Investigating the role of attention in the identification of associativity shortcuts using a microgenetic measure of implicit shortcut use

Abstract

Many mathematics problems can be solved in different ways or by using different strategies. Good knowledge of arithmetic principles is important for identifying and using strategies that are more sophisticated. For example, the problem “6 + 38 − 35” can be solved through a shortcut strategy where the subtraction “38 − 35 = 3” is performed before the addition “3 + 6 = 9,” a strategy that is derived from the arithmetic principle of associativity. However, both children and adults make infrequent use of this shortcut and the reasons for this are currently unknown. To uncover these reasons, new sensitive measures of strategy identification and use must first be developed, which was one goal of our research. We built a novel method to detect the time-point when individuals first identify an arithmetic strategy, based on trial-by-trial response time data. Our second goal was to use this measure to investigate the contribution of one particular factor, attention, in the identification of the associativity shortcut. In two studies, we found that manipulating visual attention made no difference to the number of people who identified the shortcut, the trial number on which they first identified it, or their accuracy and response time for solving shortcut problems. We discuss the theoretical and methodological contribution of our findings and argue that the origin of people’s difficulty with associativity shortcuts may lie beyond attention.

Conceptual knowledge of the associativity principle: A review of the literature and an agenda for future research

“…No studies have explored working memory and switching with associativity problems, although findings from the inversion literature indicate that they may play a role (Dubé & Robinson, 2010). Attention is theoretically expected to play a role in solving inversion problems (Siegler & Araya, 2005) but there is no empirical evidence that it is important on 'a + b − c' and 'a × b ÷ c' problems (Dubé & Robinson, 2010b;Eaves et al, 2020). Further research into the role of domain-specific and domain-general skills in strategy identification and execution is therefore warranted.…”

“…Three studies have compared performance on conducive and non-conducive associativity problems (Eaves et al, 2019(Eaves et al, , 2020Edwards, 2013). Edwards (2013) found that self-reported shortcut use was significantly higher on 'a × b ÷ c' problems that were conducive to a shortcut than those that were not conducive.…”

“…It may also be a useful approach for researchers wanting to measure strategy use in an unbiased way. To the best of our knowledge, all but one previous study (Eaves et al, 2020) that used self-reported solution strategies did so by asking participants to describe the strategy they used multiple times in a short timeframe, i.e. after every trial (e.g.…”

“…Only three published studies have investigated associativity as a standalone concept, rather than as a comparison for other principles (Eaves et al, 2019(Eaves et al, , 2020Edwards, 2013). Given the theoretical importance of associativity in algebra learning and the transition from basic to advanced mathematics, further research is warranted.…”

“…To understand how those skills help an individual select the shortcut strategy though, new methods might need to be created. For example, measures that can separate the process of strategy identification from strategy execution (Eaves et al, 2020) might be more likely to capture the contribution of the skills involved because they target mechanisms more precisely (i.e.…”