Representation and working memory in early arithmetic

“It is generally assumed that once arithmetic operations are fully mastered, the importance of spatial skills decreases and problem solving mainly relies on verbal processes (Rasmussen & Bisanz, 2005; van der Ven et al., 2013; Van de Weijer-Bergsma et al., 2015).”

“…involvement of visual–spatial skills both during the early stages of mathematics learning (Hegarty & Kozhevnikov, 1999; McKenzie, Bull, & Gray, 2003; Rasmussen & Bisanz, 2005) and during subsequent developmental phases in performing math tasks (Battista, 1990; Casey, Nuttall, Pezaris, & Benbow,…”

“…predicts the development of arithmetical attainment in school-age children, and the results seem to confirm the assumption that phonological awareness is a domain-general precursor variable of math achievement in children (Hecht et al., 2001; Koponen et al., 2007; Rasmussen & Bisanz, 2005).”

“Visuo-spatial WM is needed to acquire a basic knowledge of numbers [46,50,51], while verbal WM seems to be more useful later on, for the acquisition of more complex mathematical abilities [46,47,51], such as math fluency and word problem solving [20,52].”

“Two established predictors of word-problem solving, namely non-verbal IQ and word reading skills (Rasmussen & Bisanz, 2005; Vilenius-Tuohimaa et al., 2008; Wong & Ho, 2017), were used as the control variables.”

“…Casey, Nuttall, & Pezaris, 2001; Delgado & Prieto, 2004; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; Holmes, Adams, & Hamilton, 2008; Kyttälä, Aunio, Lehto, Van Luit, & Hautamäki, 2003; Lubinski & Benbow, 1992; McKenzie, Bull, & Gray, 2003; McLean & Hitch, 1999; Rasmussen & Bisanz, 2005).”

“It is unclear as to how the different mechanisms of WM influence the acquisition and application of knowledge in different areas of mathematics and whether the importance of one or more WM component changes with maturity (Rasmussen & Bisanz, 2005; Swanson & Kim, 2006; Vandierendonck, 2012).”

“This has been proposed in mathematics research with children (Rasmussen & Bisanz, 2005).”

“Those who perform better in spatial tasks tend to have a better performance on a test of mathematical ability [4,5].”

“Similarly, some authors found higher within- than between-component correlations (e.g. Alloway et al., 2006; Noël, 2009) and a differential involvement of the verbal and VS components in addition solving (e.g. De Smedt et al., 2009; Noël, 2009; Rasmussen & Bisanz, 2005).”

“As children progress through school they increasingly use verbal representations of quantities such as number words and the role of the VSSP has less impact (see Rasmussen and Bisanz, 2005).”

“This mechanism is crucial for a wide range of cognitive tasks (Rasmussen and Bisanz 2005; Nettelbeck and Burns 2010; Injoque-Ricle and Burin 2011).”

“Offenbar sind alle drei Arbeitsgedächtniskomponenten mit ma thematischen Kompetenzen assoziiert (David, 2012; Frisovan den Bos, van der Ven, Kroes bergen & van Luit, 2013; Rasmussen & Bisanz, 2005; Schuchardt & Mähler, 2010).”

“Other studies have shown a significant correlation between the visuo-spatial sketchpad and mathematics (Bull, Espy, & Wiebe, 2008; Geary et al., 2007; Henry & MacLean, 2003; Holmes & Adams, 2006; Kyttälä, 2008; Maybery & Do, 2003; Rasmussen & Bisanz, 2005; Intelligence.”

“An interference score was calculated for each participant by subtracting their preswitch proportion correct score from their border phase proportion correct score, and dividing that difference score by their preswitch proportion correct score (Archibald & Kerns, 1999; Rasmussen & Bisanz, 2005).”

“Previous studies highlighted that these skills are related to superior performance on counting tasks [10], nonverbal problem solving [11] as well as better overall mathematical attainment and performance [12, 13].”

“…Swanson & Jerman, 2006), and weak WM has been associated with difficulties in early numeracy acquisition (Gersten et al., 2005; Toll & Van Luit, 2013), slower learning of counting sequences (Noël, 2009), and lower accuracy in solving simple addition problems (Noël, 2009; Rasmussen & Bisanz, 2005).”

“Studies have found that performance on spatial tasks like mental rotation is correlated with mathematics achievement in school age children [1,30,36] and that visuospatial working memory is related to number and mathematics problem-solving [18,37].”

“Rasmussen and Bisanz (2005) examined the involvement of subcomponents of working memory in early arithmetic development.”

“More specifically, during the preschool period, spatial WM abilities are highly associated with performance on mathematical tasks because these tasks are underscored by the emerging ability to visually represent numbers (Rasmussen & Bisanz, 2005).”

“Some studies believe that students’ ability to maintain and operate visual spatial information plays a key role in students’ counting [61], computing [62], problem solving [63] and other mathematical abilities.”

“Previous studies demonstrated the applicability of the Corsi-Block task for children aged four or older (e.g., Bull et al. 2008; Passolunghi and Cornoldi 2008; Rasmussen and Bisanz 2005; Roebers and Zoelch 2005; Schmid et al. 2008).”

“While these have specific roots and meanings in mathematics education (Battista, 1990; Clements & Battista, 1992; Rasmussen & Bisanz, 2005), they can also be applied in science, engineering, and transdisciplinary settings (e.g., Hsi et al., 1997).”

“sketches within the framework of solving arithmetic tasks represents a strategy characteristic of younger children [96,97], while reliance on phonological, verbal information within working and long-term memory represents a more advanced strategy [98,99].”

“First of all, we replicated the common findings in the literature showing a strong association between the CE and numerical (Kroesbergen et al., 2009; Noël, 2009; Passolunghi & Lanfranchi, 2012) and arithmetical (Noël, 2009; Rasmussen & Bisanz, 2005) performance in young children.”

“…working memory uniquely explains individual differences in children’s arithmetic ability in the presence of other number-specific or general cognitive factors (e.g., De Smedt et al., 2009; Nosworthy et al., 2013; Rasmussen & Bisanz, 2005; Van der Ven, Van der Maas, Straatemeier, & Jansen, 2013).”

“…Hoard et al., 2008; Krajewski & Schneider, 2009; LeFevre et al., 2010; Rasmussen & Bisanz, 2005), especially in younger children, whereas the phonological loop predicts performance in older children (Andersson, 2008; Bull et al., 2008; Hoard et al., 2008; Noël, 2009; Rasmussen & Bisanz, 2005).”

“Studies have found that this heavier reliance on phonological working memory is seen especially during arithmetic problem solving when the children convert the mathematical symbols into verbal codes (Lee, Ng, and Ng 2009; Logie, Gilhooly, and Wynn 1994; Rasmussen and Bisanz 2005).”

“General working memory capacity has been associated with accuracy when solving simple addition and subtraction arithmetic problems (Adams & Hitch, 1997; Hecht, 2002; Seyler, Kirk, & Ashcraft, 2003), even in preschool children with no knowledge of formal mathematics (Rasmussen & Bisanz, 2005).”

“An ability to visualise (and mentally manipulate) sets of objects is an advantage in building early addition skills (Rasmussen & Bisanz, 2005).”

“Some researchers even assume that spatial processes are recruited for mathematics (Presmeg, 2006; Rasmussen & Bisanz, 2005).”

“The contribution of working memory to arithmetic word problems is not stable in elementary school students (Rasmussen & Bisanz, 2005; Meyer, Salimpoor, Wu, Geary, & Menon, 2010).”

“In a study with Canadian primary school children (Rasmussen & Bisanz, 2005) it was stated that the phonological loop represented the best predictor for achievements in verbal mathematical problems from the beginning of the first school year.”

“…better on tests of mathematical ability (Cheng & Mix, 2014); for instance, in preschoolers and first graders, spatial skills are a good predictor of math skills (Laski et al., 2013; Rasmussen & Bisanz, 2005; Verdine, Irwin, Golinkoff & Hirsh-Pasek, 2014; Zhang et al., 2014; Zhang & Lin, 2015).”

“The importance of efficient spatial layout in mathematics for cognition begins at a young age [8, 9].”

“…and with previous litera - ture regarding the crucial role of visuospatial WM (Ashke-nazi & Shapira, 2017; De Vita et al., 2022; Menon, 2016; Rasmussen & Bisanz, 2005 ) and the influence of counting (Koponen et al., 2016, 2019; Petitto, 1990; Schneider et al., 2018) in number line knowledge…”

“During the formative years of schooling, children rely on verbal WM during the verbal rehearsal of multiplication tables, as they hold the sum, its components and the answer in mind (e.g., Rasmussen & Bisanz, 2005).”

“…Lin, 2015), visuospatial skills (Cornu, Schiltz, Martin, & Hornung, 2018; Verdine, Irwin, Golinkoff, & Hirsh-Pasek, 2014), working memory (Noël, 2009; Rasmussen & Bisanz, 2005; Traverso, Tonizzi, Usai, & Viterbori, 2021) and inhibition (Blair & Razza, 2007; Espy et al., 2004; Fuhs & McNeil, 2013).”

“Sebenarnya, working memory telah berperan pada awal ketrampilan aritmatika dasar (Rasmussen & Bisanz, 2005; Nelwan et al., 2021 ).”

“The role spatial memory plays in how preschoolers solve arithmetic problems helps explains why they are more accurate when solving non-verbal arithmetic problems than verbal arithmetic problems [4].”

“Spatial thinking is positively related to mathematical thinking (Battista, 1990); that is, students who perform better on spatial tests perform well on mathematics tests (Rasmussen & Bisanz, 2005).”

“A research by Rasmussen and Bisanz (2005), conducted with elementary and kindergarten students, has revealed that answerers have difficulty in ignoring irrelevant information and this leads to decrease in their performance especially mathematics performance.”

“In their study, Ramussen & Bisanz [49] showed that for preschool children the best and unique predictor of performance was visuospatial active attention.”

“Yitong Jiang 1 · Ning Jin 2 · Xinyu Chen 3 · Jiaying Hao 3 · Xin Joe Hwang 3 · Xiaoyi Hu 3,4 it supports improving math achievement and overall cognitive development in both the short and long term (Geary et al., 2007; Otenen & Kanero, 2024; Rasmussen & Bisanz, 2005 ).”

“WM is undoubtedly an important executive function that plays a significant role in many academic achievements, including reading comprehension and mathematic problem-solving (Borella & de Ribaupierre, 2014; Caviola, Mammarella, Cornoldi, & Lucangeli, 2012; Rasmussen & Bisanz, 2005).”

“Previous studies have found a close relationship between arithmetic and these high-level cognitive abilities.(32,33) Meanwhile, numbers of studies have proved that the frontal network is essential to human’s high-level cognitive processing.”

“…of working memory on arithmetic and problem solving (Adams & Hitch, 1997; Imbo & Vandierendonck, 2007; McKenzie et al., 2003; Raghubar et al., 2010; Rasmussen & Bisanz, 2005) and arithmetic fluency on strategy development and problem-solving speed (Bull & Johnston, 1997; Carr & Alexeev, 2011;…”

“…tampil lebih baik dalam tugas-tugas spasial juga tampil lebih baik dalam tes kemampuan matematika (Casey, Nuttall, & Pezaris, 2001; Delgado & Prieto, 2004; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; Holmes, Adams, & Hamilton, 2008; McKenzie, Bull, & Gray, 2003; Rasmussen & Bisanz, 2005).”

“Rasmussen and Bisanz [24] separated working memory into 3 components and demonstrated that visual and spatial working memory predicted performance on”

“Therefore, solving a simple word problem needs extra skills that are not required for a concrete real-life problem situation (Rasmussen & Bisanz, 2005).”

“The poor performance of individuals with MD can be explained by one or more of these dimensions explored in previous studies (e.g. Hecht et al., 2001; Noel, Seron, and Trovarelli, 2004; Rasmussen and Bisanz, 2005; Wagner and Torgesen, 1987).”