Poster #12 - Children’s abilities to perform intuitive multiplicative and divisive computations

• In Event: Poster Session 10

Abstract

Children have access to perceptual representations of number, which also allow for arithmetic operations to be intuitively carried over them (Dehaene, 2011). Children can, for example, reliably identify the correct product of a set of items that doubles in amount (Barth et al., 2009; McCrink & Spelke, 2010). Results such as these, however, are not always seen as demonstrating “true” mathematical competency, primarily because they show children making relative judgements, rather than producing the absolute answers of arithmetic operations (see Barth et al., 2009). We attempt to bridge this gap by testing whether children possess the more nuanced ability to perform multiplication/division absolutely, prior to formal schooling.

Forty-five 5 to 7-year-olds (M = 6;6 [years;months]; SD = 0.82) judged “how many” items they saw in an estimation task that was speeded to prevent counting (Dramkin & Odic, 2019). Across intermixed trials, children were presented with different numerical units: “one” unit represented by either 1 dot, 3 dots, or 5 dots (Figure 1). We calculated the average slope (betas in a standard linear regression) and coefficient-of-variation (CV; Cordes et al., 2001) as an index of estimation accuracy (slope) and variability (CV) in their estimates across the target values shown.

If children’s intuitive numerical capacities support absolute multiplication/division, then children should estimate using different numerical units without prior practice/experience. For example, if told that 5 dots correspond to “one modi”, then when shown objectively 15 dots, children should respond that there are “three modies”. However, if children cannot perform absolute multiplicative/divisive operations prior to schooling, then they should estimate only according to the objective number of dots (e.g., estimating that there are “fifteen” dots, rather than “three modies”) or guess randomly. Hence, we should expect estimation slopes for the 3-dot and 5-dot units to be either flat, or closer to a beta of 3 and 5, respectively (Figure 1).

Across ages and units, children gave higher estimates for higher targets, and importantly, did not just respond with the brute number of dots (Figure 2). When shown objectively 110 dots with the 5-dot unit (i.e., 22 x 5), the median estimate was only about “eighteen modies”, suggesting that children possess absolute multiplicative/divisive capabilities prior to schooling (Figure 2). While children’s estimates were more stable (i.e., less variable) across trials when the unit was 1 dot, their estimation slopes (i.e., accuracy) did not significantly differ across the units (1- vs. 3-dot: t(42) = -1.43, p = .34; 1- vs. 5-dot: t(42) = -0.85, p = .67, 3- vs. 5-dot: t(42) = 0.45, p = .89; Figure 1). Hence, despite potentially competing links that had to be inhibited (e.g., “one” typically corresponding to a single item), and not yet having formally learned to multiply/divide, children could readily estimate using these different numeric units. In ongoing work, we further probe children’s arithmetic abilities across additional target values.

Taken together, our findings suggest that children’s intuitive quantity capacities may not only support basic relative arithmetic computations, but also more nuanced abilities to perform arithmetic absolutely.

Authors

• Denitza Dramkin, University of British Columbia (UBC)
  Presenting Author

• Darko Odic, University of British Columbia (UBC)