Math Interventions Through the Concrete-Pictorial-Abstract Process
As we return to the classroom, math interventions have become a priority. The problem is how do we “gap” the math? To first address this issue, we need to understand the concept of intervention with respect to math. Multi-Tiered Systems of Support (MTSS) or Response to Intervention (RTI) as it was known, is a current platform for math intervention. Thus, before developing a plan of action for math interventions, an understanding of the CPA process of mathematics is encouraged.
What is the CPA process of learning math? The CPA process of learning mathematics is a progression of learning math in which students will initially model math using concrete objects. Concrete objects can consist of mathematical manipulatives such as base ten blocks, color counters, linking cubes, algebra tiles, etc. Concrete objects can also consist of household items such as uncooked beans.
Next, students will model math using pictorial representations of the concrete objects initially used in modeling math.
The last progression consists of slowly transitioning to the abstract symbolic representation of mathematics.
The key in progressing through the CPA process is not to move to the next progression until students have mastered the current level of progression. For example, do not move to the pictorial representations of representing place value until students have mastered the concept with base ten blocks. Ultimately, the key is for students to progress to the abstract symbolic process of mathematical operations. Students will slowly be weaned off the concrete and pictorial progression of the CPA process.
Math interventions can be a daunting task for educators. However, breaking the process down into tiers and using concrete-pictorial-abstract representations of math can help educators better understand how to gap students’ understanding of mathematics. Utilizing the CPA process, educators can provide individualized instruction that progresses at each student’s own pace in order to ensure they fully understand mathematical concepts.
Richard Palomin and Alfonso Mendoza’s goal is to help teachers integrate physical and virtual manipulatives into their classrooms by providing interactive lessons that teach students how to solve problems while creating an interactive learning experience.
