The 2012-2013 school year was the first year for third grade to implement the Common Core Standards. Math instruction didn't change too much because the district had already implemented CGI Training for teachers.
What is CGI? CGI is Cognitively Guided Instruction (CGI) is a professional development program that increases teachers’ understanding of the knowledge that students bring to the math learning process and how they connect that knowledge with formal concepts and operations. Developed by education researchers Thomas Carpenter, Elizabeth Fennema, Penelope Peterson, Megan Loef Franke, and Linda Levi, CGI is guided by two major theses. The first is that children bring an intuitive knowledge of mathematics to school with them and that this knowledge should serve as the basis for developing formal mathematics instruction in primary school. This thesis leads to an emphasis on assessing the processes that students use to solve problems. The second thesis is that math instruction should be based on the relationship between computational skills and problem solving, which leads to an emphasis on problem solving in the classroom instead of the repetition of number facts (e.g., practicing the rules of addition and subtraction).
So basically the students are using previous knowledge, strategies, and manipulatives to solve problems and develop new strategies and understandings. What I love about this is seeing the kids really work hard to figure things out but what I don't like are the kids who really struggle without explicit instruction, they just sit or copy someone else's work and you cross your fingers that during the share time that they actually learn something from someone else explaining how they solved the problem.
So I try to incorporate both. I try to do a hands on problem at least 2 to 3 times a week. They can also be used as an assessment. Here are my Hands On Math Problems... each problem is tied to a common core standard. There are 38 total problems and you can find them here at my shop! :)