Math has always intimidated me. Well, honestly, it has always terrified me. I was never able to make a connection with numbers like I did with words, and so I struggled all through school with math. I had many great math teachers who offered a variety of methods to solve problems, but since I didn’t understand math easily, I never pushed myself to make sense of it. I did just enough to get along, enough to pass, without ever really gaining a solid grasp of the concepts.
Meeting my old math nemesis once again through viral internet memes about Common Core math problems admittedly made me defensive and dismissive of the Common Core State Standards (CCSS). Bizarre, incomprehensible math problems being shared on Facebook and YouTube by frustrated parents were basically my first introduction to the CCSS, as is probably the case for many. And there is no question that there is an abundance of bizarre math problems shared online to choose from these days.
This strange math being developed for new, common core compliant curriculum around the nation has become one of the most loudly and frequently targeted parts of the CCSS, especially in the realm of social media. This may have made it somewhat of a distraction from what I see as much more worrying complaints about common core, but because it is a valid concern, it should be addressed.
I certainly believe there are reasons to question the changes in the way math is being taught. When what should be a simple equation is made into a series of confusing and complex steps in order to find the answer, it seems reasonable to ask if this is only going to make math even more intimidating and challenging for children. Are we sacrificing speed and accuracy by moving away from rote memorization? Are we requiring students to master mathematical concepts they are not yet developmentally ready for?
Since math was so challenging for me as a student, I really tried to dig into this issue with an open mind. After all, had I been taught math fundamentals in a different way, perhaps it would have been easier for me to understand. And the truth is, I have found some explanations and examples of the reasoning behind the mad math of common core that do make sense.
Consider the ‘ten-frame’ being used in early grade level math. According to this site, “a ten-frame is a hands-on and pictorial model that teaches number sense and mental math.” This idea goes along with the concept of breaking larger numbers into groups of ten in order to make them easier to work with. When multiplication was explained to me in this way, I see the reasoning. For example, if you consider 6×12 as 6(10+2), you can do the multiplication this way: 6(10) + 6(2) is equivalent to 60+12 which equals 72. That is a simple equation, but if I apply the same method to bigger numbers, I can do multiplication in my head pretty quickly that used to take me a lot more time and thought, or a pen and paper.
I think one more good example to look at is the use of the number line. This article from Salon.com by James Goodman gives this example of solving a problem using a number line that does look confusing at first glance. However, the article goes on to explain the method this way:
If you haven’t yet made sense of the second diagram, think about the way that people used to give change at the store (perhaps a bit of a lost art these days). Suppose you purchased something that cost $8.27 and paid with a $20. The clerk would start at the value of the item purchased (in this case $8.27), then start with the change, bringing you first to $8.30, then to the 50 cent level, then to an even dollar amount, then a ten dollar amount, and so forth, until the value was brought up to the $20 you paid with:
“Okay, $8.27, 30 cents <putting three pennies in your hand>, and 20 more is 50 cents <putting two dimes in your hand>, and two quarters makes nine <dropping two quarters in your hand>, and ten <giving one dollar>, and ten more makes twenty <giving a ten>.”
This makes sense to me, and I can see many reasons for giving kids different tools to solve equations. Children all learn differently, as we well know, and it seems advantageous to allow for different problem-solving methods. Proponents of the Common Core math standards repeatedly point out that this gives greater flexibility at the classroom level, as well as stronger math fluency for all students. According to this USA Today article,
Learning math this way leads to deeper understanding, obviates the need for endless rule-memorizing, and provides intellectual flexibility to apply math in new situations, ones for which the rules need to be adapted.
That article goes on to say that the CCSS expectations for math “have been endorsed by every major mathematical society president, including the American Mathematical Society and the American Statistical Association.”
However, these arguments in defense of the Common Core math standards do not take into consideration the very real effect that high-stakes assessment testing is having on curriculum development. This is a note-worthy problem that I will get into at greater length in an upcoming post. In isolation, the ideas behind the math standards sound sensible, great even, but the reality on the ground tends to show that the benefits are quickly lost in the application.
Along with the problems associated with test-driven curriculum, there is also the question of whether these math standards are developmentally appropriate. Is it realistic to push pre-algebraic thinking on elementary school students, with the expectation that their young brains can successfully absorb the ideas for future expansion? This is certainly a difficult question to which there is no easy way to find answers. Yet it must be asked if the Common Core math standards are to be regarded as an improvement in education.
In a Huffington Post article from May 2014, it is posited that Common Core math standards are modeled on reform mathematics which it describes as math where “kids should explore and understand concepts like place value before they become fluent in the standard way of doing arithmetic.” It goes on to say,
Stanford University mathematician James Milgram calls the reform math-inspired standards a ‘complete mess’–too advanced for younger students, not nearly rigorous enough in the upper grades. And teachers, he contends, are largely ill-prepared to put the standards into practice.
‘You are asking teachers to teach something that is incredibly complicated to kids who aren’t ready for it,’ said Milgram, who voted against the standards as part of the committee that reviewed them. ‘If you don’t think craziness will result, then you’re being fundamentally naive.’
I would like to point out that James Milgram, Professor emeritus in Mathematics at Stanford University, served as a member of the Common Core validation committee, and you can find more of his opinions on CCSS here.
I do think there is much to be said for the fact that it is always hard for parents and educators to transition into something new. Remember the emergence of computers and the internet in schools, and now the increasing use of tablets (and WiFi with it’s potential dangers). I realize it can be difficult to accept having our children taught differently than we were, and, of course, we should be able to set that aside in order to be open to improvement in education. However, I also believe there are intended improvements that might actually prove to be detrimental, and it is imperative that those be questioned, highlighted, and scrutinized.
That gets to what I consider to be even deeper problems with the Common Core State Standards than math that is hard to understand out of context. Problems that these bizarre, confounding, maddening math problems all over social media may well be distracting us from. Problems I will continue to explore and write about at length in upcoming posts.