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Sarah Squire

Publications and source records attributed to Sarah Squire.

6 recordsLinked to original sources
PubMed2004

Does the cue help? Children's understanding of multiplicative concepts in different problem contexts.

BACKGROUND: Understanding arithmetical principles is a key part of a conceptual understanding of mathematics. However, very little attention has been paid to children's understanding of multiplicative, as compared to additive, principles. AIMS: This study investigated (a) children's ability to use commutative and distributive cues to solve multiplication problems, (b) whether their ability to use these cues depends on the problem context, and (c) whether separate mechanisms might underlie children's understanding of commutativity and distributivity. SAMPLE: Twenty-seven 9-year-olds (Year 5) and thirty-two 10-year-olds (Year 6). METHODS: Forty-eight multiplication problems (with a multiple-choice response format) were presented to children. There were four types of problem: Commutative, Distributive, Combined commutative-distributive (all preceded by a cue) and No cue problems. Each type of problem was presented in three different contexts: Isomorphism of measures, Area, and Cartesian product. RESULTS: Children demonstrated a good understanding of commutativity but a very poor understanding of distributivity. A common mistake in the distributive problems was to select the number that was one more, or one less, than the answer in the cue. Children's understanding of distributivity (but not commutativity) seemed to depend on the problem context. Factor analysis suggested that separate factors underlie the ability to solve commutative and distributive problems. CONCLUSIONS: Nine- and 10-year-olds understand commutativity, but are unable to use the distributive principle in multiplication. Their errors suggest that they may confuse some of the principles of multiplication with those of addition. When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems. The implications for mathematical education are discussed.

Child↗
PubMed2002

The influence of sharing on children's initial concept of division.

We report three studies that investigate young children's ability to solve partitive division problems when presented with a concrete model of a problem. In the studies, 5- to 8-year-olds were given problems about sharing "sweets" between dolls, and the sweets were grouped in one of two different ways. When the sweets were grouped by the divisor, the number of groups coincided with the number of dolls (divisor) and the number in each group was the answer (quotient). When the sweets were grouped by the quotient, the reverse was true. In all three experiments, children found it much easier to solve the problems in the Grouping-by-Divisor condition than in the Grouping-by-Quotient condition (although there was some evidence of a developmental improvement in the tasks). It is suggested that the Grouping-by-Divisor condition is easier because it coincides with the end point of sharing. The findings are discussed with reference to schemas of action in children's mathematical understanding.

Analysis of Variance↗
PubMedDate not supplied

Five steps for sustaining effective patient partnership working.

NHS organisations are to recruit and involve patients in planning and delivering health care services. This paper gives practical examples of recruiting and involving patients in this process and a 'five-step cycle' for sustaining effective partnership working between patients and NHS organisations.

Education↗