The 8 Standards for Mathematical Practice in the Common Core State

StandardsPart 2

Workshop created by:June Apaza

Vicki Kapust

Outcomes Participants will:1.Develop a deeper understanding of what it means to integrate the 8 Standards for Mathematical Practice into your classroom instruction in ways that develop these skills in your students.

1.Develop a deeper understanding of how the 8 Standards for Mathematical Practice will be assessed along with the Content Standards.

Overview Statement

The Common Core State Standards have two distinct, but totally interdependent parts: The CC Content Standards and the CC Practice Standards.

Teachers will not be successful unless they thoroughly understand both and are able to integrate them into their classroom practice. As the CCSSM document states, “These Standards are not intended to be a new names for old ways of doing business…” (CCSSM, page 5)

Standards for Mathematical Practice

Assessment and the Common Core Content &

Practice Standards

What types of evidence will students have to demonstrate to show they’ve mastered both the content and practice standards?

What types of test questions will be developed to gather this evidence?

SMARTER Balanced released a draft document outlining the content specifications that are intended to ensure that the assessment system accurately assesses the full range of the standards (including the Practice Standards).

Assessments are scheduled for full implementation in 2014.

(Field test questions are scheduled for 2013, however)

Include a variety of question types: • selected response, • short constructed response,• extended constructed response, • technology enhanced, and • performance tasks

Assessing Levels of Expertise

Level 1: Demonstrating basic procedural skills AND conceptual understanding.

Level 2: Assessing knowledge in a context where their work on complex tasks is scaffolded.

Level 3: Unscaffolded situations that call on substantial chains of reasoning.

Sample Selected Response Tasks (Level 1)

Claim #1—Conceptual Understanding and Procedural Fluency

Fraction example:

Sample Selected Response Tasks (Level 1)Claim #1—Conceptual Understanding and Procedural Fluency

Base 10 example:

Sample Selected Response Tasks (Level 1)Claim #1—Conceptual Understanding and Procedural Fluency

Integer example:

Sample Selected Response Tasks (Level 1)Claim #1—Conceptual Understanding and Procedural Fluency

HS Geometry example:

Constructed Response Task

Grade 8 example: Each day, Maria walks from home to school and then from school to home. The graphs that follow show the distance that Maria is from home at different times during the walk. Match the graphs to the descriptions of Maria’s walk shown to the right of the graphs. Next to each graph, enter the letter (A, B, C, D) of the description that best matches the graph.

Performance Task description

Performance Tasks (PT)—integrate knowledge and skills across multiple learning targets; measure capacities such as depth of understanding, research skills and/or complex analysis with relevant evidence; require student-initiated planning, management of information/data and ideas; reflect a real-world task and/or scenario-based problem; allow for multiple approaches, and so on.

Performance Tasks assess Claim #4—Modeling and Data Analysis. Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

Sample Performance Tasks—Elementary, MS, HS

Choose your grade-level task and work on the problem by yourself for about 10-15 minutes. You will not have time to complete all parts of the task. Spend enough time that you have a general understanding of what is expected. Read suggested solutions. Elementary: Grocery Store MS: Designing a Park HS: Photo Book

The cover page for your PT lists the Practice Standards being assessed in that task. Find and record the specific components of the task that assess each Practice Standard listed.

(Refer to the handout: CC Standards for Mathematical Practice—grouped into 4 categories)

If time permits, discuss your solutions, explanations, and impressions of the task with others who worked on the same problem as you did.

Sample Performance Tasks (continued)SMALL GROUP WORK

Smarter Balanced assessment tasks are designed to assess both the Content Standards AND the Practice Standards.

What actions will you need to take to prepare your students to be proficient knowing that they will be faced with similar assessment tasks? Fill out the “Teachers” column of the handout CC Standards for Mathematical Practice.

Small group discussion of your assigned category. Prepare a chart paper poster of your groups’ ideas.

Find the Reflections for the Day handout in your packet.

Complete Reflection #1: Choose some “teacher actions” that describe a change in your classroom practice. How will you implement those changes?

Web site for Smarter Balanced Assessment

Consortium:

http://www.SmarterBalanced.org

The Role of Classroom Discourse in supporting the

Common Core State Standards for Mathematical Practice

Where do you see classroom discourse in the 8 Standards for Mathematical Practice? Look for examples on all the posters and “Teacher Actions” handout that refer to anything related to classroom discourse.

High-leverage practices that impact student achievement:•Managing whole group discourse equitably and in support of all students’ learning

– Allocating turns to speak– Supporting practices of listening and speaking– Using strategies that promote participation by everyone in the

group •Establishing norms and routines for classroom discourse and work that are central to content •Setting up and managing small group work •Implementing organizational routines, procedures, and strategies to support a respectful and equitable learning environment •Designing and posing questions for specific instructional purposes •Making content (e.g. specific problems, ideas, processes) explicit through explanation, modeling, representations, and examples •Recognizing particular common patterns of student thinking and development in a specific domain (e.g. place value) •Differentiating without losing the cognitive demand of the task 

Adapted from Deborah Loewenberg Ball, University of Michigan, Teaching Words Presentation

 

The Role of Discourse in the Math Classroom

Write a paragraph or two about your personal experiences facilitating classroom discussions around mathematics. Share with one other person.

 

The Role of Discourse in the Math Classroom

Individually: Fill out both sections on the handout, Productive Discourse in the Math Classroom.

Small group:Share your ideas with others in your small group.

• When you are finished sharing, read Five Reasons Talk is Critical to Teaching and Learning and discuss as directed.

 

Math-Talk Levels Tool: Action Trajectories for Teacher and Student

Individually:

Do a quick ranking of yourself and your students using the tool (all four categories).

You do not have to share this information.

 

Math-Talk Levels Tool:

Do the math activity, Catching up or not?• Quiet think time to work on tasks• Small group discussion of the tasks

 

Math-Talk Levels Tool: Watch the video with your group’s category in mind. Find examples in the video and take notes on the index card provided.

Small group discussion of your observations and rankings.

Discuss and record ideas for integrating discourse in your own classroom, thinking specifically about the category that was assigned to your group.

Large group share

Math-Talk Levels Tool:

Do the math activity, Cube Trains• Quiet think time to work on tasks• Small group discussion of the tasks

Watch the video clip; use the other side of your index card to take notes.

 

Math-Talk Levels Tool:

Complete #2 on your Reflections for the Day sheet: What will be your next steps for integrating discourse in your own classroom?

What does it mean to “do mathematics?”

What does it mean to “do mathematics?”

The Practice Standards are descriptions of the fundamental skills needed to “do” mathematics. It’s a differing view from our traditional view of mathematics: school mathematics vs. real mathematics.

The Content Standards are the “what” of mathematics; the Practice Standards describe what it means for students to demonstrate proficiency in mathematics. They are our new “basic skills.”

We must get past the idea of mathematics as a collection of algorithms, steps, or procedures. Just getting answers, although important, is not “doing mathematics.”

 

“Doing mathematics”

Using Modeling to Make Sense of Mathematical Procedures

• Modeling subtraction with Base 10 blocks302 − 178

“Doing mathematics”

Using Modeling to Make Sense of Mathematical Procedures:

The two meanings of division

Solve using cubes to represent the cans of juice.

1. The camp counselors have 56 cans of apple juice. They are packaged in four-packs. How many four-packs do they have?

Using Modeling to Make Sense of Mathematical Procedures:

The two meanings of division (continued)

Solve using cubes to represent the cans of juice.

2. The four camp counselors have 56 cans of apple juice. They are going to divide up the 56 cans of juice equally among their four groups. How many cans of juice will each counselor get?

“Doing mathematics” Modeling multiplication across the grades using an

array model

• Model 3 times 4 using Base 10 blocks in an array

• Model 15 times 23 using Base 10 blocks in an array. Match the model to the place value operations of the standard algorithm for multiplication.

• Model ¼ times ⅔ using an array model

• Model (2x + 3)(x + 4) using an array model

“Doing mathematics”

Modeling multiplication across the grades using an array model

Small groups:– Connect the Practice Standards to the work we did

modeling subtraction, division, and multiplication.

Math-Talk Levels Tool:

Complete #3 on your Reflections for the Day sheet:

How will the Practice Standards you identified in the last set of “doing math” activities help students understand mathematical concepts?

Discussion of instructional materials

What should you do if you have instructional materials that are not well aligned with the CCSSM and in particular the Standards for Mathematical Practice?

Summing Up

Complete Reflection #4:

As you consider the CC Practice Standards and their role in classroom instruction, what changes (first steps) do you see yourself implementing in your classroom and what will you keep basically the same?

What support and/or resources will you need? 

THANK YOU!