This graphic of a Koch Snowflake (thanks wikipedia) in some ways describes what has happened to me at Twitter Math Camp (#TMC14). I started out with just a few questions, but then those questions multiplied, and the new questions multiplied, and so on, until they all started to blur together. Similarly, Koch’s Snowflake starts simple, but then each replication makes the image more complex, until it finally brings you to that snowflakey image that everyone recognizes.
In my questions, unfortunately, it isn’t that simple. I wonder, do I need to let them replicate more, before I find that big question toward which they are building? I think I at least have a feel for where they are going. I started with questions about how to help struggling students, how to reach disengaged students, how to teach multiple levels in one class, how to use project based learning to get there, how to use standards based grading to report on that learning; unh, I’m out of breath. But in my mind I can almost see the convergence point, the place where all these questions merge into one big question. I can’t quite see the shape of it, but I know it’s there.
It is something to do with teaching multiple levels in essentially the same lesson. So that kids in basic math, pre-algebra, algebra I and algebra 2 are all interacting with the same lesson at the same time, but from a perspective that fits with their level of learning. The concept of multiple entry points resonate with this question, as do the multitude of rich problem based resources from the digital math community. So for now, it seems my snowflake is this: how do I make this structure happen?
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Number sense certainly seems to be at the forefront of many math teachers’ minds these days. I know we have talked about it in my math department (high school) several times, bemoaning its lack and wondering how best to remedy that lack. And it has popped up on twitter pretty regularly. The most recent reference came from Tracy Zager with this post.
My gut response was that this was simplification of the scope of difficulties that students have in math, but Tracy asked me to look at the whole article and see what I thought. Although I had homework, I couldn’t stay away from it. As I read through it, I thought of the students I have worked with and all the different ways they have struggled in math class. Most of my math students have been identified with disabilities. The rest fall into that category of having “difficulties” in math. For many of them, number sense was at the root of their problems. However, it was often accompanied by complicating factors.
Some students have processing issues. I recall a student who would close her eyes and just think. If you could wait long enough, she would provide a response that was usually on track, although she couldn’t articulate her thought process. Another student would work a problem correctly and explain her work clearly. Five minutes later, she would get totally lost on a similar problem. Last year I had a student who seemed to have great number sense, as well as a great understanding of how things work. However, as soon as I tried to move him to the abstract or to generalize, I lost him. For students like these, the difficulty is more than just poor number sense.
In the article, Nancy Jordan does acknowledge that not all difficulties in math result from poor number sense. However, her main focus is encouraging early screening and intervention, similar to the screenings that happen for reading. She references research that supports the importance of number sense, as well as her own research that shows number sense as an early indicator of math difficulties and disabilities. She also offers some specific tasks that might help develop number sense.
So to answer Tracy’s question…After reading this article, I do agree that early identification and intervention based on number sense screenings would likely lead to improved results. I want to read more; I want to see more research in this and related areas. Further research in this area would perhaps help isolate and identify other factors that later impact success in math. And I want to know what the research can tell me to help the students that I have who struggle in math.
Jordan, N. 2007. “The Need for Number Sense.” Educational Leadership 65(2):63-65.
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