Journal of Numerical Cognition (JNC - PsychOpen)
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A Meta-Analysis of the Cross-Sectional and Longitudinal Relations Between Executive Functioning and Math in Early Childhood
No full textMath and executive functioning (EF) skills are thought to be tightly linked in early childhood. To facilitate our understanding of this link in early childhood, here we present a meta-analysis of over 1,000 different correlation values between EF and math measures in early childhood (4-6yrs). The overall average EF-Math relation was r = .350, 95% CI [.338, .361]. We then examined whether the strength of the EF-Math relation in this age-range depends on measurement factors, socio-economic status (SES), and the nature and direction of longitudinal relations. [1] Overall achievement measures of EF and math generally led to higher estimates of the EF-Math relation relative to measures of isolated EF subprocesses or specific math skills, though this may be due more to measurement than developmental factors. [2] EF measures using numerical stimuli inflate estimates of the EF-Math association by roughly 40%. [3] Low SES samples showed the strongest average EF-Math associations. [4] Longitudinal associations that do not adjust for Time-1 measurement of the outcome variable lead to inflated (as much as 120%) estimates of directional associations. After making this adjustment, we found [5a] significant, albeit reduced bidirectional relations between EF and math, and [5b] that math is a stronger predictor of future change in EF than the reverse. In sum, the results of this work contribute to theoretical models of the interaction between EF and math in early childhood, as well as to practical attempts to foster growth in children’s EF and math skills, whether in the lab, classroom or living room
When We Were Young: Memories of Early Mathematics Experiences
No full textEarly math experiences predict children’s later math abilities and beliefs. However, less is known about longer-term associations between early childhood math experiences and adult math outcomes. The present study examined emerging adults’ earliest memories of mathematics and reading experiences, asking whether characteristics of their early learning memories differ across domains of learning and relate to their adulthood math achievement and beliefs. Undergraduate students (n = 161, MAge = 19.6 years) described their earliest memories of math and reading, then completed measures of their math anxiety, math task value, and math achievement. Our results reveal significant domain differences in participants’ age during their earliest memories, the level of social interaction, and their overall rating of the experience. Emerging adults with more positive memories of their earliest math experiences had lower math anxiety, higher math task value, and higher math achievement. Our results provide additional evidence of the long-term associations between early math experiences and later math outcomes and underscore the need to promote early math experiences that are positive and engaging for young children
Embodied Magnitude Processing: On the Relation Between the SNARC Effect and Perceived Reachability
No full textMagnitude information, for instance, regarding weight, distance, or velocity, is crucial for planning goal-directed interactions. Accordingly, magnitude information, including numerical magnitude, can affect actions: Responses to small numbers are faster with the left hand than the right and vice versa (hand-based SNARC effect). Previous experiments found an influence of effector placements on the SNARC effect but also an influence of the mere distance between effectors and numbers. This indicates a sensorimotor grounding of space-number processing. In the current study, we investigated this grounding by probing the SNARC effect close to and far from the hands. We used a magnitude comparison task with a fixed standard of 5 (smaller numbers 1, 2, 3, 4; larger numbers 6, 7, 8, 9) and a sagittal response arrangement to measure hand-based and sagittal SNARC effects for digits presented at different sagittal distances to the hands, i.e., in peripersonal and extrapersonal space. A significant sagittal SNARC effect was found, with the largest effect size in extrapersonal space. Meanwhile, the hand-based SNARC effect appeared only descriptively, with the largest effect size between the hands, i.e., in peripersonal space. Additionally, a purely spatial congruency effect surfaced, prioritizing responses with the hand closer to the number. Together, these results emphasize that responses in simple decision-making tasks can be influenced interactively by a multitude of task-relevant axes and relative spatial locations, including effector placement and stimulus placement, as well as number magnitude
Assessment of Computation Competence and Non-Count Strategy Use in Addition and Subtraction in Grade 1
No full textComputation competence (CC) in simple addition and subtraction using non-counting (NC) strategies is an important learning objective in Grade 1 mathematics but many children, especially low achievers in mathematics, struggle to acquire these skills. To provide these students with the support they need, it is important to have valid and reliable tools for assessing progress in CC and NC strategy use. Developing an assessment instrument for use in Grade 1, when some children start the year unable to solve any problems, is challenging, as is ensuring measurement invariance over a school year when children generally make large achievement gains. This paper presents a new assessment tool for CC and NC strategy use in Grade 1 that was tested in a longitudinal study with N = 1,017 children. Analyses using the Rasch model revealed acceptable mean square scores (MNSQ 0.83 – 1.20). Warm’s Weighted Likelihood Estimate (WLE) reliability scores were acceptable (pre-test .77; post-test .87). Measurement invariance over time was given. The instrument is promising for assessing CC and NC strategy use efficiently and accurately in Grade 1
Examining the Role of Spatial and Mathematical Processes and Gender in Postsecondary Precalculus
No full textPassing the introductory calculus sequence is critical to undergraduate students’ retention in STEM programs. This study examines the relations between three interrelated processes found to influence mathematics learning and achievement: spatial skills, spatial anxiety, and math anxiety. Additionally, it examines the role of gender on these relations and if and how they help explain precalculus achievement. Findings revealed that spatial skills, spatial anxiety, and gender were linked to math anxiety. Furthermore, spatial anxiety and math anxiety were related to strong final exam performance, but spatial skills and gender were not related to achievement. The presented evidence is in accordance with prior research and corroborates the existence of these relational patterns in a postsecondary academic context in addition to the laboratory context. These findings have broad implications for the development and implementation of efforts aimed at improving postsecondary mathematics outcomes, and subsequent persistence, retention, and representation in STEM programs
Ninth-Grade Students’ Conceptual Understanding of the Number Line
No full textSixty (35 girls and 25 boys) 9th-grade students’ conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students’ number line descriptions and the explanations coalesced around six features: sequential ordering (i.e., numbers are sequentially represented), positivity-negativity of numbers (i.e., the number line contains positive and negative numbers), non-centrality (i.e., zero does not have to be in the center), infinity, increment flexibility (i.e., number line increments can vary), and continuity (i.e., numbers can be placed anywhere between minus infinity and plus infinity without breaks). The students’ explanations show that these six features emerge in five successive stages in the conceptual understanding of the number line. These stages are (1) no knowledge, (2) sequential ordering and positivity-negativity, (3) infinity and non-centrality, (4) incremental flexibility, and (5) continuity. The last two stages were not found in most descriptions. The results suggest that students’ understanding of the number line is incomplete and may be overestimated by commonly used quantitative assessments of number line knowledge
The Ecological Validity of Picture SFON Tasks
No full textResearch has identified that children differ in the extent to which they spontaneously focus on numerical aspects of the environment (Spontaneous Focusing on Numerosity, SFON) and that this correlates with their mathematics achievement. It is assumed that the mechanism underpinning this relationship is that children who spontaneously focus on numerical features of their environment will experience more self-initiated practice with number concepts. We explored this mechanism by investigating whether 4- to 5-year-old children’s verbal SFON scores on a picture description task related to their spontaneous focusing on number while engaged in play activities with their parent. We found that the scores derived from a picture description task were strongly correlated with the scores derived from the play sessions, rₛ = .638, 95% CI [.433, .781], providing evidence for this mechanism. We further investigated the role that verbal abilities may play in children’s performance on the picture description task, finding that general verbal abilities were not associated with verbal SFON scores. These results contribute to our understanding of the role played by verbal SFON tendencies in explaining differences in numerical development, and demonstrate the ecological validity of SFON picture tasks
From One-Half to 12th: Fraction Writing in Children and Adult Education Students
No full textLearning fractions is essential for academic and daily life success. A critical first step in acquiring fractions is learning to transcode them (e.g., writing ½ when hearing “one half”). However, little is known about how students master fraction transcoding. We addressed this gap by assessing fraction writing in two groups of Brazilian students with limited education: adults in the first year of an adult education program (AEP-1) and 2nd graders. Both groups made frequent transcoding errors. Errors were classified into three categories, Syntactic: correct numerator/denominator values with an incorrect notation (12th for “one half”); Lexical: incorrect numerals with the correct notation (⅓ for “one half”); Combined: incorrect numerals and notation (15th for “one-half”). AEP-1 students’ performance was strongly bimodal: those with weak fraction writing skills made predominantly syntactic errors, whereas those with strong fraction writing skills made mostly lexical errors. Second graders did not transcode any fractions correctly making exclusively syntactic or combined errors. Approximately half the AEP-1 students with the lowest levels of schooling (< 3 years) succeeded in writing fractions, suggesting an important role of informal experiences for this group
Capturing Math Language Use During Block Play: Creation of the Spatial and Quantitative Mathematical Language Coding System
No full textThe goals of the current study were: 1) to modify and expand an existing spatial mathematical language coding system to include quantitative mathematical language terms and 2) to examine the extent to which preschool-aged children used spatial and quantitative mathematical language during a block play intervention. Participants included 24 preschool-aged children (Age M = 57.35 months) who were assigned to a block play intervention. Children participated in up to 14 sessions of 15-to-20-minute block play across seven weeks. Results demonstrated that spatial mathematical language terms were used with a higher raw frequency than quantitative mathematical language terms during the intervention sessions. However, once weighted frequencies were calculated to account for the number of codes in each category, spatial language was only used slightly more than quantitative language during block play. Similar patterns emerged between domains within the spatial and quantitative language categories. These findings suggest that both quantitative and spatial mathematical language usage should be evaluated when considering whether child activities can improve mathematical learning and spatial performance. Further, accounting for the number of codes within categories provided a more representative presentation of how mathematical language was used versus solely utilizing raw word counts. Implications for future research are discussed