This is a gradual instructional sequence that moves students fluidly between three phases of learning.
C = Students use concrete manipulatives to model and solve problems.
R = Students use pictorial representations to model and solve problems.
A = Students use abstract numbers and symbols to model and solve problems.
Explicit Instruction: The instructional approach includes clear modeling, thinking aloud during instruction, presentation of multiple examples, and immediate, corrective feedback.
Verbalizing Thinking: The tutor/teacher teaches the material to the student and then the student teaches the material back to them. During this guided practice opportunity teachers are able to hear the verbal thinking of students allowing for immediate feedback when necessary. This verbalization helps to anchor skills (Jayanthi, Gersten, & Baker, 2008).
Multiple Strategy Use: The student learns multiple ways to approach and solve problems. In addition, to reinforcing traditional methods of multiplication, division, and fraction it also teaches alternate procedures using concrete, representational, and abstract examples.
Progress Monitoring: The materials provide opportunities for teachers to collect data daily as well as at the beginning and end of each unit.
Self-Monitoring Academic Content: At the end of each page within the Perceptions Math materials are red, yellow, and green lights. If students feel confident with the content and are ready to continue they color in the green light, if they need clarification or extra practice they color in the yellow light, and if they need to stop and go over the material a second time they color in red.