Common Core, subtraction, and the open number line: Part 4

The following picture has been making the rounds lately.


My bedrock position is simply stated: I’m for teaching any technique in elementary school that’s (1) logically correct, whether or not it’s the way it’s (mythically) “always been taught,” (2) encourages students to think mathematically, as opposed to mindlessly following a procedure with no real conceptual understanding, and (3) prepares students for algebra in a few years’ time.

That said, I have a lot of opinions about this picture, which does not necessarily align with our society’s impatient obsession with 10-second sound bites and 140-character tweets. So be it. I will divide my opinions into several categories of increasing scope.

  1. The solution of this particular question.
  2. The pedagogical reasons for using this technique (called an open number line). In other words, do we only want Jack to get the right answer, or do we want Jack to understand something about the logic behind the answer?
  3. The difficulty of assessing the depth of a student’s knowledge in a way that is developmentally appropriate.
  4. The importance of engaging parents with unorthodox ways of teaching mathematics.

Some of my opinions will line up nicely with supporters of the Common Core. Other opinions will align with the Common Core’s thoughtful critics.

green line

This is Part 4 of this series of posts: the importance of engaging parents and caregivers when unorthodox techniques of mathematics are taught.

I’ve only witnessed the implementation of the Common Core from afar, but there’s absolutely no doubt that the professional development of teachers who have been asked to teach math in a new way has left a lot to be desired. Ditto for explaining these new approaches to parents and caregivers who want to help their children.

True story: I personally did not know about the open number line until the “Meet the Teachers” night that was held for parents near the start of the school year. The teachers explained that they would be doing math a little differently and did a couple of examples using the open number line. I could feel many eyes in the room looking back at me (people know I’m a math professor) with facial expressions saying “Is this stuff really going to work for our kids?”

As this was my first exposure to the open number line, I was skeptical (I would have preferred using base-10 kits) but I held my tongue and listened carefully to the presentation. After the presentation, I was convinced that this was a completely legitimate way of teaching the subject and that the teachers had the requisite depth of understanding to teach arithmetic using this technique. After the presentation, I told anyone who’d listen that this technique was mathematically sound and pedagogically sound, even if it was different than the way that “it’s always been taught.”

Parents generally bought into the technique that evening. I’m not sure that they would have bought into it if its rationale had not been carefully explained to them.

And, as a reminder, Texas is not a Common Core state.

The failure to explain to parents and caregivers unorthodox but correct ways of teaching mathematics has been perhaps the greatest failure of the roll-out of the Common Core. It’s unacceptable that children are crying over their math homework and parents feel powerless to help (a common theme that I’ve heard over and over again from my friends).

Teachers and parents ought to be natural allies in wanting children to have a greater depth of understanding of arithmetic that will prepare them for algebra later. However, because the strategies of teaching the “why”s of mathematics have generally not been carefully explained to parents, they naturally feel somewhat helpless when trying to help their children with their homework.

My own field of research is not mathematics education. So, at professional conferences, I’ve asked friends and colleagues the same question over the years:

Letting children use their own natural curiosity to get at they “why”s of mathematics is good. Letting children use their own natural curiosity and also having the support of parents at home is better. So what research has been done on strategies on successfully engaging parents with how mathematics is currently taught versus how it was taught a generation ago (or, more accurately, what parents remember of their own experiences from elementary school)?

To my surprise, people that I greatly respect did not have an immediate answer to my question. So I’m guessing that while there’s been a lot of research into successful strategies for teaching mathematics in the classroom, there hasn’t been a lot of research into how these strategies can be supported when children are away from the classroom and asking their parents for help on their homework.

I’ll repeat the close of yesterday’s post: I won’t defend the indefensible way that the Common Core has been rolled out. Voters will be more than justified in voting out anyone who supports the Common Core if its implementation isn’t fixed in the very near future.


2 thoughts on “Common Core, subtraction, and the open number line: Part 4

  1. Reblogged this on The Twilight Zone and commented:
    If you have 20-30 minutes, I’d reco reading this guy’s assessment – best posts on Common Core I’ve read that are objective and informed. He thoughtfully analyzes one of the many emotional/viral pictures that are floating around the web, and I almost agree with everything he’s stated from the importance of knowing WHY vs just the right answer to the flaws in the textbooks/curriculum and the poor training of the educators who are trying to teach kids new methods that they may have just learned themselves. The only thing I disagree with is the idea that the parents should be taught the unconventional methods too so they can help their kids with the homework. I don’t think it’s a realistic expectation that teachers need to teach both the student and the teacher. If the parent can’t help, then they should just tell the child to ask teacher or another student for help. If anything, this may actually level the playing field of poor kids vs rich kids – finally the rich kids will need to rely only on themselves vs the help of their parents/tutors. Just like the poor kid whose parents probably have neither the time nor education to help them in school. Added bonus – all of them will potentially understand the why and fundamentals to understand higher order math later. However, I certainly can’t argue that teaching the parents will help with the implementation b/c then the parents may not feel so helpless (and dumb), so will be less angry…

    Definitely worth your time to read through all parts if you want a more clear/objective picture of the execution of common core math.

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