TY - JOUR
T1 - Children's relational knowledge of addition and subtraction
AU - Baroody, Arthur J.
N1 - Funding Information:
This research was supported, in part, by grants from the University of Illinois Research Board. I thank Jaesook Lee, Debbie Rome, Judi Stierwalt, and Sirpa Tiilikainen for collecting or analyzing the data and the staff at the Colonel Wolfe School (Urbana, IL), the University Primary School (Urbana, IL), and the Sadorus Elementary School (Sadorus, IL) for their cooperation. Thanks also to Karen Fuson and another anonymous reviewer for their thoughtful and helpful comments on an earlier draft of this manuscript.
PY - 1999
Y1 - 1999
N2 - Knowledge of addition combinations has long been thought to facilitate the learning of subtraction combinations (e.g., 8 - 5 = ? can be answered by thinking 5 + ? = 8). Indeed, it follows from Siegler's (1987) model that an associative facilitating effect should make the correct answer the most common response to a subtraction combination, even in the earliest phase of mental-subtraction development. Children in the initial or the early phase of development were examined in 2 studies. Study 1 involved 25 kindergartners and 15 first graders in a gifted program; Study 2 involved 21 first graders in a regular program. Participants were presented with pairs of items, such as 4 + 5 = 9 and 9 - 4 = ?, and asked if the first item helped them to answer the second. Many participants, particularly the less developmentally advanced ones, did not recognize they could use a related addition equation to determine a difference. Study 2 participants were also administered a subtraction timed test. Contrary to Siegler's model, developmentally less advanced children responded with the correct difference relatively infrequently on nearly all items, and even developmentally advanced children did so on more difficult items. The results of both studies are consistent with earlier findings that suggested the complementary relation between addition and subtraction is not obvious to children. They further indicate that an understanding of the complementary relation is not an all-or-nothing phenomenon. It often develops first with subtraction combinations related to the addition doubles, apparently because such addition combinations are memorized relatively early. Ready facility with related addition combinations may make it more likely that children will connect their knowledge of subtraction to their existing intuitive knowledge of part-whole relations. This process may also account for why Study 2 participants were able to master subtraction complements without computational practice. Methodological and educational implications are discussed.
AB - Knowledge of addition combinations has long been thought to facilitate the learning of subtraction combinations (e.g., 8 - 5 = ? can be answered by thinking 5 + ? = 8). Indeed, it follows from Siegler's (1987) model that an associative facilitating effect should make the correct answer the most common response to a subtraction combination, even in the earliest phase of mental-subtraction development. Children in the initial or the early phase of development were examined in 2 studies. Study 1 involved 25 kindergartners and 15 first graders in a gifted program; Study 2 involved 21 first graders in a regular program. Participants were presented with pairs of items, such as 4 + 5 = 9 and 9 - 4 = ?, and asked if the first item helped them to answer the second. Many participants, particularly the less developmentally advanced ones, did not recognize they could use a related addition equation to determine a difference. Study 2 participants were also administered a subtraction timed test. Contrary to Siegler's model, developmentally less advanced children responded with the correct difference relatively infrequently on nearly all items, and even developmentally advanced children did so on more difficult items. The results of both studies are consistent with earlier findings that suggested the complementary relation between addition and subtraction is not obvious to children. They further indicate that an understanding of the complementary relation is not an all-or-nothing phenomenon. It often develops first with subtraction combinations related to the addition doubles, apparently because such addition combinations are memorized relatively early. Ready facility with related addition combinations may make it more likely that children will connect their knowledge of subtraction to their existing intuitive knowledge of part-whole relations. This process may also account for why Study 2 participants were able to master subtraction complements without computational practice. Methodological and educational implications are discussed.
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U2 - 10.1207/S1532690XCI170201
DO - 10.1207/S1532690XCI170201
M3 - Article
AN - SCOPUS:0007347864
SN - 0737-0008
VL - 17
SP - 137
EP - 175
JO - Cognition and Instruction
JF - Cognition and Instruction
IS - 2
ER -