1. Rigor and Critical Thinking
Adding Higher Level Thinking Skills to Your Curriculum
Prepared by Peggy Ellison

2. The Definition
Rigor is the goal of helping students develop the capacity of understanding content that is complex, ambiguous, provocative, and personally or emotionally challenging. (Source: Teaching What Matters Most: Standards and Strategies for Raising Student Achievement by Strong, Silver, and Perini, ASCD, 2001)
It has real life implications.

3. Rigor
Complexity: To what extent is the curriculum organized around complex, interrelated concepts?
Emotional Engagement: To what extent does the curriculum arouse strong feelings?
Provocativeness: To what extent is the curriculum concerned with central problems in the discipline that challenge students' previous concepts? 3

4. Rigor Not difficulty but complexity
Improves students’ ability to understand complex concepts
Ability to synthesize and evaluate information to apply to new situations
Not difficulty but complexity

5. Rigor
Ambiguity: To what extent does the curriculum focus on symbols and images packed with multiple meanings? 5

6. All teachers should have a copy.
Let teachers know the students will have a copy too…provided by the district. 6

7. The Tool
The RigorMeter is a tool that is used to ensure that students are exposed to complex performance tasks.
The rigor meter is a fusion of the theory-based best practices of Bloom’s Revised Taxonomy (RT) and the Depths of Knowledge (D.O.K.).
The rigor meter facilitates the movement of knowledge from fragile to deep understanding.

8. Why do we need rigor? Rigor moves us from fragile to deep knowledge
Fragile knowledge –
- Inert knowledge: Student remembers for testing, but does not remember outside of class.
- Naïve knowledge: Simple explanations
- Ritual knowledge: Routines that work well in class but not real world
Deep knowledge – a true understanding of concepts and knowledge. The student processes the information. They can explain, apply, compare and contrast, generalize, justify, and give examples.
Perkins (1993)

9. Moving the Standard from Fragile to Deep Knowledge
Level 1 – Remembering – provides the basis for the study of various subjects by identifying facts (recognizing, listening, describing, retrieving, naming, and finding).
Level 2 – Understanding – Explains ideas and concepts (interpreting, summarizing, paraphrasing, classifying and clarifying).
Level 3 – Application – Uses information from another familiar situation (implementing, carrying out, using, and executing).
Level 4 – Analysis – breaking information into parts to explore understanding and relationships (comparing, organizing, deconstructing, interrogating, finding).
Level 5 – Evaluation – Justify a decision or course of action (checking hypothesizing, critiquing, experimenting judging).
Level 6 – Creation – Generating new ideas, products, or ways of viewing things (designing, constructing, producing, planning, and inventing).

10. How do we tell when a student has moved beyond fragile knowledge to deeper levels of understanding?
We analyze their performances for understanding.
We listen to what they say.
We examine the assignments they complete.
We expect they will be able to explain, give examples, and successfully apply what they have learned in new contexts.

11. Rigor is Not…
fifty math problems for homework when fewer will achieve mastery
more worksheets for the student who finished the assignment early
using a seventh grade text book with your high performing sixth grade students
covering more material in a shorter period of time
cold or impersonal
for a select group of students.

12. Why is Rigor Important?
Rigor is meant to improve students’ ability to understand complex concepts, but sometimes is misunderstood to mean students should work with difficult concepts.
Sometimes even the most difficult of subjects is not also a rigorous lesson. When teachers take some time to analyze their current lessons for rigor they can find where it is already present and where it might be added.
Tammy Andrew (2009)
Rigorous content demands attention, thought, and critical thinking
Rigorous content helps us handle uncertainty-simple texts make concepts seem simple and can mask complexities and interrelationships; rigorous content challenges us to deal directly with uncertainty and to search out nuance and interrelationships
Rigorous content increases flexibility in thinking –helps us build schema that is broad, flexible, and adaptable to multiple contexts
Rigorous content rewards effort and helps us develop perseverance, intellectual modesty and tolerance of others’ views
Rigorous content creates self-confidence because we know the task will be difficult, but with effort, we will be able to accomplish our goals 12

13. What is happening in the average classroom?
Behaviors
Percentage
Evidence of clear learning goals/objectives 4%
Worksheets
52%
Lecture
31%
Monitoring with no feedback
22%
Use of high yield research based instructional strategies 2%
Communication rich environments with writing and rubrics
Fewer than half the students engaged
82%
Bell to bell learning
Less than 1%
In an extensive research study conducted by Learning 24/7, 2004 of 1,500 classrooms here is what was observed:
Learning 24/7 Classroom Observation Project, 2004, Direct Observation of 1,500 K-12 Classrooms
Learning 24/7 Classroom Observation Project, 2004, Direct Observation of 1,500 K-12 Classrooms 13

14. How do we get there?
Think and plan with critical thinking and rigor in mind
Question students using DOK (Depth of Knowledge)
Pair skills from Level 2 (needed for CRCT) with Levels 3 and 4 tasks for extension – this will help students retain information if it is applied and used at higher levels
Assess students to determine present levels and compare results to the curriculum
Differentiate instruction based on student needs
Compact some of the curriculum and add tasks and assignments where needed
Use scaffolding only as needed to move students

15. CCPS Rigormeter
“Marries” Revised Bloom’s Taxonomy and DOK

16. Comparing Blooms and DOK
Knowledge/Remembering
The recall of specifics and universals, involving little more than bringing to mind the appropriate material”
Comprehension/ Understanding
Ability to process knowledge on a low level such that the knowledge can be reproduced or communicated without a verbatim repetition.
Application/applying
The use of abstractions in concrete situations
Analysis/ Analyzing
The breakdown of a situation into its component parts
Synthesis and Evaluation/ Evaluating and Creating
Putting together elements & parts to form a whole, then making value judgments about the method.
Recall – recall of a fact, information
Skill/Concept – use of information, conceptual knowledge, procedures, two or more steps, etc.
Strategic Thinking – developing a plan or sequence of steps, requires reasoning, more complex, more than one possible answer.
Extended Thinking – investigation (research) and thinking about the process and purpose and multiple conditions of the problem or task.

17. New way of thinking about Blooms with action verbs
Evaluation > Evaluating
Synthesis > Creating
Analysis > Analyzing
Application > Applying
Comprehension > Understanding
Knowledge > Remembering

18. What is DOK?
The degree of depth or complexity of knowledge reflected in the content standards and assessments - How deeply a student needs to understand the content for a given response/assessment.
You must think about what else you need to add to make a lesson deep.

19. Understanding DOK DOK is about intended outcome, not difficulty.
DOK is a reference to the complexity of mental processing that must occur to answer a question, perform a task, or generate a product.
We must understand that DOK is not about the difficulty of the objective, rather, it is about the intended outcome or the complexity of the mental processing that must occur in order to get to the intended outcome. Consider the example of adding This is easy. Students can do this by rote. It’s a DOK 1.
Increasing the difficulty of the problem by asking a student to add 4, ,530 does not increase the complexity. To solve this problem requires a child to recall the sequence of steps. The level of cognitive difficulty is still a DOK 1. It’s still recall. Knowing the rules of adding larger numbers - increasing the difficulty of the addition problem - does not affect the intended outcome. We still want the student to be able to add, just larger numbers. 19

20. Why is DOK Important
Mechanism to ensure that the intent of the standard and the level of student demonstration required by the standard matches the assessment items (required under NCLB)
Provides cognitive processing ceiling (highest level students can be assessed) for item development
Instruction, assignments, and classroom assessments must incorporate the expectation of rigor for students associated with the DOK levels of all standards and elements. 20

22. Novice Expert More sophisticated understanding
Expert vs. Novice Thinkers
Adding rigor to the curriculum moves students from:
Novice
Expert
Conversations
How much do cell phones cost?
More sophisticated understanding
What are some new trends in cell phones?
Why does thought matter? Look at Katie’s thinking. How do we as teachers modify assignments or instruction to get students to think as they learn? 22

23. Apply - Assessing Rigor
How can you implement this instructional tool in your classroom?
What are the barriers?
What are the opportunities?
What needs to be modified?
How do you analyze your curriculum to determine if it uses rigor? 23

24. Questioning
To teach students to think, you must first teach them to question.
Do you use questioning to help students develop independent thinking skills?
Do you use questioning to help students link difficult concepts?
Do your assessments contain questions that require open-ended responses?

25. Analyzing your assessments for rigor
Use your Rigormeter to assess quality of questioning
Do your questions contain the main ideas in the stem?
Do your questions or choices have distracters?
Does the format used for questioning allow opportunities for higher order thinking?

26. Why do we assess students?
Instruction – allows the teacher to determine how well students are learning and whether teaching and whether teaching strategies are working.
Formative – to provide feedback to students and teachers on learning and progress
Summative – to assign grades, or certify mastery at the end of instruction

27. Good Instruction Matters
The single greatest determinant of learning is NOT socioeconomic factors or funding levels - IT IS INSTRUCTION.
Mike Schmoker
Are these students novice or expert thinkers? What is your evidence? 27

28. Thought
The five key disciplines of thought: inquiry, knowledge acquisition, problem solving, communication, and reflection. Reflect on these disciplines as you view the video.
The Brownie Problem
The link has to opened and then you have to find the Brownie Problem on the right-hand side and click that link. The video will open in Quicktime.
Backdrop of the video: 4th grade class in a NY city public school. The video was shot in May The lesson is on fractions and is co-facilitated by the teacher and the instructional coach. The problem is who do you divide seven brownies among four friends. Teachers should review the viewing guide before watching and then jot down their thoughts afterwards. These answers/thoughts should be discussed afterwards. Once again, pose the question of what keeps us from doing this on a regular basis in our classes and in our schools. 28

29. Knowledge Acquisition
Measuring Thought
Problem Solving
To what extent do students concern themselves with pressing or problematic issues, using creative thinking to generate solutions?
[1 d2d3 d4 d]
To what extent are students encouraged to pose questions, form and test hypotheses, and use evidence and proof to substantiate their findings?
Inquiry
To what extent are students given the opportunity to speak, write, and elaborate on what they have learned?
Communication
To what extent does the curriculum engage students in acquiring and organizing information around concepts central to the topic?
Knowledge Acquisition
To what extent do students think about their own learning in order to find gaps and improve as learners and thinkers?
Reflection
DISCIPLINES OF THOUGHT
1. Knowledge acquisition-a few core ideas, graphic organizers, concept maps, variety of
experiences and media
2. Inquiry- use enduring questions, students pose questions and substantiate claims, build
research and evidence-gathering into instruction
3. Problem solving-students design easier/harder versions of problems, students discuss
problems/solutions, help students see difference between fist thoughts and second
thoughts
4. Communication- journals and logs to represent ideas/discoveries, note-taking,
representing thought, students compare ideas in pairs/small groups, whole class
discussions
5. Reflection-build units around criteria for growth, write criteria in student friendly
language, ask students to examine work at different stages. 29

30. Apply: Rigor – Questions to consider
Based on your understanding of rigor, why do you think rigor is so rare in schools today?
What are your experiences with rigor?
When do you find it challenging yet enjoyable?
When is it severe and painful?
Inform teachers that we will look at ways to assess rigor later. 30

31. Comparing Payment Plans
Activity: Answer the following question. Note your plan of attack. What are you thinking? Does this require rigorous thinking?
A video store charges $8 to rent a video game for five days. Membership to the video store is free. A video game club charges only $3 to rent a game for five days, but membership in the club is $50 per year. Compare the costs of the two rental plans. Justify your answer.
Ask participants for their definition of rigor after they complete the activity. Note the highlighted words. Ask participants why these are highlighted. 31

32. Sources
Teaching What Matters Most: Standards and Strategies for Raising Student Achievement (2001) by Strong, Silver, and Perini, ASCD
Hands On, Minds On Workshop, (2010) Clayton County Public Schools, Monique Drewry, presenter.
“Deep and Fragile Knowledge” is based upon the work of David Perkins. Perkins, David. Smart Schools. New York: Simon and Schuster, Retrieved from
Andrew, Tammie Identifying Rigor in the Curriculum: How to Determine if a Lesson Contains Rigor (2009) from
Webb, Norman, (1997) Depth of Knowledge Wheel from