Arithmetic Skills Research Articles

Effects of Gender on Basic Numerical and Arithmetic Skills: Pilot Data From Third to Ninth Grade for a Large-Scale Online Dyscalculia Screener

In this study, we analyzed the development and effects of gender on basic number skills from third to ninth grade in Finland. Because the international comparison studies have shown slightly different developmental trends in mathematical attainment for different language groups in Finland, we added the language of education as a variable in our analysis. Participants were 4,265 students from third to ninth grade in Finland, representing students in two national languages (Finnish, n = 2,833, and Swedish, n = 1,432). Confirmatory factor analyses showed that the subtasks in the dyscalculia screener formed two separate factors, namely, number-processing skills and arithmetic fluency. We found a linear development trend across age cohorts in both the factors. Reliability and validity evidence of the measures supported the use of these tasks in the whole age group from 9 to15 years. In this sample, there was an increasing gender difference in favor of girls and Swedish-speaking students by grade levels in number-processing skills. At the same time, boys showed a better performance and a larger variance in tasks measuring arithmetic fluency. The results indicate that the gender ratio within the group with mathematical learning disabilities depends directly on tasks used to measure their basic number skills.

Different complex word problems require different combinations of cognitive skills

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.

Exact arithmetic, computational estimation and approximate arithmetic are different skills: Evidence from a study with 5‐year‐olds

AbstractResearch distinguishes three types of arithmetic: exact arithmetic, computational estimation and approximate arithmetic. Little is, however, known about the interrelationship among these three arithmetic skills and the general cognitive and early numeracy skills that underlie these arithmetic skills. The current study investigates this interrelationship and underlying processes in 389 kindergartners. Exact arithmetic and computational estimation skills were assessed using a manipulative task, while approximate arithmetic was measured using a computerized task. Correlational analysis showed significant relations among the three arithmetic skills. At the same time, confirmatory factor analyses showed that they are different constructs. In addition, regression analysis showed that different general cognitive and early numeracy skills are predictive of the three arithmetic skills. Since the different arithmetic skills are related but distinct constructs and because they are driven by different processes, teaching and learning each of these skills ask for a different approach.

Alpha and theta oscillations in mental addition for high and low performers.

While many contemporary studies aim to explore the sources of notable individual differences in arithmetic skills, this study specifically aims to highlight cognitive differences between high and low math performers. Thirty-six undergraduate female students who were identified as either high or low math performers, according to an arithmetic fluency test, were recruited. In the main experiment, EEG recordings were taken, while the participants performed a mental addition task. The mental addition problems were classified as either easy or difficult, and were presented to participants in several forms. The results indicated that problem difficulty increases the gap in accuracy attainment between high and low math performers. Additionally, high performers displayed larger alpha power during mental arithmetic in P7, corresponding to the left parietal lobe. This indicated that combining behavioral and neural data can improve our understanding of the differences between high and low math performers. Interpretations and implications are discussed.

Neural representational similarity between symbolic and non-symbolic quantities predicts arithmetic skills in childhood but not adolescence.

Mathematical knowledge is constructed hierarchically from basic understanding of quantities and the symbols that denote them. Discrimination of numerical quantity in both symbolic and non-symbolic formats has been linked to mathematical problem-solving abilities. However, little is known of the extent to which overlap in quantity representations between symbolic and non-symbolic formats is related to individual differences in numerical problem solving and whether this relation changes with different stages of development and skill acquisition. Here we investigate the association between neural representational similarity (NRS) across symbolic and non-symbolic quantity discrimination and arithmetic problem-solving skills in early and late developmental stages: elementary school children (ages 7-10 years) and adolescents and young adults (AYA, ages 14-21 years). In children, cross-format NRS in distributed brain regions, including parietal and frontal cortices and the hippocampus, was positively correlated with arithmetic skills. In contrast, no brain region showed a significant association between cross-format NRS and arithmetic skills in the AYA group. Our findings suggest that the relationship between symbolic-non-symbolic NRS and arithmetic skills depends on developmental stage. Taken together, our study provides evidence for both mapping and estrangement hypotheses in the context of numerical problem solving, albeit over different cognitive developmental stages.

فاعلیة بعض أنماط التقویم فى بیئة التعلم التشارکى عبر الفصول الافتراضیة على تنمیة مهارات حل المشکلات الحسابیة لدى الطلاب القابلین للتعلم

يهدف هذا البحث إلى التعرف على بعض أنماط التقويم فى بيئة التعلم التشارکى عبر الفصول الافتراضية على تنمية مهارات حل المشکلات الحسابية لدى الطلاب القابلين للتعلم وتکونت عينة البحث من (60) طالب وطالبة من طلاب مدرسة الفکرية ببورسعيد مقسمة على مجموعتين تجريبيتين حيث المجموعة التجريبية الاولى تعتمد على التقويم الذاتى والمجموعة التجريبية الثانية تعتمد على تقويم الاقران ولتحقيق هدف البحث استخدم الباحث الاختبار التحصيلى لقياس مدى تحصيل الطلاب فى مهارات حل المشکلات الحسابية المرتبطة بمادة الرياضيات وبطاقة ملاحظة مهارات حل المشکلات الحسابية والتى ساعدت فى اخراج الباحث لمهارات حل المشکلات الحسابية المرتبطة بالبحث وتحليل محتوى لمادة الرياضيات وبيئة التعلم التشارکية القائمة على منهج الرياضيات المدعم بالانشطة والتکليفات وفق لنمط التقويم (ذاتى ـ اقران ) ويشمل البحث الحالى على متغير مستقل واحد هو أنماط التقويم ذو مستويين هما (التقويم الذاتى ، تقويم الاقران ) ومتغير تابع واحد هو مهارات حل المشکلات الحسابية وبعد دراسة المحتوى (مادة الرياضيات) وتطبيق الادوات قبليا وبعديا اسفرت نتائج البحث تفوق الطلاب الذين تم تقييهم باسلوب تقويم الاقران فى الاختبار التحصيلى وبطاقة الملاحظة عن الطلاب الذين تم تقييمهم باسلوب التقويم الذاتى . This research aims to identify some evaluation patterns in the participatory learning environment through virtual classrooms on the development of arithmetic problem-solving skills for students who are able to learn. The research sample consisted of (60) male and female students from the Fikriya School in Port Said divided into two experimental groups, where the first experimental group depends on Self-evaluation and the second experimental group depend on peer evaluation. To achieve the goal of the research, the researcher used the achievement test to measure the extent to which students’ achievement in arithmetic problem-solving skills related to mathematics and a note card for arithmetic problem-solving skills, which helped the researcher produce arithmetic problem-solving skills related to research and content analysis of mathematics and the environment. Participatory learning based on the mathematics curriculum supported by activities and assignments according to the evaluation style (self-peer) and the current research includes one independent variable which is two-level evaluation patterns (self-evaluation, peer evaluation) and one dependent variable which is arithmetic problem-solving skills and after studying the content (Article Mathematics) and the application of the tools before and after the results of the research resulted in the superiority of the students who were Evaluate them using the peer evaluation method in the achievement test and the observation card on the students who were evaluated using the self-evaluation method.

Exploring Thinking Process of Students with Mathematics Learning Disability in Solving Arithmetic Problems

The student's criterion for being diagnosed with MLD (Mathematics Learning Disabilities) can be classified as low arithmetic skills and poor working memory. The goal of this research is to understand students' process of thinking through the Polya stages when tackling arithmetic problems, as it has been expounded by Dr. Polya For students who have mathematics learning difficulties, the information is gathered by administering math problems to both females and males that ask the correct questions and have to be answered in their heads. the data gathered from the study concluded that students exhibit degrees of mental disorder that are caused by 3 distinct stages in which they must be addressed: problem-solving underachievement, when they are overreaching, and cognitive imbalance when they are overcommitted. to arrive at equilibrium, the more significant expansions must be coupled with an extensive assimilation and assimilation process As students with moderate to severe learning disability were completing multi-digit addition and multiplication, they underwent assimilation. Because of this, the cognitive fluidity present at this moment, the students have already found themselves in their present-looking-backward state of mind.

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study

Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training.Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems.Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals’ low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.

Which skills predict computational estimation? A longitudinal study in 5- to 7-year-olds

Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive of early computational estimation development. The current study longitudinally followed a group of about 350 children at four time points: second (K2, 4-year-olds) and third grades of kindergarten (K3, 5-year-olds) and first (P1, 6-year-olds) and second (P2, 7-year-olds) grades of primary school. The computational estimation task was administered in two variants: a nonverbal variant, in which the problems were presented with manipulatives and children also answered using manipulatives was administered in K3 and P1; and a verbal variant, in which the problems were presented with Arabic numerals and children had to answer verbally was administered in P1 and P2. Furthermore, children’s basic numerical skills and exact and approximate arithmetic skills were assessed in K2 and K3, respectively. Path analysis showed a positive autoregressive relationship between the verbal variants of the computational estimation task but not between the nonverbal ones. Basic numerical skills were important predictors for computational estimation at all time points. Approximate arithmetic positively contributed to nonverbal estimation, while exact arithmetic positively predicted verbal estimation. In sum, solid basic numerical and arithmetic skills support children when performing computational estimation. Future intervention research should further unravel the causal contribution of each of these basic numerical and arithmetic skills.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms.

Kindergarteners' symbolic number abilities predict nonsymbolic number abilities and math achievement in grade 1.

Research has shown that two different, though related, ways of representing magnitude play foundational roles in the development of numerical and mathematical skills: a nonverbal approximate number system and an exact symbolic number system. While there have been numerous studies suggesting that the two systems are important predictors of math achievement, there has been substantial debate regarding whether and how these basic numerical competencies may be developmentally interrelated. Specifically, the causal direction of their relation has been the subject of debate: whether children's approximate number abilities predict later symbolic number abilities (the mapping account) or the other way around (the refinement account). Our sample included 622 kindergarten children (mean age = 62 months, SD = 3.5, 279 females, 75 born outside Canada), whose dot comparison, number comparison, and mixed comparison skills were assessed over three time-points and math achievement assessed over four time-points. We contrasted multiple theoretical predictions of the interrelations between the variables of interest posited by these two developmental accounts using longitudinal random intercept cross-lagged models. Results were most consistent with the refinement account, suggesting that earlier symbolic number ability is consistently the strongest predictor of approximate number ability, mixed-comparison ability, and arithmetic skills. Notably, our results demonstrated that, when individual models are examined in isolation, model fit was adequate or near adequate for all models tested. This highlights the need for future research to contrast competing accounts, as our results suggest the examination of any one account in isolation may not reveal the best fitting developmental model. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Number line tasks and their relation to arithmetics in second to fourth graders

Considering 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.

Separable effects of the approximate number system, symbolic number knowledge, and number ordering ability on early arithmetic development

There is evidence that early variations in the development of an approximate number system (ANS) and symbolic number understanding are both influences on the later development of formal arithmetic skills. We report a large-scale (N = 552) longitudinal study of the predictors of arithmetic spanning a critical developmental period (the first 3 years of formal education). Variations in early knowledge of symbolic representations of number and the ordinal associations between them are direct predictors of later arithmetic skills. The development of number ordering ability is in turn predicted by earlier variations in arithmetic, the ANS (numerosity judgments), and rapid automatized naming (RAN). These findings have important implications for theories of numerical and arithmetical development and potentially for the teaching of these skills.

What is to be learnt? Critical aspects of elementary arithmetic skills

In this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10. Our aim is to reveal what is to be learnt and how it might be learnt by means of discerning particular aspects of numbers. The Variation theory of learning informs the analysis of 2184 observations of 4- to 7-year-olds solving arithmetic tasks, placing the focus on what constitutes the ways of experiencing numbers that were observed among these children. The aspects found to be necessary to discern in order to develop powerful arithmetic skills were as follows: modes of number representations, ordinality, cardinality, and part-whole relation (the latter has four subcategories: differentiating parts and whole, decomposing numbers, commutativity, and inverse relationship between addition and subtraction). In the paper, we discuss particularly how the discernment of the aspects opens up for more powerful ways of perceiving numbers. Our way of describing arithmetic skills, in terms of discerned aspects of numbers, makes it possible to explain why children cannot use certain strategies and how they learn to solve tasks they could not previously solve, which has significant implications for the teaching of elementary arithmetic.

Development of language and arithmetic skills: risk and protective factors. Comparative cross-sectional study.

In a literate society, linguistic/arithmetic performance is highly valued. Based on defined risk factors, strategies for promotion of better performance can be developed. To ascertain the risk and protective factors relating to development of language and arithmetic. Observational comparative cross-sectional study at a public elementary school in Ribeirão Preto (SP), Brazil. A total of 66 children (41% females) attending first to fifth grades participated in this study. They were divided into two groups: G1, children classified as presenting language or arithmetic deficits; G2, average performance. Language (oral and written) and arithmetic skills were assessed through standardized tests. Variables relating to social skills, home environment resources and behavioral problems were assessed through standardized scales. Data on other variables (pre, peri and postnatal complications, maternal variables and others) were collected through interviews. The logistic regression technique with LASSO was used (α = 0.05). Teenage pregnancy and consumption of psychoactive substances during pregnancy or complications during pregnancy were risk factors for performance regarding arithmetic and language. Higher schooling level for the mother was a protective factor in the development of arithmetic and language. Being female and having a history of otitis were risk factors for language. Altered social skills (responsibility and civility) and complaints of inattention were risk factor for arithmetic. Adequate linguistic development was a protective factor for the development of arithmetic. The risk/protective factors included variables relating to the gestational period, mother's age when pregnant, mother's schooling, social skills, behavior and development issues.

Efektivitas Metode Jarimatika dalam Meningkatkan Kemampuan Berhitung Perkalian Siswa

This study aims to determine the effectiveness of the Jarimatika method in improving the multiplication ability of grade III students of MI Manba'ul Huda Tunjungrejo for the 2019/2020 academic year. This study describes the application of the Jarimatika method to the third grade students of MI Manba'ul Huda and then analyzes the suitability of the theory with practice so that its effectiveness can be determined. Collecting data in this study used interview and documentation methods while data analysis used Milles and Huberman's model analysis, namely data reduction, data presentation, data verification. The results of this study indicate that the application of the Jarimatika method can improve students' numeracy skills. Students look active and happy when applying the Jarimatika method. The test results showed that the majority of students had good multiplication arithmetic skills. In addition, there are three criteria for the effectiveness of learning methods that must be met. First, the learning completeness of grade III students shows that the majority of students have exceeded the minimum completeness criteria. Second, there is an increase and a difference between initial understanding and after learning. Third, it can increase the interest and motivation of students who have difficulty calculating multiplication

The Implementation of the Amora Learning Model to Improve Students’ Digital Literacy Skill of Indonesia University of Education

4.0 industrial revolution known as the era of digitalization in various sectors of life. Literacy skills in the industrial revolution era 4.0, not only emphasize reading, writing and arithmetic skills, but also emphasize the importance of digital literacy skills. This study aims to examine the effectiveness of the amora learning model in increasing digital literacy of students. This quasi-experimental study uses a pretest-posttest control group design. The research instrument uses a digital literacy ability test that has been validated by an expert. Hypothesis testing using the variance test used. The increase in digital literacy ability is determined based on the results of the N-gain test. The results showed that there was an increase in digital literacy of students in both classes. The experimental class has a higher increase in digital literacy than the control class. Digital literacy skills are increasing in both classes. This shows that the amora learning model applied successfully increases digital literacy of students in foundation education courses.

Associations between working memory and simple addition in kindergarteners and first graders

This study investigated the associations between working memory and simple addition in young children. Thirty-one kindergarteners and 24 first graders participated in this study. Children’s working memory was measured using the Automated Working Memory Assessment, while addition were assessed using the Addition Test derived by the investigators based on the syllabus for early arithmetic and teacher interviews. Children’s attention was also measured in order to control for its effect on the associations. Results show that visuospatial working memory was significantly associated with the performance on double-digit addition with carrying in a small group of kindergarteners. However, this association became non-significant after controlling for attention. In Grade 1 children, significant association between visuospatial working memory and double-digit addition without carrying was found. This finding is consistent with previous studies that visuospatial working memory is the best and unique predictor for non-verbal materials. The results of this study suggest that a better understanding of the role of working memory in the development of arithmetic skills is required for early childhood education.

On Validating Cognitive Diagnosis Models for the Arithmetic Skills of Elementary School Students

On Validating Cognitive Diagnosis Models for the Arithmetic Skills of Elementary School Students

Parent and Teacher Support of Elementary Students’ Remote Learning During the COVID-19 Pandemic in Germany

The aim of the present study was to investigate the associations between parental and teacher support and elementary students’ academic skills during the COVID-19 pandemic. Building on data of an ongoing longitudinal study, we studied the roles of children’s (N = 63) academic skills before the first COVID-19 lockdown in Germany (March–June 2020) as predictors of individual differences in parental schoolwork support during the lockdown, and the contributions of parental and teacher support to students’ reading and mathematics skills after the lockdown. Findings indicated that children’s reading and mathematics skills before the lockdown predicted parental help, and reading skills predicted parental need-oriented support with schoolwork during the lockdown. Children who received more need-oriented support from parents showed a more favorable development of arithmetic skills across the lockdown. Indicators of teacher support did not explain individual differences in students’ academic skills after the lockdown period.