Intensive quantities: Towards their recognition at primary school
                  level

Howe, Christine; Nuñes, Terezinha; Bryant, Peter; Bell, Daniel A.; Desli, Despoina

doi:10.1348/97818543370009x12583699332573

Cited by 7 publications

(8 citation statements)

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“…For example, density is directly proportional to mass and inversely proportional to volume, speed is directly proportional to distance travelled and inversely proportional to time taken, and stretch is directly proportional to suspended load and inversely proportional to number of springs. As noted in Howe, Nunes, Bryant, Bell, and Desli (2010), the proportionality inherent in such concepts is often sidestepped in science education: density, speed, and stretch are typically analysed without reference to their constituent quantities. However, as a consequence, something crucial may be missed, for the difficulties that students of all ages experience with proportional reasoning have been widely documented (e.g.…”

Section: Principled Approach To Forcesmentioning

confidence: 99%

Principled Improvement in Science: Forces and proportional relations in early secondary-school teaching

Howe

Ilie

Guardia

et al. 2014

International Journal of Science Education

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In response to continuing concerns about student attainment and participation in science and mathematics, the epiSTEMe project took a novel approach to pedagogy in these two disciplines. Using principles identified as effective in the research literature (and combining these in a fashion not previously attempted), the project developed topic modules for early secondary-school teaching in the UK, arranged for their implementation in classrooms, and evaluated the results. This paper reports the development, implementation, and evaluation of one of the epiSTEMe science modules. Entitled Forces and Proportional Relations, the module covers standard curricular material in the domain of forces, while paying particular attention to the proportional nature of many key constructs. It was developed in collaboration with a small group of teachers; implemented subsequently in 16 classrooms, in all cases involving students from the first year of secondary school; and evaluated through comparison with first-year students in 13 control classrooms who were studying the topic using established methods. Evaluation addressed topic mastery and opinions about the topic and the manner in which it was taught. While further research is required before definite conclusions are warranted, results relating to topic mastery provide grounds for optimism about the epiSTEMe approach. Furthermore, student opinions about the module were positive.

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Section: Principled Approach To Forcesmentioning

confidence: 99%

Principled Improvement in Science: Forces and proportional relations in early secondary-school teaching

Howe

Ilie

Guardia

et al. 2014

International Journal of Science Education

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“…One possibility is that it is due to the strong mathematical element that undoubtedly is a part of the scientific curriculum. Scientific exercises involve a great deal of measurement and calculation, of course, and many scientific concepts, such as density and temperature, are intensive quantities Howe, Nunes, Bryant, Bell, & Desli 2010;Nunes & Bryant 2008;Nunes, Desli, & Bell 2003) and their measurement is based on ratios; children, therefore, have to be able to reason about proportions to understand several aspects of science. None of this is true of English lessons.…”

Section: Multiple Regressions: Specificity Of Predictionmentioning

confidence: 99%

“…There is also little evidence on whether these abilities, which are easy to distinguish conceptually, can also be distinguished empirically, using quantitative methods. There are longitudinal studies of how well children's number knowledge and computational skills predict their success in learning about mathematics (De Smedt, Verschaffel, & Ghesquière 2009; Durand, Hulme, Larkin, & Snowling 2005; Jordan, Levine & Huttenlocher 1994; Jordan & Montani 1997; Krajewski & Schneider 2009), and there is one study on how children's mathematical reasoning at kindergarten predicts their mathematics achievement in the first year in school (van de Rijt, van Luit, & Pennings 1999). The results of this research, on the whole, have been positive.…”

Section: Introductionmentioning

confidence: 99%

The relative importance of two different mathematical abilities to mathematical achievement

Nuñes

Bryant

Barros

et al. 2011

Brit J of Edu Psychol

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“…As argued elsewhere (Howe, Nunes, Bryant, Bell, & Desli, 2010), it is difficult to explain both the general trend in Nunes et al 's (2003) results and the exceptions unless responses to the inverse‐direct contrast are interpreted as salience effects , stemming from pragmatic consequences of how the quantities are represented in language. In particular, with many of the intensive quantities examined by Nunes et al (2003) the expression used to describe the quantity will have simultaneously defined one variable as directly proportional and rendered that variable salient.…”

Section: Comparison Problems and Variable Saliencementioning

confidence: 87%

“…Use a number or a fraction if you can’. Data on this aspect of the project are reported in Howe et al (2010).…”

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confidence: 99%

Intensive quantities: Why they matter to developmental research

Howe

Nuñes

Bryant

2010

British J of Dev Psycho

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A distinction can be drawn between extensive and intensive quantities. Extensive quantities (e.g., volume, distance), which have been the focus of developmental research, depend upon additive combination. Intensive quantities (e.g., density, speed), which have been relatively neglected, derive from proportional relations between variables. Thus, while proportional relations can be expressed with extensive quantities, these relations are constitutive with intensive quantities. One consequence is that factors, which are theorized as marginal with extensive quantities, are conceptually central in intensive contexts, and may need to be recognized in developmental models. Two such factors, termed variable salience and relational focus, are examined here, via a study where 963 Scottish children aged 7-12 years were asked to solve 42 intensive quantity problems in comparison and missing value format. Reasoning improved with age, but at all ages it was strongly influenced by variable salience and relational focus. Moreover, the manner in which these two factors interacted with other factors differed from what might be expected from models of proportional reasoning with extensive quantities. Based upon these results, it is argued that the distinction between extensive and intensive quantities is theoretically significant, and intensive quantities need to be granted more attention in the future.

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Intensive quantities: Towards their recognition at primary school level

Cited by 7 publications

References 0 publications

Principled Improvement in Science: Forces and proportional relations in early secondary-school teaching

Principled Improvement in Science: Forces and proportional relations in early secondary-school teaching

The relative importance of two different mathematical abilities to mathematical achievement

Intensive quantities: Why they matter to developmental research

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