Thirty Years of the Give-N Task: A Systematic Review, Reflections, and Recommendations

The Give-N (give-a-number) task has become a popular assessment of children’s number words and counting knowledge since Wynn’s (1990, 1992) seminal work over 30 years ago. Using the Give-N task, numerous studies have shown that children learn the first few number words slowly, before they understand how counting represents number. This learning trajectory and children's associated behaviors on the Give-N task are represented by “knower-levels” and form the basis for a large body of research assessing children’s number learning. Recent research has started to critically analyze the theoretical conceptualisation and reliability of knower-levels. We added to this work by conducting a systematic review of studies using the Give-N task. This review provides an overview of methodological practices and variations in the task’s administration and scoring of knower-levels which have theoretical and methodological implications. We argue that advancing methodology and theory for research in children’s number learning requires (1) consideration of Give-N task administration and scoring in study design and reporting and (2) reflection on the assumptions and limitations of classifying children’s performance on the Give-N task in the knower-level framework

New Editorial Team at the Journal of Numerical Cognition

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Variation in Mathematics Performance: A Multilevel Analysis With Student and School's Characteristics

Using data from the Trends in International Mathematics and Science Study (TIMSS), this study examines the student and school characteristics that contribute to students’ mathematics performance in early elementary school in Chile. Previous research has separately analyzed the association of student and school factors with mathematics performance. This study uses multilevel modeling analyses to account for those factors together and understand variability within and between schools. The sample in this study was 6,322 fourth grade students from 169 schools. The students’ mean age was 10.07 (SD = 0.50); 49.6% were girls. The results from this study show that student characteristics, such as the home mathematics environment, helped explain the variation between schools more than within schools. These findings highlight the importance of considering contextual factors, such as parent–child math interactions, when developing education policy and intervention to foster students’ mathematics skills

The Psychometric Properties of the Polish-Language Version of the Mathematical Resilience Scale

This study aims to present the psychometric properties of the Polish language version of the Mathematical Resilience Scale (MRS; Kooken et al., 2016), established in a sample of 443 adults. We confirmed the first-order three-factor structure (Value, Struggle, Growth) with the second-order factor (Total Mathematical Resilience) of the MRS and its measurement invariance across gender and field of study and profession. We also confirmed the validity of the scale: negative correlations were found between MRS scores and math anxiety, math avoidance, intellectual helplessness in mathematics; positive correlations were found between MRS scores, mathematical achievement, math learning motivation; no relationship or weak correlations were found between MRS scores, intellectual helplessness in Polish language, Polish language grades obtained in high school. Finally, we observed gender and study and profession differences in some of the MRS scores. However, further research is needed on the nature of mathematical resilience, especially to establish its relationship with general resilience

The Parity Judgment SNARC Effect: The Role of Response Mapping Order and the Nature of the Instruction

Previous research has investigated the Spatial Numerical Associations of Response Codes (SNARC) effect as a measure of spatial number coding in relation to mathematics (Cipora et al., 2020, https://doi.org/10.1111/nyas.14355). An issue that arises if one wants to correlate mathematical performance with the SNARC effect, is how individual differences in the SNARC effect are measured. Specific design choices might have an impact on the size of the SNARC effect as an individual difference measure. In the present study we investigated two design choices that have previously been neglected as possible determinants of the size of the SNARC effect as obtained in the parity judgment task. The first determinant that we investigated is mapping order. The odd-even left-right response assignments can be congruent (even-right and odd-left) or incongruent (even-left and odd-right) in terms of linguistic markedness (MARC effect: markedness association of response codes) and might be presented in two different orders (congruent first or incongruent first) possibly affecting the size of the SNARC effect. A second possible determinant is task instruction. Instructions can emphasize parity (judge numbers as odd or even) or emphasize two categories (classify numbers as 1-3-7-9 versus 2-4-6-8) as the basis for responding, perhaps requiring different levels of semantic processing. To investigate the potential impact of these variables, this study used a 2x2 between subject design, resulting in four conditions to verify the effect of mapping order and instructions. The results show that the SNARC effect is not influenced by mapping order or by the nature of the instructions, revealing the parity judgment SNARC effect as a robust marker of spatial number coding useful for individual difference research

Learning Number Notations – Comparison of a Sign-Value and Place-Value System

Although numbers are universal, there are great differences between languages and cultures in terms of how they are represented. Numerical notation can influence number processing. Two well-known types of notational systems are sign-value, such as the Roman numeral system, and place-value systems, such as the Indo-Arabic numeral system. What is involved in learning each system? Here we report a study that investigated adults’ abilities to implicitly learn an artificially created sign-value or place-value system. We asked if they could perform symbolic comparison and ordering tasks using the novel symbol system. We found adults could learn the ordinal meaning of symbols within either system and were able to extend the system to symbols not encountered during training. There was a relative advantage of the sign-value system over the place-value system for expressions encountered during the training, but also for expressions that had not previously been encountered. These results shed light on how easily the structure of place-value and sign-value systems can be learned

When We Were Young: Memories of Early Mathematics Experiences

Early 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

A Meta-Analysis of the Cross-Sectional and Longitudinal Relations Between Executive Functioning and Math in Early Childhood

Math 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

Examining a Factor Structure of Home Math Activities by Math Subdomain With Associations to Children’s Math Skills

Evidence of positive associations between the frequency of home math activities and preschool children’s math skills is mixed, and the operationalization of home math activities varies across studies. We test whether home math activities can be grouped by activity factors based on the math subdomain they target (i.e., counting and cardinality, comparison, number identification, addition and subtraction, and patterning) and examine associations between these activity factors and child math skills. Data were collected from 78 parents and their four-year-old children in the United States. Parents completed a home math activities survey, and children completed math assessments. Confirmatory Factor Analyses (CFA) indicated a well-fitting model with the five activity factors (one factor per subdomain) and a sixth factor for activities that could incorporate multiple subdomains. Structural Equation Modeling (SEM) analyses indicated positive associations between activity factors and child math skills for counting and cardinality, comparison, addition and subtraction, and patterning, but not for number identification. Results reveal that this model is appropriate for older four-year-old children closer to the beginning of kindergarten but is not appropriate for younger four-year-old children. This study suggests the possibility of operationalizing home math activities by activity factors based on math subdomains

Do Preschoolers Use Rules to Represent Their Count List?

When children first learn to count, what do they understand about the structure of the count system? The present study investigated English-speaking children’s ability to generalize the rules that structure their count list to novel contexts. A total of N = 86 children (3;0 – 6;11) completed a battery of tasks aimed at measuring their understanding of the English count list: they counted as high as they could, and were asked to generate successors to English numbers (e.g., “Fifty-seven: what comes next?”). Next, they were introduced to novel decade terms, and were asked to generate successors to numbers containing those terms (e.g., “Blicky-seven: what comes next?”). Children’s ability to generate successors was predicted by their counting ability, and a sizeable subset of children were able to generate successors both for novel numbers and for English numbers outside their productive count range. These data suggest that emerging counters can use their understanding of the structure of the English count list to generate successors to unfamiliar numbers