Common Core math is new.  The standards and methods for implementing those standards are not perfect.  This page assembles criticisms of both the standards and methods in hopes that some of them might serve to motivate and guide future improvements to the program and its instruction.

Inclusion of a criticism on this page is not an endorsement of its validity.

The Common Core Check

One father demonstrated his frustration with the new methods of teaching math by cutting a “Common Core” check to the school.

Common-Core-Check-Twitter-@JoanOfArc1920-640x480

You can read more about it here (Fox news), or here (for an explanation of the math).

What’s important about this incident is that it demonstrates a major weakness of the new model.  Parents are having trouble understanding or getting frustrated with the new methods of teaching math.  This inhibits their ability to assist their children, and thus, hinders the child’s ability to learn the math.

It’s a problem that needs to be addressed, but it is not necessarily enough reason to eliminate the program.

Arkansas Mother has a Math Problem

This video is from 2013.  In it, a mother (among other things) asks a math problem.  The question goes something like the following.  A class has 18 students.  If the class counts around by a number and ends at 90, what number did they count by?

The answer is 5.  Most adults would take 90 and divide by 18 to arrive at this answer.  Let’s first understand that this answer and method is correct.

The mother in the video suggests that if a student simply wrote 90/18=5, it would be marked wrong.  Instead, the student is expected to make 18 groups of 5 marks to illustrate the answer.

As an educator, I would not tell a student that submitted 90/18=5 that they are “wrong.”  They aren’t.  They are correct.

However, I completely understand and agree with the message this problem and the suggested solution are trying to convey.  Process is at least as important as the answer.

Let me make my point with an analogy.  Suppose I (magically) am given an opportunity to step up to the plate as a batter for the Boston Red Sox.  When the pitch is delivered, I close my eyes and swing.  By chance, I end up connecting and get a single.  After me, David Ortiz comes to bat and strikes out.  I got the “correct” answer.  David Ortiz got the “wrong” answer.  But I promise you that Ortiz had a better process.  It would be foolish for the Red Sox to release Ortiz and declare me their new DH.

Students develop mechanisms to arrive at correct answers even if they don’t understand the problem.  For example, in the above-mentioned problem, a struggling student will look at the two presented numbers, 90 and 18, and make a guess as to how to combine them.  For example, one student might write 90-18=72.

When a teacher looks at a student’s response of 90/18=5, they can’t be sure whether the student understood the problem or if they closed their eyes and swung.

Recent reforms in math education are asking students more often to explain or illustrate their response.  The theory is that this helps the students develop the underlying number sense and understanding necessary to continue into more challenging mathematics.  At the very least, it requires the students to demonstrate to the teacher that they didn’t close their eyes and swing.

Mathematics is hard.  When faced with the challenge of teaching a group of 25 young kids how to perform some math task (like multiplying small numbers), it’s easy to resort to “tricks” or memorization.  Yes, the trick or memorization will help the student answer what is 3 times 5.  However, if the tricks replace true understanding of multiplication, the student is going to have trouble understanding expressions like 7x=56 (among other things).

Tricks and memorization are great solutions for the short term, but relying on too many will leave the student with a mathematical foundation that has too many cracks to support mathematical reasoning at higher levels.

Use Your 10s

As a young child, I  would use 10s to make mental math easier.  To be honest, I don’t know if this was something that was shown to me by a teacher (and I had some excellent math teachers in early grades) or if I developed it on my own.  What do I mean by use my 10s?

Suppose I had to add 38 and 45.  I would pull 2 out of the 45 and add it to the 38 to make the problem 40 + 43.  That was and continues to be the easiest way for me to do mental addition.

As I started working with my eldest son on his addition, I found myself regularly suggesting “use your 10s.”  It seemed to work.  I think it’s important to note that I began teaching addition to my son using objects (like toy cars or pieces of candy).  Later, we moved to mental calculations.  He was adding double digit numbers in his head by kindergarten and before he was tasked with writing out  the problems on paper.

My son was familiar with the practice of “using 10s” before he was asked to write something like seen in the above video.  When he was finally asked to use number bonds (or whatever they might be called in a particular math program) he understood why he was doing it.

The act of writing out the split of 5 in the above video will appear bizarre and can be too abstract for students that haven’t first practiced the mental math of “using 10s” in their heads.

My suggestion is to put the paper and pencil away.  Ask the child to add 5 + 5, 6 + 4 and 7 + 3.  Then ask the child if she can come up with all the combinations of two numbers that add to 10.  Then ask the her to add 8 + 3 while encouraging her to use the knowledge that 8 + 2 is 10.  After some mental practice, write out the same problem and explain why 3 might be “split” into 2 + 1 so that she can rearrange 8 + 3 as 10 + 1.

When the child is ready, move to more challenging problems where the student can see the value of regrouping these numbers.  A good second grader probably has other relatively simple methods to add 8 + 5.  Why then should she learn this other new and weird approach?  Maybe if she tried 27 and 36, she might better understand the method’s utility.