Individual Differences in Children’s Early Strategy Behavior in Arithmetic Tasks

Lindberg, Staffan I.; Linkersdörfer, Janosch; Lehmann, Martin; Hasselhorn, Marcus; Lonnemann, Jan

doi:10.5539/jedp.v3n1p192

Cited by 10 publications

(12 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Children can arrive at accurate and inaccurate solutions to addition problems through a variety of strategies. Examining children’s strategies provides greater insight into their understanding of arithmetic principles and numerical magnitudes than examining only accuracy (Canobi, Reeve, & Pattison, 2003; Carpenter, Franke, Jacobs, Fennema, & Empson, 1998; Geary, Bow-Thomas, & Yao, 1992; Lindberg, Linkersdörfer, Lehmann, Hasselhorn, & Lonnemann, 2013). In fact, how children solve problems has been found to be more predictive of later mathematics achievement than the accuracy with which they solve problems (Geary, 2011).…”

Section: Addition Strategiesmentioning

confidence: 99%

Arithmetic Accuracy in Children From High- and Low-Income Schools

et al. 2016

View full text Add to dashboard Cite

This study investigated income group differences in kindergartners’ and first graders’ (N = 161) arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the magnitude of errors, with low-income first graders being less accurate than high-income kindergartners. Higher-income children were more likely to use sophisticated mental strategies than their lower-income peers, who used predominantly inefficient counting or inappropriate strategies. Importantly, this difference in strategies mediated the relation between income group and addition. Examining underlying strategies has implications for understanding income group differences in arithmetic and potential means of remedying it via instruction.

show abstract

Section: Addition Strategiesmentioning

confidence: 99%

Arithmetic Accuracy in Children From High- and Low-Income Schools

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Thus, the growth in arithmetic fluency for children in grade 2 may be reflected in better execution of both min and decomposition strategies. Notably, in the present research, I did not collect children's strategy data for the addition tasks, thus, the assumption that the improvement of the arithmetic fluency for children in grades 1 and 2 resulted from the increasing use and execution of more efficient counting and decomposition strategies was not directly tested because there is already a wealth of evidence showing how children's strategies develop as they become skilled at simple addition (e.g., Geary et al, 2004;Lindberg et al, 2013;Siegler, 1987;Shrager & Siegler, 1998;Siegler & Araya, 2005).…”

Section: Hypothesis 1: Integration Status Of Ordinal Associationsmentioning

confidence: 99%

“…On this view, ordinal processing can be viewed as the higher-level processing in the associative network than cardinal processing, because it involves a wider range of cognitive skills (cardinal, sequential and inhibitory processing). Further, arithmetic associations are integrated into the hierarchical network as arithmetic solutions require children to access their sequential and cardinal associations and thus arithmetic fluency is built upon fluent access to ordinal associations (Geary et al, 2004;Lindberg et al, 2013;Shrager & Siegler, 1998). Thus, the integration of cardinal and sequential associations into ordinal associations is critical for the development of mental arithmetic skills for children.…”

Section: Performance By Grade Andmentioning

confidence: 99%

“…that the development of cardinal associations precedes the development of ordinal associations (Colomé & Noël, 2012;Lyons et al, 2014;Knudsen et al, 2015;Sasanguie & Vos, 2018;Xu et al, under review). During the early phase of development, processing of cardinal and ordinal aspects of numbers is intertwined (Lyons et al, 2016), When children initially learn addition, they count using a sum strategy (i.e., counting both addends starting from one) or a min strategy (i.e., determining the larger of two addends to serve as the base, with the smaller operand used as the increment Groen & Parkman, 1972;Lindberg et al, 2013). Children do not consistently rely on more efficient strategies such as direct retrieval and decomposition to solve addition problems until grade 3 in North American samples (e.g., Geary et al, 2004).…”

Section: Hypothesis 1: Integration Status Of Ordinal Associationsmentioning

confidence: 99%

“…Nevertheless, the overall speed and accuracy with which children execute each strategy and the sophistication of strategy choice generally improves with age and educational experiences (Siegler, 1987). For children in grades 1 and 2, number fact retrieval is not readily available for majority of the children, and the min strategy and decomposition are usually the most dominant addition strategies (Geary et al, 2004;Lindberg et al, 2013;Shrager & Siegler, 1998;Siegler & Araya, 2005).…”

Section: Hypothesis 1: Integration Status Of Ordinal Associationsmentioning

confidence: 99%

See 2 more Smart Citations

Knowledge of Number Integration

Xu¹

View full text Add to dashboard Cite

What are the roles of cardinal and ordinal processing in the development of arithmetic? In the present dissertation, cardinal knowledge is defined as the ability to determine the quantity of number symbols whereas ordinal knowledge is defined as the ability to determine the relative relationship among number symbols. This dissertation includes two studies examining the development of the relations among cardinal, ordinal and arithmetic skills, both concurrently and predictively, for children in the early grades of elementary school. In both studies, children completed a number comparison task (e.g., which number is bigger, 4 or 5?) as an index of their cardinal knowledge. They also completed two novel order tasks: (a) missing number (e.g., which number is missing, 1 _ 3 4?), and (b) number ordering (i.e., order the three digits from the smallest to the largest, e.g., 4 5 3 or 2 7 9). Furthermore, children completed two measures of inhibitory control. Last, children's arithmetic skill (e.g., solving problems such as 4 + 5 or 7 + 6) was measured. In Study 1, I evaluated the internal consistency and validity of the novel order measures for children entering grades 1 to 3 (n = 70). In Study 2, multi-group path analysis showed that for children in grade 1 (n = 66), number ordering was strongly predicted by number comparison, but not by the missing number task or inhibitory control. Moreover, performance on the number comparison and missing number task independently predicted addition. Further, performance on the number comparison task uniquely predicted the growth of addition. In contrast, for children in grade 2 (n = 80), variance in the number ordering task was shared among the number comparison, missing number, and inhibitory control tasks. Number ordering uniquely predicted addition iii concurrently and it also predicted the growth of addition. I interpret the different patterns of results from grades 1 to 2 as reflecting different ongoing processes of integration of symbolic numerical associations. These findings suggest that development of number competence involves the integration of cardinal, ordinal, and arithmetic associations in an extensive network of relations among numbers. iv ACKNOWLEDGEMENTS First, I would like to thank the one and only Dr. Jo-Anne LeFevre for being my role model. I have been extremely lucky to have her as my mentor for eight years. She has encouraged me gently to come outside my comfort zone to achieve more than I could have imagined. I will be forever thankful to her from the core of my heart.

show abstract

Fostering Computation Competence with Non-Counting Strategies and Conceptual Subitizing in Grade 1: An Intervention Study in Inclusive Classrooms

Leuenberger,

Diener,

Wehren-Müller

et al. 2024

J Math Didakt

View full text Add to dashboard Cite

Computation competence (CC) with non-counting (NC) strategies is an important aim of Grade 1 mathematics education, but studies have shown that many students struggle to acquire these skills and continue to rely on counting strategies in later years. Therefore, even though counting is an important first strategy for young children, it is vital to support the development of CC with NC strategies from the earliest stages of mathematics education. This study examined the success of an intervention to promote the use of CC and NC strategies and conceptual subitizing (CS). The study was conducted with a sample of N = 1017 Grade 1 students, and investigated whether the achievement gain was affected by the intervention setting: cooperative learning, individual support for low achievers, a combination of the two settings, and a control group. Students in the combined setting had greater achievement gains in CC with NC strategy use and CS than the control group and outperformed those in the other intervention groups in CS. The combined setting also benefitted low achievers in mathematics for CS, but not for CC and strategy use. A combination of cooperative learning and individual support seems to be the best option for improving the CS and CC and NC strategy use of first graders, especially low achievers in mathematics.

show abstract

Individual Differences in Children’s Early Strategy Behavior in Arithmetic Tasks

Cited by 10 publications

References 21 publications

Arithmetic Accuracy in Children From High- and Low-Income Schools

Arithmetic Accuracy in Children From High- and Low-Income Schools

Knowledge of Number Integration

Fostering Computation Competence with Non-Counting Strategies and Conceptual Subitizing in Grade 1: An Intervention Study in Inclusive Classrooms

Contact Info

Product

Resources

About