Sunday, September 30, 2012

Facilitate Deeper Thinking with 
Open-Ended Math Problems

Costa and Kallick(2000) say that careful, intentional, and mindful questioning is one of the most powerful tools a skillful teacher possesses. Good questions are open-ended, whether in answer or approach. Open ended questions promote students’ mathematical thinking, understanding, and proficiency. By asking purposeful questions, dynamic learning environments can be created and students can make more sense of math.

One of my goals this year with my fifth grade students was to encourage deeper thinking in math. My reasoning was two-fold. First, with the the new Common Core State Standards, there is a greater emphasis on this. Second, I have a high population of students that are identified as being gifted in math. My students tend to always like to look for the quick or simple solution and they are used to solving problems very quickly, yet cannot explain or justify their reasoning. My colleagues and I have begun using open-ended questions to guide our instruction. 

These questions:
  • help our students make sense of math concepts.
  • encourage our students to find more than one way to solve problems or more than one answer.
  • empower students to unravel their misconceptions.
  • encourage students to make generalizations and connections along with requiring the application of facts and procedures.
  • lead to questions posed by students during their investigations that prompt deeper thinking. 

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