Role of Reasoning Strategies in Promoting Students' Understanding With Basic Combinations

• In Event: Marriott Roundtable Session 9
  In Roundtable Session: Exploring Cognitive Processes in Mathematics

Abstract

Reasoning strategies play a critical role in promoting basic combinations computational fluency and their use has been widely supported by research (NCTM,2006;NMAP,2008;NRC,2001). Study 1 involved assessing 74 first graders’ understanding and use of the near-doubles (6+6=12 and 12+1=13, so 6+7=13) and make-a-ten (9+8=17 as 9+(1+7)=(9+1)+7=10+7) strategies after an intervention. Study 2 entailed assessing 81 grades K-3 participants’ understanding and use of the subtraction-as-addition strategy (13-7=6 as 6+7=13). Participants’ knowledge and reliable use of the strategies was examined using a computational shortcut task (presenting a “helper sum” such as 5+7=12 before 12–7=?). The results indicate that the majority of participants who received the instructions had learned and reliably used the reasoning strategies to avoid the laborious computation using counting/inefficient methods.

Authors

• Veena Paliwal, University of West Georgia

• Arthur J. Baroody, University of Denver and the University of Illinois at Urbana-Champaign

• Ajay K. Das, Empire State College - SUNY