Procedural Fluency and Conceptual Understanding: Two Sides of the Same Coin

Procedural Fluency and Conceptual Understanding: Two Sides of the Same Coin

• Examine how Conceptual Understanding supports Procedural Skill & Fluency

• Explain the role of task sequences in building Procedural Skills & Fluency supported by Conceptual Understanding

• Discuss the pitfalls of learning with procedures disconnected from Conceptual Understanding

Schedule:

5 minutes –     Settle in, take attendance, Intro question: Think of a mathematical concept that you have struggled with in the past. Why do you think you might have struggled with this concept?

10-15 minutes –     Participants’ implementation share-out

3-5 minutes –     Transition into current module, connection between concepts: When teachers at your school talk about rigor, are they usually referring to more procedural skill and fluency or more conceptual understanding?  

10-20 minutes –     Workbook reflection: 

1. What might be some benefits of starting with conceptual understanding before developing procedural fluency? What might be some challenges?

2. Can you think of an example when using reasoning is more efficient than using the standard United States algorithm?

3. What connections do you see between the 8 standards of mathematical practice and conceptual and procedural understanding?

4. Were there any prompts in this section of the workbook that you wanted to discuss with the rest of the group? What about them were you looking to explore further?

20-30 minutes –     Application discussion prompts: 

1. Which aspect of procedural fluency (accuracy, efficiency, flexibility) do your students struggle with the most? How might you make connections to conceptual understanding to improve this aspect of their procedural fluency?

2. How might collaboration lead to deeper understanding of math concepts?

3. Think of a concept you have taught recently or plan to soon. What might be a sequence of 3-4 tasks to build conceptual understanding that supports procedural skill and fluency? How might your current instructional materials support this sequencing?

5-10 minutes -     Wrap up: Each individual brainstorms "What can you do between now and our next meeting to incorporate or emphasize this topic more in your classroom?" and a few participants volunteer for the next session’s implementation share-out