Executive Function

Executive Function is a term given to cognitive skills relating to the conscious control of thoughts and actions including basic processes of memory (particularly working memory), inhibitory control, attention and planning (see Figure 2.3). Researchers have suggested that important executive function skills form part of a central executive component of working memory (see Baddeley, 1992) and evidence has supported a

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relationship between these various working memory measures and arithmetic development (Blair & Razza, 2007; Bull, Espy & Wiebe, 2008; Bull & Lee, 2014; Chu et al., 2016). Bull and Lee (2014) suggest that executive function may be related to high academic achievement because children with good executive function may show good school-related behaviours including good attention in class, high focus on working activities and ability to refrain from disruptive behaviour in a classroom. Despite a growth of interest in executive function in recent years, it is still an ill- defined construct and there continues to be discrepancies in the way that executive function is defined and measured (Zelazo & Müller, 2002). Moreover, there exists some debate within the literature about the true nature of executive function, with some researchers arguing that these skills are in fact separate constructs rather than a unitary factor (e.g. van der Sluis, de Jong, & van der Leij, 2007).

In numerical development literature, executive function is commonly (although not consistently) defined as a measure encompassing three main skills: inhibition (overriding a dominant response), shifting (switching flexibly between tasks and rules) and updating (monitoring the contents from working memory). Other skills also examined can include selective attention, planning, goal setting and self-regulation. Working memory is an active part of the memory system, responsible for temporarily storing information and mentally working on and processing the information. It has been implicated in executive function since the earliest definitions and remains a common measure in more recent executive function tasks. Working memory and updating are clearly linked to arithmetic because in order to compute a calculation, an individual needs to consider the sum (phonologically or orthographically) and actively hold the digits in memory whilst retrieving results. Inhibition may be important for ensuring the correct use of a calculation method. For example, a child may be experienced in addition and thus have to inhibit this response for a less well practiced subtraction question. For more advanced number skills, inhibition of irrelevant information may be important, for example selecting appropriate information from a word problem.

Shifting skills are useful in a range of numerical processing tasks including computing different types of arithmetic sum (e.g. moving quickly from addition to subtraction) and moving between different forms of notation (verbal and orthographic).

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Figure 2.3 Simplified model adapted from (Diamond, 2013). Executive function and related terms.

The tasks used to measure these constructs in children vary across different studies, although there are a number of key tasks that are commonly used in the literature. Updating is often measured using a working memory task, for instance a backward digit or word span task (e.g. Wechsler Adult Intelligence Scale; WAIS-III; Wechsler, 1997). A simple forward digit or word span task is a good measure of a child’s short- term memory (simply repeat the words you hear in increasing number of words within an item). However, as working memory and updating is assessing the ability to process information stored in a short-term (limited capacity) store, a backward span task (repeat the words/digits heard backwards) requires the use of processing upon the information held. Note that the use of a backward digit task may confound results for

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numerical development, and therefore a backward word span is a preferred working memory task within this literature.

Inhibition is commonly measured via a Stroop test (Stroop, 1935) or Head Toes Knees and Shoulders Task (HTKS; e.g. Burrage et al., 2008). Both of these assess the child’s ability to inhibit an automatic (or dominant response). The HTKS task is suitable for young children and it requires them to control the dominant reaction when asked to “touch your head” by doing the opposite and touching their toes (or similarly for knees and shoulders). A common measure for a shifting task is the Wisconsin Card Sorting Task (e.g. Struss et al., 2000) whereby children learn to associate a rule with a set of cards but then this rule is switched, and the participant must deduce what the new rule is. For younger children, similar but simpler card sorting tasks have been used to measure the ability of a child to switch between different perspectives (e.g. shifting task; Dick, 2014).

Developmental studies have examined if these separate measures relate to a unitary underlying construct, using factor analysis. There is evidence to support this, and moreover to show that this factor correlates with general learning attainment including arithmetic (Bull et al., 2011; Bull & Scerif, 2001; Hughes, Ensor, Wilson, & Graham, 2009). However, some studies have suggested that these skills may be tapping into slightly different constructs, with a possible-two factor model; inhibition and shifting as one factor and working memory as a second (Lee et al., 2011; Van der Ven et al., 2012). For example, Miyake et al. (2000) showed through exploratory factor analysis that although correlated, three executive function tasks measuring shifting, updating and inhibition are clearly separable to one another. This finding suggests that it is important to consider the unity and diversity of executive functions. One potential reason for the different findings within the literature may be partly due to the measures used to examine executive function and the ages of the children within the study. In general, researchers examining numerical development assess executive function as one main factor although it is not completely clear if this is consistently the case (Fuhs, Hornburg, & McNeil, 2016).