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The Good and Bad of Common Core Mathematics

21 Dec

Initially I was opposed to Common Core Mathematics and in general, I would say that I am still anti-common core but not for the same reasons that many others are anti-common core.  Since I was against CC, I joined some Stop Common Core groups and visited some groups who support doing away with Common Core.  I listened to a very interesting debate with a Pro Common Core Side and Stop Common Core side and was very disappointed in the ability of the side that was against Common Core to debate its argument effectively.  I also became very disappointed with the arguments of many of the people who were anti-common core.  I don’t believe the larger political argument that it is Bill Gates trying to take over the world and any generalized arguments on that point.  To be honest, I would support a common core if it was good and effective. My feelings of anti-common core (and I am mostly speaking in the area of mathematics because that is the area I am qualified to address) are solely with respect to the effectiveness and appropriateness of the curriculum and its ability to improve mathematics in the classroom.

As a mathematics educator, someone who has a Ph.D. in mathematics education, and someone who actually works with kids at all grades and all levels of ability, I applaud and understand the INTENT behind the goals of the mathematics common core.  When you look at the goals, the expectations, the curriculum, and what the educators who wrote it had in mind, I can clearly see what they WANTED to achieve and on many levels it is wonderful.  The problem that they failed to see is that the implementation of these goals was not feasible and has created utter chaos.  Let’s take an example.

In elementary school, one “common core” objective is working with the decomposition of numbers.  This means the ability to break numbers apart into pieces to create more friendly numbers to make math easier to work with, often in your head and sometimes on paper.  For example, if you were adding 213 + 23 in your head, a mathematician might first add 210 plus 20 to get 230 and then add the 3 afterwards to get 233.  Mathematicians (read Ph.D.’s in math education here too) have a natural number sense to regroup numbers that allow you to add and subtract more efficiently in your head.

So… our wonderful creators of Common Core, thought, “well if this is what good mathematicians do automatically, this is what we should TEACH all kids to do.”  First it will allow them to build more number sense since they will have to understand how numbers are broken up and go back together (place value, etc) and second they will learn how to do math more efficiently.  All of this is good intent, it makes sense on a pedagogical level.

HOWEVER – what did this TRANSLATE to into the hands of TEACHERS and CURRICULUM WRITERS and in the eyes of PARENTS (and filtered down to CHILDREN)…

First, some children will just naturally decompose numbers – the kids that math comes easy to anyway, will just do it on their own!  The kids that math does not come to easily, do not tend to decompose numbers on their own for a reason, it is hard for them, they don’t build number sense at the same rate as the child who would naturally decompose numbers – so the age at which our CC creators choose for us to have kids LEARN to decompose numbers may not be DEVELOPMENTALLY APPROPRIATE for all children. This is a common problem with lots of Common Core Mathematics.

Second, elementary teachers are teaching children to decompose numbers – this is not something they were taught to do, elementary teachers get VERY LITTLE training in how to teach math and even less time in how to teach math this NEW way, the common core way, which is certainly not how THEY learned math.  So, the lessons may be confusing for students and the reasoning behind WHY they are decomposing numbers may be lost because these elementary teachers are not the ones with Ph.D.’s in mathematics education who understand the theory and the why’s behind all of this.

Third, the reason for decomposing numbers is usually to provide the ability to do math quickly in one’s head, not to do it long hand on paper – but again this got lost in translation, the teachers and curriculum writers don’t understand the REASON behind the goal, they just know the goal:  Decompose numbers and learn to add this way (because this is what the higher ups say is good to do).  So, now kids are learning to add numbers on paper using friendly numbers where it takes 5 minutes to do a problem that should take 1 minute if using the most effective way.  By this I mean, if it is small enough to do in your head, you should use the friendly number approach and decompose your numbers BUT if they are big numbers, you should use the traditional algorithm and do it on paper.  Students should be learning to take the most efficient approach and that the reason for decomposition and friendly numbers is that it will help them with mental math but there is still a place for the traditional algorithm and this method is not meant to replace it.

It got to the point where parents would post “bad” math common core homework assignments on this Stop Common Core site so everyone could see and comment.  At first, there were legit bad assignments –

  • some were developmentally inappropriate
  • some were new common core ideas that had no directions so both parent and child were lost or used vocabulary that the teacher had never provided to student / parent
  • some were things that I just mentioned, where it was something that was completely out of context, long tedious multi-step problems that could and should be done more effectively with a traditional algorithm

but, it reached a point that parents began to just be ANTI-COMMON CORE and ANY and ALL math homework was bad in their mind and they were posting things that were:

  • assignments that you have seen pre-common core
  • very good assignments that taught strong math concepts
  • anything that was slightly different or didn’t require the memorization of math facts was considered BAD

So, I want to make a point that being anti-common core doesn’t mean you agree that all of common core is bad.  I see a lot of merit is the ideas behind common core math, however, the implementation is a disaster and I feel strongly until (and if) that can be fixed, we are simply confusing students more.  Teachers are requiring students to “only do it the common core way,” instead of saying, “here is a tool box,” use this tool box but as long as you get there – both procedurally and conceptually, I don’t care how you do it.  I also think that Common Core pushes the concept and the why too much at the expense of the procedure.  Again, to do math, you need to have a tool box of procedures, the why and the applications come for students who are successful with strong procedural knowledge and when we over-focus on the concepts and the essay writing, students lose the practice time which also helps the light bulbs go off.  There has to be a balance.

 

Lynne Gregorio, Ph.D. Mathematics Education

 
 

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