Algorithms, Quadcopters, and the CCSS-M

So, as usual, the end of the school year (and then subsequent visit from my in-laws) ended up leaving not enough time to do my self-assigned homework around #algorithmchat in a timely manner. But, in keeping with my belief that it's more about the learning then the exact date of that learning, here's the results of my thinking.

First, I think my general thinking hasn't changed that much from the original post, where I stated:

algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning

I appreciated the detailed descriptions and explanations of the various algorithms in the Fuson and Beckmann article and they certainly got me thinking. The authors argue that the CCSS-M includes the meaning and sense-making as part of students' development and understanding of algorithms, which I agree with. They also state that in the past the algorithm was often taught without that meaning and sense-making portion, and I think most of us agree that is not a great approach.

The part I still disagree with the CCSS-M (and maybe Fuson and Beckmann as well, I'm not sure) on is the idea of the standard algorithm. I think the crux of this argument boils down to folks who argue for one specific standard algorithm because it is the most "efficient." I would argue that the most efficient way to do most of these calculations is with Siri or Google Glass or Wolfram Alpha. I'm more interested in students understanding the mathematical underpinnings of the algorithm(s) then in being able to quickly apply them. I want them to have number sense and mathematical understanding, but I don't think that necessarily means being able to "efficiently" compute a four digit by four digit multiplication problem by hand.

So, as long as I can change the standard algorithm to a standard algorithm that makes both mathematical sense and is most helpful to that particular student (which, I admit, doesn't flow quite as freely), then I'm good.

As a side note, this TED Talk happened to get posted just as I was trying to compose this blog post.


I think it's interesting in and of itself, but I also found it interesting how often he refers to "algorithms" and "mathematical modeling." I think this shows the power of algorithms, but also the need for our students to understand the algorithms, and also to understand that algorithms are first and foremost developed by humans and are not always set in stone, as when the algorithms appear to "adjust" or "learn" in the flipping sequence.

If our students can be begin to understand that algorithms don't supersede our understanding, but can help enhance it, then I think we're on the right track.

Algorithm Nation

As many of you are aware, I'm the "Director of Technology" (read, "building level technology coordinator) for my high school, but I also teach one section of Algebra. As a result I often find myself drawn into the math conversations happening on Twitter and on folks' blogs. This weekend I somehow ended up deciding to join a "reading group" around an article (pdf) titled "Standard Algorithms in the Common Core State Standards" from the Fall/Winter issue of the NCSM Journal.

Basically the conversation on Twitter began with some folks describing ways in which algorithms got in the way of learning and understanding mathematics. Then other folks pushed back a bit and asked if perhaps there was some value in algorithms. Christopher Danielson then pointed us toward the article in NCSM and suggested a "reading group" to discuss the issue. Feel free to "join" the group, which basically means you read the article and discuss it on Twitter or blogs using the hashtag #algorithmchat.

I thought I'd take a moment to put down my thoughts about algorithms in mathematics before I've read and begun discussing the article, just so I/we could see if my thoughts change after the discussion. While this is certainly a topic I have thought about, I also have not done a "deep dive" into the research or people's thoughts about algorithms. Right now I think I come down squarely in the middle (if that's possible). I agree that there are many times when algorithms have gotten in the way of learning and understanding mathematics. That we try to get our students to master the algorithms as quickly as possible so that they can be "efficient", even if it's at the expense of understanding. Then later we complain when they don't seem to have what we would consider basic number sense.

On the other hand, I don't see that as an inherent problem with algorithms, just the way that we sometimes deploy them. I do see algorithms as a valuable tool in working with mathematics (and other content and problems, for that matter). I think as long as we focus on understanding before (and while) we use algorithms, they can be very valuable in ways at making our thinking and processing "efficient" in order to then move on to thinking about more advanced mathematics, as well as to apply the mathematics.

So I guess my position right now, before this discussion, is that algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning. Feel free to join our reading group and contribute your own thoughts (on Twitter, on a blog, heck, even face-to-face if you have someone to talk to in your own building).