ABSTRACT
How do adults produce the answer of a single-digit (simple) number combination such as 3×4 or 6+9? This question has dominated research on adult mathematical cognition since Ashcraft and Battaglia (1978) proposed experts retrieve answers from memory by activating associative links between combinations and solutions. Nearly all subsequent research on the topic has been based on the assumption adults directly retrieve the answer of a simple combination from some form of mental network (e.g., Ashcraft, 1982, 1987, 1992; Campbell, 1987a, 1987b, 1995; Geary, Widaman, & Little, 1986; LeFevre, Bisanz, & Mrkonjic, 1988; Miller, Perlmutter, & Keating, 1984; Rickard & Bourne, 1996; Stazyk, Ashcraft, & Hamann, 1982; Widaman, Geary, Cormier, & Little, 1989; but cf. Baroody, 1983, 1984, 1985, 1994). In contrast, researchers who examined addition or multiplication performance in children found that they use a mixture of counting procedures, other reconstructive strategies, and retrieved solutions (e.g., Ashcraft, Fierman, & Bartolotta, 1984; Baroody, 1992, 1993, 1995; Cooney & Ladd, 1992; Groen & Parkman, 1972; Jerman, 1970; Siegler, 1988a; Siegler & Shrager, 1984). The development of arithmetic knowledge, therefore, was typically hypothesized to proceed from flexible and adaptive selection from among a variety of procedures by children to the use of a single, efficient, and invariant approach (i.e., direct retrieval) by adults (Ashcraft, 1987; Siegler & Shipley, 1995).
