Unit 4Connecting Standards for

Mathematical Practice to Content

Produced under U.S. Department of EducationContract No. ED-VAE-13-C-0066, with StandardsWork, Inc. and

Subcontractor, Reingold, Inc.

December 2014

The InstructionalAdvances in

MathematicsCCR Standards for Adult Education

2

The Three Key Advances Prompted by the CCR Standards

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.

3

Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regularity in repeated reasoning.

4

Unit 4 ObjectivesConnecting 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.

5

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.”

6

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.

7

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

8

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

9

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.

10

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.

11

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

12

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.

13

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?

14

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?