has chosen (we use Engage NY) seem to teach them how to decompose numbers as required by this standard. The standard does NOT dictate how to teach them that.
What Started It for Me?
Well, someone posted a video on Facebook titled “Arkansas Mother Obliterates Common Core in 4 Minutes!” (You can watch it HERE). It has well over 2 million views as of the time I am writing this and is one of the first videos that comes up when you search “common core” in youtube. I watched the video when I saw it posted on Facebook and quite frankly I was very surprised at the title of the video and all the praise for the woman in the video. It actually made me mad. I found the woman condescending and in no way would want her thought process to be the basis of my children’s education. In my opinion, she does not obliterate common core in any way in the video. She actually made me feel better about it. Here is the scenario in the video:
- The Math Problem: There is a class of 18 students. The teacher has them count around the room by a number (as in counting by 2’s or 5’s or 10’s) and when they get to the last student they are at 90. What number did they count around the room by?
- The Arkansas mother’s way of doing the problem: Divide 18 into 90 to get 5. Simple.
- The Common Core way: Draw 18 circles, put one hash mark in each circle and keep going around until you have drawn 90 hash marks. How many hash marks are in each circle? Answer = 5. As the video points out, this takes “108 steps”.
Then, I went down a few videos in the Youtube suggestions on the right hand side and found another video that was titled “Proof That Common Core is Killing Common Sense”. Also one of the most watched videos on Common Core in Youtube and also highly condescending and also actually made me feel even better about common core. You can watch it HERE. This one starts with a simple problem that is made “harder” by common core and then finishes with conspiracy theory. The person in this video makes the point that she would never draw circles and hash marks at the grocery store to do something simple like add the price of milk to the price of bread. That is probably true, but she also would not do the standard algorithm on paper by carrying ones and all that! She would do “common core math” in her head. Here is the main scenario in this video:
- The Math Problem: 530 – 270.
- The “right” way according to the video: Just do the algorithm. Write 530 on top of 270, draw a line under it, subtract each column, borrow from other columns if needed, etc. The standard arithmetic algorithm. If you do it right, you get 260.
- The Common Core Way: Add 30 to both numbers to get 560 and 300 and then subtract. Clearly, the answer is 260.
Finally, I saw this Math problem going around on the internet. It’s probably the most viral math problem out there related to CC and widely used to prove how dumb CC is.
This one makes me like common core even more, too! I will tell you why in a minute.
Why I Actually LIKE These 3 Problems
1) Let’s start with the last problem in the picture above. 32 – 12 = 20. The “common core way” (which is actually not dictated by CC) seems to take way longer and doesn’t even really seem to make sense the way it is written. Let me try to give you the thought process behind it though. It goes something like this:
- If I start at 12 and count up to 32, I can figure out the difference between 32 and 12.
- I know how to count easily by 1’s, 2’s, 5’s, and 10’s (most kids do by 1st grade). So, one option is to get to the nearest number ending in 5 or 10. There are many options here but I will choose to count up 3 to get to 15.
- Now, I can easily count by 5’s to get to the nearest number ending in 0 (10, 20, 30, etc). That takes me to 20 and the total I have now counted is 8 (3 + 5).
- Now, I can easily count by 10’s. So, I will add 10 to get to 30. The total I have now counted is 18 (3 + 5 + 10).
- Now, I can see that I am only 2 away from 32. So, I will count up 2 more. The total I have counted is now 20 (3 + 5 + 10 + 2)
Clearly, this takes longer than doing the algorithm marked as the “old fashion” way in the picture. However, the “new” way demonstrates an understanding of manipulating numbers that can be done in your head. It’s actually not even close to the only way to do that problem the “new” way. For instance, you could simply count by 10’s from 12. First to 22 (+10) and then to 32 (+10 more) and arrive at 20. You did the same thing but in fewer steps. You could also count down to 10 (-2) and then up by 10 twice to get to 30 (+20) and then up by 2 (+2). The answer is still 20, but you can demonstrate that you understand numbers well enough to get to the answer several different ways.
Oddly enough, it’s probably the way you actually do math problems in your head every day. Maybe you just don’t realize it because you have learned it only through practical application and necessity rather than through school where you were only taught the algorithms. Let me give an example:
- You go to Starbucks (or your favorite coffee shop…no coffee discrimination here) and buy a coffee for $3.27 and pay with a $20 bill. How much change are you owed?
- If you were asked this question on the spot, my guess is that you would not write 20.00 on top of 3.27 and draw a line under it and do the algorithm. If you were going to just do that, why not pull out your phone and use the calculator?
- Here is an example of how you MIGHT think this problem out in your head: $3.27 + 3 cents = $3.30. $3.30 + 70 cents = $4.00 (total added is now 73 cents). $4.00 + $16.00 = $20.00. Change should be $16.73 (3 cents + 70 cents + $16). That is just ONE way you might do it. It’s no different than the 32-12 problem shown above.
If this type of skill is what they are trying to teach my child starting in Kindergarten, then I am all for it.
2) I’ll try to make this one shorter! Let’s talk about the problem 530 – 270 = 260. This was reported as a second grade math problem. To me, the “new” way to teach this problem does two things:
- It begins teaching kids concepts that they will NEED for higher level math such as algebra where subtracting or adding things to both sides of an equation is essential to solving the problem. It teaches them that they can manipulate the numbers to see the problem differently and still get the right answer.
- It teaches them that they can manipulate the numbers in ways to make the problem easier to do in their head (much like the coffee example above). In this case, when you add 30 to both numbers, the answer becomes much easier to simply SEE. You most likely won’t need the algorithm when you see 560 – 300, and even if you do, there is no borrowing from other columns like you would have to do in the original problem (which makes no logical sense…it’s just a learned operation/trick).
3) Finally, the problem that “Obliterates” Common Core in 4 minutes says that it takes 108 steps to do the same thing that you can do in one step. My thoughts:
- The point of the “108 step” exercise is not to get the answer in the fastest way. The point is to understand WHY dividing 18 into 90 gives you the right answer.
- You could argue that the circle and hash mark method is a dumb way to show students why the answer is 5. However, again, that is a curriculum thing and not a CC thing. There are many ways to teach students how that works visually. This is just one way. The point here is NOT efficiency but rather understanding.
Let me see if I can give a counter-example to show why I think the hype about these math methods is not the right way to think about it. Let’s imagine a scenario where the standard method of teaching math has always been the “new” way shown in the picture above and we didn’t have the standard algorithms. Imagine I came along with these new algorithms to teach math and taught nothing about why they work. Would it be hated? I think so
Check this out:
Why does that work? Why does borrowing from the other column work? It doesn’t make logical sense, but many of the anti-CC material out there is talking about how our standard algorithms just “make sense”. They only make sense because we have learned them and know the rules. If they came to us as adults and gave us these rules they would NOT make sense. I just don’t see how borrowing a one from the next column makes logical sense. I know it works…but that’s all.
In the “old fashion” way in this example, it’s quite easy to do in your head. I can start at 47,299 and add 1 to get to an easier number to deal with: 47,300. Then, I can easily count by tens to get as close as possible to 47,397. That gets me to 47,390 and I have counted a total of 91. Then, I can either go to the next 5 or easily just count up 7 more to get at total of 98. Is this not how you would do the problem in your head at the grocery store?
One Last Example
For this part of the blog, I want to give one last example/resource in the form of a video. This video, in my opinion, is a short and very good explanation of why we are teaching kids math this way now. It is less than 8 minutes and will give you a few more examples of why this is a GOOD way to prepare kids for math in regular life as well as in higher level courses.
VIDEO: https://vimeo.com/110807219
More To Say
I have more to say. So, please make sure you read the other parts (and the requests at the beginning of this blog) before making any comments. When part 2 is complete, there will be a link at the bottom of this post.
In the rest of this blog, I will cover things like:
- The Standard algorithms are STILL TAUGHT!
- Teaching math this way is not new.
- How my childhood prepared me for Common Core Math
- What I think parents can do to help their kids with Common Core Math
- Why I think it’s too early to throw this out
- How I think we are sabotaging ourselves by opposing CC because we don’t understand it
- The problems I see with Common Core
Part 2
Thank you. I have been saying this since CC became the new set of standards. While it is far from perfect, at least public schools are trying to improve. Kudos to you for speaking up for your kids in the face of controversy.
Thank you, Kara. Appreciate your comment.