Teaching Math to Students With Disabilities

Teaching math to students with disabilities can be challenging especially if you’re trying to use the same program that the entire school is using. Luckily, there is a researched-based method that has been proven extremely effective and can be used with any math concept. It is called the CRA method. 

The CRA (concrete, representational, and abstract) Method is a way to provide instruction for students. Concrete is the stage where the student will be able to work with tactile (hands-on) objects to help them solve the problem physically. Representational is the stage where they can draw pictures to solve a problem. Abstract is the final stage where the student can solve the problem using only numbers. 

There are many special education teachers that will justify the lack of progress with a student to an absence of direct instruction programs in the area of math. Although this is a valid reason to feel frustrated, it doesn’t matter what program you use; it matters how to teach concepts. The book, “Building Number Sense Through the Common Core” by Bradley S. Witzel shows you the method CRA:  Concrete, Representational and Abstract. Using this method will help all teachers focus on number sense and not just getting students to the right answer.

CONCRETE

Let’s talk about “Concrete”. This refers to students having actual objects or manipulatives to use when learning a concept. This is an important stage in learning a math concept because the student is allowed the opportunity to “do” what is being taught. The teacher models how to use and label the objects in order to come up with the answer and allows the students to replicate the process. Mastery of this stage would show the student can independently use the objects, label each part (the red circles are the number of cookies that Suzie made and the yellow circles are how many cookies her brother ate), and solve the problem accurately. 

You will find concrete steps used in Kindergarten, First and Second grades, but it seems to lose its traction in the older grades. Some teachers feel that it seems unnecessary and childish to use objects when teaching a new concept, but this should be used in all grades. That physical act of moving and manipulating objects allows the student to have a better understanding or sense of the problem. Skipping this step may result in a lack of generalization to a new skill and/or holes in their progression in math.

REPRESENTATIONAL

Once the student has a solid grasp on solving a problem with concrete (pun intended), then they are ready to move into the representational stage. This stage is the progression from objects to pictures. This is where the student gets to “see” what is being taught. Once again, the teacher would model how to represent solving the problem but this time only uses pictures. The student may come up with various ways to pictorially represent this problem as the teacher guides them through to make sure they fully understand what they are representing. Mastery of this stage would include the student independently creating a picture of the problem, appropriately labeling each part of the picture (the tally marks are how much money I started with and the x’s are each dollar that I spent), and solving with accuracy.

ABSTRACT

Finally, once representational is mastered, then the student can move to the last step:  abstract. Teachers would model with the student how to use the symbols (numbers) to work through the math problems. Lots of practice and review is required to master this step. It’s also beneficial to create connections with previous concepts that have been taught so the student can generalize these skills. Mastery of this stage would show that the student can independently label what each number represents (the “5” is how many hours Jack spent watching TV and the “3” is how many hours Sarah spent watching TV) and solves the problem with accuracy.

ISOLATION OR SIMULTANEOUS?

Each stage of the CRA method can be done in isolation or simultaneously. It is understood that the teacher will be introducing a concept for the first time when implementing this method. It is meant to teach each stage in isolation to strengthen the understanding of one before moving on to the other. With this in mind, before moving on from Concrete to Representational, the teacher would introduce the new stage by connecting this stage to the previous. This helps the student understand how the stages are related by seeing them side-by-side. The process would be the same when moving from Representational to Abstract. 

This process with the stages is typically used for new instruction. However, there is an appropriate instance in which to teach each stage simultaneously:  when a student has already been exposed to this concept for a long period of time. For example, I had a student that was shown how to subtract 2-digit by 2-digit with regrouping in her second and third grade class using only that abstract stage. She partially had the procedure down, but not enough to be accurate. 

At this point, I divided a paper into 3 columns. The first column was for unifix cubes to “do” the problem, the second column was used to draw the numbers using lines for the tens and dots for the ones to “see” the problem, then the third column was to write the abstract numbers to solve the problem. With each step of solving, she would move from column one, then two then three. This continued for a couple of days until she told me that she was ready to solve using only pictures (representational) and numbers (abstract). After a few days of using both stages, she was able to understand the abstract strategy that was taught in her classroom. 

Following the CRA method in math will help special education teachers focus on “how” they are teaching math concepts instead of what page of the teacher’s manual we need to look at. This model creates a pattern and flow of how the teacher is introducing any new concept along with increasing the number sense that is needed in order to generalize these new math skills into future concepts and the confidence and practice to problem solve.