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

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

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

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

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.

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)

Conceptual Flow

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.

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

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.

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)

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)

Conceptual Flow Example

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?

Connect Standards to the Conceptual Flow

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

Identifying Assessments

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.

Selecting the Concept for a Lesson

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?

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?

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