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Common Core and Cognitively Guided Instruction in Mathematics

At Richmond Street School, we approach math instruction and math learning through the lens of Cognitively Guided Instruction (CGI). Cognitively Guided Instruction is:
  • An approach that positions students as sense-makers who actively participate in the learning process as they grow as mathematicians
  • An opportunity for teachers to pose a variety of tasks to engage students in problem solving, expecting students to author their own strategies and learn from each others' thinking
  • A way for teachers to use knowledge of children's problem solving strategies to plan instruction 
How Can I as a Parent Engage in Mathematical Dialogue with My Child?
Consider asking your child the following questions to engage in a dialogue around mathematics:
  • Probing
    • Can you tell me how you did that?
    • How did you figure that out?
    • Parents points to one part of the strategy (or child chooses) and ask child to tell you more about that.
  • Extending
    • Reflection: How do you know you got the right answers? Can you prove it?
    • Multiple Strategies: Can you think of another way to solve the problem?
    • Mathematical Representation: Ask your child to write an equation or number sentence that shows how she solved the problem.
 Our Changing Role as Parent Educators
Then Now
Check assignments only for accuracy. Focus on correct answers.  Ask your child to explain her thinking and reflect on the process of solving. Try to make connections to previously solved problems. 
Explain steps to child so they can replicate the procedure.  Pose a problem and let your child work through the problem before you intervene. 
Make sure child does many problems of the same problem type. Give fewer problems and encourage the use of multiple strategies.
Drilling students to memorize facts. Expect your child to explain her thinking, especially with new concepts. Students should develop conceptual understanding before procedural fluency. Realize that fluency is NOT synonymous with automaticity. 
More information about CGI can be found here: What is CGI
Common Core and Mathematics
This video by Dr. Jo Boaler, professor of mathematics at Stanford University, provides parents with research evidence on the reasons Common Core Mathematics is needed in the United States.  It addresses the tasks and questions used in mathematics classrooms, mindset, problem-solving, and advancement and tracking.
The CA Math Council's website has a link specifically for families: with resources that include "Math at Home" a downloadable PDF booklet.

Another excellent resource for parents by grade level are the "Parent Roadmaps to the Common Core Standards - Mathematics" from the Council on the Great City Schools.  These publications provide guidance to parents about what their child will be learning and how they can support that learning in each grade level K-8.  They also provide a three-year snapshot that shows how selected progress from year to year to prepare students to be "college and career ready" upon high school graduation.