Page 80 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 3
However, most of the relevant research has focused on only the mathematical problem-solving of relatively young children (up to third grade or the age of about 7 years; e.g., Rasmussen & Bisanz, 2005; Swanson et al., 2008). As a result, only the solution of simple, single- step math problems has been studied (e.g., Fuchs et al., 2006; Swanson & Beebe-Frankenberger, 2004; Zheng et al., 2011). Relatively little is known about the predictive roles of arithmetic fluency and executive functioning for advanced mathematical problem-solving. However, both of these are important in light of the complexity of problem- solving tasks requiring advanced mathematical problem-solving and multi-step calculations for their solution. In addition, in grade 4 new domains of mathematics are being taught that also include certain necessary knowledge and skills (e.g., mastery of multiplication and fractions). Development of advanced mathematical reasoning and analytic thinking may not be a matter of simply mastering the required mathematical knowledge; it is possible that there is also a need for sufficient arithmetic fluency and executive cognitive functioning. Additional research on the roles of arithmetic fluency and executive functioning in the mathematical problem-solving skill of older elementary school children is thus needed.
Arithmetic fluency and mathematical problem-solving
During early elementary school, teachers focus on number, counting, and simple arithmetic competence (Geary, 2011). Children gradually master key arithmetic facts for quick and accurate responding (Andersson, 2008; Fuchs et al., 2006). When solving more advanced mathematical problems, children must be able to quickly retrieve these arithmetic facts from long-term memory and store this information in short-term memory (Baddeley, 2000). To be able to solve mathematical problems, it is necessary that children understand mathematical concepts (conceptual knowledge), know the procedural steps to solve a problem (procedural knowledge) and have sufficient knowledge of basic facts (factual knowledge; Geary, 2004, 2011; Geary & Hoard, 2005). Cragg et al. (2017) offered a framework presenting a refined hierarchical structure for mathematical development, based on the framework of Geary (2004). In that framework, the underlying cognitive