**Difficulty**

http://tinyurl.com/DoKSurvey

Jamie Marantz

Director

Core Learning

December 2014

Building a Cognitively Rigorous Math Classroom:

Integrating the Common Core Into Secondary Math

1. I will be able to describe rigor in relation to Webb’s Depth of Knowledge framework.

2. I will be able to evaluate the rigor of assessment items or student tasks using Webb’s Depth of Knowledge (DoK) Levels.

3. I will be able to scaffold student success with high Depth of Knowledge problems and questioning strategies.

4. I will be able to scaffold students' cognitive rigor through the Mathematical Practices.

**Learning Targets**

http://padlet.com/acoecore/FUSD-Rigor

**Why is Depth of Knowledge (DoK) Important?**

**DO NOW**

Define cognitive rigor on your note guide.

Discuss with your group.

Develop one

‘Basic’

and one

‘Rigorous’

question

Share with your partner:

What makes your question

‘rigorous’,

or

‘basic’

?

Difficulty is about how many

students answer a question

correctly.

“How much is: 2 + 2?”

“How much is: 2,385,786.21 + 37,848.97?”

**DoK**

DoK refers

to-

The complexity of the mental processing students must perform

and

…

how deeply they have to know the content to complete the task.

DoK is about

COMPLEXITY

DoK-1 : Recall and Reproduction

DoK-2 : Skills & Concepts

DoK-3 : Strategic Thinking

DoK-4 : Extended Thinking

DoK Levels

Ingrid Roberson

Professional Expert Assessment

Transitioning to

Next Generation Assessments:

I will be able to assess the Depth of Knowledge required of individual questions.

I will be able to identify key differences between the California Standards Test (CST) and SBAC.

Learning Targets

TASK: Compare and contrast the CST and the SBAC

CST/SBAC

How DO They Compare?

1. CST REVIEW:

http://www.starsamplequestions.org

As a pair, select 4 CST questions across different strands

As a pair, reviews the first CST question together, assigning a Depth of Knowledge level and citing evidence for your answer.

Individually, review the 3 remaining CST questions

Now, share your results and reasoning with your partner.

CST/SBAC

Compare and Contrast Activity

Assessment DoK Analysis

I will be able to evaluate the rigor of assessment items or student tasks.

DoK and Transitioning to Next Generation Assessments

As a pair, select 3 Assessment questions across different domains.

As a pair, review the first assessment question together,

assign a Depth of Knowledge level, and cite your evidence.

Individually, review the 2 remaining Assessment questions.

Now, share your results and reasoning with your partner.

CST/SBAC

Compare and Contrast Activity

http://www.smarterbalanced.org

Increasing the Depth of Knowledge on Classroom Tasks

In your Grade Level group (2-3 people), select a question or task from an upcoming topic, lesson, or unit from your textbook/curricular materials at a Dok 1 or 2. Modify it to a higher DoK.

Document your work on Chart Paper:

Old Question/Task

Modified Question/Task

Old and New DoK--Convince Us!

Scaffolding Rigor for Students

DoK 1. Microwave a pizza.

DoK 2. Make mac & cheese from a recipe.

DoK 3. Make a dish from two recipes.

DoK 4. Craft a 3 course meal from what is in the fridge.

**What Are the DoK Levels?**

Examine your original RIGOR definition. Any changes?

Assign DoK Levels to the questions you made.

Now create a level 3 Question!

Share out!

Use

the data provided

or

What comes after

the verb determines DoK:

**VERBS**

**DoK**

DoK 1: Students will graph the point (1,6) in the first quadrant of the coordinate plane.

Adapted from a Prezi originally by:

Celine Liu

Math Specialist

**Cooking tasks examples:**

**Activity:**

1. Look at your slip.

2. Go to the corner you think it fits in.

3. Discuss with your corner. Prepare

to share.

4. Name your DoK level.

Write

Pair

Share

Examine the Math Practices Rubric. Where is Rigor embedded in the Practices? How could you use the MPs to support students' development towards increased Cognitive Rigor?

Discuss with a shoulder partner.

One Big Idea to share with the whole group.

Thank you for your participation! Please share feedback about today by going here:

and clicking on "Take the Survey."

Jim Town

jtown@acoe.org

Juwen Lam

juwenl@acoe.org

Celine Liu

cliu@acoe.org

DoK 2: Students will graph the vertices of the reflected image of a triangle.

DoK 3: Given the coordinates for three vertices of a rectangle, students will graph the coordinates of the fourth vertex.

DoK 4: Students will graph the vertices of a triangle onto positive coordinate planes using different scales and analyze what changes in the figure are affected by the changes in scales and explain why.

Scaffolding for Rigor

Which mix is more "orangey?"

http://tinyurl.com/corelearning

It should be noted that while the majority of the mathematics content knowledge as described by the Standards for Mathematical Content was rated at DOK Levels 1 and 2, it is not necessarily the case that assessment items would be developed at the same DOK levels. Developers of the summative assessment items/tasks may decide to require students to apply the Standards for Mathematical Practice in varied and complex ways, resulting in assessment items/tasks at DOK Levels 3 or 4.

--from Smarter Balanced CCSS Eligible Content, http://www.smarterbalanced.org/wordpress/wp-content/uploads/2011/12/Smarter-Balanced-CCSS-Eligible-Content-Final-Report.pdf

Depth of Knowledge and the Standards for Mathematical Practice

Increasing the Depth of Knowledge on Classroom Tasks

Open the task so there are multiple methods, pathways, representations

Add a visual component, ask students how they see mathematics

Include inquiry opportunities

Extend the task to make it lower floor, higher ceiling

Ask the students to convince and reason--be a lawyer

Ask the problem before teaching the method

-Dr. Jo Boaler, Professor of Math Education, Stanford Graduate School of Education

Presentation at CMC-North 2014

Fremont Unified School District

**Increasing the Depth of Knowledge on Classroom Tasks**

http://robertkaplinsky.com/why-does-depth-of-knowledge-matter

Sample group: 10/10 students answered both correctly

District (396 7th graders):

68.26% correctly answered circumference question

78.59% correctly answered area question

Sample group:

1/10 students earned 2 points with SBAC-like rubric

6/10 earned 1 point

District (396 7th graders):

12.12% earned 2 points