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Post date: Aug 29, 2017 8:56:56 PM
While the Common Core State Standards in mathematics has two sections, the Content section is the most familiar to educators. This is a list of facts, procedures, conventions, etc that students need to know and understand, organized by grade (K-8, & HS) and then topic. The build on each other, and address the mathematical content that is the result of mathematical thinking. But there is a second section -- The Standards for Mathematical Practice.
So why the separate section for the Standards for Mathematical Practice? It was an in an effort to clarify that these practices - the ways mathematically proficient people do math - are essential at all grade levels, and cut across all content topics. In fact, these practices being included in the CCSSM emphasize that the content is to be taught through the practices and to ensure the connections drawn between content and practice are genuine and integrated.
The Mathematical Practices, as they are also called, are the "essential mathematical habits of mind and action" and should be infused throughout the curriculum and pedagogy of mathematics in age-appropriate ways:
2) Reason abstractly and quantitatively
3) Construct viable arguments and critique the reasoning of others
4) Model with mathematics
5) Use appropriate tools strategically
6) Attend to precision
7) Look for and make use of structure
8) Look for and express regularity in repeated reasoning
Although listed as eight different and seemingly separate items, the mathematical practices are interconnected.
1) Make sense of problems and persevere in solving them
The image to the right showcases the relationships among the practices. Practices 1 and 6 are the overarching habits of mind in mathematical problem solving. Practices 2 and 3 are directed at reasoning and justifying, which are essential for constituting the validity of mathematical work. Practices 4 and 5 are important to prepare students to mathematics in their work, and finally practices 7 and 8 connect patterns and structure in math and calculations. These Mathematical Practices represent the thinking and skills necessary to develop and apply mathematics.
It may seem difficult at first to wave the mathematical practices into your curriculum content, but understanding their connections, and the part they play in math tasks helps tremendously. Also understanding how fundamental these practices are to rich tasks and problem solving gives way to the conviction that it is imperative for all students to develop these practices. Preparing students for our knowledge-based economy requires them to be able to approach a never-seen-before problem with confidence, explore the possible ways to solve it, have stamina to stick with it through multiple trials, then use various methods to communicate their thinking of the situation. Connecting, and crossing between, mathematics content and the Mathematical Practices will help transform math learning from insignificant memorization of facts and procedures to engagement with seeing and exploring math in the world around us. As we engage students in the Mathematical Practices, we prepare them for our ever-changing world.
Here are some resources to support your understanding and application of the Standards for Mathematical Practice in your classroom are linked below:
->Chart with descriptions of the Standards for Mathematical for each grade level:
Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade High School
->Classroom posters:
General - all 8 on one page & one per page By Grade Span (for age appropriate vocab & images) - K-1st 2nd-3rd 4th-5th 6th
This will the first of a series of blog posts dedicated to the Standards for Mathematical Practice. Each month I will dig deeper into one of the Mathematical Practices, and provide resources for you to watch, read, and learn more about what each practice looks like in application, why it is important, and how to measure student progress on the math practice. I will update this post to have links to each of the following posts in the series.
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