Unit 4 Connecting Standards for Mathematical Practice to Content Produced under U.S. Department of Education Contract No. ED-VAE-13-C-0066, with StandardsWork, Inc. and Subcontractor, Reingold, Inc. December 2014 The Instructional Advances in Mathematics CCR Standards for Adult Education

The Three Key Advances Prompted by the CCR Standards 2 1.Focus: Focus strongly where the CCR Standards focus. 2.Coherence: Design learning around coherent progressions from level to level. 3.Rigor: Pursue conceptual understanding, procedural skill and fluency, and application—all with equal intensity.

Standards for Mathematical Practice MP.1Make sense of problems and persevere in solving them. MP.2Reason abstractly and quantitatively. MP.3Construct viable arguments and critique the reasoning of others. MP.4Model with mathematics. MP.5Use appropriate tools strategically. MP.6Attend to precision. MP.7Look for and make use of structure. MP.8Look for and express regularity in repeated reasoning. 3

Unit 4 Objectives Connecting Standards for Mathematical Practice to Content  Recognize the Standards for Mathematical Practice as important processes and proficiencies with long-standing importance in mathematics education.  Understand how to recognize opportunities for observing the Standards for Mathematical Practice in the requirements of both standards and lessons.  Develop an understanding of how to integrate the Standards for Mathematical Practice with content in lessons as a means to enrich student learning. 4

Rationale for the Standards for Mathematical Practice Relevance and Importance Based on the Research  The Standards for Mathematical Practice rest on “processes and proficiencies” with established significance in mathematics education (NCTM and NRC).  When Standards for Mathematical Practice are connected to content, deeper understanding can occur, enabling students to extend them to new situations (ACT National Curriculum Survey).  Attention to the Standards for Mathematical Practice shifts the emphasis from just “how to get the answer” to also “learning how to learn.” 5

Implications of the Standards for Mathematical Practice on Instruction  The Standards for Mathematical Practice are applied across all levels.  Not all Standards for Mathematical Practice are appropriate for every lesson.  Students need opportunities to experience all of the Standards for Mathematical Practice over the course of the unit or the level of study. 6

7 Now let’s do some hands-on work with the Standards for Mathematical Practice...

Materials (Part One)  Directions for Participants  Worksheet: Matching Standards for Mathematical Practice to Content Standards  Resource: CCR Standards for Mathematical Practice  Resource: CCR Standards for Adult Education 8

Directions (Part One) 1.Carefully read the CCR Level B content standard on the worksheet. 2.Imagine a lesson that targets the standard. Then follow these steps: –Use the code X to mark Standards for Mathematical Practice that are central to the lesson you envision. –Use the code O to mark Standards for Mathematical Practice that support the lesson you envision. –Leave blank any Standards for Mathematical Practice that are not relevant to the lesson you envision. 9

Directions (Continued) 3. Working first independently and then with a partner, evaluate the relevance of each Standard for Mathematical Practice to the requirements of the content standard listed. 4. Discuss individual decisions and rationales at your table, including how the different types of lessons imagined would affect the relevance of a particular Standard for Mathematical Practice. 10

Materials (Part Two)  Directions for Participants  Worksheet: Enriching a Mathematics Lesson  Resource: Math Lesson—Equivalent Fractions  Resource: CCR Standards for Mathematical Practice  Resource: CCR Standards for Adult Education 11

Directions (Part Two) 1.Scan the lesson and make notes about how the Standards for Mathematical Practice might be observed in the activities of the lesson. 2.Use codes X and O to mark the central and supporting Standards for Mathematical Practice. Leave blank any Standards for Mathematical Practice that are not relevant to the requirements of the lesson. 3.Discuss individual decisions and rationales at your table. 12

Reflections  What are some of the Standards for Mathematical Practice that you think are central to the lesson?  What are some of the Standards for Mathematical Practice that you think might serve in a supporting capacity to the lesson?  Why is it important to emphasize the Standards for Mathematical Practice at all levels of adult learning? 13

Next Steps  How has participating in this activity changed your thinking about the CCR Standards?  How will you use the information and understanding you have acquired to improve your teaching practice and student learning?  What additional training and tools would strengthen your ability to do so? 14