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Monday, October 26, 2015

I Want to Understand: How Do You Teach Math Well?

I'm still mulling over the math debate at our PLC last week, a debate that frustrated me. It's not uncommon to have math debates in school since there are many ways to teach math well and there's limitless resources today when it comes to teaching math.

Our debate essentially arose from a discussion of when to teach decimals related to specific algorithms and problem solving. I tend to use the curriculum outline as a guide and embed the teaching of multiple concepts again and again while following the guide. I repeat concept, knowledge, and skill work often as I embed and connect new learning concepts and perspectives. Hence rather than teach decimals at one or two points throughout the year, I connect decimals to each unit regularly to a greater or lesser degree depending on student needs and interest as well as the content focus. I find that this repetition and multi-dimensional study of each concept helps students to gain understanding. Yet, as mentioned at the meeting, I recognize that you have to be cautious with regard to concept overload especially for those students who have difficulty integrating too many concepts at once. As I often say, teaching is a dance, and as a dance, you have to be conscious of each student's current understanding, readiness for learning, and academic need. It's not a one size fits all.

So as I continue to think, I reached out and posed a number of questions for my colleagues. I essentially asked the following:
  • Do we want too-tight programs that don't give us the ability to weave important concepts into the curriculum in multiple ways throughout the year as one way to make numerous connections?
  • How do we teach concepts? Do we embrace the notion of blended learning?
  • How are we embedding new tools while also using tried-and-true traditional tools to teach math well?
  • Where are we making time and space for the Standards of Mathematical Practice (SMPs)?
  • When we discuss math are we focused on the deep questions that matter or are we focused on rules and parameters more?
  • Do we rush the curriculum too  much, and by doing this do we negate the strength of deep project and problem base learning?
As I read a number of university students' blog posts, I was prompted to write this post. The university students quickly grasped the need for vocabulary development and math games as important elements of the math program yet many could not understand where coding fits in. That sent me on a quest as I intuitively know that coding is wonderful for math learning. My students who code understand math with much greater speed, depth, and efficiency. In a sense, their work with coding creates the brain paths possible to learn math well, and their coding experience has led to lots of joy, creativity, problem solving, and engagement with mathematical thinking. Hence, I see the positive impact that coding has on math daily. Yet when it came to explaining that to my university students, I struggled as I didn't have the language to do that. I found a number of articles that will help me make the connection this week, articles that basically support the notion that to code is to do math, and by doing math we ready ourselves for math learning and comprehension. If I find the time to complete Google's computational thinking course, I'll be able to explain this even better. 

In the meantime, if you have thoughts or perspectives on this rambling post, please let me know. What and how we teach continues to evolve, and that evolution will profit from our discussion and debate about what work and why it works when it comes to teaching and learning math well.

Addition: Coding Links I Plan to Share with University Students