Concrete and Visual Representation
by Hannah Johnson
1. Virtual Manipulatives
1.1. fall between the C and R; do not replace concrete, but great tool
1.2. Illuminations
1.3. National Library of Virtual Manipulatives
2. Suggestions
2.1. follow the continuum
2.2. explicitly link C, R, & A
2.3. manipulatives should be clear model of concept
2.4. have students represent concept multiple ways
2.5. have students translate among different representations
2.6. have students explain their thinking
2.7. gradually fade use of manipulatives
3. Representation Standard
3.1. create and use representations to organize, record, and communicate math ideas
3.2. select, apply, and translate among math representations to solve problems
3.3. use representations to model and interpret physical, social, and math phenomena
4. Research on CRA
4.1. benefits
4.1.1. increased motivation
4.1.2. more meaningful
4.1.3. increased understanding
4.2. explicit inquiry routine
4.2.1. Ss develop the model through guided questioning of the T
4.3. notes
4.3.1. Ss need to understand relationship between C and R
4.3.2. Ss with disabilities need 3 lessons at C level, and 3 at R level before moving to A
4.3.3. to progress from one level to another, Ss need 80% proficiency