Chapter 5: Whole-Number Operations
Introduction
- NCTM Standards
- Definition of Proficiency
- Computational Fluency
- Conceptual Understanding
- Procedural Fluency
Conceptual Understanding
Conceptual Understanding
- Components of Conceptual Understanding
- Digit Computation
- Embedded Fluency
- Application
Instructional Considerations
Instructional Considerations
- Levels of Learning - such as CRA
- Manipulatives
- Connect Operations to Daily Experiences
- Consistent use of Vocabulary
- Concepts in Addition and Subtraction (Figure 5.2)
- Consistent Procedures at each Learning Level (Figure 5.3)
- Developmental Readiness
- Discussions and Opportunities for Verbal Reasoning
- Addition and Subtraction Problem Types (Figure 5.4)
Multiplication and Division
- Appropriate Readiness
- Multiplication: an efficient way of counting or adding equal-sized groups
- Division: (1) separating a given number of elements into equal-sized groups and (2) separating a given number into a certain number of groups
- Introduction through Concrete Materials and Pictorial Representations from their Real World
- Three Categories Identified from Research
- Types of Grouping Problems (Figure 5.6)
- Importance of Place Value
- Graduated CRA Sequence (Figure 5.7 through Figure 5.11)
- Summary of presented Information (p. 87)
Meeting Instructional Needs
Meeting
Instructional Needs
- Metacognitive Strategies
- Schema-Theory or Schema-Based Instruction
- Technology and CAI
- "Careful planning, teaching, and assessment of students' learning; strategic use of evidence-based instructional practices, including various cognitive and metacognitive strategies; and specific interventions" (p. 89)
- Incremental Rehearsal Delivery
- IES Practice Guide