Basic Numeracy Skills Research Articles

Arithmetic fluency and number processing skills in identifying students with mathematical learning disabilities

BackgroundStudents with mathematical learning disabilities (MLD) struggle with number processing skills (e.g., enumeration and number comparison) and arithmetic fluency. Traditionally, MLD is identified based on arithmetic fluency. However, number processing skills are suggested to differentiate low achievement (LA) from MLD. AimsThis study investigated the accuracy of number processing skills in identifying students with MLD and LA, based on arithmetic fluency, and whether the classification ability of number processing skills varied as a function of grade level. Methods and proceduresThe participants were 18,405 students (girls = 9080) from Grades 3–9 (ages 9–15). Students’ basic numerical skills were assessed with an online dyscalculia screener (Functional Numeracy Assessment –Dyscalculia Battery, FUNA-DB), which included number processing and arithmetic fluency as two factors. Outcomes and resultsConfirmatory factor analyses supported a two-factor structure of FUNA-DB. The two-factor structure was invariant across language groups, gender, and grade levels. Receiver operating characteristics curve analyses indicated that number processing skills are a fair classifier of MLD and LA status across grade levels. The classification accuracy of number processing skills was better when predicting MLD (cut-off < 5 %) compared to LA (cut-off < 25 %). Conclusions and implicationsResults highlight the need to measure both number processing and arithmetic fluency when identifying students with MLD.

Age-related effects in magnitude and place-value processing

While general cognitive skills decline during aging, numerical skills seem to be mainly preserved. Such skills are essential for an independent life up to old age, e.g., when dealing with money or time. Operating with numbers usually requires number magnitude and place-value processing. The question is whether these processes are negatively affected by aging due to the general cognitive decline or positively affected due to lifelong experience with numbers. Therefore, we investigated age-related changes in the distance and compatibility effects in single-digit, two-digit, and four-digit number comparison. On the one hand, older adults took longer for number processing and showed a smaller distance effect, indicating altered number magnitude representations. On the other hand, older adults were better in place-value processing as indicated by a smaller compatibility effect than in younger adults. We conclude that aging differentially affects basic numerical skills.

Field of Study and Gender Moderation of the Association of Personality and Math Anxiety with Numeracy

Math anxiety and personality influence numeracy, although the nature of their contribution has been overlooked. In the present study, we investigated whether their association with numeracy depended on field of study and gender in higher education. Participants were Italian undergraduates in either the humanities (N = 201) or Science, Technology, Engineering and Math (STEM; N = 209) fields of study. These participants remotely completed standardized tests assessing numeracy, math anxiety, personality, intelligence, and basic numerical skills. We tested whether math anxiety and personality interacted with field of study and gender in predicting numeracy. Results showed that math anxiety was negatively associated with numeracy independently of field of study and gender, while the effect of personality, especially neuroticism, on numeracy interacted with field of study over and above intelligence and basic numerical skills. Specifically, humanities undergraduates with higher neuroticism levels scored lower in numeracy than STEM undergraduates. These findings underscore the importance of emotional experience for a good performance in mathematics, beyond math anxiety and the other personality traits, in the students that are less familiar with mathematics. Finally, no robust gender moderation emerged, suggesting that its role may be overridden by differences associated with career choice.

Implementation of Basic Continuity and Recovery Plan, Teacher Engagement, and Parental Involvement in Public Secondary School: A Basis for School-Home Framework

As the face-to-face classes progress schools reopen their ground for the school year 2022-2023. Although expected, it is discovered that many learners do not meet the expected outcomes in mastery of basic numeracy and literacy skills and competencies. The Department of Education instantly developed a recovery learning plan framework to guide schools in addressing learning gaps. The main thrust of this paper was to determine the level of implementation of the Basic Continuity and Recovery Plan, Teacher Engagement, and Parental Involvement in public schools. The findings of the study revealed that the implementation level of basic continuity and recovery plan as assessed by the school head in terms of the development and implementation of long-term and catch-up plans to accelerate learning and reintegration of learners’ safe return to the school system was implemented. in terms of establishment of teachers' and learners' support systems through community and stakeholders' collaboration, literacy and numeracy assessment levels and learners' overall situation, especially the marginalized and modification learning package focused on fundamental skills towards resiliency were fully implemented. The level of teacher engagement in terms of vigor, dedication, and absorption were very often. The level of parental involvement was highly involved. There was no significant difference amongst respondents’ assessment on Implementation of Basic Continuity and Recovery Plan, Teacher Engagement, and Parental Involvement. There was a significant relationship between basic continuity and recovery Plan, teacher engagement and parental involvement. A localized School-Home Framework that focused on the four pillars of school-home partnership and connection was proposed.

Parental Involvement and Children Acquisition of Literacy and Numeracy Skills in Uganda

The aim of the study was to investigate the relationship between parental involvement and children’s acquisition of literacy and numeracy skills in Uganda. The objectives of the study were threefold; to examine the level of competence in children’s literacy and numeracy skills; to establish the relationship between parental involvement and children’s competences in literacy and numeracy skills as well as to predict parental factors in determining children’s competences in literacy and numeracy skills in Uganda. Secondary data from Uwezo 2021dataset were analysed using descriptive statistics, the correlational coefficient and logistic regression analysis was used to explore the levels of competence in literacy and numeracy skills among children, the association between competence levels in literacy and numeracy and parental involvement was analysed; as well as parental factors as predictors in children’s acquisition of literacy and numeracy skills were investigated. The study findings revealed that children in Uganda were at different competence levels in literacy and numeracy. Parental involvement in children’s education also significantly enhanced the acquisition of basic literacy and numeracy skills. However, there was a low positive correlation between parents’ participation in reading with their children and acquisition of literacy and numeracy skills. Noteworthy, findings revealed that numeracy skills of 4-16-year-olds increased with TV and mobile telephone access in households. In conclusion, parental factors play a significant role in predicting the development of literacy and numeracy abilities among children in Uganda. The odds ratio for increased literacy skills was lower in male-headed households but higher in households with parents who completed Ordinary School Certificate, Advanced School Certificate, and tertiary diploma/degree. Thus, the Ministry of Education and Sports should provide free adult education to parents in order to encourage them to be involved in their children’s education. The findings of this study inform education policy review to enhance children’s acquisition of basic skills in literacy and numeracy.

Delayed development of basic numerical skills in children with developmental dyscalculia.

Research suggests that children with developmental dyscalculia (DD) have deficits in basic numerical skills. However, there is conflicting evidence on whether basic numerical skills in children with DD are qualitatively different from those in typically developing children (TD) or whether basic numerical skills development in children with DD is simply delayed. In addition, there are also competing hypotheses about deficits in basic numerical skills, assuming (1) a general deficit in representing numerosities (Approximate Number System, ANS), (2) specific deficits in an object-based attentional system (Object Tracking System, OTS), or (3) deficits in accessing numerosities from symbols (Access Deficit, AD). Hence, the purpose of this study was to investigate whether deficits in basic numerical skills in children with DD are more indicative of a developmental delay or a dyscalculia-specific qualitative deviation and whether these deficits result from (selective) impairment of core cognitive systems involved in numerical processing. To address this, we tested 480 children (68 DD and 412 TD) in the 2nd, 3rd, and 4th grades with different paradigms for basic numerical skills (subitizing, counting, magnitude comparison tasks, number sets, and number line estimation tasks). The results revealed that DD children's impairments did not indicate qualitatively different basic numerical skills but instead pointed to a specific developmental delay, with the exception of dot enumeration. This result was corroborated when comparing mathematical profiles of DD children in 4th grade and TD children in 2nd grade, suggesting that DD children were developmentally delayed and not qualitatively different. In addition, specific deficits in core markers of numeracy in children with DD supported the ANS deficit rather than the AD and OTS deficit hypothesis.

Remedial Teachers’ Needs for Developing New Basic Numeracy Teaching Aids: A Needs Analysis

Appropriate teaching aids can assist remedial pupils in mastering basic numeracy skills effectively. However, issues persist of remedial pupils struggling to grasp basic numeracy skills, potentially due to the lack of suitable teaching aids tailored for Malaysia’s Special Remedial Programme. Thus, this quantitative study aimed to identify remedial teachers' needs for developing new basic numeracy teaching aids in the Special Remedial Programme. This study adapted McKillip's Discrepancy Model to guide the needs analysis. A quantitative survey methodology was used with 143 remedial teachers respondents in Melaka state, Malaysia. A validated questionnaire measured the levels and discrepancies in remedial teachers’ utilisation, perceptions, constraints, and skills regarding proposed basic numeracy teaching aids by the Ministry of Education Malaysia. Descriptive statistics were calculated. Findings showed moderate utilisation, high positive perception, moderate constraints, and high skills levels in using existing basic numeracy teaching aids. Discrepancies were identified in each construct, indicating the need for improvements tailored for better remedial learning. The results suggest modifying and developing new basic numeracy teaching aids that meet remedial pupils’ learning characteristics, fostering their creative thinking, facilitating self-directed learning activities, improving time efficiency in teaching and learning mathematics, providing various customisable teaching aid templates that are easy to reproduce with affordable everyday materials, and developing user-friendly technology teaching aids. Addressing these needs can enhance remedial teaching practices and pupils’ numeracy achievement. This study provides an important initial evidence base for designing and developing appropriate basic numeracy teaching aids based on remedial teachers’ current needs.

Pengaruh Kemampuan Pemecahan Masalah Matematik dan Motivasi Belajar terhadap Numerasi Siswa Kelas 4 SD

Numeration has an important role in the future of students. Train students' basic numeracy skills from an early age to prepare the next generation. The motivational boost factor in learning is one of the things that needs to be raised in learning efforts at school. The type of research used is quantitative research. The population of this study was 33 grade 4 students at SDN Sindanglaka Cianjur Regency. The student motivation questionnaire instrument for learning motivation is 25 statements, while problem-solving or problem-solving uses 2 questions. The dependent variable is numeracy ability in grade 4 elementary school, with the form of a test instrument as many as 2 questions. The results of the study concluded that there was no influence of mathematical problem-solving ability and learning motivation on numeracy in grade 4 students at SDN Sindanglaka. Because the application of numeracy in schools has just been implemented in the independent curriculum students do not understand numeracy.

Corrigendum: The changing nature of basic skills in numeracy

Corrigendum: The changing nature of basic skills in numeracy

Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School.

Mathematical anxiety (MA) and mathematics performance typically correlate negatively in studies of adolescents and adults, but not always amongst young children, with some theorists questioning the relevance of MA to mathematics performance in this age group. Evidence is also limited in relation to the developmental origins of MA and whether MA in young children can be linked to their earlier mathematics performance. To address these questions, the current study investigated whether basic and formal mathematics skills around 4 and 5 years of age were predictive of MA around the age of 7-8. Additionally, we also examined the cross-sectional relationships between MA and mathematics performance in 7-8-year-old children. Specifically, children in our study were assessed in their first (T1; aged 4-5), second (T2; aged 5-6), and fourth years of school (T3; aged 7-8). At T1 and T2, children completed measures of basic numerical skills, IQ, and working memory, as well as curriculum-based mathematics tests. At T3, children completed two self-reported MA questionnaires, together with a curriculum-based mathematics test. The results showed that MA could be reliably measured in a sample of 7-8-year-olds and demonstrated the typical negative correlation between MA and mathematical performance (although the strength of this relationship was dependent on the specific content domain). Importantly, although early formal mathematical skills were unrelated to later MA, there was evidence of a longitudinal relationship between basic early symbolic number skills and later MA, supporting the idea that poorer basic numerical skills relate to the development of MA.

The changing nature of basic skills in numeracy

The changing nature of basic skills in numeracy

Learning stations in enhancing remedial pupils’ basic numeracy post-pandemic: A case study

This case study aims to explore the usage of learning stations to teach basic numeracy and to engage level one remedial pupils to learn basic numeracy after pandemic. After the pandemic, many factors will determine whether remedial pupils struggle to grasp basic numeracy skills, especially in light of the new educational norm that the COVID-19 pandemic has provoked. However, learning stations can assess pupils’ understanding through its unique features, improving pupil’s learning numeracy, especially in this post-pandemic COVID-19. Data was collected from three remedial officers via interview and five remedial primary level one pupils in Sandakan, Sabah through observations. On top of that, analysis of documents such as APDM data and numeracy screening data were performed to gain a comprehensive picture of this usage of learning stations. Findings reveal that learning stations were potentially useful to teach basic numeracy for that remedial primary level one pupil, in particular, 30.95% of the remedial pupils passed the numeracy screening test after learning at the learning stations. At the end of this study, that remedial pupil was able to achieve the learning goals through learning stations.

Acquisition of new arithmetic skills based on prior arithmetic skills: A cross-sectional study in primary school from grade 2 to grade 5.

In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. In order to address this question, our goal was to determine the predictive power of previously taught operations on newly taught ones above general cognitive skills and basic numerical skills. More than one hundred children in each school level from Grades 2 to 5 from various socio-cultural environments (N= 435, 229 girls) were tested. Children were assessed on their abilities to solve the four basic arithmetic operations. They were also tested on their general cognitive abilities, including working memory, executive functions (i.e., inhibition and flexibility), visual attention and language. Finally, their basic numerical skills were measured through a matching task between symbolic and nonsymbolic numerosity representations. Additions and subtractions were presented to children from Grade 2, multiplications from Grade 3 and divisions from Grade 4. We show that addition predicts subtraction and multiplication performance in all grades. Moreover, multiplication predicts division performance in both Grades 4 and 5. Finally, addition predicts division in Grade 4 but not in Grade 5 and subtraction and division are not related whatever the school grade. These results are examined considering the existing literature, and their implications in terms of instruction are discussed.

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data.

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

Learning Mathematics with Interactive Technology in Kenya Grade-one Classes

While countries in sub-Saharan Africa have made significant progress towards achieving universal school enrolment, millions of students lack basic numeracy skills. This paper reports the results of a pilot study that aimed at using the Emergent Literacy in Mathematics (ELM) software to teach mathematics in early primary grades in Kenya. Designed as a pre- and post-test non-equivalent group research, the study unfolded in 14 grade-one classes from 7 primary public schools. After having learned with ELM for about two terms, the experimental students (N = 283) considerably outperformed their peers (N = 171) exposed to traditional instruction with the effect sizes of +0.37 on the overall skills measured by a standardised test of mathematics. The impact of ELM activities was the greatest on students’ ability to take language and concepts of mathematics and apply appropriate operations and computation to solve word problems. On this set of skills, the magnitude of difference between the experimental and control groups was +0.77. This study also revealed some positive shifts in the teachers’ perceptions about their practice. The teachers who adopted ELM in their practice reported having gained more confidence in mathematics and comfort in teaching mathematics with computers.

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

Predicting fraction and algebra achievements online: A large‐scale longitudinal study using data from an online learning environment

AbstractBackgroundMastering fractions seems among the most critical mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and operations) is highly relevant. However, almost all existing studies identifying more basic numerical skills as predictors of fraction understanding rest on data acquired in face‐to‐face testing—mostly in classrooms.ObjectivesIn this article, we evaluated whether results obtained in these previous studies generalized to data from the curriculum‐based online learning environment Bettermarks for mathematics used in schools in the Netherlands.MethodsWe considered data from more than 5000 students who solved over 1 million mathematical problem sets on basic mathematical skills, fractions, but also algebra.Results and ConclusionsIn line with previous findings, we found that fraction understanding was predicted significantly by more basic mathematical skills. Our analyses also indicated that algebra achievement was predicted significantly by fraction understanding beyond influences of more basic mathematical skills.ImplicationsTogether, these findings generalized previous results based on face‐to‐face testing to the context of data from online learning environments and thus, indicate that data from such large‐scale online learning environments may well qualify to provide significant insights into the hierarchical development of mathematical skills.

Gender Similarities in the Mathematical Performance of Early School-Age Children

The role of gender in mathematical abilities has caught the interest of researchers for several decades; however, their findings are not conclusive yet. Recently the need to explore its influence on the development of some foundational mathematic skills has been highlighted. Thus, the current study examined whether gender differentially affects young children’s performance in several basic numeracy skills, using a complex developmentally appropriate assessment that included not only standard curriculum-based measures, but also a non-routine task which required abstract thinking. Further, 136 children (68 girls) aged 6 to 8 years old completed: (a) the third edition of the standardized Test of Early Mathematical Ability (TEMA-3) to measure their mathematical knowledge; (b) the Kaufman Brief Intelligence Test (K-BIT), and (c) a non-routine counting detection task where children watched several characters performing different counts, had to judge their correctness, and justify their answers. Furthermore, frequentist and Bayesian analyses were combined to quantify the evidence of the null (gender similarities) and the alternative (gender differences) hypothesis. The overall results indicated the irrelevance or non-existence of gender differences in most of the measures used, including children’s performance in the non-routine counting task. This would support the gender similarity hypothesis in the basic numerical skills assessed.

Arithmetic (Re-)Learning in Neurological Patients

Abstract. Background: Numbers are an integral part of our life. Being competent with numbers is crucial for coping with the challenging demands of our modern times. Anyone who lacks basic numerical and calculation skills due to, for example, lower education, developmental disorders or acquired brain damage is socially disadvantaged and destined to remain marginalized. Improvement of basic numerical and calculation skills must therefore be an important goal of cognitive rehabilitation and intervention. Methods: We summarize the most recent studies regarding the rehabilitation of simple calculation deficits in adult neurological patients. Results: Over the last decades, several studies have reported acquired selective deficits in number processing and calculation skills in adult brain-damaged patients. It has also been shown in single case-studies that targeted rehabilitation based on theoretical neuropsychological models may lead to significant improvements of acquired deficits. Discussion: Systematic interventions may be successful in the case of acquired calculation deficits. Improvement of numerical competence in adult patients are possible even in very unfavorable circumstances (e.g., chronic stage, older age, severe deficits). This finding is of high relevance as numbers are essential in our daily life, and deficits in number processing may have a strong impact on a person's every-day autonomy.

The positioning of GCSE and Functional Skills in Further Education: how do vocational students make sense of post-16 mathematics pathways?

ABSTRACT Continuing to study mathematics is currently a requirement for low attaining 16- to 18-year olds in Further Education, as part of an ongoing drive to raise basic numeracy skills in England. However, these students, widely regarded as demotivated, often fail to make any progress in mathematics over the two years. This research explores how students make sense of the complex relationship between the two main post-16 qualifications, GCSE and Functional Skills, and its effect on students’ opportunities to succeed in mathematics. The study was conducted with vocational students (N = 187) at one Further Education college in the academic year 2018–19, using both a questionnaire and examination results. Findings suggest multiple dimensions that students valued in mathematics qualifications, while GCSE and Functional Skills were viewed either as a single linear progression or as two divergent pathways. Success was linked to features of the qualification taken, raising questions about inequality of opportunity.