Child-methods in secondary mathematics

Booth, Lesley R.

doi:10.1007/bf00386044

Cited by 34 publications

(18 citation statements)

References 2 publications

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“…Many children do not understand the idea of letter as a variable (Booth, 1981). They tend to interpret letter as standing for a specific number, and different letters must necessarily represent different numbers (Collis & Romberg, 1975;Kuchemann, 1981).…”

Section: The Misconceptions In Algebramentioning

confidence: 99%

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An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

Lim

2017

EJREP

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Section: The Misconceptions In Algebramentioning

confidence: 99%

“…All these items were adopted and adapted from various educational studies on this topic (e. g. Ayres, 2000b;Booth, 1981;Demby, 1997;Hart et. al., 1981;Liebenberg, 1997;Sakpakornkan & Harries, 2003;Swafford & Brown, 1989;Teng, 2002;Vaiyavutjamai, 2001;Vlassis, 2002).…”

Section: Instrumentsmentioning

confidence: 99%

An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

Lim

2017

EJREP

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“…Related studies have indicated that children's informal strategies may be developed prior to instruction (Carpenter, Hiebert & Moser, 1981;Fuson, 1982;Gelman & Gallistel, 1978;Groen & Resnick, 1977;Hughes, 1986;Steffe et al, 1988), and that children may continue to use these despite formal instruction (Booth, 1981;Fischbein, Deri, Nello & Merino, 1985;Hart, 1981). When children experience formal instruction it cannot be assumed that their conceptualisations are linked with oormal mathematical ideas, or that their own strategies match those encouraged by instruction.…”

Section: Informal and Forma! Strategiesmentioning

confidence: 99%

Children’s solutions to multiplication and division word problems: A longitudinal study

Mulligan

1992

Math Ed Res J

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Children's solution strategies to a variety of multiplication and division word problems were analvsed at foor interview stages in a 2-year longitudinal study. The study followed 70 children Erom Year 2 into Year 3, from the time where they had received no formal instruction in multiplication and division to the stage where they were being taught basic multiplication facts. Ten problem structuren, five for multiplication and five for division, were classified on the basis of differences in semantic structure. The relationship between problem condition (i..e. small or large number combinations and use ofphysical objects or pictures), on performance and strategy use was also examined.The results indicated that 75% of the children were able to solve the problems using a wide variety of strategies even though they had not received formal instruction in muitiplication or division for most of the 2 year period. Performance level generally increased for Bach interview stage, but few differences werefound between multiplication and division problems except for Cartesian and Factor problems.Solution strategies were classified for both multiplication and division problems at three levels: (i) direct modelling with counting; (ii) no direct modelling, with counting, additive or subtractive strategies; (iii) use of known or derived facts (addition, multiplication).A wide range of counting strategies were classified as counting-all, skip counting and double counting. Analysis of intuitive models revealed preference for a repeated addition model for multiplication, and a 'building-up 'model for division.In recent years there has been a steady growth in mathematics education research investigating how children develop mathematica) concepts and processes (Bel)

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“…and yet have difficulty counting coUections of Bienes blocks in units of ten and one, (p. 1). It may also be the absence of semantics that prompted Booth (1981) to remark ~~It was as ir two completely different types of mathematics were involved; one where the children could use common sense, the other where 'they had to remember a rule,, (p, 35).…”

Section: Rules and Principles Of Concept Learningmentioning

confidence: 99%

Concept-referenced testing

Horne¹

1987

Eur J Psychol Educ

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It is suggested that … criterion-referenced tests to have any educational vatue, they must be linked to the categories o[ learning that have beert demonstrated in learning theory.These categories lorm the basis oŸ ,the test domains. The nature of the two mare ccttegories, conoepts and rules, is reviewed and it is suggested that the errors produced by pupils that indieate faulty cortcept learning or rules application should forro the basis for the production of tests. Examptes of such tests are also discussed.As this approa~h to testing is markedly diHerent to the current psychometric approa~h to criterion-re~erenced testing it is suggeste• that the forro oŸ testing described here be called concept-referenced testing to distinguish it Ÿ other Ÿ o… criterion-reference• measures.

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Child-methods in secondary mathematics

Cited by 34 publications

References 2 publications

An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study

Children’s solutions to multiplication and division word problems: A longitudinal study

Concept-referenced testing

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