Aging, rule-violation checking strategies, and strategy combination: An EEG study in arithmetic

https://doi.org/10.1016/j.ijpsycho.2017.07.003Get rights and content

Highlights

  • We report an EEG study of strategy execution in arithmetic problem solving.

  • Strategy combination was found when both five- and parity-rule were violated.

  • ERPs revealed distinct time-courses for one- and both-rule violation problems.

  • The time course of these modulations differed for young and older adults.

  • Time-frequency analyses revealed several changes with aging.

Abstract

In arithmetic, rule-violation checking strategies are used while participants solve problems that violate arithmetic rules, like the five rule (i.e., products of problems including five as an operand end with either five or zero; e.g., 5 × 14 = 70) or the parity rule (i.e., when at least one of the two operands is even, the product is also even; otherwise the product is odd; e.g., 4 × 13 = 52). When problems violate both rules, participants use strategy combination and have better performance on both-rule than on one-rule violation problems (i.e., five or parity rule). Aging studies found that older adults efficiently use one-rule violation checking strategies but have difficulties to combine two strategies. To better understand these aging effects, we used EEG and found important age-related changes while participants used rule-violation checking strategies. We compared participants' performance while they verified arithmetic problems that differ in number and type of violated rule. More specifically, both-rule violation problems elicited larger negativity than one-rule violation problems between 600 and 800 ms. Five-rule violation problems differed from parity-rule violation problems between 1100 and 1200 ms. Moreover, rule-violation checking strategies and strategy combination involved delta, theta, and lower alpha frequencies. Age-related changes in ERPs and frequency were associated with less efficient strategy combination. Moreover, efficient use of one-rule violation checking strategies in older adults was associated with changes in ERPs and frequency. These findings contribute to further our understanding of age-related changes and invariance in arithmetic strategies, and in combination of arithmetic strategies.

Introduction

To accomplish a wide variety of cognitive tasks, people know, select, and execute multiple strategies (see Siegler, 2007, for a review). A strategy can be defined as “a procedure or a set of procedures for achieving a higher level goal or task” (Lemaire and Reder, 1999, p. 365). Previous research revealed that, with aging, older adults use fewer strategies, use available strategies in different proportions, select the best strategy (i.e., which yields the best performance) less often, and execute strategies less efficiently (e.g., Mata et al., 2007, Hertzog and Dunlosky, 2004, Touron and Hertzog, 2009; see Lemaire, 2016, Hinault and Lemaire, 2016a, for reviews). However, the neural correlates of these age-related changes in strategic variations are poorly documented. The main goal of this study was to investigate age-related differences in electrophysiological signatures of cognitive strategies. We pursue this issue in the specific context of arithmetic, but findings generalize to cognitive domains where young and older participants are known to use multiple rule heuristics rule-violation checking strategies and strategy combination.

In arithmetic, strategy use and strategy performance have been investigated with two types of tasks, production and verification tasks. In verification tasks, like the one used in the present study, participants are shown arithmetic equations like 8 × 4 = 32, or 8 × 4 = 31, and have to say whether these equations are true or false. Previous research found that participants can rely on calculation strategies (i.e., calculate the exact answer, then compare it to the proposed answer) and non-calculation strategies like rule-violation checking strategies (i.e., reject proposed answers that violates arithmetic rules). Previous research has found that participants use the parity-rule violation checking strategy if the equation violates the parity rule (i.e., when at least one of the two operands is even, the product is also even; otherwise the product is odd; e.g., 4 × 13 = 52) and the five-rule violation checking strategy if the equation violates the five rule (i.e., products of problems including five as an operand end with either five or zero; e.g., 5 × 14 = 70). Participants are faster to correctly reject a proposed product that violates arithmetic rules (e.g., 5 × 14 = 62) than when a false product respects arithmetic rules (e.g., 5 × 14 = 60; Krueger and Hallford, 1984, Krueger, 1986, Lemaire and Fayol, 1995, Lemaire and Reder, 1999, Masse and Lemaire, 2001, Siegler and Lemaire, 1997). These differences in participants' performance between rule-violation problems and no rule-violation problems have been accounted for by assuming that participants use fast rule-violation checking strategies on rule-violation problems and slower calculation strategies on no rule-violation problems. Moreover, previous research found that some rule violation checking strategies are faster than others (e.g., five-rule violation checking strategy is faster than parity-rule violation checking strategy; Lemaire and Reder, 1999, Masse and Lemaire, 2001). Recently, Hinault et al., 2014a, Hinault et al., 2015 found that participants had better performance to reject rule-violation problems that violated both the five- and the parity-rules than problems that violated only the five-rule or only the parity-rule. The authors proposed that participants combined both five- and parity-rule violation checking strategies on both-rule violation problems. This strategy combination led people to determine whether an equation with 5 and an odd operand had an odd product, and whether an equation with 5 and an even operand had an even product.

Among factors that influence arithmetic strategy use, participants' age strongly influences which and how strategies are used. Aging studies revealed both age-related differences and similarities in how young and older adults use rule-violation checking strategies. Hinault et al. (2015) found no differences between young and older adults in the five-rule and the parity-rule violation effects, suggesting that young and older adults can use rule-violation checking strategies as efficiently. Moreover, although Hinault et al. found effects of strategy combination in both young and older adults, older adults showed smaller effects of strategy combination, with reduced differences between both-rule violation problems and one-rule violation problems in older than in young adults. This suggests that the efficiency of strategy combination decreases with age.

Despite previous interesting findings on aging and strategies, a number of issues remain unaddressed regarding how young and older adults differ in rule-violation checking strategies and in strategy combination. For example, we ignore whether smaller benefits associated with both-rule violation problems in older adults than in young adults come from the same processes being implemented later and/or less efficiently in older adults than in young adults. Alternatively, aging could affect specific processing steps such as encoding of problem features or co-activation of rule-violation checking strategies before strategy combination. Moreover, we do not know if age invariance in behavioral performance associated with five- and parity-rule violation checking strategies results from the same processes to reject one-rule violation problems in young and older adults or whether the same behavioral outcomes result from different sets of mechanisms used in each age group.

The approach adopted here rests on the logic that neural correlates of rule-violation checking strategies and of strategy combination could provide crucial information to determine the processes involved and further characterize age differences and similarities in rule-violation checking strategies (see Hinault and Lemaire, 2016b for a review). As an example, El Yagoubi et al. (2005) studied age-related differences in split effects (i.e., better performance when false proposed answers are far from correct answers than when splits are small). They found that, although both groups were similar regarding behavioral performance, ERPs differed between young and older adults. Indeed, ERPs associated with large and small-split problems were similar in older adults, while, in young adults, a larger positivity for large-split than for small-split problems was observed about 250 ms after problem presentation. These findings suggest that older adults used only one strategy to solve both types of problem, and demonstrate the high sensitivity of EEG to detect group differences, even when both groups do not differ in behavioral measures.

Recently, Hinault et al. (2014a) used electroencephalography (EEG) in young adults to investigate rule-violation checking strategies and strategy combination. They found that both-rule violation problems resulted in a larger negativity than one-rule violation problems between 550 and 850 ms after problem presentation. These differences in event-related potentials (ERPs) were interpreted as the result of problem features activating both rule-violation checking strategies and leading to combination into a single strategy after encoding problem features. ERPs associated with five-rule and parity-rule violation problems were found to differ between 850 and 1400 ms, with a larger positivity for five- than for parity-rule violation problems. These findings were interpreted as reflecting higher consciousness of using the five-rule violation checking strategy relative to the parity-rule violation checking strategy (e.g., Krueger, 1986, Lemaire and Fayol, 1995, Lemaire and Reder, 1999, Masse and Lemaire, 2001). By comparing ERPs associated with rule-violation effects in young and older adults, here, we aimed at determining whether rule-violation effects show similar electrophysiological signatures in both age groups.

We pursued three goals in the present study. First, we investigated age-related differences in ERPs signatures of rule-violation checking strategies and of strategy combination. Following previous works using ERPs in arithmetic, we expected ERPs to reveal differences between young and older adults that behavioral measures sometimes fail to detect (e.g., El Yagoubi et al., 2005). Thus, such findings could bring crucial information to unravel the cognitive processes engaged by older adults during the execution of the five-rule and the parity-rule violation checking strategies. Furthermore, age-related differences in ERPs signatures of strategy combination could further our knowledge about why older adults showed smaller effects of both-rule violation (i.e., as seen in both-rule violation problems being rejected more quickly than one-rule violation problems) than young adults. We predicted that the difference between both-rule violation problems and one-rule violation problems will be of decreased amplitudes and/or duration relative to young adults. Such differences would account for less efficient combination of both rule-violation checking strategies to solve problems. Regarding one-rule violation checking strategies, we expected that older adults show larger and/or earlier differences between five-rule and parity-rule violation problems than young adults to maintain performance equivalent to that of young adults when rejecting problems that violate the five or the parity rule. Alternatively, older adults could be as able as young adults to activate and execute rule-violation checking strategies systematically and efficiently on each rule-violation problem, resulting in similar patterns of activation in both age groups.

The second goal of the present study was to use time-frequency analyses to unravel cognitive processes involved in rule-violation checking strategies and in strategy combination. Until now, no studies were conducted to investigate oscillatory activities underlying rule-violation checking strategies. We expected increased delta, and theta in both-rule violation problems compared to one-rule violation problems. Such modulations were expected, as these frequencies were previously associated with retrieval of arithmetic procedures and rules (see Hinault and Lemaire, 2016b, for a review). As an example, Dimitriadis et al. (2010) observed increased power in the delta band (1–3.5 Hz) when participants executed calculation strategies to solve multiplication problems. Also, theta power (4–8 Hz) has been associated with retrieval strategy for increased power in left hemisphere (e.g., Earle et al., 1996, Grabner and De Smedt, 2011, Grabner and De Smedt, 2012, Klimesch et al., 2005), and working memory efforts for frontal power increase (e.g., Klimesch et al., 1996, Klimesch et al., 1997, Micheloyannis et al., 2005, Pivik et al., 2012). Moreover, reduced power in the lower alpha band (8–10 Hz) widespread over the scalp had been reported during calculation strategies (Earle et al., 1996, Glass, 1968, Micheloyannis et al., 2005, Yu et al., 2009, Yu and Zhang, 2012). During strategy combination, co-activation of several arithmetic rule-violation checking strategies and combination into a single strategy is expected to involve these frequencies. Moreover, power differences in such frequencies were also expected in five-rule violation problems relative to parity-rule violation problems. Indeed, results are expected to better distinguish the processes involved in rule-violation checking strategies. Furthermore, the frequencies involved, or their latencies, should differ between one-rule and both-rule violation problems to underlie the behavioral differences found during the resolution of these problems. Such differences were expected in a similar latency range than in our previous ERPs study (Hinault et al., 2014a). These results will enable a better specification of the processes involved during strategy combination, as well as the differences between mechanisms underlying verification of the five-rule and the parity-rule violation.

The third and final goal of the present study was to investigate age-related changes in time-frequency patterns associated with strategy combination and with rule-violation checking strategies. The rationale for carrying out these analyses was to show qualitative differences between young and older adults during the selection and execution of rule-violation checking strategies and during strategy combination. These findings will provide a deeper understanding of aging effects on strategic processing in arithmetic. Overall, we expected decreased power in older adults, compared to young adults, in line with previous works (e.g., Finnigan and Robertson, 2011, Gajewski and Falkenstein, 2014). Moreover, as previous works showed that strategy combination is less efficient with age (Hinault et al., 2015), delayed modulations of oscillatory activities, or differences in the frequency bands involved were expected. For one-rule violation problems, increased power in older adults compared to young adults was expected to document how older adults manage to reach similar behavioral performance to young adults. Alternatively, in line with similar behavioral performance, similar oscillatory patterns could be observed in young and older adults for parity- and five-rule violation problems.

Section snippets

Participants

Fifteen young adults and 15 older adults participated in this experiment (see participants' characteristics in Table 1). All participants were right-handed, and reported normal or corrected-to-normal vision. Participants were not informed of the purpose of the experiment. An informed consent was obtained prior to participation. Behavioral and ERP data of young adults were analyzed and published previously (Hinault et al., 2014a).

Stimuli

The stimuli were multiplication problems presented in a standard

Behavioral analyses

Participants' performance on false five problems were analyzed with 2 (Age: young adults, older adults) × 4 (Rule Violation: no-rule, parity-rule, five-rule, both-rule) mixed-design ANOVAs (Šidák corrected; Šidák, 1967; Table 2, Table 3, Fig. 2), separately for RTs and percentages of errors. To discard an interpretation in terms of different speed/accuracy tradeoff between young and older adults, additional analyses were run with error rates as a covariate in ANOVAs, but the same results were

Discussion

The aim of the present study was to investigate age-related differences in electrophysiological signatures of strategy combination and of rule-violation checking strategies. First, behavioral results replicated previous findings showing that older adults were as efficient as young adults to reject parity-rule and five-rule violation problems, but were less efficient on both-rule violation problems (Hinault et al., 2015). Error rates were included as covariates in analyses without changing the

Acknowledgements

We would like to thank Amandine Parlanti for her help with data collection. We also would like to thank three anonymous reviewers for their help with the manuscript and their helpful comments.

This work was supported in part by the CNRS (French NSF) and by a grant from the Agence Nationale de la Recherche (Grant # ANR-13-BSH2-0005-01).

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