Problem size effect and processing strategies in mental arithmetic

Abstract

We investigated the event-related brain potentials elicited by arithmetical operations whose solution requires direct memory retrieval or non-retrieval strategies. The problem size effect--the increment in reaction time for arithmetical problems with large operands--appears to be due to the selective use of non-retrieval procedures, and studies with event-related potentials have demonstrated an amplitude modulation of a late positive slow wave (range between 400-800 ms) related to the problem size effect. Two arithmetic operations (additions and subtractions) and three levels of problem size (adding or subtracting 2, 4 or 6) were used. We found an amplitude modulation of the late positive slow wave in subtractions, where non-retrieval procedures are mainly used. This amplitude modulation was not evident in additions, where direct retrieval strategies are believed to be used. Our results suggest that the problem size effect is related to non-retrieval procedures of calculation.

The arithmetic problem size effect in children: an event-related potential study

“…The late slow wave, i.e., late positivity component (LPC), which has been put forward as a brain signature of the problem size effect, was defined as having a mean amplitude value in the 500–675 ms range. This time window was chosen because it is the window where the LPC has been described in previous ERP research in adults (Niedeggen and Rösler, 1999; Núñez-Peña et al, 2005, 2006, 2011; Núñez-Peña and Escera, 2007; Núñez-Peña, 2008) and children (Prieto-Corona et al, 2010). We only analyzed the mean amplitude of the LPC, and not the peak amplitude or peak latency of the LPC because the LPC is a slow wave component without a clear starting point, peak, and ending point.…”

“…Event-related potentials during arithmetic in adults also revealed the existence of a late positive slow wave (e.g., Pauli et al, 1994, 1996; Niedeggen and Rösler, 1999; Iguchi and Hashimoto, 2000; El Yagoubi et al, 2003; Núñez-Peña et al, 2005, 2006; Szucs and Csepe, 2005; Núñez-Peña and Escera, 2007; Núñez-Peña, 2008; Prieto-Corona et al, 2010; Szucs and Soltesz, 2010; Chen et al, 2013). This late component, which shows a posterior distribution and starts at about 400 to 500 ms post-stimuli, may be the brain signature of the problem size effect.…”

“…Numerous behavioral studies have reported this problem size effect in adults and children (see for a review Zbrodoff and Logan, 2005). The electrophysiological correlates of this problem size effect have been well documented in adults (Jost et al, 2004a,b; Núñez-Peña et al, 2005, 2006, 2011; Núñez-Peña, 2008), which makes this effect an excellent paradigm to investigate mental arithmetic. To the best of our knowledge, there are no studies that have examined this problem size effect in children.…”

“…This late component, which shows a posterior distribution and starts at about 400 to 500 ms post-stimuli, may be the brain signature of the problem size effect. More specifically, the amplitude of this late positive slow wave increases as the problem size increases (Pauli et al, 1994, 1996; Núñez-Peña et al, 2005, 2006; Núñez-Peña, 2008). This amplitude modulation has been reported for multiplication (Pauli et al, 1994, 1996), addition and subtraction (Núñez-Peña et al, 2005, 2006).…”

“…More specifically, the amplitude of this late positive slow wave increases as the problem size increases (Pauli et al, 1994, 1996; Núñez-Peña et al, 2005, 2006; Núñez-Peña, 2008). This amplitude modulation has been reported for multiplication (Pauli et al, 1994, 1996), addition and subtraction (Núñez-Peña et al, 2005, 2006). The amplitude of this positive slow wave is reduced by practice, probably because practice strengthens the memory trace and encourages the use of retrieval (Pauli et al, 1994; Núñez-Peña, 2008).…”