Children's Estimation Research Articles

Evaluating the Nolla Method for Dental Age Estimation in Children from Northwestern Romania

Background/Objectives: Dental age estimation plays a critical role in pediatric dentistry, orthodontics, and forensic medicine. The Nolla method, widely applied globally, has shown variable accuracy across different populations. This study aimed to evaluate the applicability and accuracy of the Nolla method in estimating the dental age of Romanian children and to identify potential discrepancies between dental and chronological ages. Methods: A retrospective analysis was conducted on 860 panoramic radiographs from pediatric patients aged 3–15.9 years in Oradea, Romania. The Nolla method was applied to estimate dental age, and the results were compared with chronological age. Statistical analyses, including Wilcoxon signed-rank and Mann–Whitney U tests, were performed to evaluate the accuracy and consistency of the Nolla method. Results: The study analyzed 860 panoramic radiographs (356 boys and 504 girls). The average chronological age was 9.95 ± 2.48 years, while the average dental age, as estimated using the Nolla method, was 8.43 ± 2.13 years. Dental age was consistently lower than chronological age, with a median difference of 1.5 years (IQR: 0.9–2.2 years). Among the 13 age groups, the highest representation was found in the 8–8.9-year (14.7%) and 9–9.9-year (13.3%) groups. Gender differences were statistically significant (p < 0.001); girls demonstrated a larger median discrepancy of 1.7 years (IQR: 1.1–2.3 years) compared to boys at 1.15 years (IQR: 0.6–1.8 years). Notably, discrepancies increased with age, peaking at 2.6 years in the 14–14.9-year group (4.7% of the sample). The youngest group (3–3.9 years) showed the smallest difference of 0.3 years. Significant differences between chronological and dental ages were observed in 87.5% of the sample. Conclusions: The Nolla method consistently underestimated dental age in Romanian children, with greater discrepancies in older age groups and among girls. These findings highlight the need for the population-specific calibration of the method to improve its accuracy in both clinical and forensic contexts.

Questioning weber-fechner law in young children's numerical estimation strategies

The subjective number-space mapping and, especially, its evolution in young children has been the subject of intense controversy among different competing models. Many studies point out that: (i) young children's innate estimates follow a logarithmic mapping (Weber-Fechner law) and (ii) driven by education, children evolve into a linear mapping. In this paper we show, in consonance with other investigations, that innate numerical intuitions of young children are in fact a linear mapping, and not a logarithmic one. We found that young children extrapolate linearly from a reference point. The apparent logarithmic mapping is an artifact produced by placing a huge range of numbers within a small number line. We show how the appearance of the mapping can be modulated by changing the size and contour conditions of the number lines used in experiments.

Demirjian's and Cameriere's Methods for the Assessment of Dental Age Estimation in Children from a Southern Brazilian City.

The chronological age estimation of living individuals is a crucial part of forensic practice and clinical practice, such as in orthodontic treatment. It is well-known that methods for age estimation in living children should be tested on different populations. Ethnic affiliations in Brazil are divided into several major groups depending on the region, with the south of Brazil being known for its German immigration. (1) Background: This study aimed to evaluate the correlation between chronological age and dental age using Demirjian's method and Cameriere's method in a group of children from Joinville, South Brazil to investigate if both methods can be used to estimate dental age in this population. (2) Methods: The sample consisted of 229 panoramic radiographs (119 were males and were 110 females) from Brazilian children (ages ranging from 6 to 12 years). The chronological age at the time of the panoramic radiographic exam was calculated for each child. The dental age was estimated according to Demirjian's method and Cameriere's method. All continuous data were tested for normality by using the Shapiro-Wilk test. The Pearson correlation coefficient test was applied. An alpha of 5% (p < 0.05) was used for all analyses. (3) Results: The mean chronological age was 8.75 years. According to Demirjian's method, the mean dental age was 9.3 years, while according to Cameriere's method, the mean dental age was 8.66 years. A strong correlation between chronological age and dental age according to Demirjian (r = 0.776 and p < 0.0001) and Cameriere (r = 0.735 and p < 0.0001) was observed for both genders. (4) Conclusions: Both methods presented a good correlation with chronological age in the studied population and could be used to assess dental age in this population.

A Review on Dental Age Estimation in Children and Adolescents

Abstract Children are seen as beings who exist from birth through puberty, while teenagers are regarded as existing from puberty until around the age of 20 years. For a number of legal processes, including child labor, employment, the age of majority, rape, adoption, marriage eligibility, and situations where the birth certificate is unavailable, age estimation in children and adolescents is crucial. Despite the wide range of methods available, dental age estimation techniques that take into account tooth maturation are thought to be the most reliable predictors of chronological age in subadults. This is because genetic factors predominate and environmental factors, particularly between birth and age ten, tend to have little impact on tooth maturation. The eruption of teeth holds greater significance in the deciduous dentition, where genetic factors predominantly govern the process, compared to the permanent dentition. Conversely, tooth calcification serves as a viable indicator for estimating dental age in both primary and permanent dentitions. Current dental age estimation methods are based on age-related changes in teeth, such as tooth growth and development, changes that occur after teeth form, and biochemical changes. Therefore, in this review article, we will explore the several methodologies used for dental age assessment in children and adolescents.

An examination of measures of young children's interest in natural object categories

Developmental research utilizes various different methodologies and measures to study the cognitive development of young children; however, the reliability and validity of such measures have been a critical issue in all areas of research practices. To address this problem, particularly in the area of research on infants' interests, we examined the convergent validity of previously reported measures of children's interests in natural object categories, as indexed by (1) parents' estimation of their child's interest in the categories, (2) extrinsic (overt choices in a task), (3) intrinsic (looking time toward objects), and (4) physiological (pupil dilation) responses to objects of different categories. Additionally, we also examined the discriminant validity of all the aforementioned measures against the well-established and validated measure of parents' estimations of children's vocabulary knowledge. Children completed two tasks: (a) an eye-tracking task, where they were presented with images from a range of defined categories, which collected indices of looking time and pupillary activity; (b) a sticker-choice task, where they were asked to choose between two sticker-images from two different categories belonging to the range of categories assessed in the previous task. Parents completed two questionnaires to estimate (i) their child's interests and (ii) vocabulary knowledge in the categories presented. We first analyzed the discriminant validity between the two parent measures, and found a significant positive association between them. Our successive analyses showed no strong or significant associations between any of our measures, apart from a significant positive association between children's looking time and parents' estimations of children's vocabulary knowledge. From our findings, we conclude that measures of infants' interests thus far may not have sufficient reliability to adequately capture any potential relationship between these measures, or index different components of interest in young children. We suggest next steps for further validation studies in infant research.

Children's number line estimation strategies: evidence from bounded and unbounded number line estimation tasks.

This study investigates the number line estimation (NLE) strategies utilized by children aged 4-7 across both bounded and unbounded NLE tasks. Drawing on prior research, it hypothesized that younger children would predominantly employ benchmark-based strategies, with endpoints as reference points, in bounded tasks, while older children would utilize a wider range of reference points including midpoints and quartiles. For unbounded tasks, it was anticipated that both younger and older children would adopt the scalloped strategy. A total of 181 Chinese children participated, representing three educational backgrounds: Middle Class (kindergarten), Senior Class (kindergarten), and Grade 1 (elementary school). They completed the bounded and unbounded NLE tasks with numbers ranging from 0 to 50. Data analysis focused on estimation accuracy using Percent Absolute Error (PAE) and contour analyses to examine strategy use. Results revealed that all age groups employed benchmark-based strategies using endpoints and midpoints in both bounded and unbounded tasks, and applied the scalloped strategy with units of integers 5 or 10 across all tasks. Findings suggest a coexistence of benchmark-based and scalloped strategies across task types, reflecting children's intuitive estimation strategies. Furthermore, children aged 4 to 7 exhibited consistent strategy utilization, indicating a developmental stage characterized by reliance on specific reference points for estimation. This study contributes to understanding the developmental trajectory of number line estimation strategies in early childhood and emphasizes the importance of task type, learning experiences, and other factors in eliciting different estimation strategies.

How Did Spain Perform In PISA 2018? New Estimates Of Children’s PISA Reading Scores*

ABSTRACT International large-scale assessments have gained much attention since the beginning of the twenty-first century, influencing education legislation in many countries. This includes Spain, where they have been used by successive governments to justify education policy change. Unfortunately, there was a problem with the PISA 2018 reading scores for this country, meaning the OECD refused to initially release the results. Therefore, in this paper we attempt to estimate the likely PISA 2018 reading scores for Spain, and for each region within. The figure finally published by the OECD for Spain – in terms of reading scores – was 476.5 points, which is between the lower and upper bound of the interval we find (475 to 483 test points in 2018). Additionally, we report some robustness checks for the OCED countries participating in PISA 2018, which show that the difference between the actual scores and the ones we found with the imputation methods are quite close.

Potential moderators of the left digit effect in numerical estimation

Recent work reveals a left digit effect in number line estimation such that adults' and children's estimates for three-digit numbers with different hundreds-place digits but nearly identical magnitudes are systematically different (e.g., 398 is placed too far to the left of 401 on a 0-1000 line, despite their almost indistinguishable magnitudes; Lai et al., 2018, https://doi.org/10.1111/desc.12657). In two preregistered studies (N = 218), we investigate the scope and malleability of the left digit effect. Experiment 1 used a typical forward-oriented 0-1000 number line estimation task and an atypical reverse-oriented 1000-0 number line estimation task. Experiment 2 used the same forward-oriented typical 0-1000 number line estimation task from Experiment 1, but with trial-by-trial corrective feedback. We observed a large left digit effect, regardless of the orientation of the line in Experiment 1 or the presence of corrective feedback in Experiment 2. Further, analyses using combined data showed that the pattern was present across most stimuli and participants. These findings demonstrate a left digit effect that is robust and widely observed, and that cannot be easily corrected with simple feedback. We discuss the implications of the findings for understanding sources of the effect and efforts to reduce it.

Are parent-reported sleep logs essential? A comparison of three approaches to guide open source accelerometry-based nocturnal sleep processing in children.

We examined the comparability of children's nocturnal sleep estimates using accelerometry data, processed with and without a sleep log. In a secondary analysis, we evaluated factors associated with disagreement between processing approaches. Children (n = 722, age 5-12 years) wore a wrist-based accelerometer for 14 days during Autumn 2020, Spring 2021, and/or Summer 2021. Outcomes included sleep period, duration, wake after sleep onset (WASO), and timing (onset, midpoint, waketime). Parents completed surveys including children's nightly bed/wake time. Data were processed with parent-reported bed/wake time (sleep log), the Heuristic algorithm looking at Distribution of Change in Z-Angle (HDCZA) algorithm (no log), and an 8 p.m.-8 a.m. window (generic log) using the R-package 'GGIR' (version 2.6-4). Mean/absolute bias and limits of agreement were calculated and visualised with Bland-Altman plots. Associations between child, home, and survey characteristics and disagreement were examined with tobit regression. Just over half of nights demonstrated no difference in sleep period between sleep log and no log approaches. Among all nights, the sleep log approach produced longer sleep periods (9.3 min; absolute mean bias [AMB] = 28.0 min), shorter duration (1.4 min; AMB = 14.0 min), greater WASO (11.0 min; AMB = 15.4 min), and earlier onset (13.4 min; AMB = 17.4 min), midpoint (8.8 min; AMB = 15.3 min), and waketime (3.9 min; AMB = 14.8 min) than no log. Factors associated with discrepancies included smartphone ownership, bedroom screens, nontraditional parent work schedule, and completion on weekend/summer nights (range = 0.4-10.2 min). The generic log resulted in greater AMB among sleep outcomes. Small mean differences were observed between nights with and without a sleep log. Discrepancies existed on weekends, in summer, and for children with smartphones and screens in the bedroom.

Simultaneous Recording of Objective Sleep in Mothers and School-aged Children with Developmental Disabilities: A Pilot Study of Actigraphy and Videosomnography.

Mothers of school-aged children ages 3 to 17 years with developmental disabilities (DDs) commonly report sleep problems in their children associated with impaired maternal sleep. However, existing research relies heavily on mothers' self-reported sleep. This study aimed to determine the feasibility of objectively measuring child and mother sleep-wake patterns using actigraphy and videosomnography. This was an observational pilot study. Mothers wore actigraphy watches and video-recorded their child's sleep for 7 nights. Mothers also completed a7-day sleep diary and questionnaires on sleep quality, depressive symptoms, stress, and child sleep problems. Ten mothers (32-49 years) and ten children with DDs (8-12 years) completed this study. Half of the children were boys with autism spectrum disorders. We successfully recruited 77% of eligible mothers for the study during the pandemic. Eight mothers successfully wore the actigraphy, and nine successfully video-recorded their child's sleep. Mothers rated their participation positively and considered the data collection protocol acceptable. While mothers' sleep patterns from actigraphy were mostly within recommendations, self-reported sleep quality was poor. Child's sleep estimates from videosomnography showed children slept substantially less than recommended sleep hours. Mothers also reported a high frequency of child sleep problems. Consistent with this pattern, mothers also endorsed elevated stress and depression. The use of actigraphy and videosomnography is feasible. Objective sleep measurement for mothers' and children's sleep is needed with self-report to measure multidimensional aspects of sleep and discrepancies between objective and self-report sleep measures. Future studies can use multi-methods sleep measures and work toward interventions that can improve family sleep and reduce mothers' stress and depression.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm.

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Energy Expenditure Estimation in Children, Adolescents and Adults by Using a Respiratory Magnetometer Plethysmography System and a Deep Learning Model.

Purpose: Energy expenditure is a key parameter in quantifying physical activity. Traditional methods are limited because they are expensive and cumbersome. Additional portable and cheaper devices are developed to estimate energy expenditure to overcome this problem. It is essential to verify the accuracy of these devices. This study aims to validate the accuracy of energy expenditure estimation by a respiratory magnetometer plethysmography system in children, adolescents and adults using a deep learning model. Methods: Twenty-three healthy subjects in three groups (nine adults (A), eight post-pubertal (PP) males and six pubertal (P) females) first sat or stood for six minutes and then performed a maximal graded test on a bicycle ergometer until exhaustion. We measured energy expenditure, oxygen uptake, ventilatory thresholds 1 and 2 and maximal oxygen uptake. The respiratory magnetometer plethysmography system measured four chest and abdomen distances using magnetometers sensors. We trained the models to predict energy expenditure based on the temporal convolutional networks model. Results: The respiratory magnetometer plethysmography system provided accurate energy expenditure estimation in groups A (R2 = 0.98), PP (R2 = 0.98) and P (R2 = 0.97). The temporal convolutional networks model efficiently estimates energy expenditure under sitting, standing and high levels of exercise intensities. Conclusion: Our results proved the respiratory magnetometer plethysmography system’s effectiveness in estimating energy expenditure for different age populations across various intensities of physical activity.

From integers to fractions: The role of analogy in developing a coherent understanding of proportional magnitude.

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one another. To address this, we asked 177 third, fourth, and fifth graders (M = 9.85 years, 87 girls, 69% White, 19% low income) to estimate the position of proportionally equivalent integers and fractions on number lines (e.g., 3 on a 0-8 number line vs. 3/8 on a 0-1 number line, Study 1). With increasing age, children's estimates of implicit and explicit proportions became more coherent, such that a child's estimates of fractions on a 0-1 number-line was a linear function of the same child's estimates of equivalent integers. To further investigate whether preexisting integer knowledge can facilitate fraction learning through analogy, we assigned 100 third to fifth graders (M = 10.04 years, 55 girls, 76% White) to an Alignment condition, where children estimated fractions and integers on aligned number lines, or to a No Alignment condition (Study 2). Results showed that aligning integers and fractions on number lines facilitated a better understanding of fractional magnitudes, and increased children's fraction estimation accuracy to the level of college students'. Together, findings suggest that analogies can play an important role in building a coherent understanding of proportions. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The Impact of Speaker Diarization on DNN-based Autism Severity Estimation.

This paper presents a speech-based system for autism severity estimation combined with automatic speaker diarization. Speaker diarization was performed by two different methods. The first used acoustic features, which included Mel-Frequency Cepstral Coefficients (MFCC) and pitch, and the second used x-vectors - embeddings extracted from Deep Neural Networks (DNN). The speaker diarization was trained using a Fully Connected Deep Neural Network (FCDNN) in both methods. We then trained a Convolutional Neural Network (CNN) to estimate the severity of autism based on 48 acoustic and prosodic features of speech. One hundred thirty-two young children were recorded in the Autism Diagnostic Observation Schedule (ADOS) examination room, using a distant microphone. Between the two diarization methods, the MFCC and Pitch achieved a better Diarization Error Rate (DER) of 26.91%. Using this diarization method, the severity estimation system achieved a correlation of 0.606 (Pearson) between the predicted and the actual autism severity scores (i.e., ADOS scores). Clinical Relevance- The presented system identifies children's speech segments and estimates their autism severity sc30:310ore.

Estimation of Children's Soil and Dust Ingestion Rates and Health Risk at E-Waste Dismantling Area.

Due to environmental health concerns, exposure to heavy metals and related adverse effects in electronic waste (e-waste) dismantling areas have attracted considerable interest in the recent years. However, little information is available about the Soil/Dust Ingestion Rates (SIR) of heavy metals for children living in such sites. This study estimated the soil ingestion of 66 children from e-waste disassembly areas by collecting and analyzing selected tracer elements in matched samples of their consumed food, feces, and urine, as well as soil samples from their play areas. The concentrations of tracer elements (including Al, Ba, Ce, Mn, Sc, Ti, Y, and V) in these samples were analyzed. The SIR was estimated to be 148.3 mg/day (median) and 383.3 mg/day (95th percentile) based on the Best Tracer Method (BTM). These values are somewhat higher than those observed in America, Canada, and other parts of China. Health risk assessments showed that Cr presented the greatest carcinogenic risk, at more than 10−6 in this typical polluted area, while As was second. These findings provide important insights into the exposure risks of heavy metals in e-waste dismantling sites and emphasize the health risk caused by Cr and As.

About the Recent Chilean Immigration Phenomenon: A Scoping Review on Radiographic Methods for Dental Age Estimation in Children

The objective of this review was to identify original studies describing radiographic methods for dental age estimation applied in Chilean children, considering that it is a country with a long history of natural disasters and it has shown an unprecedented increase in the number of migrants in recent years, with significant percentages of individuals under 18 years of age. A scoping review was carried out following the methodology for the Joanna Briggs Institute scoping reviews and PRISMA guidelines. A specific search strategy was implemented in PubMed/Medline database, with complementary use of the Google Scholar website searching for full articles in English and Spanish. Five documents responded to the search objective, of which only 3 were published in refereed journals. Two documents focused their study on the maturation of upper and lower third molars, one on the maturation of the second and lower third molars, and two documents on the maturation of the seven mandibular teeth according to classical methodologies. The scarce existing literature, the almost absence of validated methods for the Chilean population, as well as the reported mass immigration phenomenon make a new and profound scientific research approach necessary for the application of updated methods.

Hearing aid use in 11-year-old children with mild bilateral hearing loss: Associations between parent and child ratings and datalogging

ObjectiveThis study examined the hearing aid use in older school-aged children with mild bilateral hearing loss. More specifically, it investigated children's and parents' estimation of use in comparison to datalogging as well as explored the situations children used their hearing aids. Methods and materialsSixteen children with mild bilateral hearing loss and their parents participated. Of those, 14 children used hearing aids. Children and parents completed a questionnaire on hours of hearing aid use and situations hearing aids were used. Datalogging of the hearing aids was recorded and compared to the outcome of the questionnaires. ResultsDatalogging indicated average hearing aid use time was 6.6 h. Children significantly overestimated their use of their hearing aids while approximately half the parents overestimated their child's use. Children used their hearing aids most often at school and in the car. ConclusionChildren with mild bilateral hearing loss overestimate the amount of time they are wearing their hearing aids. This may impact counselling and intervention on the use of hearing aids. Therefore, school-aged children should be included in the discussions around potentially increasing use of hearing aids.

Accuracy of Weight Estimation in Children Using the Broselow, PAWPER XL, PAWPER XL-MAC, and Mercy Tapes.

Quick and accurate estimate of a child's weight is often required for medical interventions like drug dose calculation when scale measured weights cannot be obtained safely. Length-based methods of weight estimation are more accurate than age-based methods, with the most accurate being the length-based, habitus-modified methods. This study sought to determine and compare the accuracies of the 2017 Broselow tape, Paediatric Advanced Weight Prediction in the Emergency Room Extra-Long (PAWPER XL) tape, Paediatric Advanced Weight Prediction in the Emergency Room Extra-Long Mid-Arm Circumference (PAWPER XL-MAC) tape, and the 2-dimensional (2D) Mercy tape in Ghanaian children. A cross-sectional study was conducted at the Tamale Teaching Hospital in Ghana. Eight hundred forty children between 2 months and 13 years had their weights estimated by the 2017 Broselow, PAWPER XL, PAWPER XL-MAC, and 2D Mercy tapes. Accuracy of the methods was determined by percentage of weight estimated to within 10% and 20% of actual weight. Mean percentage error and the Bland-Altman analysis were used to assess bias and precision. The proportion of weight estimates within 10% and 20% of actual weight for Broselow tape were 47.5% and 82.3%, for 2D Mercy tape were 73.1% and 96.3%, for PAWPER XL-MAC were 77.6% and 97.5%, and for PAWPER XL were 81.7% and 96.8%, respectively. The Broselow tape had the greatest bias and least precision among the 4 methods. The Mercy, PAWPER XL-MAC, and PAWPER XL tapes had similar performance, but all performed significantly better than the Broselow tape in pairwise comparison. The best weight estimation method overall was the PAWPER XL tape as it also had the least bias and greatest precision. The Mercy, PAWPER XL-MAC, and PAWPER XL tapes were more accurate than the 2017 Broselow tape and should be used in preference in Ghana and countries with similar population structure.

Age Estimation in Children by the Measurement of Open Apices in Teeth: A Study in the Western Indian Population.

In forensic sphere and clinical dentistry, age estimation is a topic of utmost importance. Various techniques are employed in children to determine age; however, dental development has proven to be an appropriate method because of its low variability. Cameriere's method is a widely accepted method of age estimation in children, which is carried out by measuring the projections of open apices and also the heights of developing permanent teeth seen on panoramic radiographs. The aim of this study is to establish a new formula for age estimation in the Western Indian population by measuring the open apices of mandibular teeth using Cameriere's European formula. For this study, we included 311 panoramic radiographs of healthy children living in Western India (Maharashtra, Gujarat, and Goa) aged 4–15 years which were analysed by two independent researchers. Seven left permanent mandibular teeth were assessed for length and width of open apices. Dental maturity was evaluated using measurements of the left seven permanent mandibular teeth (xi = Ai/Li, i = 1,…, 7), the sum of the normalized open apices (s), and the number (N0) of teeth with complete root formation. A linear relationship between open apices, N0, age, and other factors was evaluated with the aid of a stepwise multiple regression model. A stepwise linear regression showed that all parameters, gender, s, N0, and x5, were significantly associated with age (R = 85%). No statistically significant difference was found between the predicted and actual chronological age of children in the age group of 4–13 years using the regression equation for the Western Indian population. The present research suggests that the new regression formula developed will be more accurate for age assessment in the Western Indian population.

Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal.

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model-a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult-like, linear estimates when to-be-estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults' estimates were subject to inter-trial differences regardless of stimulus order. In contrast, children were not able to use the trial-to-trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial-to-trial changes in number-line tasks.