Exploring the Common Core Standards for Mathematical Practices
The Common Core State Standards for Mathematics (CCSSM) describe eight Standards for Mathematical Practice applicable to students of all grades. Different than the grade-specific Standards for Mathematical Content, these practices describe the habits of mind—the ways of thinking about math—that mathematicians and successful students use. In this course, participants will explore and unpack the eight math practices, learning what they mean and how they can be developed across all grades. Participants will read articles to deepen their understanding of the practices, watch videos to see how other teachers are fostering the practices in their curricula, listen to interviews with experts, and collaboratively develop ideas and strategies for developing the practices with students. Participants will create or rework a lesson to promote one or more of the mathematical practices in their classrooms that can be used now, regardless of whether or not the Standards for Mathematical Content are addressed.
Goals and Objectives
During this course, participants will learn skills and strategies to:
understand the math practices as habits of mind,
understand that the math practices are developed throughout all the grades,
gain strategies for developing a classroom culture that promotes and values this kind of thinking,
explore rich math tasks through the lens of promoting the practices,
identify evidence that students are using the practices in their work, and
gain a model for the structure and interrelatedness of the practices.
Create a lesson that promotes one or more practice.
This course provides professional development aligned to the CCSSM through readings, activities and classroom applications of teaching strategies. The CCSSM establish what students should know but not how teachers should teach. This course is designed to help teachers learn instructional strategies that guide students to reach these new challenging standards.
This course will help participants learn and apply the relevant CCSSM in their teaching. © 2012. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
This course is designed for mathematics teachers, curriculum specialists, professional development specialists, or other school personnel. Participants are expected to have regular access to computers and be proficient with using email and web browsers.
Session One: Looking at the Practice Standards
The developers of the CCSSM describe the Standards of Mathematical Practices as habits of mind that bring coherence to the topics described in the content standards. In this session, participants will review the eight practice standards. They’ll hear from one of the developers of the standards to gain some history about how they were developed and why they are important. Throughout the session, participants will think about how they can promote the practices with their existing curriculum.
Session Two: Overarching Habits of Mind
Bill McCallum, the lead writer of the CCSSM refers to Mathematical Practices 1 and 6 as, “overarching habits of mind of a productive mathematical thinker.” These practices describe problem solving, perseverance, and precision—things that students should be working on all the time. In this session, participants will examine these practices in greater depth. They will watch videos of students engaging with these practices and explore sample tasks and lessons they might use to help develop them. Participants will also interview students and share what they have learned about students’ mindset with the other participants.
Session Three: Reasoning and Explaining
The CCSSM asks for students to understand the “why” of mathematics, not just the “how.” Mathematical Practices 2 and 3 are the “reasoning and explaining” standards and they describe the practices of students engaged in reasoning, explaining, and defending their ideas, as well as critiquing the ideas of others. In this session, participants will unpack these math practices by reading more about them, watching videos of the practices in action, and exploring tasks that can help promote these habits of mind.
Session Four: Modeling and Using Tools
Mathematical Practices 4 and 5 discuss the importance of students of knowing how to use math to make sense of problems in context or in the world around them through the use of modeling with manipulatives and representations such as tables, diagrams, and graphs. As this practice is developed through K–12, students gain sophistication and flexibility in their understanding of not only what is being asked, but choosing the best tools to help them solve the problem. In this session, participants will explore these practices in greater depth by watching videos of the practices in action. They will learn about an instructional strategy and assessment tool that can be used to help students with modeling and use it to design a quick activity sketch of a lesson or unit in their curriculum.
Session Five: Seeing Structure and Generalizing
Of the eight Standards for Mathematical Practice, the language in Practices 7 and 8 —“look for and make sure of structure” and “look for repeated reasoning”—may be the least familiar. In this session, participants will explore what is meant by “structure” through worked examples in a video presentation. They’ll make sense of both practices by seeing them in action and explore tasks that they could use to help develop this kind of thinking in their students.
Session Six: Starting With the Practices
Phil Daro, one of the authors of the CCSSM has said, “There is no reason to wait on the mathematical practices—it is a good starting point." In this session, participants will think about and discuss what this statement means to them and how they want to approach implementing the Standards for Mathematical Practice in their classroom or school. Participants will also finish and submit their final projects to their facilitator.