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Building a Rigorous Math Classroom: Strategies for Success

DOK depth of knowledge, what is it, why is it useful?

on 12 December 2014

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Transcript of Building a Rigorous Math Classroom: Strategies for Success

What's The Depth?
Jamie Marantz
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
Why is Depth of Knowledge (DoK) Important?
Define cognitive rigor on your note guide.
Discuss with your group.
Develop one

and one
Share with your partner:

What makes your question

Difficulty is about how many
students answer a question

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

The complexity of the mental processing students must perform


how deeply they have to know the content to complete the task.
DoK is about
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
How DO They Compare?
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.
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.
Compare and Contrast Activity
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!
the data provided
What comes after
the verb determines 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:
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.


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
Juwen Lam
Celine Liu
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?"
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
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
Full transcript