The Common Core State Standards for Math actually include two types of standards: the content standards and the standards for mathematical practice. The content standards define the specific skills that are to be mastered at each grade level. For example, multiplication, division, and fractions are all content standards for 3rd grade. The standards for mathematical practice, however, outline how students go about doing the math. They are skills, based on the NCTM process standards, which students should utilize on a daily basis, regardless of the content being taught. In other words, they should be embedded into daily math instruction, rather than taught in isolation. Too often, however, teachers focus their attention and energy on the content standards and neglect the mathematical practices, resulting in students with only a surface-level understanding of the math they are doing.
So what are the standards for mathematical practices, and how can teachers go about incorporating them into their lessons? Let’s start by taking a look at the standards:
- Make Sense Of Problems And Persevere In Solving Them—understand the meaning of the problem, determine entry point, analyze information, plan a solution pathway, apply problem-solving strategies, check for reasonableness
- Reason Abstractly And Quantitatively—make sense of quantities and their relationships in problem situations, use different properties of operation and objects with flexibility, create a coherent representation of the problem at hand
- Construct Viable Arguments And Critique The Reasoning Of Others—justify conclusions, communicate them to others, and respond to the arguments of others
- Model With Mathematics—apply known mathematics to solve problems arising in everyday life, society, and the workplace
- Use Appropriate Tools Strategically—consider the available tools when solving a mathematical problem
- Attend To Precision—communicate precisely to others using clear definitions, meaning of symbols, and computational accuracy
- Look For And Make Use Of Structure—discern a pattern or structure
- Look For And Express Regularity In Repeated Reasoning—look for general methods and shortcuts, maintain oversight of a process while attending to details
Click here to grab a bookmark listing the mathematical practices and keep it with you while planning.
Now that we know what they look like, here’s my secret for embedding them into your instruction…talk less!! That’s right. You talk less, and let your students talk more. To increase the capacity of our young mathematicians, we need to deliberately plan ways for them to communicate, both orally and in writing, about the math they are doing. The “turn and talk” strategy is great for increasing student participation and engagement during a whole group lesson. Simply present an idea, or better yet ask a great question, and then have your students “turn and talk” to a partner. Routines like this one send the message that all students are expected to communicate their mathematical thinking, and it also gives students a safe forum for trying out new ideas. If you’re looking for visual aids on the Mathematical Practices for your classroom, check out my primary and intermediate poster sets.