Automatizing arithmetic: Using intensive training to examine how first graders learn single-digit addition.

The ability to rapidly and efficiently provide answers to simple additive problems (e.g., 2 + 3 = 5) is a paradigm case of automaticity in human learning. Achieving such automaticity is classically explained as a shift from procedural strategies (e.g., counting) to retrieval of learned addends-result associations from semantic memory (e.g., Ashcraft, 1992; Logan, 1988). However, the counting procedure that is used by children at the beginning of learning might also become automatized and become as efficient as retrieval of association from memory, supporting single-digit addition even in adults (Barrouillet and Thevenot, 2013; Uittenhove et al., 2016). Although this automatized counting model is supported by findings in adults, there is no longitudinal study investigating precisely how children learn single-digit addition. It is therefore unclear whether such learning stems from procedural automatization or semantic retrieval. Using an intensive training paradigm to accelerate arithmetic learning in 1st grade, the present study aims to investigate whether achieving automaticity with single-digit addition may be related to procedural automatization or semantic retrieval. Twenty-six first-grade students are currently completing a 10-week training program on tablet (iPad A16), practicing single-digit addition problems via 5-minute production tasks, three times a week (30 sessions total). Before and after training, participants are asked to verify whether addition equations are true (e.g., 2+3 = 5) or false (e.g., 2 + 3 = 4 or 2 + 3 = 6). Self-reported strategies of participants are also collected. Finally, episodic memory, working memory, processing speed and subitizing range are acquired as exploratory measures. Problems will be classified as automatized if no explicit counting strategy is reported after training. The opportunistic stopping phenomenon (Zbrodoff, 1995, 1999) will be used to evaluate whether such problems are solved through automatized counting or retrieval of association. That is, if automatized problems are counted, children should reject equations presenting an intermediate step of counting as the result (e.g., 2 + 3 = 4) faster than equations that are out of the counting range (2 + 3 = 6). Since we specifically expect problems solved through automatized counting to include only addends up to 4, as the maximum number of elements that can be apprehended simultaneously (Cowan, 2001), we will also compare the slope of the problem-size effect for these problems with those involving addends above this range. Exploratory analyses will investigate the relations between different phases of learning and measures of episodic memory, working memory and processing speed (Beaunieux et al., 2006) as well as subitizing range. Evidence of opportunistic stopping on automatized problems would support the automatized counting model. Evidence of a difference in slope between categories of automatized problems would support the coexistence (horse race model from Logan and Cowan, 1984) of the automatized counting and retrieval models. Overall, these findings should clarify current theoretical stances on the development of automaticity in mental addition and could also yield educational implications.