Start off by watching this video designed to explain why Common Core math problems look so weird.
The video does a good job at what it does but it is incomplete. The video gives attention to the fact there are a lot of ways and not just one right way to work a problem. It does acknowledge that students still need to learn the standard algorithms. The video does not provide additional information that would complete the story. Here are two pieces of information that aren’t considered.
One. The Common Core has a two year delay for the teaching of the standard algorithm for each operation. This means students are being taught and practicing other methods for two years before being taught the standard algorithm. It is not easy to get students to make the shift from an inefficient method they have used for two years to using the standard algorithm for that operation. The two year delay and other issues with the Common Core are addressed in a a document called Common Does Not Equal Excellent.
Two. The strategies promoted by the Common Core are not new. They have been taught to students for years as way to help them understand how things work. In the past, students were shown these methods and were moved on to using the standard algorithm rather than using and practicing inefficient strategies. A look at math text books from the 1950s and 1960s indicates that teaching for understanding was important and included. Barry Garelick often addresses this in his articles like The Myth About Traditional Math Education. In addition to having numerous articles and a couple of fun to read books, Barry blogs at Traditional Math.