Individual differences in children’s addition and subtraction knowledge

Canobi, Katherine H.

doi:10.1016/j.cogdev.2003.10.001

Cited by 79 publications

(127 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Geary (2011) also reported similar findings. Canobi (2004) highlighted that 6 to 8 year old children with good levels of conceptual understanding may have widely varying levels of procedural skill. Consequently, mathematics achievement measurements may not be good indicators of children's combination of conceptual and procedural skills (Gilmore & Bryant, 2006).…”

Section: Interactions Among Predictorsmentioning

confidence: 99%

“…However, there may be individual differences in the relationship between conceptual understanding and procedural skill, such that, for example, children with the same level of procedural skill may have differing levels of conceptual understanding (Canobi, 2004;Gilmore & Papadatou-Pastou, 2009). Aside from research into the development of conceptual understanding itself, large longitudinal studies of the development of mathematics achievement have tended to place more attention on procedural skills or basic numerical processing, compared with conceptual understanding (e.g.…”

mentioning

confidence: 99%

See 1 more Smart Citation

The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement

et al. 2017

View full text Add to dashboard Cite

Large individual differences in children's mathematics achievement are observed from the start of schooling. Previous research has identified three cognitive skills that are independent predictors of mathematics achievement: procedural skill, conceptual understanding and working memory. However, most studies have only tested independent effects of these factors and failed to consider moderating effects. We explored the procedural skill, conceptual understanding and working memory capacity of 75 children aged 5 to 6 years as well as their overall mathematical achievement. We found that, not only were all three skills independently associated with mathematics achievement, but there was also a significant interaction between them. We found that levels of conceptual understanding and working memory moderated the relationship between procedural skill and mathematics achievement such that there was a greater benefit of good procedural skill when associated with good conceptual understanding and working memory. Cluster analysis also revealed that children with equivalent levels of overall mathematical achievement had differing strengths and weaknesses across these skills. This highlights the importance of considering children's skill profile, rather than simply their overall achievement.

show abstract

Section: Interactions Among Predictorsmentioning

confidence: 99%

mentioning

confidence: 99%

The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Preschoolers' informal knowledge can differ significantly [e.g., Dowker, 2005;Baroody et al, 2006a;National Mathematics Advisory Panel, 2008]. Gaps in everyday knowledge can interfere with understanding formal instruction or engaging in mathematical thinking (e.g., devising problem-solving strategies, reasoning logically about problems) and, thus, greatly delay or hamper the learning of school mathematics [Baroody, 1987[Baroody, , 1996[Baroody, , 1999bJordan et al, 2003;Canobi, 2004].…”

Section: Active Construction View: Difficulties Mastering Basic Combimentioning

confidence: 99%

Why can't Johnny remember the basic facts?

Baroody

Bajwa

Eiland

2009

Dev Disabil Res Revs

View full text Add to dashboard Cite

Memorizing the basic number combinations, such as 9 þ 7 5 16 and 16 2 9 5 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage View), memorizing a basic fact is a simple form of learning-merely forming and strengthening an association between an expression and its answer. The two primary reasons this simple form of learning does not occur are inadequate practice or, in cases where adequate practice has been provided, a defect in the learner. According to the number sense perspective (Active Construction View), memorizing the basic combinations entails constructing a well-structured or -connected body of knowledge that involves patterns, relations, algebraic rules, and automatic reasoning processes, as well as facts. In effect, fluency with the basic number combinations begins with and grows out of number sense. Aspects of number sense critical to such fluency begin to develop in the preschool years. According to the Active Construction View, the primary cause of problems with the basic combinations, especially among children at risk for or already experiencing learning difficulties, is the lack of opportunity to develop number sense during the preschool and early school years.

show abstract

“…This work has attempted to measure, and in a few cases account for, individual differences in children's arithmetic performance (Hecht, Close, & Santisi, 2003;Swanson & Kim, 2007), conceptual understanding (Canobi, 2004Canobi, Reeve, & Pattison, 1998;Dowker, 1998) and strategy use (Imbo & Vandierendonck, 2007;Kerkman & Siegler, 1997). These studies reveal the importance of considering the variety of ways in which children develop understanding of arithmetic.…”

mentioning

confidence: 99%

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Gilmore

Παπαδάτου-Παστού

2009

Mathematical Thinking and Learning

View full text Add to dashboard Cite

Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual differences in the way this concept develops. To determine whether these differences are reliable and reflect alternative paths of development, we examined data from 14 studies of children's understanding of inversion. Cluster analyses and meta-analytic techniques were used to quantify the size of the inversion effect and examine factors influencing its size and to test the stability of patterns of individual differences across the studies. Evidence was found for reliable patterns of individual differences, which have implications for current theories of concept development. Individual Differences Meta-Analysis 3Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-AnalysisAn enduring question in mathematical cognition concerns how children develop understanding of mathematical concepts. This has attracted attention from researchers in both cognitive psychology and mathematics education. One of the key questions for both fields is how children's understanding of mathematical concepts develops in relation to their ability to perform mathematical procedures.

show abstract

Individual differences in children’s addition and subtraction knowledge

Cited by 79 publications

References 36 publications

The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement

The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement

Why can't Johnny remember the basic facts?

Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Contact Info

Product

Resources

About