Early Understanding of Intensive Properties of Matter: Developmental and Cultural Differences

Early Understanding of Intensive Properties of Matter: Developmental and Cultural Differences Julia L. Hill (julia.hill@ucl.ac.uk) Anne Schlottmann (a.schlottmann@ucl.ac.uk) Michelle R. Ellefson (mre33@cam.ac.uk) Keith S. Taber (kst24@cam.ac.uk) Venus W. S. Tse (wingsum1216@gmail.com) Tiffany S.W. Yung (see.yung.11@ucl.ac.uk) Psychology and Language Sciences, University College London Faculty of Education, University of Cambridge Abstract Many properties of substances/materials are intensive, and children are widely believed to have difficulties with reasoning about intensive quantities. Here we used a novel judgment method, together with a cross-cultural paradigm to study 4- to 9-year-olds’ understanding of the intensity/ concentration (sweetness) of sugar-water solutions. UK children knew from the youngest age that intensity increases with amount of solid, and a significant, but small effect for decreasing amount of liquid appeared by age 7, a couple of years prior to the age typically reported. Hong Kong children were more advanced, with strong liquid effects and the normative concentration pattern from the youngest age. Problems with intensive quantity reasoning may not reflect a universal cognitive limitation, but seem to depend on cultural experience. This has implications for children’s chemistry reasoning and education. Keywords: intensive properties, chemistry, reasoning, cognitive development. Introduction We have learnt much about young children’s understanding of objects, but far less is known about how they understand the substances/materials of which these objects are composed. Matter has extensive and intensive properties, those that depend on amount (e.g. weight, height, volume) and those that hold independent of amount, for every bit of homogenous matter (e.g., density, strength, temperature, colour, taste). Many properties we consider basic characteristics of substances/materials are of the latter, intensive kind. Here we consider children’s understanding of the taste intensity of mixed substances (sweetness of solutions of sugar in water). Prior work concludes that children have little understanding of intensive properties, including sweetness, until the late primary years. This study re-opens the case, applying an Information Integration approach, previously successful in eliciting understanding in other domains deemed difficult for children, and using a cross-cultural paradigm, studying children in the UK and Hong Kong. Prior work on intensive properties: Which cup is sweeter? Much work documents that children have great difficulty with intensive quantities. Some attribute this to conceptual problems, such as insufficient differentiation of extensive and intensive concepts (Jager & Wilkening, 2001; Piaget & Inhelder, 1974; Smith, Carey, & Wiser, 1985) or logical incongruence of intensive concepts (Kloos, 2007). Another set of accounts focuses on measurement of intensive quantities as ratio of two extensive quantities, e.g., sweetness depends on the ratio of sugar to water, or density depends on the ratio of mass to volume. In this view, children’s problems reflect difficulties with proportional thinking (Nunes, Desli, & Bell, 2003; Stavy, Strauss, Orpaz, & Carmi, 1982). Most studies used choice tasks, e.g., children chose which of two cups of water was sweeter, one half full or one full, both with the same quantity of sugar added. Children up to 9 or 10 years either said that both were equally sweet, containing the same amount of sugar, or that the full glass was sweeter, mistaking the indirect, diluting effect of the water for a direct effect (Stavy et al., 1982). Nunes et al. (2003) had similar findings for a range of intensive properties, but also reported that problems with intensive quantities go beyond those with indirect variables: Children were worse on intensive than extensive problems even when both involved indirect variables. The reasons remain unclear, but it is clear that in choice paradigms children have problems until fairly late. Information Integration Approach: How sweet is this cup? In other domains, choices turn out to be insensitive measures of children’s competence. When a densely spaced row of pennies is pushed further apart, children say that the longer row has more – centration and lack of number conservation (Piaget, 1965). But when making graded judgments of numerosity on graphic, not numerical scales, as used within Information Integration Theory (Anderson, 1981, 1996), children as young as 3 take both length and density of the row into account (Cuneo, 1982). When asked to choose which of two plates with red winner and clear loser marbles is better for winning in a blind draw, many 8-year-olds still choose based on the number of winners only (Siegler, Strauss, & Levin, 1981). But when making judgments of how easy it is to win in a blind draw, even 4-year-olds consider both winners and losers (Anderson & Schlottmann, 1991). This may come about because choice tasks tend to elicit analytic, system II forms of reasoning, with dimension- by-dimension comparison (Siegler et al., 1981), while graded judgment tasks tap into more synthetic, intuitive system I forms of thinking (Schlottmann & Wilkening, 2011). This intuitive understanding can be dramatically more advanced than children’s analytic understanding. Here, we use an Information Integration approach to study children’s concepts of taste intensity, sweetness, as a function of both amounts of solid/sugar and liquid/water