• Home
  • Using CRA to Develop Conceptual Understanding and Fluency in Multiplication and Division

Using CRA to Develop Conceptual Understanding and Fluency in Multiplication and Division

Session Type: 
Session Day: 
Session Location: 
Brazilian B
Session Time: 
2:30-3:45 pm
Instructional Strategies
Policy that Impacts Student Outcomes
Teaching Content to Diverse Learners

Watch a VIDEO about this session

The concrete-representational-abstract sequence (CRA) emphasizes conceptual understanding of operations prior to developing fluency. This session will describe how researchers used CRA to teach elementary students with disabilities the relation between multiplication and division while developing fluency in basic facts. Attendees will learn how to design similar CRA interventions. This presentation is supported by research and practices that will improve education of students with disabilities. To progress in mathematics, students must conceptually understand the meaning of operations and their relations, but understanding the relation can be difficult (Bisanz, Watchorn, Piatt, & Sherman, 2009; Robinson & LeFevre, 2012). Visual representations such as CRA are effective in teaching operations to students with disabilities (Agrawal & Morin; Jitendra, 2013). The presentation will show a 20-minute intervention which will allow teachers to learn how to teach critical concepts related to multiplication and division to elementary students with diverse learning needs. The study used a mixed method design in which a multiple probe across students design measured the effects of CRA on percentage of correct facts and fluency as well as a qualitative design to analyze videos of students explaining their computation process. Researchers demonstrated a functional relation between CRA and mastery and fluency in facts.

Learning Outcomes and Next Steps:

At the end of this session, attendees will:

(a) describe two ways in which CRA is effective for teaching conceptual knowledge of multiplication and division facts to elementary aged students, and
(b) describe how they can use readily available materials to teach multiplication or division at the concrete or representational levels of CRA.

Follow KUCRL 


Countdown to

48 nationally ranked graduate programs.
—U.S. News & World Report
Pharmacy school No. 2 nationally for NIH funding
Hall Center receives 3rd NEH challenge grant to support humanities research collaboration
Regional leader in technology commercialization
12 graduate programs rank in top 10 nationally among public universities.
—U.S. News & World Report
KU Today