Kaitlyn has 6 boxes of pencils with the same number of pencils in each box. All together she has 24 pencils. How many pencils are in each box?
What was your strategy for solving this problem? Did you look for a key word/phrase? Did you skip over the story and go straight to the numbers to help you solve? If you answered "yes" to either or both of these questions, I want to explain why this approach causes problems for students in math. According to the research of Clement & Bernhard (2005), the key word strategy sends a terribly wrong message about doing mathematics. The most important approach to solving any contextual problem is to analyze it and make sense of it. What I have discovered is that the key word approach encourages students to ignore the meaning of the problem. When this happens students don't take the time to think about what's being presented in the story; instead they look for an easy way out of persevering through a problem based on the information presented.
If you are a teacher reading this post, please don't feel guilty because I did the same thing for many years when teaching my students how to solve word problems. I had posters with specific key words displayed on poster boards and I even encouraged students to use those posters as a reference when they needed to. I did it that way because that was the way my teachers taught me, it worked, and I would do the same for my students. Over the years as more research has surfaced and math programs have been revamped in a way that is now designed to provide opportunities to develop students conceptual understanding of mathematics. My philosophy has definitely shifted as well. Before leaving the classroom a few years ago, I really found myself enjoying teaching math lessons that allowed my students to find several ways of tackling problems.
Now as a Math Coach, I especially love listening to children's mathematical thinking. I also appreciate hearing them explain their approach to making meaning of numbers; this concept of math reasoning is part of what is known as Cognitively Guided Instruction (CGI). My challenge for you this week is to read the article in the Intentional Toolkit titled "What is CGI and what does it look like in a classroom?" This short article outlines some specifics of how this type of instruction transforms teaching and learning in the classroom. I'm also sharing an article titled "Key Word Strategy". This article list four ideas that teachers often overlook when introducing story problems to students.
As always, I hope you find this information useful, perhaps your school is currently using the CGI framework and if so, feel free to comment on its impact in your classroom. Until next time...go out there and be GREAT!
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