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Students with mature number sense "make sense" of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; R. Reys et al., 1999; Yang, 2005). Although national standards and policy documents (e.g., CCSS, 2010; NCTM, 2000, 2014) emphasize the importance of number sense, limited research exists on the association between students' mature number sense and other important psychological constructs in mathematics education, such as grade-level mathematics achievement. The present study addressed this gap through a longitudinal design, advancing fundamental knowledge of number sense as a construct. At the start of the school year, middle school students (N = 129 at Time Point 1) completed measures of mature number sense and several related constructs, including grade-level mathematics achievement, executive functioning, and fraction and decimal computation. Students returned in the spring (N = 115 at Time Point 2) to complete an end-of-year mathematics achievement assessment as a measure of grade-level content learned during the year. We found mature number sense to be measurably distinct from related constructs and uniquely predictive of students' grade-level mathematics achievement at the end of the school year, controlling for their beginning-of-year mathematics achievement. Educational Impact and Implications Statement: This study showed that middle school students' number sense uniquely predicts how much grade-level mathematics content students learn over a school year. Students completed a series of assessments at the start and end of a school year, and we analyzed which factors are most predictive of students' learning in math over the school year. Students' number sense was more predictive of grade-level mathematics achievement than was their executive functioning skills or even their fraction and decimal computation skills. These results suggest that teachers can view developing students' number sense and their grade-level math learning as complementary rather than competing goals. When students construct high levels of number sense, they are laying a strong foundation of math knowledge to build upon as they encounter new grade-level content and skills. [ABSTRACT FROM AUTHOR]

This article aims to identify the knowledge that enables a prospective secondary school teacher to mobilize number sense components during a pre-professional practicum. Using a qualitative case study approach, four classroom episodes focused on fractions, percentages, and algebraic language are analyzed. The study involves one prospective teacher and 23 students from a multigrade school in central-southern Chile. The analysis integrates teacher's specialized knowledge and mathematical working spaces to explore how these frameworks inform the teacher's knowledge. The findings reveal that the teacher employs personal theories, real-life examples, and graphical aids to enhance students' understanding, though there is a reliance on rules and algorithms. While specialized knowledge aids in teaching, there is less emphasis on fostering students' conceptual understanding and judgement. The study recommends improving teacher training programs to better equip prospective teachers in grasping number sense components, highlighting the need for more focused training on its development. [ABSTRACT FROM AUTHOR]

In order to succeed in advanced mathematics and other related courses while in college, students must have a strong foundation in the subject of mathematics. Thus, this study aimed to determine the level of students' fundamental skills in mathematics in the areas of number sense, mathematical representation, spatial skills, estimation, patterns, and problem-solving when they are grouped according to the school of origin, strand, and program enrolled. Likewise, to test if there is a significant difference in fundamental mathematics skills when grouped according to the demographics. A descriptive comparative research design was utilized, and 278 first-year students participated. The results revealed that students performed better on their fundamental skills in mathematics in the area of patterns and performed lowest mean in spatial skills. Students who graduated from public schools performed well in all areas compared to private school students; in terms of program enrolled, fundamental skills in math varies. Furthermore, there is a significant difference in students' fundamental skills in mathematics when grouped according to the school of origin and strand, otherwise in program enrolled. This study suggests that mathematics teachers must utilize a different teaching strategy suited to students' needs following the learner-centered approach in teaching. [ABSTRACT FROM AUTHOR]

Introduction: The model of quantity-to-number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German "Mengen, zählen, Zahlen" (MZZ)]. Methods: We assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention. Results and Discussion: Multi-level analyses confirmed both significant shortand long-term effects in the specifically trained quantity-number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6  months and remained stable even 15  months after training. Effect sizes ranged from d=0.32 to d=1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model. [ABSTRACT FROM AUTHOR]

Background: Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks—'Fluency hypothesis'. Aims: The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels. Sample: Four hundred and thirty‐seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later). Methods: Number sense, arithmetic (addition and subtraction), spatial ability, visuo‐spatial working memory, perception, reaction time, character reading and general intelligence were measured. Results: Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta =.15 for addition and.06 (ns) for subtraction) compared to Grade 2 (.23–.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2. Conclusion: Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense‐arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2. [ABSTRACT FROM AUTHOR]

Number sense is fundamental to the development of numerical problem‐solving skills. In early childhood, children establish associations between non‐symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non‐symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross‐format neural representational similarity (NRS) between non‐symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short‐term training (STT) can induce similar changes as long‐term development. In this study, children aged 7–10 years underwent a theoretically motivated 4‐week number sense training. Using multivariate neural pattern analysis, we investigated whether short‐term learning could modify the relation between cross‐format NRS and arithmetic skills. Our results revealed a significant correlation between cross‐format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long‐term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. Research Highlights: We tested the hypothesis that short‐term number sense training induces the dissociation of symbolic numbers from non‐symbolic representations of quantity in children.We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training‐induced neurocognitive changes in the relation between number sense and arithmetic problem‐solving skills.Neural representational similarity between non‐symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training.Short‐term training recapitulates long‐term neurodevelopmental changes associated with numerical problem‐solving from childhood to adolescence. [ABSTRACT FROM AUTHOR]

The aim of this study is to determine the number sense skills of preschool (Kindergarten) children. In the study, survey design, one of the quantitative research methods, was used. The study group consists of a total of 114 children attending all the kindergartens (5 kindergartens) in the city center of Tunceli in the 2020-2021 school year. The data collection tool used in the study is the "Preschool Number Sense Test" developed by the researchers. In the analysis of the data, the correct answers obtained by using number sense skills, the correct answers obtained by using rule and operation-based methods, the false answers obtained by using number sense skills, the false answers obtained by using rule-operation-based methods and the questions left unanswered were considered. As a result of the analysis made, it was determined that preschool students used rule- and operation-based methods more in problem-solving when dealing with questions, and it was seen that they used number-sense-based methods less frequently. [ABSTRACT FROM AUTHOR]

Number sense is a skill that contributes significantly to learning mathematics. However, number sense is often positioned as a fundamental skill whose development is more focused on children. The contribution of number sense in mathematics is even more apparent at higher levels of education. Ironically, number sense seems ignored and has become a rarely studied topic in higher education. Thus, the student’s number sense ability profile seems buried with various problems. This study aims to reveal the profile of prospective elementary school teachers’ number sense abilities and the factors causing their failure in solving math problems during the implementation of blended learning. This study uses a qualitative approach with 37 prospective elementary school teachers as research subjects. The observation of the test and lecture activities is the data collection method. The results showed that the prospective elementary school teachers’ number sense ability was still relatively low. Based on the components, the order of number sense abilities is from the highest, namely: (1) knowledge and number facilities with the achievement of 14.41%; (2) knowledge and facilities for number operations with the achievement of 8.12%; and (3) knowledge and facilities of numbers and operations for computing settings with an achievement of 1.8%. The low number sense ability is caused by the habit of solving problems procedurally and the failure to solve problems due to misconceptions, not understanding concepts, inaccuracy, inability to understand questions, and difficulty representing fractions. Various factors causing the failure arose due to the limitations of implementing blended learning.

Empirical research on number sense to date has been conducted with preschoolers and elementary school students. Despite their contributions to the literature, these studies have used variable-centered analytic approaches that may prevent distinct number sense profiles for preschoolers and first graders from being identified. This study aimed to determine the number and proportions of distinct number sense profiles, the variables influencing these profiles, and the characteristics of the children with different profiles in the transition from preschool to elementary school. We conducted a quantitative study using a cross-sectional design for this purpose and used latent profile analysis to identify and describe distinct number sense profiles for preschoolers and first-grade students. A total of 1688 children, 848 from preschool and 840 from the first grade of elementary school, took part in the study. A Number Sense Screener was used to determine number sense profiles. The data collection tool used in the study was found to be reliable. Based on the findings of the study, we identified three profiles for both the preschoolers and first graders, namely, moderate very low, moderate low, and moderate high. We examined family and household income variables to help predict the profiles. We then took the characteristics and components of number sense that caused the differentiation in the profiles as revealed by the results of the study and discussed them in light of the literature. [ABSTRACT FROM AUTHOR]

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240 first-grade students with mathematics difficulties in a new geographical region. Participating students were randomized into one of three conditions: (a) 2:1 mathematics intervention group, (b) 5:1 mathematics intervention group, or (c) business-as-usual instruction. Relative to the original study, findings from the replication varied. When comparing the treatment groups to the control, results suggested positive effects on all outcome measures, including a follow-up assessment administered one year later. However, differences between the two treatment groups based on group size were not found in the mathematics outcome measures. Both groups also received commensurate levels of observed instructional interactions. Implications for unpacking contextual differences between original research and their replications as well as using future research to explore the quantity and quality of instructional interactions as ways to explain variation in findings of group size are discussed. [ABSTRACT FROM AUTHOR]

Mathematics teachers face significant challenges in developing number sense among students. This study investigates the teaching practices of Saudi Arabian primary school mathematics teachers for fourth-grade female students. Using a descriptive-analytical approach and validated observation cards, the study sampled 20 teachers and analyzed data through statistical measures. Results revealed teaching practice levels as low in planning, moderate in implementation, and high in evaluation, with overall moderate effectiveness. No significant differences were found based on teaching experience, academic degree, class size, training programs, or teaching load. The study recommends the Saudi Ministry of Education enhance teaching practices via targeted professional development and suggests future research on instructional methods across different educational levels and the use of digital tools. [ABSTRACT FROM AUTHOR]

The political and social environments in which learners with disabilities live often cause more limitation on the individual abilities of these learners than the disability itself (Capri et al., 2018:2). Likewise, mathematical thinking for learners who are severely mentally disabled is often limited to concretisation or memorisation, which tends to undermine mathematical number sense. This study was undertaken against the background of a lack of methodological guidelines for the teaching of mathematics in the new adapted curriculum for learners who are severely intellectually disabled. Context-rich mathematics tasks for the development of mathematical thinking in learners who are severely intellectually disabled were used during the study. A qualitative research approach was followed in which empirical data were generated through three action research cycles. Data were collected through in-depth discussions, field notes, a literature review and learner work. Vygotsky’s (1978:6) sociocultural theory was used as a theoretical framework because it highlights the importance of social interactions and mediated learning. The Reality, Abstraction, Mathematics and Reflection (RAMR) framework of Cooper and Carter (2016:177) is used as a didactic framework for a practical approach to mathematics education in the study. According to the data from in-depth discussions with five educators, learners with intellectual disability are perceived to have limited number sense knowledge. These educators also indicated that their choice of learning tasks only included number facts, arithmetic fluency, memorisation, and teaching with concrete apparatus. Data from the in-depth discussions with two mathematics subject advisors working in special education pointed out educators’ limited didactical knowledge for teaching mathematics to learners who are severely intellectually disabled. Based on these data, a teaching intervention was designed and implemented for six months. The purpose was to investigate the effect on participation and learning of changing the researcher’s practice to focus on mathematical reasoning in context rich tasks. The lived experiences of the ten learners who were involved in the teaching intervention were included as a background to mathematics problems to design context-rich tasks. The guidelines from the research entail that real-life contexts in which mathematical problem types are embedded are conducive to learning experiences that are rich in discussion for learners who are severely intellectually disabled. Such an approach has the potential to make mathematics more meaningful to learners who are severely intellectually disabled, improve their mastery of contexts, and develop critical thinking. Findings from the action research process can be adapted to similar mathematics teaching practices. [ABSTRACT FROM AUTHOR]

Teachers' perceptions of their teaching and learning activities are critical, especially given that the Malaysian preschool curriculum has undergone multiple revisions recently. The purpose of this study was to measure Malaysian teachers' perceptions on teaching early mathematics. The study aimed to assess teachers' perception of six constructs, namely, (1) knowledge about early mathematics, (2) readiness to involve in the early mathematics, (3) understanding of the importance of early mathematics, (4) past experience in mathematics, (5) attitudes towards early mathematics, and (6) importance of knowledge about teaching early mathematics. This study gauged the 76 Malaysian preschool teachers using a set of questionnaire. As this research discovered, the teachers in this study believed that they knew about early mathematics, were eager to get involved in early mathematics activities at preschool, understood the importance of Mathematics literacy, were positively disposed towards it, and considered mathematical knowledge regarding preschoolers to be critically valued. [ABSTRACT FROM AUTHOR]

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation). [ABSTRACT FROM AUTHOR]

To examine the relationship between early number sense and later symbolic arithmetic competence and how they are connected in young Chinese children. The present study utilized a longitudinal sample of 115 Chinese children aged 3 to 6. Young children completed measures to assess number sense, visual spatial skills (in the fall of their second kindergarten year, K2), arithmetic competence (in the spring of their second kindergarten year, K3), working memory, verbal comprehension, and inhibitory control (in the fall of their first kindergarten year, K1). The results showed that number sense predicted arithmetic competence six months later. Meanwhile, visual spatial skills played a mediating role in this association, but it became non-significant when working memory, verbal comprehension, and inhibitory control were added as covariates. These longitudinal findings confirm the close association between number sense and arithmetic competence in young Chinese children. [ABSTRACT FROM AUTHOR]

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Copyright of Gazi University Journal of Gazi Educational Faculty (GUJGEF) is the property of Gazi University Journal of Gazi Educational Faculty (GUJGEF) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of International Journal of Educational Studies in Mathematics (IJESIM) is the property of International Journal of Educational Studies in Mathematics (IJESIM) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

IntroductionThe model of quantity–to–number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German “Mengen, zählen, Zahlen” (MZZ)].MethodsWe assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention.Results and DiscussionMulti-level analyses confirmed both significant short-and long-term effects in the specifically trained quantity–number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6 months and remained stable even 15 months after training. Effect sizes ranged from d = 0.32 to d = 1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model.

Background: South African teachers’ mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics. Aim: The aim of this article is to share how pre-service teachers (PSTs) used the empty number line (ENL) to demonstrate the jump strategy (JS) for efficient mental computation, related to the national Mental Starters Assessment Project (MSAP). Setting: This study was conducted at a tertiary institution in the Eastern Cape province of South Africa, with 40 first-year intermediate phase PSTs, during their mathematics didactics course. Methods: The data comprised 40 micro-teaching videos, analysed thematically, following an analytical model for video-recorded data. Videos were categorised according to the way they faithfully followed or departed from the MSAP teacher resources. Results: Findings suggest that more than 70% of the PSTs faithfully followed the teacher resources to teach the JS on the ENL, with regards to use of at least three of the four key elements, namely: ENL, jumps, gesturing, and key phrases and terminology. Conclusion: We suggest PSTs receive explicit instruction on the above-mentioned key elements for teaching mental calculation strategies with the ENL and opportunities to practise teaching these to their peers. Contribution: Most PSTs successfully used the ENL to demonstrate the JS for efficient mental computation, enabled by the opportunity to engage in developing (and reflecting on their) micro-teaching videos.

Background: National and international assessments show South Africa’s underperformance in mathematics. As many learners already fall behind in the early grades, where foundational number sense should be established, addressing the challenges of number sense in the Foundation Phase (FP) is important. Research recognises the need to better develop pre-service primary teachers’ (PSTs’) mathematical content knowledge (CK) and pedagogical content knowledge (PCK). Understanding the importance that CK PSTs bring to their tertiary studies is needed. Aim: The study explores, what knowledge do third-year FP PSTs have of additive reasoning mental mathematics strategies? Setting: We share data from a larger study of PSTs’ CK and PCK of additive reasoning strategies (a key aspect of number sense) before additive reasoning lectures with 80 third-year FP PSTs during their mathematics methodology course at a private institution. Methods: Participants included 54 of the 59 PSTs who agreed to take part in the study and were present in the first session when the pre-questionnaire (the focus of this article) was administered. Quantitative and qualitative analysis of PSTs’ methods used, performance on the pre-questionnaire calculation items and explanations of methods and strategies were carried out. Results: Results highlight the need for explicit teaching of efficient calculation strategies along with required fluencies for using strategies. Conclusion: Knowledge of additive reasoning strategies cannot be taken for granted as established at school. Contribution: The findings of the study highlight the need for explicit teaching of efficient mental strategies such as Bridging Through Ten, Jump Strategy and Rounding and Adjusting in PSTs’ studies.

Background: South African learners face the double disadvantage of living in low socio-economic conditions with access to few resources and attending schools with challenging learning conditions. Mathematics performance reflects such conditions with extreme performance gaps between wealthier and poorer learners. The need for early intervention is increasingly acknowledged. Aim: In this conceptual article, we draw out the features of mathematics games that can be used to develop learners’ foundational number sense that will impact their learning trajectories. Setting: Based on our experience in working with learners from low socio-economic backgrounds in after-school mathematics clubs, we propose that these are opportune spaces for intervention. Methods: Drawing both on the research literature and our experience, we exemplify and discuss key features of mathematics games and argue why these are important to support the development of number sense. Results: We argue that to meaningfully develop young learners’ number sense, activities need to be sufficiently engaging to retain their interest and be presented in a manner that club practitioners, who might not be teachers, are able to facilitate. Drawing on our experiences of designing and running mathematics clubs, we discuss why components like built-in checks, readily available resources, connection to calculation strategies and transferability to home settings are important design features. Conclusion: Particular design features are important to enable maths games to support learners’ development of efficient and effective calculation strategies. Contribution: This article contributes a framework of key features for effective use of games to develop mental mathematics strategies for number sense.

Number sense merupakan kemampuan dasar dari kemampuan matematika lainnya. Namun, dalam praktik pembelajarannya masih jauh dari sesuai karakteristik dan tahap perkembangan anak usia dini. Tujuan dari penelitian ini adalah untuk mendeskripsikan penggunaan Ten Frame dengan loose parts dalam mengembangkan number sense pada anak usia dini. Ten Frames merupakan sebuah bingkai sebanyak 2 × 5 dimana akan diletakkan berbagai benda untuk merepresentasikan bilangan satu sampai sepuluh. Loose parts ialah bahan-bahan yang terpisah, dapat dibawa, dipindahkan, digabungkan yang terdiri dari bahan alam, plastik, logam, kayu dan bambu, kaca dan keramik, benang dan kain, serta bekas kemasan. Metode penelitian yang digunakan adalah metode penelitian deskriptif untuk mengetahui praktik pembelajaran menggunakan Ten Frame dengan loose parts dalam mengembangkan number sense anak usia dini. Kesimpulan yang diperoleh adalah dengan menggunakan Ten Frames dengan loose part anak lebih mudah memahami tentang konsep bilangan, hubungan angka dan jumlah benda serta operasi bilangan dengan cara yang menyenangkan.

Global and country-specific mathematics performance constitutes a major challenge, both for educators and policymakers. Realisation of the African Union Agenda 2013 hinges significantly upon transformation of education. In this regard, mathematics and science education, specifically, are instruments for scientific and technological development to position Africa on the same level as the global league of continents in the future. It is, therefore, important to develop amongst learners a good understanding of a mathematical concept such as number sense from an early age, given that students who have a good sense of numbers can manipulate figures to simplify calculations and have the confidence to approach problems in a variety of ways. It is for this reason that the present study investigates the intervention strategies implemented by educators in enhancing learners’ understanding of number sense in the Ekurhuleni North District schools, Gauteng Province, South Africa. The study used a case study design and a qualitative research approach, both of which were supported by an interpretivist paradigm. The study made use of a semi-structured interview to gather data from mathematics teachers, learners, and a principal in the selected school. Research findings revealed that although mental computation, use of concrete props, use of the number line, and a counting strategy are some of the various strategies employed to enhance learners’ understanding of number sense, teachers need to develop a sound understanding of number sense and be flexible in their approaches in order to assist learners. Based on the findings, it was recommended that curriculum designers and teachers concentrate on teaching methods to help students develop learners’ number sense, as this can lead to potential mathematics success.

When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? We investigate the role of specific spatial frequencies to the encoding of number through cross-adaptation. In two experiments, observers were peripherally adapted to six randomly generated sinusoidal gratings varying from relatively low-spatial frequency (M = 0.44 c/deg) to relatively high-spatial frequency (M = 5.88 c/deg). Subsequently, observers judged which side of the screen had a higher number of dots. We found a strong number-adaptation effect to low-spatial frequency gratings (i.e., participants significantly underestimated the number of dots on the adapted side) but a significantly reduced adaptation effect for high-spatial frequency gratings. Various control conditions demonstrate that these effects are not due to a generic response bias for the adapted side, nor moderated by dot size or spacing effects. In a third experiment, we observed no cross-adaptation for centrally presented gratings. Our results show that observers' peripheral number perception can be adapted even with stimuli lacking any numeric or segmented object information and that low spatial frequencies adapt peripheral number perception more than high ones. Together, our results are consistent with recent number perception models that suggest a key role for spatial frequency in the extraction of number from the visual signal (e.g., Paul, Ackooij, Ten Cate, & Harvey, 2022), but additionally suggest that some spatial frequencies – especially in the low range and in the periphery – may be weighted more by the visual system when estimating number. We argue that the cross-adaptation paradigm is also a useful methodology for discovering the primitives of visual number encoding. [ABSTRACT FROM AUTHOR]

Animals employ quantitative abilities to gauge crucial aspects of their environment, such as food or predator density in a given area or the number of eggs in a nest. These quantitative skills hold ecological implications and can impact an animal's fitness. However, our comprehension of how these abilities intersect with environmental challenges remains limited. We tested for spontaneous quantity discrimination in the sleepy lizard (Tiliqua rugosa), a long-lived species known for forming life-long pair bonds in which pairs come together for the breeding season. We subjected lizards to a Y-maze experiment presenting both discrete (comparisons involving two vs. four, two vs. six, two vs. eight, four vs. six, four vs. eight, and six vs. eight pieces) and equivalent continuous combinations (single pieces differing in size) of pumpkin pieces. Our findings revealed that sleepy lizards exhibited spontaneous quantity discrimination, favoring the larger quantity in three discrete comparisons (eight vs. two, two vs. six, four vs. six) and two continuous comparisons (eight vs. two, eight vs. four). However, low accuracy may be attributable to difficulty in visual acuity exacerbated by difficulty discriminating quantities at small ratios. Furthermore, we found no evidence for a speed-accuracy trade-off in their decision-making process. Our results suggest that sleepy lizards likely employ multiple cues to estimate quantity accurately. Considering these results in the context of previous studies on various lizard species, it becomes apparent that lizards, as a group, offer a valuable model for unraveling the evolution of cognition, given their diverse ecology and sociobiology. [ABSTRACT FROM AUTHOR]

This Brief Report presents an example of assessment validation using an argument-based approach. The instrument we developed is a Brief Assessment of Students’ Mature Number Sense, which measures a central goal in mathematics education. We chose to develop this assessment to provide an efficient way to measure the effect of instructional practices designed to improve students’ number sense. Using an argument-based framework, we first identify our proposed interpretations and uses of student scores. We then outline our argument with three claims that provide evidence connecting students’ responses on the assessment with its intended uses. Finally, we highlight why using argument-based validation benefits measure developers as well as the broader mathematics education community. [ABSTRACT FROM AUTHOR]

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Considering the negative situations faced by the migrating societies, it is known that the language and culture factors exert a stronger influence on the mathematics course than the other undesirable conditions. From this perspective, it is known that the mathematical performance of individuals is likely to increase by placing the concept of number sense in the center. Therefore, the present study aimed to examine the number sense skills of Syrian immigrant students with reference to gender and duration of stay as an immigrant as well as to determine their conceptual awareness of number sense-related components. The descriptive correlational design was used in this study in which 152 immigrant students participated. Web-based two-tier test was used in the data collection process, and descriptive statistical values and t-test for independent samples in the analysis of the data. As a result, it was found that male students compared to female students, as well as those who had been immigrants in Turkey for a long time compared to those for a shorter time showed higher number sense performances, though most of the students were at a low number sense level. In addition, the differences appeared significantly in relation to the variables of gender and duration of stay as an immigrant. A surprising result is that most students preferred number sense-based solutions as the basis for their answers. It can thus be concluded that the number sense performances of Syrian immigrant students are lower than expected and that future studies are needed not only to focus on teachers but also on teaching methods and materials in order to take immigrant problems under control and to come up with solutions with a view to overcome such challenges. [ABSTRACT FROM AUTHOR]

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The nonsymbolic comparison task is used to investigate the precision of the Approximate Number Sense, the ability to process discrete numerosity without counting and symbols. There is an ongoing debate regarding the extent to which the ANS is influenced by the processing of non-numerical visual cues. To address this question, we assessed the congruency effect in a nonsymbolic comparison task, examining its variability across different stimulus presentation formats and numerical proportions. Additionally, we examined the variability of the numerical ratio effect with the format and congruency. Utilizing generalized linear mixed-effects models with a sample of 290 students (89% female, mean age 19.33 years), we estimated the congruency effect and numerical ratio effect for separated and intermixed formats of stimulus presentation, and for small and large numerical proportions. The findings indicated that the congruency effect increased in large numerical proportion conditions, but this pattern was observed only in the separated format. In the intermixed format, the congruency effect was insignificant for both types of numerical proportion. Notably, the numerical ratio effect varied for congruent and incongruent trials in different formats. The results may suggest that the processing of visual non-numerical parameters may be crucial when numerosity processing becomes noisier, specifically when numerical proportion becomes larger. The implications of these findings for refining the ANS theory are discussed. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the relationship between number sense, algebraic reasoning, and mathematical achievement among 8th grade students. This study aims to describe an existing situation in the research, and so uses a survey model as quantitative research. The Algebraic Reasoning Assessment Tool (ARAT); and number sense test, as developed by Kayhan Altay (2010) were used. This study used the graded score scale, adapted from Marzano (2000), to evaluate students' responses to the ARAT questions. This research was conducted with 290 8th grade students. On evaluation, the results of this research were as expected, because algebraic reasoning is based on number concept and number sense. Accordingly, in order for students to be able to think and reason using algebra, it is necessary that they learn algebra without any problems and they understand the basics of algebra well. On the other hand, arithmetic knowledge is shown to be the basis of algebraic learning. On examination, the definitions of algebra state that it is a generalized form of arithmetic. Arithmetic knowledge is related to a complete understanding of the concept of number. It is concluded that, a student who fully learns the concept of number may also has a developed number sense. This study showed that the algebraic reasoning ability of students with a high number sense is high. Besides, it was determined that students often had difficulty using different solution strategies while answering the questions. In addition, it is concluded that the students' number sense scores were a significant predictor of algebraic reasoning scores, and that 36% of the variance in algebraic reasoning scores could be explained by number sense scores. [ABSTRACT FROM AUTHOR]

Copyright of Bolu Abant Izzet Baysal University Journal of Faculty of Education / Bolu Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi is the property of Bolu Abant Izzet Baysal University Journal of Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, it is aimed to examine performance of number sense of gifted students in terms of gender, grade levels,number sense self-efficacy and number sense components. In line with the studies in the literature, due to the insufficent research on the number sense on students who diagnosed with special talents in our country, it is felt that in this research we need to study with these student and examine the level of student of this category in the scope of relevant study in terms of various variables. A quantitative descriptive research model was used to determine carefully and completely the level of students' number sense and their existing situations that is related to it. The study group consists of 6th and 7th-grade students attending Science and Art Centers located in 12 provinces in the Eastern Anatolia Region during the 2022-2023 academic year .286 students attended in this research that included 184 students in the 6th grade and 102 students in the 7th grade. This study included the Number Sense Scale and the Number Sense Self-Efficacy Scale as a data collection tools. It is indicated that in this research students diagnosed with special abilities didn't show high level of number sense performance; instead, they prefer rule-based solutions.It is revealed that, the component "flexibility in calculation" is the most succeded one among the components of number sense.When the students' grade level increases, it has been observed that, the number sense performance of students improves.When number sense performance was examined based on gender, it was seen that male students used number sense more than female students.When the relationship between the number sense test scores and number sense self-efficacy scores of gifted students was examined, an expressive positive correlation was found between the scores. [ABSTRACT FROM AUTHOR]

One model of numeric perception is a density-area mechanism: a process that estimates both density and area of an array, then multiplies them to create an estimate of number. One line of evidence that supports this is the surprising numeric Ebbinghaus illusion: smaller context circles lead to greater perceived number than larger context circles, potentially via larger perceived area. This registered report re-tested this effect with a number of simple but potentially important improvements in the method and analysis. Participants were asked to indicate the number of blue dots in arrays that were surrounded by grey context circles of three different sizes. Both experiments confirmed that larger context circles lead to a proportional increase in perceived number. Experiment 1 (N = 50) did so with denser, more texture-like arrays (50-100 dots filling 35% of the area). Experiment 2 (N = 50) did so with sparser, more scatter-like arrays (10-30 dots filling 5% of the area). These findings confirm the existence of the numeric Ebbinghaus effect. This in turn confirms a specific prediction derived from a density-area mechanism and rules out alternatives that begin by stripping away context to non-verbally count discrete entities. No further significant evidence was found to suggest that this depends on the array being particularly dense or texture-like, nor to suggest that anything moderates the impact of increasing perceived area as a direct proportional effect on increasing perceived number. This further builds the case that this kind of numeric perception relies on a density-area mechanism.

Dyscalculia is a specific learning difficulty that affects an individual's ability to perform mathematical tasks. The research was aimed at investigating whether gender and age have a differential influence on the number sense, arithmetic operations, and working memory dimensions of dyscalculia. The research design was an expo facto research design. The population was all 87320 junior secondary school 1 and 2 students in Obio-Akpor local government area. The sample consists of 453 students who have been diagnosed with dyscalculia. This sample was randomly drawn using a multistage sampling procedure. A standardized instrument, the Dyscalculia Test by Eteng-Uket, was used for data collection. High validity and reliability indices were obtained for the test. The data were analyzed using mean, standard deviation, one-way, and two multivariate analyses of variance. The result showed that gender and age independently and in interaction had a differential influence on dyscalculia dimensions, but this differential influence was not significant. Based on these findings, it is recommended that educators use a variety of individualized instructional strategies and materials, including visual aids, manipulatives, and adaptive technologies that are effective for different genders and age groups of dyscalculics

In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into account that there are non-numerical methods of assessing numerosity, which opens up the possibility that cognitive agents lacking numerical abilities may still be able to represent numerosity. In this paper, I distinguish between numerical and non-numerical methods of assessing numerosity and show that the most common models of the internal mechanisms of the so-called number sense rely on non-numerical methods, despite the claims of their proponents to the contrary. I conclude that, even if it is established that agents attend to numerosity, rather than continuous properties of stimuli correlated with it, an answer to the question of the existence of the number sense is still pending the investigation of a further issue, namely, whether the mechanisms the brain uses to assess numerosity qualify as numerical or non-numerical.

This text focuses on the development of number sense, specifically addressing the challenges associated with understanding the number system, including the connections to and difficulties in early arithmetic learning. It provides a synthesis of the scientific literature related to this development. It concludes by proposing a hypothesis for the development of number sense, associated with the construction of dynamic and pictorial mental representations. This continuum proposes five key phases: perception of small quantities, additive thinking, multiplicative thinking and pre-place value, passage to tens and passage to hundreds and understanding place value.

本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項。 Background and Purpose The main purpose of teaching number sense to young children is to establish a core knowledge framework for number concepts, thereby enabling young children to understand a wide range of number problems and providing a basis for children to learn more complex number concepts in the future. Number sense is also fundamental for learning formal mathematics later in life. Studies have associated a lack of number sense in early childhood with a subsequent decline and difficulty in mathematical learning. Therefore, cultivating number sense in early childhood is essential for future mathematics achievement. The development of young children’s numerical cognition and mathematical skills is closely linked to the establishment of a mental number line. Additionally, studies have discovered a strong correlation between an individual’s innate perception of the mental number line and their proficiency in a range of mathematical abilities, including understanding number concepts, estimating quantities, and performing arithmetic. With the goal of developing young children’s number sense and basic arithmetic skills, this study designed a set of targeted intervention tools in the form of digital number line games. These tools were designed to help young children develop an understanding of mental number lines, thereby improving their number sense and basic arithmetic skills. This study also compared the improvement effects of the number line game and a non-number line game on the aforementioned learning objectives to determine which game was more effective at improving the relevant learning outcomes. Literature Review The meaning of number sense Number sense can be described as an individual’s ability to understand, relate, and connect numbers. Children with number sense can understand the relevant concepts and principles of numbers. Number sense includes several mathematical aspects, such as the ability for estimating small quantities, counting and cardinality, comparing numbers, recognizing number patterns, and transforming numbers. The concept of number sense in early childhood refers not to a single mathematical ability but rather encompasses a set of essential cognitive components that aid in comprehending numbers and abstract numerical symbols. These components include a conceptual understanding and the ability to perform practical numerical operations. Development of a mental number line and the relationship between a mental number line and number sense in children The ability to place numbers on a mental number line is associated with the development of number sense, which is the ability to understand, relate, and connect numbers. Relevant studies have suggested that an individual’s perception of the mental number line influences their development of several number sense components (e.g., estimating, counting, and transforming numbers). Therefore, as soon as young children are capable of counting, connecting, and estimating the size of numbers and have learnt the numeral system and the spatial arrangement of numbers, they may acquire the ability to perceive a mental number line. Through educational activities, children can learn how to spatially arrange numbers (i.e., visualize a mental number line) and effectively develop a complete understanding of advance number concepts, including number transformation. Relationship between the construction of a mental number line and basic arithmetic The construction of a mental number line involves spatially arranging numbers by size in the mind. Numbers are arranged in a continuous, quantity-based analogical format in ascending order (from left to right). When constructing a mental number line, basic arithmetic is performed. For example, the number after 6 is 7. To arrive at 7, addition arithmetic (6 + 1) must be performed. Therefore, the construction of a mental number line plays an important role in the development of basic arithmetic skills. Methods This study employed an experimental research design. A total of 105 preschool children from rural areas in eastern Taiwan were enrolled into this study. Participants were randomly divided into three groups: two experimental groups and a control group. A pretest-posttest analysis was performed to explore the influence of number line games on number sense and basic arithmetic skills. One-way analysis of covariance was performed to determine whether significant differences were present between the pretest and posttest results and between the three groups to eliminate the influence of confounding variables. Results Results for the number sense Covariate analysis revealed significant differences in posttest scores between the three groups (F(2,101) = 64.47, p < .05, eta squared η 2 = .56). Furthermore, the improvement in number sense in the two experimental groups was significant. Both interventions (a number line game and a non-number line game) significantly improved the number sense to a similar extent. Results for basic arithmetic skills Significant differences were observed in the improvement of addition and subtraction skills between the two experimental groups and the control group. Basic arithmetic skills were better in the two experimental groups than in the control group. Additionally, the group that played the number line game performed significantly better than the group that played the non-number line game. Conclusion This research is one of the few studies that has explored the development of number sense among young children by using a number line game. The findings indicate that the number line game, which was designed in accordance with the mental number line concept, can effectively enhance number sense among young children. However, in terms of improving number sense, similar learning outcomes can also be achieved by using non-number line games. In terms of improving basic arithmetic skills (addition and subtraction), the number line game was more effective than the non-number line game (traditional number decomposition and synthesis game). Furthermore, the non-number line game was more effective than the intervention in the control group. Overall, the digital game intervention aimed at improving mathematical learning among young children (whether it involves a number line game or a traditional non-number line game) had a positive effect on improving numerical ability, including number sense and basic arithmetic. The number line game was more effective than the non-number line game and the intervention in the control group. These findings are expected to advance the theoretical literature of mathematics education in early childhood and the teaching practices of mathematics for young children.

Preverbal infants spontaneously represent the number of objects in collections. Is this 'sense of number' (also referred to as Approximate Number System, ANS) part of the cognitive foundations of mathematical skills? Multiple studies reported a correlation between the ANS and mathematical achievement in children. However, some have suggested that such correlation might be mediated by general‐purpose inhibitory skills. We addressed the question using a longitudinal approach: we tested the ANS of 60 12 months old infants and, when they were 4 years old (final N = 40), their symbolic math achievement as well as general intelligence and inhibitory skills. Results showed that the ANS at 12 months is a specific predictor of later maths skills independent from general intelligence or inhibitory skills. The correlation between ANS and maths persists when both abilities are measured at four years. These results confirm that the ANS has an early, specific and longstanding relation with mathematical abilities in childhood. Research Highlights: In the literature there is a lively debate about the correlation between the ANS and maths skills.We longitudinally tested a sample of 60 preverbal infants at 12 months and rested them at 4 years (final sample of 40 infants).The ANS tested at 12 months predicted later symbolic mathematical skills at 4 years, even when controlling for inhibition, general intelligence and perceptual skills.The ANS tested at 4 years remained linked with symbolic maths skills, confirming this early and longstanding relation in childhood. [ABSTRACT FROM AUTHOR]

Types of mathematical learning disability (MLD) are very heterogeneous. Lower scores on mathematics and several cognitive skills have been revealed in samples with MLD compared with those with typical development (TD), but these studies vary in sample selection, making it difficult to generalize conclusions. Furthermore, many studies have investigated only one or few cognitive skills, making it difficult to compare their relative discrepancies. The current meta-analysis (k = 145) was conducted to (a) give a state-of-the-art overview of the mathematical and cognitive skills associated with MLD and (b) investigate how selection criteria influence conclusions regarding this topic. Results indicated that people with MLD display lower scores not only on mathematics but also on number sense, working memory, and rapid automatized naming compared with those with TD, in general independently of the criteria used to define MLD. A profile that distinguishes people with more serious, persistent, or specific MLD from those with less severe MLD was not detected. [ABSTRACT FROM AUTHOR]

Numbers are fundamental mathematical concepts that underlie various other mathematical principles. This research investigates the relationship between number sense and the numeracy abilities of fifth-grade elementary school students. A cross-sectional survey method was used, with 205 respondents voluntarily participating. The results showed a reciprocal relationship between number sense and numeracy in elementary school students. Emphasising number sense can enhance flexibility in numeracy solutions. Number sense can be developed through assigning math tasks related to the students' environment or associating it with other learning processes. The study emphasises the importance of number sense in the primary school mathematics curriculum. [ABSTRACT FROM AUTHOR]

This study aims to examine the relationship between number sense skills and mathematical reasoning skills of preservice mathematics teachers. The research was conducted with 124 preservice mathematics teachers in the 2018-2019 academic year. Correlational model, one of the quantitative research methods, is used in the research. Data was analysed by the simple linear regression analysis, and the multiple regression analysis. As a result of the analysis, it was determined that the mathematical reasoning skills and the number sense skills of the preservice mathematics teachers were at "High" level. A statistically significant relationshi was observed between preservice mathematics teachers' mathematical reasoning skills and their number sense skills, both in general and in some of its factors. Besides, the main findings of this study was determined that mathematical reasoning skill was a significant predictor of the number sense skill. It was seen that the strongest predictor of number sense was "solving non-routine problems" and the weakest predictor was "recognizing and using mathematical patterns". Thus, it is thought that this study is particularly important in that it emphasizes the strong relationship between number sense and non-routine problems and illustrates that this aspect has a great importance in terms of number sense skills of preservice mathematics teachers. [ABSTRACT FROM AUTHOR]

This study investigated whether mathematics education based on a multi‐tiered response to intervention (RTI) model can support students' arithmetic competence in primary schools in Sweden. The intent was to identify and support students at risk of failure. In this study, 113 students participated in the intervention, and 30 students participated in the control group. Both groups were followed from Grade 1 to the end of Grade 2 and compared. During the first semester in Grade 1, all students were taught basic addition and subtraction with explicit instructions in Tier 1. Those who did not respond to Tier 1 after one semester were provided support within Tier 2 during the second semester. The same was repeated in grade 2 and the students that did not respond to Tier 2 were supported within Tier 3. At the end of Grade 2, students in the intervention group performed significantly higher on the basic arithmetic competence in the number range 1–9 than the control group. No significant difference was found in a test measuring basic arithmetic competence in the number range 10–19. This study shows that using multi‐tiered RTI might be sufficient to identify and support students at risk in early arithmetic competence. [ABSTRACT FROM AUTHOR]

Copyright of JMD: Journal für Mathematik-Didaktik is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)