CRA Mathematics

ARIN IU is pleased to offer a Concrete-Representational-Abstract Instructional Sequence (CRA) training. CRA is an intervention for mathematics instruction that research suggests can enhance the mathematics performance of students in a classroom. The CRA instructional sequence/approach provides a graduated, conceptually supported line of work to create meaningful connections among concrete, representational, and abstract levels of understanding. The CRA sequence of instruction provides the framework for meeting the goals outlined by the National Mathematics Advisory Council and the requirements of the Pennsylvania Academic Standards.

The CRA sequence of instruction is for all grade levels, not just the primary grades. The addition/subtraction and multiplication/division strategies can be used to introduce basic arithmetic concepts to students in younger grades and help them develop algorithms for more complex calculations. Older students can also benefit from use of CRA strategies to bridge skill deficits, and increase their procedural fluency, strategic competence, and productive disposition. The fractions CRA strategy can be used to introduce concepts of fractions in earlier grades. It can also be used with students in middle and high school for more complex problems involving proportions and rational numbers. Likewise, the integers and equations CRA strategies can be used to introduce concepts of solving for unknown values during core instruction and during interventions to fill gaps and increase conceptual understanding.

The “doing” stage uses concrete objects to model problems. In the concrete stage, the teacher begins instruction by modeling each mathematical concept with concrete materials (e.g. red and yellow chips, cubes, base ten blocks, pattern blocks, fraction bars, geometric figures).

The “seeing” stage uses representations of the objects to model problems. In this stage, the teacher transforms the concrete model into a representational (semiconcrete) level, which may involve drawing pictures; using circles, dots, and tallies; or, using stamps to imprint pictures

for counting.

The “symbolic” stage uses abstract symbols to model problems. At this stage, the teacher models the mathematical concept at a symbolic level, using numbers, notation, and mathematical symbols to represent the number algorithm. The teacher uses operation symbols (+, × ,÷, –) to indicate addition, subtraction, multiplication, or division.

CRA may be implemented at all grade levels individually, in small groups, or for the entire class. It can be used with children at the elementary or secondary level. When using CRA, the teacher is able to provide multiple opportunities for practice and demonstration helping students achieve mastery of the mathematical concept.

Concrete manipulatives such as algebra tiles, cups, sticks, or base ten blocks can be used in the CRA sequence. The teacher should use the manipulative and movements that match the conceptual understanding behind the algorithm. In addition, there are many free, virtual manipulative applications available for use.

Manipulatives will be provided for you during the training.

WHEN

Monday March 14 & Tuesday March 15, 2022

8AM - 3PM

WHERE

ARIN Central Office

2895 West Pike Rd

Indiana, PA 15701

MORE INFORMATION

The cost for participation is $5 per participant; lunch will be on your own

Click the link to register: http://www.solutionwhere.com/arin/cw/main.asp