Distinguishing conceptions of multiplicative reasoning in Chinese elementary students: What sense correct and incorrect solutions might make to them?

Abstract

We address the question: What may be the conceptual sources of Chinese elementary students’ correct and incorrect solutions to multiplicative problem situations? We focus on situations for eliciting evidence about their ability to add and subtract sets of composite units—mental structures that underlie conceiving of whole numbers as a single entity composed of smaller units (e.g., “3” is composed of three “1s”). A conception postulated to underlie this ability is termed Same-Unit Coordination (SUC). We attribute student errors to reasonable-to-them spontaneous use of a previously established, repetitively practiced way of operating on 1s (“Ones”) contained within composite units—a conception we term Totaling. We analyze qualitative data to illuminate this phenomenon and quantitative data to depict its scope. These analyses support our claim that student solutions, seen by an observer as correct or erroneous, can be explained as (a) reasonable from the students’ frame of reference and (b) possibly arising from instructional focus on mastering multiplication facts to find totals of 1s in equal-size sets.