Identifying Mathematics Levels of Cognitive Rigor (DOK)

Office of Curriculum , Instruction & Professional Development - Mathematics February 19, 2015

Module 9 K-12 Mathematics

Connector:You have three broomsticks:The RED broomstick is three feet longThe YELLOW broomstick is four feet longThe GREEN broomstick is six feet long1. How much longer is the GREEN broomstick

than the RED broomstick?

2. How much longer is the YELLOW broomstick than the RED broomstick?

3 feet twice as long/ 2 times as long

1 foot times as long

Source: http://tedcoe.com/math/wp-content/uploads/2013/10/broomsticks-for-nctm.doc

OutcomesUnderstand how the Hess’ Cognitive Rigor Matrix is used to guide increased cognitive demand through examining effective questioning and quality mathematical tasks.

Recognize and name ways in which the use of effective questioning supports Culturally Responsive instruction.

Norms

•Equity of Voice•Active Listening•Respect for All Perspectives•Safety and Confidentiality•Respectful Use of Technology

Today’s Focus:•Shifts Review

•Questioning for higher levels of complexity

•AzMERIT Math & DOK 1, 2 and 3

•Mathematical Tasks Analysis

Review 3 Key Math Shifts

1. Focus strongly where the Standards focus

2. Coherence: Think across grades, and link to major topics within grades

3. Rigor: In major topics, pursue with equal intensity: Procedural Skill & Fluency, Conceptual Understanding and Application.

Revisiting Math Talk Moves

Positive influences of Math Talk

•can reveal understanding and misunderstanding.

•supports robust learning by boosting memory.

•supports deeper reasoning.

•supports the development of social skills.

•supports language development AND is essential for quality writing in the math class.

Depth of Knowledge (DOK) - A Four Level System

Level 1 Recall

Level 2 Skill/Concept

Level 3 Strategic Thinking/Reasoning

Level 4 Extended Thinking/Reasoning

Lesson Transcript Task1) Choose Table 3 or Table 42) Read the transcript of the lesson (on the left).3) Then read the hypothetical scenario (on the

right).4) Discuss what you notice. You may consider…

• How does the level of DOK and Bloom affect the level of cognitive demand required of the student?

• How does the level of DOK and Bloom affect the amount of teacher and student talk?

• Why did the authors assign the levels to the questions?

A New Lens for our Standards for Mathematical Practice…

With a partner….

•Review the SMP Questioning handout.

•Find two questions that might have been appropriate for the lesson you examined. How would you classify the questions.

•How would you anticipate the question impacting student learning?

As defined by Geneva Gay, principles of culturally responsive teaching apply to mathematics (Gay, 2009 & 2010).

•Acknowledging cultural heritages•Bridging school, home, and sociocultural

realities•Variety of instructional strategies• Importance in all school subjects •All students can learn and deserve the

opportunity to do so 

Gay, G. (2009). Preparing culturally responsive mathematics teachers. In B. Greer, S. Mukhopadhyay, A. B. Powell & S. Nelson-Barber (Eds.), Culturally responsive mathematics education (pp. 189-205). New York & London: Routledge. Gay, G. (2010). Culturally responsive teaching: Theory, research and practice (2nd edition). New York: Teachers College Press.

Variety of Instructional Strategies: Effective QuestioningWalsh and Sattes (2005) point out that what educators likely intuitively sense:“Teachers, through quality questioning techniques, can transform typical mathematics classrooms into more student –centered, inquiry based classrooms in which students are thinking and reasoning at high levels.” Mathematics Teaching in the Middle School “A Tool for Rethinking Questioning” Vol. 20, No. 5 December2014/January 2015 NCTM Journal

How does effective questioning support Culturally Responsive teaching?

•Student-centered discourse

•Inclusive of student voices, experiences, prior knowledge

•Multiple perspectives shared

•Students are engaged and active participants

AzMERIT Arizona’s Measurement of Educational Readiness to Inform Teaching

On the ADE website, these are given on the Mathematics Assessment Blueprint:

Percentage of Points by Depth of

Knowledge LevelGrade DOK

Level 1DOK Level 2

DOK Level 3

3-11 10% - 20%

60% - 70%

12% - 30%

Grade Level task and analysis

You need: •a partner •Grade level sample task

1. Review the standard your task is aligned to.• Where does this standard fall on the

Cognitive Rigor Matrix?

2. Review the task. • What level would you categorize this

task? How would you justify your answer? What is the evidence?

3. How would you modify the task to increase the cognitive demand? Give two examples.

4. Construct a question that will help students have access to a high cognitive demand. (use your SMP handout)

Grade Level task and analysis

•Share with your table how you increased the cognitive demand of the task.

Based on your work analyzing a task….

Quick Write:

Complete the sentence and write two more sentences to explain.

•As I think about using the Hess’ Cognitive Rigor Matrix to increase cognitive demand …

•Planning effective questions and quality tasks will impact student learning…..

Culturally Responsive

Bibliography• Mathematics Teaching in the Middle School “A Tool for

Rethinking Teachers’ Questioning” , by A. Simpson, Vol. 20, No. 5 December2014/January 2015. NCTM Journal

• Cotton, Kathleen. "Classroom Questioning." (n.d.): n. pag. Web.

• Walsh and Sattes (2005) “Quality Questioning: Research-Based Practice to Engage Every Learner”, Thousand Oaks, CA, Corwin Press.

• Schuster, L., & Anderson, N. (2005). Good questions for math teaching why ask them and what to ask, grades 5-8. Sausalito, CA: Math Solutions Publications.

• Sullivan, P., & Lilburn, P. (2005). Good Questions for math and teaching: Why ask them and what to ask Grades K-6. Sausalito, CA: Math Solutions.