Early math instruction often prioritizes rapid retrieval of mathematical facts, (e.g. 4 + 6 = ; 10), an approach thatpromotes quick recall of sums but with limited transfer to unstudied problems. We consider how this pattern changeswhen the learning scenario highlights the quantities that underlie symbols. Adult participants learned a novel base 8addition task using alphabetic symbols to indicate quantities (e.g. AG + AF = ). They practiced with symbols onlyor with symbols grounded in quantitative representations. When tested in the same format as participants were trained,studied problems were learned equally well but symbol-only learners transferred only to identical-elements problems (e.g.AG + AF transferred to AF + AG). Grounded learners showed better transfer to problems involving novel quantities.The results suggest, in contradiction to some other recent findings, that arithmetic transfer is boosted when the learningscenario highlights quantitative meaning denoted by number symbols.

Previous studies on numeric cognition have focused primarily on magnitude, based on its role as a core feature of number knowledge. In this paper, we report the results of three experiments investigating adults’ sensitivity to properties of number apart from magnitude. In Experiment 1, we use a triadic judgment task to replicate a classic study of number properties. In Experiment 2, we compare these representations among expert and non-expert groups. In Experiment 3, we examine whether instruction can tune representation of number properties. Results indicate that the triadic comparison task is a reliable method of assessing sensitivity to number properties. We found that magnitude is difficult to suppress among non-experts, who are primarily attuned to magnitude and parity. Mathematically sophisticated participants were sensitive to a range of number properties compared with the non-expert group. We discuss implications for theories of number concepts and their relation to special populations