Pathways to arithmetic fact retrieval and percentage calculation in adolescents

Abstract

There are both similarities and differences in the cognitive mechanisms underlying arithmetic fact retrieval and percentage calculation in adolescents. Adolescents' symbolic-number processing, arithmetic fact retrieval, and percentage calculation continue to rely on the linguistic pathways, whereas the reliance upon the spatial pathway has ceased. The reliance upon the quantitative pathway varies depending on the task.

Examining the Differential Role of General and Specific Processing Speed in Predicting Mathematical Achievement in Junior High School

“…According to the Cattell–Horn–Carroll (CHC) theory of cognitive abilities, processing speed typically includes: perceptual speed, decision speed, arithmetic fluency, and reading fluency ( Schneider and Mcgrew 2012 ). Several existing studies reported that processing speed is associated with children’s mathematical achievement ( Bull and Johnston 1997 ; Cowan et al 2011 ; Fuchs et al 2006 ; Fung et al 2014 ; Geary 2011 ; Hecht et al 2001 ; Lambert and Spinath 2017 ; Leikin et al 2014 ; Lin 2020 ; Passolunghi and Lanfranchi 2012 ; Rohde and Thompson 2007 ; Taub et al 2008 ; Träff et al 2017 ).…”

“… Rohde and Thompson ( 2007 ) reported that processing speed, which is assessed by symbolic visual matching—letters and numbers stimuli, constantly accounted for a significant amount of additional variance in mathematics performance. Additionally, processing speed could also predict mathematic achievement longitudinally ( Cowan et al 2011 ; Geary 2011 ; Passolunghi and Lanfranchi 2012 ; Träff et al 2017 ). Path analyses models revealed the following findings about processing speed: (1) prediction power of number symbolic visual matching for numerical competence among pre-schoolers, and (2) prediction power for mathematical achievement among followed-up first graders ( Passolunghi and Lanfranchi 2012 ).…”

“…Processing speed is divided into general processing speed (perceptual and decision speed) and specific processing speed (number facility/arithmetic and reading fluency [representing the academic fluency]) ( Schneider and Mcgrew 2012 ). For example, the specific processing speed measured by number facility ( Fuchs et al 2006 ; Passolunghi and Lanfranchi 2012 ; Träff et al 2017 ) or arithmetic fluency ( Cowan et al 2011 ; Geary 2011 ; Hecht et al 2001 ; Lambert and Spinath 2017 ) can significantly predict mathematical achievement; however, this relationship is not shared by general processing speed ( Andersson and Lyxell 2007 ; Fuchs et al 2006 ; Jordan et al 2003 ; Tikhomirova et al 2020 ).…”

Logical Reasoning, Spatial Processing, and Verbal Working Memory: Longitudinal Predictors of Physics Achievement at Age 12–13 Years

“…This test was developed by the first author and has been used in a number of studies on children aged 6–15 years (e.g., Träff et al, 2017a,b,c). The child was presented with sequences of words read by the experimenter, spanning from a minimum of two words to a maximum of seven words.…”

Time Reading in Middle and Secondary School Students: The Influence of Basic-Numerical Abilities

“…In line with previous research as described above, we expected basic numerical abilities to predict time reading in general significantly. In particular, addition (reflecting magnitude manipulation) and arithmetic fact knowledge (e.g., multiplication) were shown to be significant predictors of mathematical achievement in general (e.g., Geary, Nicholas, Li, & Sun, 2017;Jordan, Hanich, & Kaplan, 2003;Krajewski & Schneider, 2009;Träff, Skagerlund, Olsson, & Östergren, 2017) and digital time reading but also to a lesser extent analog time reading in particular (e.g., Friedman & Laycock, 1989). Even tough studies are missing, it seems reasonable that subtraction skills also reflecting magnitude manipulation (e.g., Dehaene & Cohen, 1997) should also be a relevant predictor of time reading in general.…”