But I also tutor students on the side, and one student I tutor is just starting a geometry class. And so I showed him pages posted on this blog -- Lessons 1-6 and 1-7, plus the Opening Activity on Euler’s bridges, and he succeeded on these first assignments -- and he quickly thought to add an extra bridge to make the impossible network into a traversable one. He also enjoyed the story of why students should learn math.
As promised, today I discuss the pros and cons of the Common Core Standards in Math, from kindergarten through grade three. The plan is to address many concerns that teachers and parents have regarding the standards, and suggest how I would change the standards in order to solve the problems caused by the current Common Core. I will only discuss Common Core on its mathematical merits. In particular, I will not discuss:
Constitutionality: Many people believe that anything other than 50 different sets of standards, one for each state, is unconstitutional and violates the Tenth Amendment. One good thing about national standards is that they make it easy for a family that does not want to change standards be able to avoid changing standards (that is, a family forced, because of a job, to move to another state). On the other hand, one bad thing about national standards is that they make it hard for a family that wants to change standards to be able to change standards.
Politics: As I mentioned earlier, much of the opposition to Common Core is political. Many of those who oppose the standards are Republicans, as it was a Democratic administration that proposed them.
The ELA standards: The ELA standards for Common Core have their own pros and cons. One major point of contention is their emphasis on informational nonfiction.
AP US History and other subjects: Earlier on this blog, I mentioned that some people are mentioning changes to the way AP US History is taught in their arguments against Common Core. And recently, I found a counterargument to my statement that the Common Core Standards have nothing to do with US History -- someone claimed that the Common Core and the AP US History standards have a common author. But of course, this all goes back to politics again -- the claim is that because of Common Core, AP US History will now be taught with a liberal slant.
The Next Generation Science Standards: Once again, my focus will be on math, not science -- but I may mention science only to the extent that math and science are closely related. After all, I just mentioned that much of what one learns in Algebra I shows up again in AP Physics 1.
And now enough about what I won’t discuss, and on to what I will discuss. Many Common Core horror stories begin with a photo of a math worksheet that a young student brings home. As I mentioned earlier, I was drawn into a debate on Facebook, where the following photo was posted:
Now this second grade worksheet begins by noting that the whole number 227 stands for 2 hundreds, 2 tens, and 7 ones. But the problem is that later on, it states that 227 is 1 hundred, 12 tens, and 7 ones. So, the second-grader and her parent are left to wonder, what’s going on here?
We begin by asking, what should a second-grade worksheet look like? Well, one thing we might expect to see is a subtraction problem -- for example, what is 227 - 132? And we begin by subtracting 2 from 7 in the ones place, leaving 5. Now we move to the tens place, but we can't take 3 away from 2. So we borrow 1 from the hundreds place and make the 2 a 12, so now we can subtract 3 from 12 to give us 9. Now look at the top -- after borrowing, the top row now reads 1, 12, 7 -- 1 hundred, 12 tens, and 7 ones!
So now we see the problem -- the student and her mother alike were confused when they saw 1, 12, 7 on this worksheet, but I bet there would have been no problem if the paper had simply asked for the answer to 227 - 132. So why wasn’t this question on the worksheet instead?
The so-called Math Wars have been fought for much of the 20th century, and they have spilled into the 21st with the advent of Common Core. There are two main schools of thought -- the traditionalists and the progressives. Here are some of the differences between these two philosophies:
A progressive teacher is often described as “a guide on the side.”
A traditionalist teacher is often described as “the sage on the stage.”
A progressive teacher abhors worksheets full of math facts as “drill and kill.”
A traditionalist teacher adores worksheets full of math facts as “drill and skill.”
A progressive teacher focuses on the end result -- applying math to the real world.
A traditionalist teacher focuses on the beginning -- mastering basic skills.
Around the year 2000, there were two websites that corresponded to these philosophies -- Mathematically Correct took the traditionalist side of the Math Wars, and Mathematically Sane took the progressive side.
Now undoubtedly, Common Core leans toward progressivism. Some Common Core defenders point out that nowhere in the standards is progressivism recommended. But even if the Common Core Standards don’t themselves recommend progressivism, many progressive teaching methods are being implemented in the name of Common Core. For example, if the mother whose daughter brought home the above worksheet were to ask why so many strange questions were being asked, the teacher would certainly reply that it was because of Common Core.
Second, it’s not as much what the standards say, but what material appears in the PARCC and SBAC assessments. If the standards mention traditional math but the test questions are progressive, then progressive math is what will be taught.
Finally, although the Mathematically Correct website no longer exists (and disappeared before the Common Core debate), the Mathematically Sane site still does (though it’s rarely update). About Common Core, Mathematically Sane writes:
“The release of the Common Core State Standards (CCSS) is a welcome milestone in the standards movement that began more than 20 years ago when the National Council of Teachers of Mathematics published Curriculum and Evaluation Standards for School Mathematics.”
And so this clinches it -- a known progressive website calls the Common Core a “welcome milestone.” Even if Common Core doesn’t directly promote progressivism, it is the de facto cause of the sharp increase in progressivism in the classroom and progressive worksheets for the students to take home.
Now I am sympathetic to both the traditionalist and progressive philosophies -- both of them have a purpose. In particular, many of the arguments for progressivism apply more to older students. For example, oppositional teenagers may resent adult authority. They may not want a “sage on the stage” forcing them to do “drill and kill” worksheets. They may ask, “When are we ever going to do this in real life?” -- implying that they will do no more than the bare minimum of math required to survive in the real world. Unless it is obvious from the beginning the applications of the math they are learning, they won’t even begin to do the work at all. And this is where progressivism shines -- it focuses on the real-world applications of the math that the students are supposed to learn.
But that’s just it -- this argument focuses on oppositional teenagers. Younger students, on the other hand, are often eager to learn. They want to please the adults in their lives and prove to them how smart they are. And one place where little children can prove how smart they are -- to demonstrate their skills -- is on “drill and skill” worksheets! And so we actually want “drill and skill” for these students.
And so I prefer traditionalism in the lower grades. But now I must define what exactly the “lower grades” are. Certainly, the grades that are too young to take the PARCC or SBAC assessments are too young for progressivism. If we make the third grade -- the youngest PARCC/SBAC year -- traditionalist, then that would automatically make all grades younger than that grade traditionalist as well, since the primary teachers would have to prepare the students for the traditionalist third grade.
I’ve mentioned in passing that my opinion of Common Core is mixed. For the youngest students, my opinion isn’t so mixed -- but instead is crystal clear. The official position of this blog is to support traditionalism from kindergarten to third grade. And so, I am opposed to the Common Core Standards in math for grades K-3.