Concreteness Fading

Knowledge Refinement

Principle in Action

DreamBox Learning Math offers adaptive math program that integrates curriculum and continuous formative assessment. To help learners build a mathematical understanding of numbers, the learning program begins with highly concrete, manipulatable tools like the math rack, where students can physically see and interact with quantities through beads, providing a tangible foundation for number sense. As learners demonstrate mastery at this concrete level, the program gradually fades into more abstract representations of pure numbers.

DreamBox Learning Math

Practice counting to 13 using different bead combinations

Use beads to calculate and identify specific numbers like 8

Practice counting to 13 using different bead combinations

Discuss in your team

What are some concrete ways to represent your target concepts?

What are some abstract ways to represent your target concepts?

What are some ways of bridging the concrete and abstract representations?

How can you show the learners this bridging (visual instruction, text feedback, or other ways)?

Principle Definition

Start with concrete examples when introducing new concepts, then gradually replace them with more abstract representations. When explaining key concepts, use both abstract and concrete representations and highlight how they represent the same critical takeaways.

Concreteness Fading

Knowledge Refinement

Principle Definition

Start with concrete examples when introducing new concepts, then gradually replace them with more abstract representations. When explaining key concepts, use both abstract and concrete representations and highlight how they represent the same critical takeaways.

Relevant Principles

Relevant Principles

Principle in Action

DreamBox Learning Math

DreamBox Learning Math offers adaptive math program that integrates curriculum and continuous formative assessment. To help learners build a mathematical understanding of numbers, the learning program begins with highly concrete, manipulatable tools like the math rack, where students can physically see and interact with quantities through beads, providing a tangible foundation for number sense. As learners demonstrate mastery at this concrete level, the program gradually fades into more abstract representations of pure numbers.

Practice counting to 13 using different bead combinations

Use beads to calculate and identify specific numbers like 8

Discuss in your team

What are some concrete ways to represent your target concepts?

What are some abstract ways to represent your target concepts?

What are some ways of bridging the concrete and abstract representations?

How can you show the learners this bridging (visual instruction, text feedback, or other ways)?