Representation and working memory in early arithmetic

“Rasmussen and Bisanz (2005) have suggested that young children use non-verbal mental models to solve mathematical tasks and, in general, during kindergarten and preschool years children are dependent on visuo-spatial resources (Hitch et al., 1988; Walker et al., 1994).”

“Thus, the relationships between a single cognitive process and math skill found in younger children may not necessarily generalize to older children (Andersson, 2008; Rasmussen & Bisanz, 2005).”

“Young children with higher performance in phonological memory have been shown to be more accurate in arithmetic processes such as addition (Noel et al., 2003; Rasmussen & Bisanz, 2005).”

“Early arithmetic is performed on non-symbolic quantities, such as dots ( ), and this direct presentation of quantity could encourage the use of quantity calculations (e.g., visually grouping) (cf. Rasmussen & Bisanz, 2005).”

“This finding is consistent with those of other studies (Gathercole & Pickering, 2000; Holmes & Adams, 2006; Rasmussen & Bisanz, 2005) that have shown the visual–spatial sketchpad to be important to math performance because it is responsible for the processing of visual and spatial information, such…”

“Younger children prefer visual strategies like pointing compared to older children who use verbal strategies like rehearsal [31].”

“Although children with SB had difficulty on large set objectbased arithmetic, which is related to visual–spatial memory in preschoolers (Rasmussen & Bisanz, 2005), their performance on tasks measuring counting knowledge and procedures was equally disrupted.”

“In addition, they must understand the underlying arithmetic operations (Rasmussen & Bisanz, 2005) and be capable of manipulating and understanding number relations (Fuchs et al., 2006).”

“By the same token, working memory was found to be strongly related to arithmetic problem solving (Rasmussen & Bisanz, 2005).”

“Results such as these imply that visuo-spatial working memory is especially relevant for mathematics performance (Alloway and Passolunghi, 2011), although some studies suggest that verbal working memory becomes more relevant with age (Rasmussen and Bisanz, 2005).”

“Later, starting from school age, learning is more dependent on verbal rehearsal to preserve information in memory, thus recruiting more the phonological loop (Hitch et al., 1988; Rasmussen and Bisanz, 2005).”

“…underlying visual-spatial WM was based on recent findings highlighting the role of visual-spatial WM processes in solving arithmetic problems and number writing before school entry and within the first grade (Grube & Seitz-Stein, 2012; Rasmussen & Bisanz, 2005; Simmons, Willis, & Adams, 2012).”

“…(Swanson, 2011), and the finding that only the phonological loop, but not the visual-spatial sketchpad, significantly predicted number-sentence construction is consistent with the suggestion that school-age children tend to represent arithmetic problems in verbal format (Rasmussen & Bisanz, 2005).”

“…may be a particularly important correlate in young children during the early stages of learning single-digit arithmetic, during which children rely heavily on finger counting, which may be visuospatial in nature (eg, McKenzie et al., 2003; Raghabur et al., 2010; Rasmussen and Bisanz, 2005).”

“…older than nine years may rely more on the phonological loop while performing WM required tasks (Andersson & Lyxell, 2007), whereas young children may rely more on different WM resources (i.e., visuospatial) through analogous mental models (Kytta¨la¨ et al., 2010; Rasmussen & Bisanz, 2005).”

“It has been argued that when younger children solve number word problems they rely on an analogous mental representation of the quantities, that is, tokens that can be manipulated (Rasmussen & Bisanz, 2005).”

“This measure has been used in previous research as a valid measure of the central executive (e.g., Gathercole & Pickering, 2000; Rasmussen & Bisanz, 2005 ).”

“Working memory resources are thought to be especially involved in encoding, calculating, and response generating (Adams & Hitch, 1997; Campell & Xue, 2001; Imbo & Vandierendonck, 2008; Rasmussen & Bisanz, 2005 ).”

“The results of the study highlight the link between mental imagery processes and math skills, and in particular the connection between the capacity to use mental representations from a preschool age and the ability to compute during the early stages of math learning, confirming the recent literature (Rasmussen and Bis…”

“This would allow for controlling for visual–spatial working memory capacities, as these are related to QNCs (e.g., Krajewski & Schneider, 2009; Rasmussen & Bisanz, 2005; Simmons et al., 2008).”

“…the three of us?," the child must understand the problem (Lee, Ng, & Ng, 2009), understand the arithmetic operations presented in the statement (Rasmussen & Bisanz, 2005), manipulate and understand the numerical relations established therein (Fuchs et al., 2006), understand the type of problem…”

“Indeed, children with poorer visual-spatial abilities might experience problems with non-symbolic magnitude processing (Rasmussen & Bisanz, 2005), which in its turn might impede the development of symbolic numerical magnitude representations.”

“…between visuospatial working memory and mathematical ability have often been reported (Bull & Lee, 2014; De Smedt et al., 2009; Friso-Van den Bos, van der Ven, Kroesbergen, & van Luit, 2013; Holmes & Adams, 2006; rasmussen & Bisanz, 2005; van der Ven, van der Maas, Straatemeier, & Jansen, 2013).”

“It is the most frequently used model to explain WM in studies concerning WM and mathematics (e.g., Alloway, Gathercole, Willis & Adams, 2004; Bull, Espy & Wiebe, 2008; Kroesbergen, Van de Rijt & Van Luit, 2007; Rasmussen & Bisanz, 2005).”

“Moreover, younger children rely more on visuospatial working memory to retrieve numerical information, while older children use more sophisticated techniques, such as retrieval of numerical information and using verbal working memory (Rasmussen & Bisanz, 2005).”

“133,134 For example, visuospatial abilities are important in holding and manipulating information in mental and complex calculation.”

“Among older children, the contribution of the PL appears to be significant in solving calculus problems or performing exact mental calculations, when using verbal counting strategies, or when required to transform symbols and numeric models into language codes [21,37].”

“A possible explanation for this change might be a shift from initially relying on visuospatial representations of magnitude and problem-solving strategies like finger counting (Rasmussen and Bisanz, 2005) to verbal retrieval strategies (De Smedt et al.”

“The third is that the predictive value of working memory is influenced by the period of childhood growth, where visio-spatial memory seems very strong [39], [40].”

“In pre-kindergarten, VSWM predicts counting skills (Kyttälä, Aunio, Lehto, Van Luit, & Hautamäki, 2003) and nonverbal addition (Rasmussen & Bisanz, 2005).”

“…and Shinn 2004), and domain-general variables such as visual-spatial memory (Geary et al. 2007; Krajewski and Schneider 2009) and verbal working memory (Berg 2008; Chard et al. 2005; Passolunghi et al. 2008; Rasmussen and Bisanz 2005; Hecht et al. 2001, also controlled for general verbal ability).”

“Past research suggests that children who are able to do so have better working memory (Dubé & Robinson, 2010; Rasmussen & Bisanz, 2005), are better inhibitors (Robinson & Dubé, 2013), and have stronger arithmetic skills (Gilmore & Papadatou-Pastou, 2009).”

“Such a visuospatial weakness might account for some numerical difficulties of children in arithmetic (Rasmussen & Bisanz, 2005) or inmore basic number processing (Bachot et al., 2005; Koontz & Berch, 1996).”

“On the other hand, Rasmussen and Bisanz (2005) observed that when simple additions were presented visually using concrete materials, performance in addition tasks was associated with visuospatial WM resources.”

“Children may also depend on different subcomponents within the working memory as a function of age (Andersson & Lyxell, 2007 ; Rasmussen & Bisanz, 2005 ).”

“For instance, Brocki et al. (2007) and Rasmussen and Bisanz (2005) observed a significant relationship between backward span performance and this variant of the day/night task in preschoolers.”

“…1994), magnitude representation (Pelegrina et al., 2015), arithmetical problems (Passolunghi & Siegel, 2001; Passolunghi & Mammarella, 2010; Rasmussen & Bisanz, 2005), quantitative central conceptual structures (Morra et al., 2019), and geometrical achievement (Giofr e et al., 2013, 2014).”

“…Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; Geary, Saults, Liu, & Hoard, 2000; Holmes, Adams, & Hamilton, 2008; Kytt€al€a, Aunio, Lehto, Van Luit, & Hautam€aki, 2003; McKenzie, Bull, & Gray, 2003; McLean & Hitch, 1999; Rasmussen & Bisanz, 2005; Thompson, Nuerk, Moeller, & Kadosh, 2013).”

“…in a variety of ways (Bull & Scerif, 2001; Floyd et al., 2003; Gathercole et al., 2004; Geary, 1993; Hale et al., 2008; McGrew & Wendling, in press; Osmon et al., 2006; Passolunghi & Siegel, 2001; Rasmussen & Bisanz, 2005; Swanson, 1994; Swanson & Beebe-Frankenberger, 2004; Swanson & Jerman, 2006).”

“…Uttal, Meadow, Tipton, Hand, Alden & Warren 2012; Wai, Lubinski & Benbow, 2009) and in early academic skills (e.g., math, reading, writing; Assel, Landry, Swank, Smith & Steelman, 2003; Cheng & Mix 2012; Holmes, Adams & Hamilton, 2008; Passolunghi & Mammuarella 2010; Rasmussen & Bisanz, 2005).”

“…consistent with findings that phonological processes such as fact retrieval are more strongly related to adults’ calculation skills whereas visual-spatial processes are more strongly related to children’s arithmetic skills (McKenzie et al., 2003; Raghubar et al., 2010; Rasmussen & Bisanz, 2005).”

“For instance, younger children rely more on visual representations, but as they get older they tend to use verbal strategies (e.g. rehearsal) that allow them to recode visual information in verbal codes (Alloway, Gathercole, & Pickering, 2006; Rasmussen & Bisanz, 2005).”

“…this task constitutes a measure of the executive control of attention, some have also acknowledged that as it requires the verbal recall of numbers, this information must be maintained in the phonological loop (Bull et al., 2008/this issue; Geary, Hoard, & Hamson, 1999; Rasmussen & Bisanz, 2005).”

“Estudos longitudinais sugerem que o processamento viso-espacial é crucial nos primeiros anos de aprendizagem da matemática para a representação de modelos mentais de quantidade que não envolvam rótulos verbais (Huttenlocher, Jordan, & Levine, 1994; Rasmussen & Bisanz, 2005).”

“Previous research showed that younger children mainly rely on resources of the visuospatial sketchpad to solve mathematical problems [52,53].”

“To be more precise, the visual–spatial sketchpad was found to be associated with finger counting (Rasmussen & Bisanz, 2005), whereas the phonological loop was found to be related to more mature strategies that relied on verbal counting or fact retrieval (De Smedt, Holloway, & Ansari, 2011; Hecht,…”

“…study could add valuable results because previous research (e.g., De Smedt et al., 2009; DeStefano & Lefevre, 2004) has shown that working memory—particularly its visuospatial component (e.g., Rasmussen & Bisanz, 2005)—is a strong predictor of first-grade children’s mathematical achievement.”

“However, most of the relevant research has focused on only the mathematical problem-solving of relatively young students (up to the age of about 7 years; e.g., Rasmussen & Bisanz, 2005; Swanson et al., 2008).”

“Noel, Seron, and Trovarelli (2004) and Rasmussen and Bisanz (2005) reported statistically significant relationships between central executive and performance in single-digit arithmetic.”

“Hitch et al. (1988) found that preschool children rely on visuospatial working memory more than older children do, and Rasmussen and Bisanz (2005) found visuospatial working memory to be the best and only unique predictor of preschool performance on standard nonverbal arithmetic problems.”