Karen Ford wrote a post entitled, "Ten Things Parents Should Know About the Common Core State Standards", that includes a basic definition, goals, and additional sources of information. Dialog with parents about the CCSS will look different depending on your school population. You may choose to include information on school web sites, create monthly podcasts, or sponsor information parent nights. What important items would you include on a '10 top things parents should know list'? What would you tell parents about the CCSS?
From a parent to another parent, I would promote the Common Core Standards because I can be sure that my child is learning the same important core concepts and skills as other kids their age across the US. We are a military family and move every couple of years. Now that there are Common Core Standards across the States, I can be reassured that my kids won’t have big gaps in their education when they move schools. For example, with the Common Core Standards the concept of multiplication is introduced in 2nd grade with skip counting and then taught more intensely in 3rd grade. I taught 5th grade and I had many students who didn’t know the times tables and didn’t fully understand the concept of multiplication. Now with the Common Core Standards I feel confident that my kids will have a good understanding of multiplication well before 5th grade regardless of where they go to school in the US.