1. Building a Conceptual Flow
Coherence, Rigor, and Focus for
Units of Instruction
Kathy DiRanna
NEA Teacher Ambassador Training
San Francisco
February 21, 2014

2. Session Outcomes
Experience the development of a conceptual flow to align with CCSS―Mathematics
Understand the value of a conceptual flow as a guide for: planning instruction, assessment points, and evaluating instructional materials

3. New Opportunities for All Learners
Common Core State Standards (ELA and Mathematics)
Next Generation Science Standards
21st-Century Skills

4. How People Learn Prior knowledge Conceptual frameworks Metacognition
(Bransford et al., 2000)

5. Conceptual Flow and How People Learn (Key Finding #2)
To develop competence in an area of inquiry, students must:
 have a deep foundation of factual knowledge,
understand facts and ideas in the context of a conceptual framework, and
organize knowledge in ways that facilitate retrieval and application.

6. Conceptual Flow Basics
Details the important concepts
Identifies an instructional sequence
Identifies important concepts for assessment of student understanding
Serves as a tool for evaluation of instructional materials
(DiRanna, Osmundson, Topps, Gerhardt, Barakos, Cerwin, Carnahan, Strang, 2008)

7. Conceptual Flow

8. Steps to Create a Conceptual Flow Overview
Individual pre-think to “what should a student know?” prompt; transfer ideas to sticky-notes.
Collaborative pre-think: share with your team and determine one “sticky- notes flow.”
Read the instructional materials and note the concepts for the IM conceptual flow.
Match collaborative pre-think to concepts addressed in the instructional materials.
Align concepts from the collaborative pre-think and instructional materials to content standards.
Review progression of concepts and place them in an instructional sequence with the strongest possible links for student understanding.
Flag assessments.

9. Quick Write Prompt
What should an exiting (middle school) student know about (ratios and proportions)?

10. CONCEPTS
Facts or definitions are pieces of information. The focus is on verifiable and discrete details.
In teaching, facts are often presented without making connections to the big ideas in mathematics.
Concepts are overarching ideas that clearly show the relationships between facts. They are frequently abstract.
In teaching, concepts are often presented with connections to the real world and to the big ideas of mathematics.

11. Create a Conceptual Flow
Pre-think:
Answer the prompt in a paragraph
Use complete sentences
No behavioral objectives
No questions
Transfer ideas to appropriate-size sticky-notes (biggest idea on large sticky-note; medium idea on medium note; facts, algorithms on small notes)

12. Create a Conceptual Flow
Collaborative pre-think:
Play “sticky-note” game with colleagues
Begin with largest idea
Build from there
Negotiate size of idea
Determine instructional sequence (conceptual flow)

13. Conceptual Flow Example

14. Match to Standards
Where are the standards on your conceptual flow? Write the standard on an orange sticky- note and post on the flow where you find a match.
Are there standards that are not in your flow? Should they be? Add if appropriate.
Where would you place the standards for mathematical practice?

16. Connect Standards to the Conceptual Flow

17. Assessment Check Review your conceptual flow
Identify where you would put assessments
Place a flag at a point where you think you would need to know what students understand before moving on in their study

18. Identifying Assessments

19. Conceptual Flow in Instructional Materials
Conduct an individual pre-think of the important concepts a student should know about a big idea.
Create a collaborative pre-think from the individual pre- thinks.
Read and identify the conceptual flow in the instructional materials. Write the concepts facts on appropriate-size sticky notes.
Match collaborative pre-think to concepts addressed in the instructional materials and align with content standards.
Review progression of concepts and place them in an instructional sequence with the strongest possible links for student understanding.

20. Selecting the Concept for a Lesson

21. Reflection
How did using the conceptual flow protocol make you think differently about the instructional flow of a unit?
What ahs did you have about your instructional materials after building a conceptual flow?
To what extent did developing a conceptual flow help you gain a deeper understanding of the breadth and depth of the CCSS and what is meant by making progress toward college and career readiness?
Are the materials sufficient? Do they need to be augmented? How can you use the mathematical practices to make the content stronger?

22. Working with Others
What additional support do you need to replicate this process for another unit of instruction?
To replicate this process with other teachers?

23. Find Out More Smarter Balanced can be found online at:
SmarterBalanced.org