Journal of Numerical Cognition (JNC - PsychOpen)
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Reciprocal Associations Between Executive Function and Academic Achievement: A Conceptual Replication of Schmitt et al. (2017)
No full textThe goal of the current study was to conduct a conceptual replication of the reciprocal associations between executive function (EF) and academic achievement reported in Schmitt et al. (2017, https://doi.org/10.1037/edu0000193). Using two independent samples (N (STAR) = 279, and N (Pathways) = 277), we examined whether the patterns of associations between EF and achievement across preschool and kindergarten reported in Schmitt et al. (2017) replicated using the same model specifications, similar EF and achievement measures, and across a similar developmental age period. Consistent with original findings, EF predicted subsequent math achievement in both samples. Specifically, in the STAR sample, EF predicted math achievement from preschool to kindergarten, and kindergarten to first grade. In the Pathways sample, EF at kindergarten predicted both math and literacy achievement in first grade. However, contrary to the original findings, we were unable to replicate the bidirectional associations between math achievement and EF in either of the replication samples. Overall, the current conceptual replication has revealed that bidirectional associations between EF and academic skills might not be robust to slight differences in EF measures and number of measurement occasions, which has implications for our understanding of the development EF and academic skills across early childhood. The present findings underscore the need for more standardization in both measurement and modeling approaches – without which the inconsistency of findings in published studies may continue across this area of research
Number Line Tasks and Their Relation to Arithmetics in Second to Fourth Graders
No full textConsidering the importance of mathematical knowledge for STEM careers, we aimed to better understand the cognitive mechanisms underlying the commonly observed relation between number line estimations (NLEs) and arithmetics. We used a within-subject design to model NLEs in an unbounded and bounded task and to assess their relations to arithmetics in second to fourth grades. Our results mostly agree with previous findings, indicating that unbounded and bounded NLEs likely index different cognitive constructs at this age. Bounded NLEs were best described by cyclic power models including the subtraction bias model, likely indicating proportional reasoning. Conversely, mixed log-linear and single scalloped power models provided better fits for unbounded NLEs, suggesting direct estimation. Moreover, only bounded but not unbounded NLEs related to addition and subtraction skills. This thus suggests that proportional reasoning probably accounts for the relation between NLEs and arithmetics, at least in second to fourth graders. This was further confirmed by moderation analysis, showing that relations between bounded NLEs and subtraction skills were only observed in children whose estimates were best described by the cyclic power models. Depending on the aim of future studies, our results suggest measuring estimations on unbounded number lines if one is interested in directly assessing numerical magnitude representations. Conversely, if one aims to predict arithmetic skills, one should assess bounded NLEs, probably indexing proportional reasoning, at least in second to fourth graders. The present outcomes also further highlight the potential usefulness of training the positioning of target numbers on bounded number lines for arithmetic development
An Examination of Third- and Fourth-Graders’ Equivalence Knowledge After Classroom Instruction
No full textThe present correlational study examined third- and fourth-graders’ (N = 56) knowledge of mathematical equivalence after classroom instruction on the equal sign. Three distinct learning trajectories of student equivalence knowledge were compared: those who did not learn from instruction (Never Solvers), those whose performance improved after instruction (Learners), and those who had strong performance before instruction and maintained it throughout the study (Solvers). Learners and Solvers performed similarly on measures of equivalence knowledge after instruction. Both groups demonstrated high retention rates and defined the equal sign relationally, regardless of whether they had learned how to solve equivalence problems before or during instruction. Never Solvers had relatively weak arithmetical (nonsymbolic) equivalence knowledge and provided operational definitions of the equal sign after instruction
A Commentary on “Not Toeing the Number Line for Simple Arithmetic: Two Large-n Conceptual Replications of Mathieu et al. (Cognition, 2016, Experiment 1)”
No full textNo abstract available
Second and Fifth Graders’ Use of Knowledge-Pieces and Knowledge-Structures When Solving Integer Addition Problems
No full textIn this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. Fifty-one out of 102 second graders and 90 out of 102 fifth graders read or used negative signs at least once across the 11 problems. Among second graders, one of their most common strategies was subtracting numbers using their absolute values, which aligned with students’ whole number knowledge-pieces and knowledge-structure. They sometimes preserved the order of numbers and changed the placement of the negative sign (e.g., −9 + 2 as 9 – 2) and sometimes did the opposite (e.g., −1 + 8 as 8 – 1). Among fifth graders, one of the most common strategies reflected use of integer knowledge-pieces within a whole-number knowledge-structure, as they added numbers’ absolute values using whole number addition and appended the negative sign to their total. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change. Adding to prior findings, we found that entrenchment of previously learned patterns can be useful in unlikely ways, which should be taken up in instruction
The Unexplored Role of Handshape Similarity in Processing Numbers on the Hands
No full textWith two simple experiments we investigate the overlooked influence of handshape similarity for processing numerical information conveyed on the hands. In most finger-counting sequences there is a tight relationship between the number of fingers raised and the numerical value represented. This creates a possible confound where numbers closer to each other are also represented by handshapes that are more similar. By using the American Sign Language (ASL) number signs we are able to dissociate between the two variables orthogonally. First, we test the effect of handshape similarity in a same/different judgment task in a group of hearing non-signers and then test the interference of handshape in a number judgment task in a group of native ASL signers. Our results show an effect of handshape similarity and its interaction with numerical value even in the group of native signers for whom these handshapes are linguistic symbols and not a learning tool for acquiring numerical concepts. Because prior studies have never considered handshape similarity, these results open new directions for understanding the relationship between finger-based counting, internal hand representations and numerical proficiency
Three Addend Addition: Who Goes Out of Order and Why?
No full textSingle-digit, three addend sums of the type a + b + c offer a rich opportunity to directly observe the range of strategies that different participants may use because they afford the possibility of measuring a partial sum (i.e., a + b or a + c or b + c). For example, while computing the sum 9 + 7 + 1, do participants go in order by first adding 9 + 7 and then adding 1, or do they incur the cost of going out of order by adding 9 + 1 in order to obtain the partial sum of 10, which makes the subsequent addition of 7 less effortful? Informed by findings in simple and complex arithmetic, we investigated the problem types and participant characteristics that can predict out of order switching behavior in such three-addend sums. To test our hypotheses, we tasked participants, first in an online study, and then in an in-person study to complete 120 single-digit, three addend problems. We found that participants switched the order of addition to prioritize efficiency gains in contexts in which the partial sum addends were small or equal to each other, or when doing so led to a partial sum of 10, or led to a partial sum that is equal to the third remaining integer. Response latency data confirmed that participants were deriving efficiencies in the manner we expected. Related to individual differences, our findings showed that participants with higher levels of math education were most likely to seek efficiency benefits whenever they were on offer
Next Directions in Measurement of the Home Mathematics Environment: An International and Interdisciplinary Perspective
No full textThis paper synthesizes findings from an international virtual conference, funded by the National Science Foundation (NSF), focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children’s outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct – focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars