Making Connections

How Is Mathematical Thinking Portrayed in the Common Core State Standards?

How familiar are you with the Common Core State Standards? Across the United States, states and school districts have implemented the Standards to varying degrees. Some of you may have been teaching with the Common Core Standards in mind for a few years now, and others of you may only be newly familiar with them. Access the Common Core State Standards official website and explore its components. In the Mathematics section, there are content standards listed by grade level, high school course, and mathematical domain (e.g., geometry, counting, or functions). Please spend a few minutes examining the Standards as listed by the grade level or content domain that interests you most. (Keep in mind that states that have or will be adopting the Core Standards make modifications to these areas.)

Within the Common Core Standards, the Standards for Mathematical Practice are often overlooked. The Common Core authors have developed a list of eight of these practices, which relate to the ways students should interact with mathematical content across grade levels and across content domains. We can think of these eight practices as the authors' description of what it means to think mathematically. Please read the Standards for Mathematical Practice.

As the introduction to the Standards for Mathematical Practice states, these Standards are descendants of earlier documents that addressed what it means to do mathematics and to think mathematically.  You may have heard of some of the documents: the National Council of Teachers of Mathematics (NCTM) Process Standards, published in 2000, and Adding It Up: Helping Children Learn Mathematics, published by the National Research Council in 2001. You will read more about these—and other authors' ways of describing mathematical thinking—in the readings for this lesson.

Let's begin by reading a selection from the book Smarter Than We Think: More Messages About Math, Teaching, and Learning in the 21st Century. It was written for educators, school administrators, parents, and anyone interested in K–12 math teaching. It was written by Cathy Seeley, a former president of the NCTM. Are you familiar with this organization? If not, you should be. It's the primary national professional organization for mathematics teachers. If you're not familiar with the Council, please spend a few minutes looking around the NCTM website. The organization offers membership packages for teachers, teachers in preparation, and schools. All of these packages offer benefits, such as access to online resources, web-based videos on a variety of professional development topics, and a subscription to one of the organization's magazines (Teaching Children Mathematics, Mathematics Teaching in the Middle School, or Mathematics Teacher). Whether or not you are or may consider becoming a member, it's important for you to be familiar with this important organization, which has done a lot to professionalize and advance the field of mathematics teaching.

Smarter Than We Think was written as a series of short "messages." For this lesson, you will be reading Message 31, which offers what I consider one of the best summaries of the Common Core Standards for Mathematical Practice. The piece connects the Common Core Standards to the NCTM Process Standards and the Five Strands of Mathematical Proficiency from Adding It Up.

As you read Message 31, note the terms and ideas you find most interesting and compelling. You should incorporate these into your concept map--one of your assignments for this course which you will work on at the beginning and the end of this course. (Please read the description of the Concept map assignment now by referring to its description on the Activities page) You will notice that Figure 31.1 on page 250 is a sort of concept map; you might use it to inform your own (but note that the author herself writes on page 251 that her personal graphic would be different from that one!).