Understanding of Derived-Fact Strategies in Addition and Subtraction

Putnam, Ralph T.; Bettencourt, Laurie U. de; Leinhardt, Gaea

doi:10.1207/s1532690xci0703_3

Cited by 37 publications

(28 citation statements)

References 10 publications

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“…For example, learning subtraction combinations can be facilitated if children see the connection between subtraction and addition [e.g., if 5 þ 3 5 8, then 8 2 5 is 3; Putnam et al, 1990;Baroody, 1999a], and 2xn/nx2 combinations can be meaningfully memorized by recognizing the relation between multiplication and (repeated) addition of a like term [e.g., 2 3 7 5 7 þ 7 5 14; Baroody, 1993]. Ideally, learning opportunities should be purposeful (personally relevant and engaging), meaningful (build on what children know), and inquiry-based (directed at promoting autonomous mathematical problem solving and reasoning).…”

Section: Why Is Structured Discovery Learning Of Patterns and Relatiomentioning

confidence: 99%

Why can't Johnny remember the basic facts?

Baroody

Bajwa

Eiland

2009

Dev Disabil Res Revs

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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.

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Section: Why Is Structured Discovery Learning Of Patterns and Relatiomentioning

confidence: 99%

Why can't Johnny remember the basic facts?

Baroody

Bajwa

Eiland

2009

Dev Disabil Res Revs

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“…Perhaps the most systematic study to date of children's understanding of compensation and equivalence constraints is that of Putnam, deBettencourt and Leinhardt (1990). They asked third grade students to watch puppets demonstrate "derived fact strategies" for addition and subtraction, to complete the calculations, and then to justify them.…”

Section: Compensation and Equivalencementioning

confidence: 99%

“…For example, equation (15) General relationships of this kind are reflected in the rules for derived fact arithmetic described by Putnam, deBettencourt, and Leinhardt (1990) and shown in Table 1.…”

Section: The Psychological Origin Of Mathematical Principlesmentioning

confidence: 99%

An Investigation Into 3-, 4-, and 5-Year-Old Children’s Nonsymbolic Magnitude Comparison Ability According to Ratio Limit and Task Condition

Cho¹,

Yi²

2017

Korean J Child Stud

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“…2012,, 390 unter Bezug auf u.a. BAROODY 1983BAROODY & GINSBURG 1986;PUTNAM ET AL. 1990;THORNTON 1990;FUSON 1992b;BEISHUIZEN 1997;TREFFERS 2001;CAMPBELL 2008 Rather, they were constantly applying the strategy evoked by the presentation format.…”

Section: Gebrauch Der Grundvorstellungen Und Darauf Aufbauendenmentioning

confidence: 99%

Grundvorstellungen und Vorgehensweisen bei der Subtraktion

Wessel¹

2015

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Understanding of Derived-Fact Strategies in Addition and Subtraction

Cited by 37 publications

References 10 publications

Why can't Johnny remember the basic facts?

Why can't Johnny remember the basic facts?

An Investigation Into 3-, 4-, and 5-Year-Old Children’s Nonsymbolic Magnitude Comparison Ability According to Ratio Limit and Task Condition

Grundvorstellungen und Vorgehensweisen bei der Subtraktion

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