Does the cue help? Children's understanding of multiplicative concepts in different problem contexts

Abstract

Nine- and 10-year-olds understand commutativity, but are unable to use the distributive principle in multiplication. Their errors suggest that they may confuse some of the principles of multiplication with those of addition. When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems. The implications for mathematical education are discussed.

Children’s understanding of the arithmetic concepts of inversion and associativity

“…In general, the results indicate that as children get older, their conceptual understanding of inversion becomes stronger, a finding that is not unexpected and is consistent with previous research on children's development of conceptual knowledge in arithmetic (e.g., Rasmussen et al, 2003;Squire, Davies, & Bryant, 2004;Vilette, 2002). The results revealed several important and unexpected findings.…”

Children's understanding of multiplication and division: Insights from a pooled analysis of seven studies conducted across 7 years

“…Children's conceptual understanding of basic mathematical operations is crucial in the development of their mathematical skills (Bisanz, Watchorn, Piatt, & Sherman, 2009; National Council of Teachers of Mathematics, 2014). However, most of the research on how children acquire and develop their understanding has focused on the operations of addition and subtraction (Cowan & Renton, 1996;Squire, Davies, & Bryant, 2004). This is unfortunate as children's conceptual understanding of multiplication and division is considered to be both a greater challenge for children (Cowan & Renton, 1996;Fuson, 1988) and a critical precursor for complex mathematical skills such as algebra and calculus (Kilpatrick, Swafford, & Findell, 2001;Nunes, Bryant, & Watson, 2009).…”

Children Have the Capacity to Think Multiplicatively, as long as …

“…In noting that this is indicative of students not understanding the structure of the mathematics, they stated that this lack of understanding is largely due to the use of computational procedures rather than the exploration of mathematical relationships (Warren and English, 2000). Squire, Davies and Bryant (2004) also noted the importance of students developing a conceptual understanding of the mathematics that underpins multiplication facts and algorithms. They note a number of benefits from students developing a strong conceptual understanding including greater flexibility in their thinking, working quicker, deriving unknown facts from known facts, and being more efficient at solving problems (Squire et al, 2004).…”

“…Squire, Davies and Bryant (2004) also noted the importance of students developing a conceptual understanding of the mathematics that underpins multiplication facts and algorithms. They note a number of benefits from students developing a strong conceptual understanding including greater flexibility in their thinking, working quicker, deriving unknown facts from known facts, and being more efficient at solving problems (Squire et al, 2004). They discuss the results of a study showing students being more efficient at identifying and using the commutative property than the distributive property but at no stage were children asked to consider why the property works.…”

“…They discuss the results of a study showing students being more efficient at identifying and using the commutative property than the distributive property but at no stage were children asked to consider why the property works. Indeed, in noting the underlying importance of commutativity, they added that it is vital for educators to consider how to develop children's understanding of commutativity (Squire et al, 2004). This must go beyond describing in terms of a 'switch around' as discussed by Anthony and Walshaw (2000).…”