Explicit C-R-A Instruction
Purpose
The purpose of Explicit CRA Instruction is to provide
struggling learners access to key features of target
mathematics concepts that make them distinct in order to
develop conceptual understanding.
What is it?

This instructional practice incorporates two teaching
strategies: teaching through a concrete-torepresentational-to-abstract (CRA) sequence of
instruction and using explicit teaching techniques.

A CRA sequence of instruction provides students a
scaffolded way to develop conceptual understanding of
target concepts moving from more tangible representations
to less tangible ones. At the concrete level, students
work with tangible materials that accurately represent
the target concept. At the representational level,
students learn drawing strategies for replicating their
concrete level experiences. At the abstract level
students use mathematical symbols only to represent their
understandings and to problem solve.

Explicit teaching involves the use of several techniques,
all of which help students access key features of target
mathematics concepts that make them distinct and
meaningful. These techniques include use of authentic
contexts, multisensory methods, structured language
experiences, cuing, graphic organizers, and use of
examples and non-examples.

CRA and Explicit instruction are integrated into a single
instructional approach whereby explicit teaching
techniques are used at each CRA level.
What are the critical elements of this strategy?

Target concepts are introduced and students have many
opportunities to apply their developing understandings
(practice) at each level of understanding: concrete,
representational, and abstract.
o Concrete Level – commercial and non-commercial
materials are used to represent target concepts.
Students manipulate these materials in ways that
accurately demonstrate the meaning of different
mathematical processes and to problem solve.
o Representational Level – students learn to use
simple drawings to recreate the materials and
actions used at the concrete level for
representing a target concept and to problem
solve.
o Abstract Level – students use only mathematical
symbols to represent the target concept and to
problem solve.

Mathematics symbols are explicitly associated with their
representations at the concrete and representational
levels in order to facilitate meaning for students of
abstract mathematical symbols.

Explicit teaching techniques are integrated at the
concrete, representational, and abstract levels to ensure
that students have experiences that allow them clear
access to the key features of the target concept. They
include:
o Authentic Contexts – target concepts
introduced and practiced by students
contexts that are meaningful to them
to learning new mathematics concepts
its relevance to students’ lives).
are
within
(in contrast
devoid of
o Multisensory Methods/Cuing of Key Featuresteachers identify those features/steps of a
target mathematics concept that make it distinct.
Students are provided multiple ways to experience
each key feature: visual, auditory, tactile,
kinesthetic.
o Structured Language Experiences – students are
provided structured experiences to use their
language to describe their understandings of
target concepts. “Language” can be expressed in
multiple ways including speaking, writing,
performance, drawing, etc.
o Graphic Organizers – Visual displays are used to
assist students to organize their thinking about
target mathematics concepts, their meaning,
including how two or more concepts related to
each other.
o Examples and Non-examples – As students begin to
demonstrate initial understandings of a target
concept through appropriate models (examples),
non-examples are used to assist students in
refining their understandings of the concept.
Examples are compared to non-examples to examine
each for key features that make the target
concept distinct. Students are provided multiple
opportunities to determine why certain nonexamples do not accurately represent the target
concept based on it lacking one or more of the
target concept’s key features.
How do I implement the strategy?
Concrete Level
1. Identify the key features (typically 3-5) of the target
concept
2. Choose appropriate concrete materials as a model for the
target mathematics concept such that the key features of
the target concept are evident.
3. Provide multiple models using the selected concrete
materials, integrating the explicit teaching techniques
described above. Place particular emphasis on
highlighting the identified key features of the concept.
4. Clearly associate the concrete materials with the
abstract mathematical symbols they represent for the
target concept.
5. Continuously check for student understanding.
6. Provide multiple opportunities for students to apply
their developing understandings using concrete
materials.
7. Provide timely corrective feedback and provide
additional models using explicit teaching techniques as
needed.
8. When students are able to accurately represent the
target concept with 100% accuracy multiple times begin
teaching them drawing techniques (Representational
Level)
Representational Level
1. Continue to highlight the key features of the target
concept from concrete level instruction.
2. Choose an appropriate drawing technique for representing
what students did at the concrete level.
3. Continue with the same process used in steps 3-8 for
Concrete Level, except for using drawings rather than
concrete materials.
Abstract Level
1. Continue to highlight the key features of the target
concept from concrete level and representational level
instruction.
2. For those concepts that involve procedures or steps, make
sure that the procedure/process used is consistent across
concrete, representational, and abstract levels.
3. Continue with the same process used in steps 3-8 for
Concrete and Representational Levels using mathematical
symbols without the use of materials or representational
drawings.
How Does This Instructional Practice Help Struggling
Learners?

Provides students a scaffolded process for developing
conceptual understanding of target mathematics concepts.

By emphasizing the key features of target concepts and by
providing explicit ways for them to access these
features, students are afforded a transparent process for
understanding what makes the target concept distinct.
This also assists students with attention difficulties to
focus on what is relevant rather than what is not
relevant.

Provides students a way to develop meaningful
associations to the abstract nature of mathematics.

Helps students move from concrete to abstract
understanding.
Examples of Research Support for the Instructional Features
of This Strategy: Allsopp (1997); Borkowski (1992);
Jitendra, Hoff, & Beck (1999); Lenz, Ellis, & Scanlon
(1996); Miller & Mercer (1993); Miller, Strawser, & Mercer
(1996); Montague (1992); Morroco (2001); Owen & Fuchs
(2002); Paris & Winograd (1990); Strichart, Mangrum, &
Iannuzzi (1998); Swanson (1999).