The Effects of Instruction on Children's Understanding of the "Equals" Sign

Baroody, Arthur J.; Ginsburg, Herbert P.

doi:10.1086/461356

Cited by 163 publications

(214 citation statements)

References 6 publications

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“…Conceptual errors were frequent, and many students omitted the equal sign altogether, even on typical addition problems. These findings converge with other work indicating that understanding of the equal sign is limited in children in this age range (Baroody & Ginsburg, 1983;Kieran, 1981;McNeil & Alibali, 2000). Understanding of equations should be a target for instruction in elementary school.…”

Section: Discussionsupporting

confidence: 87%

You'll see what you mean: Students encode equations based on their knowledge of arithmetic

2004

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This study investigated the roles of problem structure and strategy use in problem encoding. Fourthgrade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + or 6 + 4 + 5 = + 5). Next, they completed an encoding task in which they reconstructed addition and equivalence problems after viewing each for 5 s. Equivalence problems of the form 4 + 3 + 6 = 4 + overlap with a perceptual pattern found in traditional arithmetic problems (i.e., answer blank in final position), and students' encoding was poorest on problems of this type. Individual differences in encoding the equivalence problems were related to variations in strategy use. Some students solved blank-final equivalence problems using the standard arithmetic strategy of performing all given operations on all given numbers. These students made more errors in encoding problem structure, but fewer errors in encoding the numbers, than did students who solved the problems using correct or other incorrect strategies. Moreover, students who expressed many strategies for solving the blank-final equivalence problems made fewer errors in encoding problem structure, but more errors in encoding the numbers, than did students who expressed only a single strategy. Results highlight that encoding is intended to guide action and that prior experience can simultaneously facilitate and interfere with accurate encoding.

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Section: Discussionsupporting

confidence: 87%

You'll see what you mean: Students encode equations based on their knowledge of arithmetic

2004

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“…In contrast, in counting up, children start from s and increment until m is reached, with the solution being the number of times the counter has been incremented. Many studies have shown that counting down is more difficult and error prone than counting up (Baroody, 1984;Baroody & Ginsburg, 1983;Fuson, 1984;Fuson, 1992;Siegler, 1987), with the main reason being that counting backward is more difficult than counting forward (Fuson, Richards, & Briars, 1982). Thus, counting down probably is one of the slowest and least accurate algorithmic strategies that children use to solve arithmetic problems, and it can be imagined that counting down results in weak associations that probably are difficult to retrieve.…”

Section: Discussionmentioning

confidence: 99%

Strategies in subtraction problem solving in children

Barrouillet

Mignon

Thévenot

2008

Journal of Experimental Child Psychology

112

111

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The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lépine. Although the pattern of relationship between individual differences in working memory, on the one hand, and strategy choices and response times, on the other, was the same in both operations, subtraction and addition differed in two important ways. First, the strategy of direct retrieval was less frequent in subtraction than in addition and was even less frequent in subtraction solving than the recourse to the corresponding additive fact. Second, contrary to addition, the retrieval of subtractive answers is confined to some peculiar problems involving 1 as the subtrahend or the remainder. The implications of these findings for developmental theories of mental arithmetic are discussed.

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“…Specifically, children often begin solving mathematics problems with the equal sign at the end of the problem (e.g., 7 + 3 = _). These early experiences often lead students to misperceive the equal sign as meaning Bget the answer^or Bfind the total^ (Baroody & Ginsburg, 1983;Carpenter, Franke, & Levi, 2003;McNeil & Alibali, 2005). This misperception leads to difficulty in learning to solve and understand mathematical equivalence problems.…”

Section: Implications For Educational Practicementioning

confidence: 99%

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

DeCaro

2016

Mem Cogn

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An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth-and sixthgrade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcutfirst condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

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The Effects of Instruction on Children's Understanding of the "Equals" Sign

Cited by 163 publications

References 6 publications

You'll see what you mean: Students encode equations based on their knowledge of arithmetic

You'll see what you mean: Students encode equations based on their knowledge of arithmetic

Strategies in subtraction problem solving in children

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

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