Summary:

Deliberate practice is crucial for developing mental representations and providing opportunities for students to struggle. Mental representations, supported by neuroscience, are enhanced through visual and physical mathematical representations. Techniques like "groupitizing" and finger perception are strong predictors of future math achievement, even more so than early test scores. 

It's vital for students to experience numbers in various ways, such as visually, physically, and playfully. For example, asking students to design a foot parade for addition or using area models for multiplication fosters engagement and understanding. Teaching algorithms too early can hinder students' ability to think flexibly, a phenomenon known as cognitive interference. Starting lessons with visual prompts encourages diverse ideas and open discussions, promoting a more inclusive and dynamic learning environment.

Key Math-ish Principle(s): 

Utilizing a visual and physical approach to math.

The importance of connected and flexible knowledge.

Key Ideas/Themes:

• Deliberate Practice and Mental Representations: Deliberate practice is crucial for developing mental representations and encouraging students to struggle, which enhances learning. Neuroscience supports the importance of mental representations in understanding mathematics.
  
  

• Visual and Physical Representations: Student learning is significantly enhanced by visual and physical representations of mathematics. Techniques like "groupitizing" and using finger perception as predictors of math achievement highlight the importance of these methods.
  
  

• Diverse and Playful Approaches to Mathematics: It is essential for students to experience numbers in various ways, including visually, physically, and playfully. Examples include creating a foot parade for addition and using area models for multiplication, which foster deeper engagement and understanding.
  
  

• Impact of Algorithmic Teaching on Sense-Making: Teaching algorithms too early can hinder students' ability to think flexibly, known as cognitive interference. Encouraging diverse perspectives through visual invitations at the start of lessons promotes open discussions and a dynamic learning environment.

Reflection Questions:

After reading this chapter reflect on the following questions. Think about:

1. What makes sense? 

2. What can you apply in the classroom right now? 

3. What do you still need help with?