Rigor for Math Classrooms

2. Rigor for Math Classrooms Rigor has been in the front of most of our minds throughout the transition to the CCRS.  Come and think deeply about what rigor means for student expectations, activities, and assessments in the math classroom.  What does it look and sound like?  How can you plan for it effectively?  How can you work to raise it without leaving students behind?

3. Presenter Introduction: • Stephanie Darley • East Valley RttT Math Coach • Curriculum Coach at DHHS • Highly Qualified in Math, Spanish and English • Been with TLG for 6 years

4. This Session’s Goals: • Participants will develop a shared understanding of the concept of Cognitive Rigor. • Participants will apply Depth of Knowledge to instructional tasks, questions and assessments. • Participants with utilize the Hess Cognitive Rigor Matrix in designing unit and lesson plans.

5. Research Based Support for Today’s Session: • Bloom, B.S. (ed.) 1956. Taxonomy of educational objectives Handbook 1. The cognitive domain, New York: David McKay. • Karin K. Hess, Ed. D., Senior Associate Center for Assessment, Dover, NH khess@nceia.org • Presentation adapted from “Cognitive Rigor” by Amanda Bachler, PAHS • Students learn skills and acquire knowledge more readily when they can transfer their learning to new or more complex situations, a process more likely to occur once they have developed a deep understanding of content (National Research Council, 2001). • Learning is optimized when students are involved in activities the require complex thinking and the application of knowledge. Expert teachers know how to enhance both surface and deep learning of content (Hattie, 2002).

6. Do Now . . . • Take a minute to write your personal definition of “cognitive rigor” as it relates to instruction, learning and assessment. • Give an example of the most “rigorous” activity you have used or created. • Compare your definition and example with a shoulder partner.

7. Now let’s apply your rigor definition: Imagine your class is working on solving two-step equations and has the problem 2x+5=17. • What is a basic comprehension question you could ask? Share with your shoulder partner. • What is a more rigorous question you might ask? Share with your shoulder partner.

8. Developing the Cognitive Rigor Matrix There are different models to describe cognitive rigor. Each addresses something different. Blooms Taxonomy- What type of thinking (verbs) is needed to complete the task? Webb’s Depth of Knowledge- How deeply do you have to understand the content to successfully interact with it? How complex is the content?

9. Bloom’s (Revised) Review

10. https://vimeo.com/20998609 Webb’s Depth of Knowledge • DOK-1: Recall & Reproduction- Recall of a fact, term, principle, concept, or perform a routine procedure • DOK-2: Basic Application of Skills/Concepts - Use of information, conceptual knowledge, select appropriate procedures for a task, two or more steps with decision points along the way, routine problems, organize/ display data, interpret/use simple graphs • DOK-3: Strategic Thinking - Requires reasoning, developing a plan or sequence of steps to approach problem; requires some decision making and justification; abstract, complex, or non-routine; often more than one possible answer • DOK-4: Extended Thinking - An investigation or application to real world; requires time to research, problem solve, and process multiple conditions of the problem or task; non-routine manipulations, across disciplines/content areas/multiple sources

11. DOK is about complexity- not difficulty! • The intended student learning outcome determines the DOK level. What mental processing must occur? • Don’t rely on the verbs, it is what comes after the verb that is the best indicator of the rigor/DOK level.

12. DOK is about Complexity • Level 1 requires students to use simple skills or abilities. • Level 2 includes the engagement of some mental processing beyond recalling. • Level 3 requires some higher level mental processing like reasoning, planning, and using evidence. • Level 4 requires complex reasoning, planning, developing, and thinking over an extended period of time

13. Do Now (Revisited) . . . Using the CRM, review your “rigorous” activity from the Do Now with a partner. • Where would the activity fall on the CRM? • What other tasks might be developed and where would they fall on the CRM?

14. Math Tasks to Analyze • Working in your group, place each math task in the appropriate DOK quadrant. • Be prepared to justify your choice of DOK for each question.

15. The CR Matrix: Mathalicious “Pandemic”http://www.mathalicious.com/lesson/pandemic/ • With your shoulder partner, identify or create a task for each DOK level. • Be able to justify why each task belongs to the assigned DOK level. • Choose one task to share with the rest of the participants.

16. Some General Rules of Thumb . . . If there is only one correct answer, it is probably level DOK 1 or DOK 2 • DOK 1: you either know or you don’t • DOK 2 (conceptual): apply one concept, then make a decision before going on applying a second concept If more than one solution/approach, requiring evidence, it is DOK 3 or 4 • DOK 3: Must provide supporting evidence and reasoning (not just HOW solved, but WHY – explain reasoning) • DOK 4: all of “3” + use of multiple sources or texts

17. Quiz Time!! • From your computer, phone or tablet, log in to Socrative at m.socrative.com • Use room #118706 • Complete the DOK Quiz with a partner.

18. Thank You!!! • A session survey will be emailed to you this week through a Googledoc. Kindly complete it so we can reflect and improve future PD efforts. • Travel safely!