Saturday, September 28, 2013

What happens when I add this?

My preservice elementary teachers are just finishing up a unit on patterns. Coming into the unit, one thing some of them struggled doing was writing an explicit rule for a pattern reflecting linear growth. In my opinion, this represents a gap in experience not a lack of ability. Since all of them have had some background in Algebra, the question is what experience are they missing?

Coincidentally, a post by Dan Wekselgreene on Linear Patterns in Algebra 1 showed up in my Twitter feed this morning. (Thanks MTBoS!) It is a good example of immersing learners in different representations and supporting them in making connections that can result in deeper understanding of linear relationships. I had my students do something similar (see the example on the right) but for some it was not enough. There was still something missing. It is for this reason that I add one more representation (an idea I learned from literacy instruction) - a recount.

From Mooney's (2001) Text Forms and Features:
Recounts: Why? To give a sequential and detailed account of an incident, a series of incidents or a conversation
What? A written record of recall of events, with attention to sequence and accuracy, and often to detail
Doing a detailed account of each step provides learners with an added experience for seeing the structure of the linear pattern. A recount is demonstrated in the think-aloud provided below.

This seems to provide many of my learners with an experience that was lacking from previous math classes - a missing piece to the puzzle that bridges some cognitive gap. However, I am also aware that they have had experiences that the typical freshman in Algebra 1 might be lacking. What do you think, would adding a recount to your linear pattern unit help?

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