 Alright, so a question that I get asked a lot about is, what is the common core? So let's talk a little bit of history. In 2001, then-President George W. Bush signed the No Child Left Behind NCLB Act, and this act required three important things. First, that all states develop rigorous learning standards to be reviewed by the federal government, all public school students to take the same test regardless of learning disability status based on the state's standards, and that schools and teachers that fail to demonstrate adequate yearly progress to be held accountable. And here's the important thing. The tests are not the standards. The tests are on the standards because the tests have to be on something, but the standards can exist without the test, and the tests are independent of the standards. For standards you adopt, there are going to be some tests that are associated with them. So with that in mind, let's think about what those math standards are. So non-common core states, these are Texas, Virginia, a couple of others, they base their standards on principles and standards for school mathematics published just before No Child Left Behind in 2000 by the National Council of Teachers of Mathematics. They base their standards on 60 or more years of research on how children learn mathematics, and a comparison to standards in countries that routinely outperform U.S. students on international mathematics exams. And these are what non-common core states base their standards on. In contrast, the common core state standards in mathematics are based on principles and standards for school mathematics, 60 years of research on how children learn mathematics, and comparison to standards in other countries that outperform U.S. students on international mathematics exams. And what this means is that there is no real difference between the standards that are adopted by common core states and the standards that are adopted by non-common core states. Now, there is one minor difference, states that adopt the common core state standards are also eligible for additional federal education funds. So what this means is that states that don't adopt the common core will base their standards on a set of documents and produce their own standards at their own expense, and they will not be eligible for these additional funds. On the other hand, states that do adopt the common core state standards will have a set of standards that are based on the same documents, the same information that the non-common core states have used. The standards will have been developed and paid for by somebody else. The standards are freely available incidentally. And in addition, if they adopt the common core state standards in mathematics, they will also be eligible for additional federal education funds. Well, so the question is, well, what are these standards? Independent of whether you're a common core or a non-common core state, independent of whether your state is going to receive additional federal money for not having to develop its own standards. What are these standards? And a lot of the standards are going to be based on an important document called Adding It Up. This was put together by the National Research Council in 2001. And this document, again, freely available online, this was published by the National Research Council, and you could look it up and download the entire document if you want. This is an influential document for developing both the common core state standards and the non-common core state standards in mathematics. And the focus on this document is on K-5 topics, whole number operations, however, if you change the K-5 curriculum, you have to change the curriculum in grades 6 through 12 as well. So what's in this document? Well, there's three key concepts. Regardless of whether you're a common core or a non-common core state, you're going to incorporate three concepts into the math standards. If I were to put a name to them, I would say that these standards are, these concepts are parts, problem solving, and passing it along. Parts. Well, so for example, here's a problem, and we'll talk about that more in a second, 16 times 26. And I'll say, multiply this in your head. So most of us were taught the following method of multiplication, 26 times 16. We wrote down some digits, we did some multiplication, we wrote some things in some places because we were told to do that, and we end up with an answer 416. Now, if I try to do this method in my head, I'm going to run into a little bit of a problem. I am a mathematician, I've been teaching mathematics for more years than I care to remember, and I can't do this in my head. On the other hand, one approach of many different approaches is to think about this multiplication and to break the number into parts. So one thing I might do is I might think of the number 26 as consisting of the parts 25 and 1. Now here's the most important thing to remember, which is, why did I choose 25 and 1? Well I chose 25 and 1 because I felt like choosing 25 and 1. Now why did I feel like choosing 25 and 1? Well part of the reason that I did that is that I think about 25 as a quarter and 1 of course is as a penny. And here's a useful fact, we're good at thinking in terms of quarters. Multimals of 25 are easy for us if we think about them as quarters. And so this viewpoint allows us to consider this multiplication in the following way. 16 times 25, well that's 16 quarters and 16 pennies. A quarter and a penny is 26, 16 of these, well 16 quarters is $4, that's 400, 16 pennies is of course 16, so 16 times 26 is going to be 416. Now a question that parents often ask is, well what about, how do I help my child with this sort of problem? And so here's a useful question to think about, how else can you think about this? If you want to think about these numbers as parts, how else can you think about the numbers? Again 26, I am an adult, I'm used to thinking about quarters and pennies so that's the idea that 26 as 25 and 1 comes somewhat naturally. And there's other things we can do, 26 is any number of other ways we can look at it. Second thing that the standards also suggest is their focus on problem solving. And an important goal in modern mathematics education is to provide as many opportunities for problem solving as possible. And well here's an interesting notion, this is not a problem, find 16 times 26, that is not a problem. Why is it not a problem? Well it's not a problem because you already know in theory how to multiply. You know how to solve this, this is a task that we have to do, and what we have to do is apply something that we know how to do. It's a task to be completed, it's not a problem, at least not in the sense of problem solving. There is a problem, invent a new way to multiply then use your method to find 16 times 26. And this is a problem, but it's actually a very hard problem because we have to create something completely new. And most of us, if we were confronted with this we would probably not be able to create a completely new way of multiplying because quite frankly people have been inventing ways of multiplying for 4,000 years and all of the ways, all of the obvious ways to multiply have already been invented. Well here's a problem your child can solve, invent a way to multiply that is new to you then use it to find 16 times 26. Or equally, equally relevant, here's a problem, 16 times 26, but at this point you don't know how to multiply. How would you do it? Well this kind of raises the question, why don't I just teach them how to multiply? Why don't I just teach them the standard algorithm? 60 or more years of research on how children learn mathematics shows two important things. Students can solve arithmetic problems using their own informal algorithms without being taught how to multiply 16 times 26 if they understand what this is, what it means to multiply. They're able to solve problems like this using their own methods. When they use their own methods, they tend to outperform their peers who have been taught using the standard algorithm even when both groups are given the same total instructional time. And most importantly, these informal algorithms can be the basis to promote student understanding and proficiency when they eventually do learn the standard algorithm. So if we don't teach them the standard algorithm from the get-go, they figure it out. They do better and they understand and apply the standard algorithm more efficiently when they are eventually introduced to it. And this means that if you introduce the standard algorithm too early, you are going to deprive your child of a unique educational opportunity. Your child has one chance to figure out for themselves how to do products like this. If you tell them how, they may learn this standard algorithm, but they will have lost a unique educational opportunity of figuring something out for themselves. So again, one thing that you can help your child if you want to promote this, what does it mean? When you do this thing, what are you doing? What does it mean? Finally, one important one of the third component of the state standard, whether they're common core or not, comes along with the idea of passing it along. And there's an old saying, those who can do, those who can't teach, utter nonsense, complete garbage. You cannot teach something effectively that you do not understand. If you don't understand it, you may be able to repeat it, but you cannot teach it effectively. The other important thing is that explaining something confronts you with the limits of what you do understand. And most importantly, communication is the key to success in any field. No matter what you're going to do in life, you have to be able to communicate. So the other thing is, it's also important to be able to understand how another person is thinking. If you can communicate and if you can get into the mind of somebody else, you have a winning combination. And so, by explaining the solution to the problem, your child gives the listener insight into what they understand and also what they have difficulties with. And this leads to one of the most reviled problems that show up on the common core, which is the finding correct type problems, and they are generally something like this, George added 28 plus 35 this way, and what did George do wrong and help him to find the correct answer? Well, note that there's two parts to this problem. Identify the error that George made, fix it, and so here's a good answer. Well, let's see, what did George do? So again, getting into the mindset, getting into the mind of George, how did George think a useful thing to think about? Because again, useful skill in any field that you're going to go into, what's the other person thinking? Well, let's see, what did he do? He added two, thirty and five, he added thirty, oh, he added thirty-seven here. He didn't want to add thirty-seven, he wanted to add thirty-five. So what should he have done? Well, he should have added two, thirty and three. So again, George is adding thirty-seven. Well, he doesn't want to do that. He wants to add thirty-five. Well, if I want to help George, I'll say, well here, look, what you really want to do is add two, thirty and three and get your answer. And so we've identified George's error, he added the wrong total, and then he, we've presented a way that George can get the correct answer by adding the correct numbers. And so a useful question to ask when your child is confronted with the problem like this, why did they do what they did? Let's put a summary on all of this. The future is going to belong to three groups of people. Those who can break a big problem part into smaller problems, those who can create original solutions to problems, and those who can communicate solutions to problems. The Common Core State Standards and Mathematics help prepare your child for this future. And again, you can help your child at home by asking three key questions. How else can you think about it? How can you break this into smaller problems? What does it mean? And why did they do that? These are three key things to think about when you see those Common Core Worksheets being sent home with your kids.