Based Math Interventions - Concrete Representational Abstract
If you know anything about the alphabet
soup that special
education can sometimes be, then you've likely heard of
acronyms like RTI (response to intervention) and SRBI (scientific
research based interventions). What do these two acronyms mean
to school staff? Basically, that there needs to be a research
base to the interventions they use to help struggling
students. What this means to parents is that research based
interventions are likely being tried to help their children every
day. Speaking of research based interventions, or in this case
research based math
interventions, one that has shown some promise is the Concrete
Representational Abstract Approach.
Yep, that is a pretty scary name. But if you want to improve
fraction skills, algebra, place value, and more, the Concrete
Representational Abstract Approach is one you'll want to become
familiar with. So read on to find out what this math
intervention is, and what the research says about it.
What is the
Concrete Representational Abstract Approach?
The Concrete Representational Abstract Instructional Approach (CRA)
is a research based math intervention that is broken down into
stages by its name. These stages are:
Most that run in educational circles realize that multimodal
instruction can help students learn. In other words, adding
words to tactile representations or visuals (tactile, visual,
auditory) helps. In CRA, the concrete stage refers to the use
of concrete materials (ex.- blocks, marbles, chips) to introduce
In the representational stage, the teacher moves things to a higher
level by transitioning instruction from the concrete level to a less
concrete platform. In other words, students might go from
using blocks to using dots, picturer, or some other type of drawing.
Math is about symbols, right? Well, in this stage instruction
moves to the symbols and numbers we've become so accustomed to in
math. You've seen them before- +, -, %, etc.
An Example of the Concrete
Representational Abstract Approach
Learn about reading and writing fractions.
The teacher might offer students 10 marbles. Five of them are
red, five are yellow. He/she might ask the group to count the
total number of marbles, then how many are red, how many are yellow.
The teacher might discuss the fact that the total number of marbles
is 10. Since that is the total number of marbles, it
represents the whole thing or the whole in the following fractional
The teacher might then ask students to write 10 where the word
"whole" is in the aformentioned representation.
From there, the teacher does not necessarily need to go back to the
concrete stage. Rather, they might transition back to the
representational stage to ask their students, "how many marbles are
yellow?" When they say five, the teacher might conclude for them
that the yellow marbles represent part of the whole. The
instruction would then once again enter the abstract phase, where
the students would likely write down the number 5 where the word
"part" is in the aformentioned representation, leaving the fraction
The Research Supporting the Use of
Concrete Representational Abstract Instructional Intervention as a
Research Based Math Approach
Drum roll, please. After all, we've promised you that the CRA
is a research based math intervention. So check out some of
the online research that supports its use by following the links