An Analysis of the Relationships among Computation-Related Skills Using a Hierarchical-Clustering Technique

The role of number words in preschoolers’ addition concepts and problem‐solving procedures

“…In this study, younger preschoolers made more accurate judgements of commutativity than associativity, and eight children (the commutativity cluster) consistently rejected the associativity principle and accepted the commutativity principle, but the reverse conceptual profile was not present. These results support previous findings among schoolchildren and older preschoolers (Canobi et al, 1998(Canobi et al, , 2002(Canobi et al, , 2003Close & Murtagh, 1986;Langford, 1981) and imply that children who understand one conceptual relation do not necessarily understand another. Instead, preschoolers appear to learn about increasingly complex part-whole relations with experience.…”

“…Specifically, in keeping with previous findings among older children (Canobi, Reeve, & Pattison, 1998, 2002Close & Murtagh, 1986;Langford, 1981), we hypothesised that preschoolers would make more accurate commutativity than associativity judgements, performing above chance for commutativity but not associativity. Our second hypothesis was that older preschoolers would outperform younger *Corresponding author.…”

“…However, little attention has been directed towards preschoolers' understanding of associativity. Research has indicated that schoolchildren have a stronger grasp of commutativity than associativity (Canobi et al, 1998(Canobi et al, , 2003Close & Murtagh, 1986;Langford, 1981). In addition, a study by Canobi et al (2002) has suggested that exploring preschoolers' understanding of addition concepts that vary in complexity sheds light on their developing understanding of the structure of arithmetic.…”

Educational Data Mining

“…Gagné coined the term "learning hierarchy" to describe the prerequisite relationship among skills, and developed methods for extracting learning hierarchies from student data. Following this work, there were a number of studies in the education literature on estimating prerequisite structure in mathematics curriculums, including work by Miller and Phillips [1974], Uprichard and Phillips [1977], and Close and Murtagh [1986].…”