The Common Core: Mathematics
The Common Core State Standards for Mathematics have been adopted by 45 states. (Learn more about Common Core implementation in your state.) The Standards are divided into two categories that intersect: the Standards for Mathematical Practice and the Standards for Mathematical Content. These Standards call for a shift from shallow coverage of a variety of topics to focused, coherent instruction in a continuous progression from grade to grade. The goal is to give students the time and support needed to grasp important mathematical concepts and solve complex problems.
The central theme of the Standards for Mathematics is a dual emphasis on mathematical fluency and deep understanding. These are not competing goals; rather, they mutually support each other.
The Standards require intense practice that becomes increasingly challenging as students progress from one grade to the next. This repeated practice is designed to help students develop the skills needed to carry out mathematical procedures accurately, efficiently and flexibly. From there, students can begin to recognize the patterns and structures underlying the operations they are performing.
As students practice solving problems and learn to move with ease between concrete situations and their symbolic representations, they will further improve their fluency in applying procedures appropriately. Students will become adept at choosing the correct tools to solve problems and explaining the basis for their decisions.
The Standards discourage mechanical approaches to mathematics that rely on mnemonics and other tricks. Students should not just get the right answer. They should know why an answer is right.
To facilitate students’ reasoning skills, have them check their work. Encourage them to get in the habit of asking, “Does my answer make sense? Why or why not?” This practice will help students develop strategic thinking and build math vocabulary. In later grades, students can build on a solid Math foundation to model real-world situations, construct arguments and critique others’ reasoning.
The ultimate goal of the Common Core’s focus on skills and understanding is to help students appreciate the usefulness of Math in navigating a range of real-world challenges. Students will begin to see the value of perseverance in solving problems and be confident in their ability to arrive at a satisfactory solution.
Two consortia, the Partnership for Assessment of Readiness for College and Career (PARCC) and Smarter Balanced, are creating computer-adaptive assessments that will be administered for the first time in the 2014-15 school year. The assessments will require students to understand mathematical concepts and solve problems according to their grade level. Students will also be asked to explain their reasoning.