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Online one-on-one tutoring serves as a personalized approach to supplement classroom instruction. However, with the growing tutoring market, a single tutor often handles inquiries from students across primary, middle, and high school levels. Consequently, the extent of tutors’ interactions with students of varying grades and their use of tutoring strategies to enhance student learning remains unclear. To address this gap, we collected and analyzed 1500 tutoring dialogues from amateur mathematics tutors concurrently instructing students from primary, middle, and high school levels. These dialogues were annotated using a coding scheme and a well-trained powerful artificial intelligence (AI) model. The interaction dynamics were subsequently examined using epistemic network analysis and lag sequential analysis, yielding findings on the occurrences, co-occurrences, and sequential patterns of dialogic strategies. First, the results reveal that tutors frequently engaged in off-topic behaviors and direct instruction, regardless of students’ educational level. Second, tutors’ constructive questions and knowledge sharing and instruction were more associated with greater constructive expressions from students at higher educational levels, while primary students primarily demonstrated simple acknowledgment. Third, tutors exhibited limited sequential patterns of dialogic strategies when tutoring primary and middle school students, mainly focusing on question-asking behaviors and evaluation and feedback. In contrast, tutors displayed diverse patterns across various categories of dialogic strategies when instructing high school students, emphasizing the facilitation of students’ reasoning and metacognition. These findings underscore the importance of training tutors to develop dialogic skills and adopt tailored pedagogical approaches for different educational levels, ensuring effective and efficient online one-on-one mathematics tutoring. [ABSTRACT FROM AUTHOR]

Grasha–Riechmann Teaching Styles have a high potential to be applied in Mathematics especially to help increase teacher educators’ knowledge. However, very little attention has been paid to the study of identifying the teaching style patterns of Mathematics teachers at the primary school National-Type Chinese Primary Schools or Sekolah Jenis Kebangsaan Cina SJKC. There is increasing concern about how this teaching style related to the teaching experience. This study aims to identify the patterns of Grasha– Riechmann Teaching Styles among primary school Mathematics teachers and the relationship between Grasha–Riechmann Teaching Styles with teaching experience. The quantitative approach through a survey was applied to 97 Mathematics teachers of SJKC Kepong, Kuala Lumpur using the simple random sampling method. The instrument was adapted from the Grasha–Riechmann Teaching Styles Questionnaire (1996), which measures five teaching styles such as Personal Model Teaching Style, Expert Teaching Style, Formal Authority Teaching Style, Delegator Teaching Style, and Facilitator Teaching Style. The patterns showed that the Personal Model Teaching Style is the most dominant, and the Facilitator Teaching as the least dominant style. The Spearman’s Rho Correlation also reported a very weak significant correlation between Grasha–Riechmann Teaching Styles with the teachers’ Mathematics teaching experience, specifically for Expert, Formal Authority, and Facilitator Teaching Styles. The study provides practical implications for educators’ professional development to diversify the training of teachers by experience and adapt them to the needs of student learning in primary school. These findings trigger ideas to get a better understanding by other demographic variables such as gender, age, and complexity of Mathematics subject. [ABSTRACT FROM AUTHOR]

Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size (g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propose recommendations for future research and classroom practice. [ABSTRACT FROM AUTHOR]

Comics engage students in learning mathematics through their interactive nature and the relatively simple language they use. Not only that, it also helps expand students' thinking through the introduction of contextualized mathematics. This is also in line with the latest math education trend to engage students with math problems in a real-world context. As a result, there is a great potential for the use of comics as a teaching tool in primary school mathematics lessons. The current research works pointed out that comics increase the efficiency of teaching and strengthen the relationship between teacher and students. The purpose of this study is to determine the effect of educational comics-supported instruction on academic achievement of primary school students in division concept. The study used quasi-experimental design with pretest-posttest control group. The study group consists of 42 second grade pupils (21 for experimental and 21 for control group) studying in a public primary school located in Niğde, Turkey. As for data collection, academic achievement test was developed based on the learning outcomes of the mathematics curriculum. The pilot study was conducted to determine the statistics and the quality of test items. In order to ensure the validity of this test, evidences were collected and the reliability of the test calculated. The results of this study showed that the students who learn division via educational comics-supported instruction is more successful than the students who learn division via traditional instruction. Two of the reasons could be listed as (1) division is a complex and abstract concept so that traditional instruction have some difficulty in making the understanding easier, (2) educational comics strengthen the communication between student and teacher, attract attention of the students. This study is considered important in terms of emphasizing that educational comics are a preferred tool for some concepts of mathematics instruction. [ABSTRACT FROM AUTHOR]

This study explores the relationship between play-based learning and achievement in mathematics in Palestinian elementary school children. Forty teachers from eight schools received training in play-based pedagogies and follow-up support visits from programme staff (intervention group); four matched schools served as the control group. Grade-appropriate tests were administered to all students in two consecutive school terms. A total of 859 students (458 females, 401 males) and 832 students (477 females, 355 males) completed maths tests in term 1 and 2, respectively. Results revealed that the intervention group attained higher test scores than the control group in both terms (P < 0.01). Furthermore, in term 2 an interaction effect between group and gender was found (P < 0.05), with girls in the intervention group achieving the highest scores. Our finding suggest that play-based learning approaches may enhance academic achievement. [ABSTRACT FROM AUTHOR]

The use of technology can make the students interested in getting more involved in teaching and learning process. Encouraging technology utilization in learning is supported to influence the student interests in learning. This study aims to develop android based educational games to enhance elementary school student interests in learning mathematics. The method used in this study is ADDIE (Analyze, Design, Development, Implement, Evaluation) model to develop the product. The effectiveness of the product developed in this study was tested through experimental research using posttest only control group design. The results of Kolmogorov-Smirnov test show that significance value reaching 0.200 larger than 0.05 confirming that experimental and control group are normally distributed. Test of variance homogeneity shows that significance arrives at 0.547 meaning that the data are homogeneous. Independent sample test reveals that the significance attaining 0.001 less than 0.05 expressing that Ho is rejected. The conclusion drawn from this research is that android based educational games are proven to increase the interest in learning mathematics for sixth grade elementary school students in Matraman District, East Jakarta, Indonesia. [ABSTRACT FROM AUTHOR]

Star Math (SM) is a popular computer adaptive test (CAT) schools use to screen students for academic risk. Despite its popularity, few independent investigations of its diagnostic accuracy have been conducted. We evaluated the diagnostic accuracy of SM based upon vendor provided cut-scores (25th and 40th percentiles nationally) in predicting proficiency on an end of year state test in a sample of highly achieving grade three (n = 210), four (n = 217), and five (n = 242) students. Specificity exceeded sensitivity across all grades and cut-scores. Acceptable levels of sensitivity and specificity were achieved in grade three and four but not grade five when using the 40th percentile. [ABSTRACT FROM AUTHOR]

This article reviews and proves nine necessary and sufficient properties of orthogonal circles. The first six properties are known to some degree, while the last three are unknown, to the best of our knowledge. [ABSTRACT FROM AUTHOR]

In this paper, we will show a characterization for pairs of commensurable diagonals of regular n-gons. This result gives a positive answer to a recent question. [ABSTRACT FROM AUTHOR]

In 2005, Osler et al. showed that algebraic irrational numbers of the form k n for n , k ∈ N can be approximated using specific Greek ladders (Osler, T. J., Wright, M., & Orchard, M. (2005). Theon's ladder for any root. International Journal of Mathematical Education in Science and Technology, 36(4), 389–398. https://doi.org/10.1080/00207390512331325969). In 2018, Herzinger et al., showed that every algebraic number of degree 2 or less can be approximated using rung ratios generated by a specific Greek ladder (Herzinger, K., Kunselman, C., & Pierce, I. (2018). Greek ladders via linear algebra. International Journal of Mathematical Education in Science and Technology, 49(7), 1119–1132. https://doi.org/10.1080/0020739X.2018.1440326). Using techniques from linear algebra, in particular the companion matrix of a polynomial, we will prove that every real algebraic number can be approximated by a Greek ladder, as well as show how to construct such a ladder. [ABSTRACT FROM AUTHOR]

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are introduced to the key concept of distributivity of multiplication over addition. The results show that modelling activities designed through the heuristics of didactical phenomenology, guided reinvention and emergent modelling may support the accessibility of distributivity, as these students were able to reinvent this concept solving an experientially significant problem. This result can be attributed to a combination of several factors: the choice of a realistic and rich problem, that stimulated students to elaborate formal mathematical concepts mathematizing their informal solving strategies, rooting new understandings in experientially real phenomena; the use of a suitable artifact, that presented mathematics as a means of interpreting and understanding reality and increasing the opportunities for observing mathematics outside of the school context; the role of the teacher, who guided students in reinventing mathematics in an active way. [ABSTRACT FROM AUTHOR]

Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not pictures or numbers only). Researchers are exploring integrating the phases of CRA, referred to as concrete-representational-abstract–integrated (CRA-I), because it may be a more efficient method of instruction. The CRA-I integrates all phases starting with the first lesson (e.g., Lesson 1 includes manipulatives, pictures, and numbers only) and then fades concrete and representational instruction. The purpose of this article is to provide information about a CRA-I Tier 2 mathematics intervention on additive reasoning for second-grade students in a rural school in the southeastern United States. The researchers describe CRA-I, the lessons implemented, and implications for teacher use. [ABSTRACT FROM AUTHOR]

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction. providing insight into how fractions might be introduced to improve learning. We designed a card game to teach first and second grade children (N = 195, including a racially and economically diverse sample from the United States) about fractions in one of three ways. In the Actively Divided condition we iteratively divided an area model into equal-sized units, in the Predivided condition we used an area model with the end-state of the Actively Divided condition, and in the Nondivided condition we used a continuous representation of the fraction magnitude that was not divided into unit-sized parts, Children in the actively divided condition demonstrated larger improvements matching symbolic fractions and visual fractions (i.e., pie charts) than children in the other two conditions. Posthoc analyses of children's gameplay revealed that the actively divided condition may have provided a more optimal level of difficulty for young children than the predivided condition, which was particularly difficult, and the nondivided condition, which was trivially easy. These differences in gameplay performance provide insights into possible mechanisms for our results. We discuss open research questions highlighted by this work and implications of these findings for both the development of proportional reasoning and fraction learning. [ABSTRACT FROM AUTHOR]

Previous studies have demonstrated the association between visual perceptions (i.e., form, luminance, area, and colour perception) and numerosity processing; however, there is a lack of evidence on the different roles of visual perceptions that contribute to the close relationship between numerosity processing and arithmetic computation. Using a sample of 259 Chinese primary students, this study investigated the visual perception properties that underlie the relationship between numerosity processing and arithmetic ability. A series of cognitive tasks were used to assess their numerosity processing, arithmetic fluency, visual perception, and other general cognitive abilities as cognitive covariates. Visual perceptions were measured through figure matching, luminance matching, colour matching, and area matching tasks. The results showed that form, luminance, area, and colour perception significantly correlated with numerosity processing. Only form perception fully accounted for the close relationship between numerosity and arithmetic fluency. These results suggested that visual form perception was fundamental for numerosity processing and arithmetic fluency. [ABSTRACT FROM AUTHOR]

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual‐spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual‐spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual‐spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual‐spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older. [ABSTRACT FROM AUTHOR]

Research on the associations among adversity, executive function (EF), and academic outcomes in low- and middle-income countries, where developmental risk factors are more prevalent and impoverished environments are more widespread than in high income countries, is sparse. This study examines the relations among cumulative risk. EF, and learning outcomes measured 2-years later in Ghanaian third- and fourth-graders (N = 371,49% female), shedding light on underlying mechanisms of how risk can undermine learning. A cumulative risk index was created based on a set of four child-reported risk factors: home aggression, unsafe home neighborhood, hunger. and having worked for pay. Cumulative risk and EF were negatively correlated. Learning outcomes (literacy and math test scores) were negatively correlated with earlier measures of cumulative risk and positively correlated with earlier measures of EF. EF mediated the association between cumulative risk and later learning outcomes, accounting for 65.3% of the total effect for literacy and 100% for math. This mediated pathway was robust to controls for child and household sociodemographic characteristics. The findings contribute to a small evidence base on the mediating role of EF in linking adversity and learning outcomes in a global context. [ABSTRACT FROM AUTHOR]

Using a cluster randomized trial, we investigated the effects of mathematics professional development on student achievement in elementary schools. Pairs of schools were matched on prior mathematics; percentage of students receiving free or reduced-price lunch and percentage of limited English proficient students were randomly assigned to two groups. One received professional development on mathematics that focuses on diagnosing student thinking and the other received professional development on formative assessment. Student-level achievement data (pretest and posttest performance on a standardized test of mathematics) were nested within grades and schools and analyzed using mixed-effects multi-level linear modeling. The results indicate students in schools that were provided the mathematics professional development had greater mathematics achievement than students in schools in a control condition. The effect held across grade levels. [ABSTRACT FROM AUTHOR]

BACKGROUND: Breakfast after the bell (BAB), an alternative way to deliver breakfast after the school day begins, has been shown to increase participation in the School Breakfast Program. However, BAB occupies time that could otherwise be used for instruction and may affect academic performance. This study examined whether BAB affects math and literacy scores in third grade, an age not adequately studied in earlier literature. METHODS: Using data on Arkansas students, we compared schools adopting BAB to corresponding "synthetic" control schools by minimizing preadoption differences in observables that can influence test scores. RESULTS: We found little evidence of positive or negative effects on test scores. We also found little evidence of meaningful program effects over subsamples of schools by district enrollment size and BAB delivery method. Schools that adopted grab‐and‐go delivery and schools in districts with small enrollments, less than 600 students, showed statistically negative effects on math after BAB adoption. However, these effects were transitory and no longer present by the time the first fully exposed cohort reached third grade. CONCLUSIONS: BAB can be incorporated into the school day without adversely impacting academic achievement, especially if adopting schools seek input from educators and nutrition personnel already experienced with BAB. [ABSTRACT FROM AUTHOR]

The article discusses problems with ambiguous conditions, the solution of which leads to several variants of answer. Such problems are called variative problem. The role of variative problems in intellectual development of schoolchildren in mathematics classes are described in this article. Proposed a methodology for including variative problems in the process of teaching mathematics. [ABSTRACT FROM AUTHOR]

The sustaining environments hypothesis theorizes that the lasting effects of PreK programs are contingent on the quality of the subsequent learning environment in early elementary school. The current study tests this theory by leveraging data from students (N = 462) who did and did not enroll in the Boston Public Schools (BPS) prekindergarten (PreK) program as well as features of their kindergarten instruction measured at the child- and classroom-levels using surveys and observations. Taken together, findings revealed limited evidence for the sustaining environments hypothesis. The bulk of the results were null, indicating that in general, associations between enrollment in BPS PreK and language, literacy, and math skills through the spring of kindergarten did not vary by kindergarten instructional experiences. When examining distinct types of instructional experiences, there were some inklings that child-level observational measures of kindergarten learning experiences--particularly those capturing constrained versus unconstrained instruction--were more predictive of PreK persistence than observed global classroom quality measures or survey-based measures of advanced instruction. However, these associations were not always specific to outcomes matching the content delivered during this instruction (math vs. literacy), consistent with the possibility of either cross-domain effects or that instructional variables are proxies for more general instruction;il practices. Findings for future research and theory are discussed. [ABSTRACT FROM AUTHOR]

In the study, the effects of STEM activities applied to primary school fourth grade students on students' attitudes towards STEM, 21st century skills and mathematics achievement were analyzed. Sequential exploratory design was used in the research, which was carried out as a mixed method. In the quantitative part of the research, time series design, one of the semi-experimental designs, was used. The study group consists of 34 primary school fourth grade students. Quantitative data were collected with the STEM Attitude Scale, the 21st Century Creativity and Renewal Skills Scale, the Scratch Achievement Test and the Mathematics Achievement Test. On the other hand, qualitative data were collected with a Semi-Structured Interview Form. Descriptive statistics, ANOVA for Repeated Measures, and dependent groups t-test statistics were used in the analysis of quantitative data. Qualitative data were analyzed using descriptive and content analysis techniques and presented in tables. As a result of the research, it was determined that STEM education has a significant effect on the attitudes of primary school fourth grade students towards STEM and their 21st century skills. It has been figured out that the effect of STEM education on increasing the mathematics achievement of primary school fourth grade students is not significant. Students reported that STEM education activities were fun, useful and instructive. With STEM implementations, students' attitudes towards science, technology, engineering and mathematics have changed positively; They stated that 21st century skills such as communication, cooperation, creativity and critical thinking have developed. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate primary school students' proof schemes for four operation problems in mathematics. Based on qualitative research design, the data were collected through document analysis and interview method in the study. In the first stage of the study, 4 open-ended four operational problems were asked to al of 1st, 2nd and 3rd Grade students in a primary school located in the city center of Elazig. Students who answered the problems correctly were invited for interviews. In the interviews, the students were asked to explain aloud how they solved the problems. The interview data were analyzed using descriptive analysis based proof schemes categorization of Harel and Sowder (1998), and the proof schemes and proof-making approaches of the participants were investigated. The findings revealed that the participants mostly used external conviction proof schemes regardless of grade and operation type. It was also found that although 1st Grade students used the authoritarian proof scheme more, 2nd and 3rd Grade students mostly employed ritual proof scheme to explain their solutions. [ABSTRACT FROM AUTHOR]

Background: Previous research showed a significant association between mathematics and working memory (WM). However, evidence regarding the different effects of verbal and visuospatial WM on mathematical abilities was very limited. Aims: The current research aims to explore the relationship between verbal and visuospatial WM with mathematical abilities, and how this relationship is moderated by age and math domains. We also wonder whether the results would change when we use several tests for each component and use a latent variable approach for more reliable measurement. Sample: 131 first graders and 144 fifth graders from a primary school in Hangzhou, Zhejiang province, China, participated our research. Methods: All participants completed three verbal and three visuospatial WM tasks, mathematics tests, and fluid intelligence test. Hierarchical multiple regression analysis was used to examine the pattern of relations among these constructs. Results: The results of hierarchical multiple regression analysis showed that verbal WM significantly predicted mathematics achievement for fifth graders, while failed for first graders. However, visuospatial WM played a substantive role in both graders' mathematical performance. The different role of the two WM components also depend on various fields of mathematics. Conclusion: Our results indicated the distinct influence of verbal and visuospatial WM on primary school students' mathematical abilities and highlighted the developmental and domain‐specific effects of WM on mathematics. [ABSTRACT FROM AUTHOR]

Limited quantitative research has examined similarities and differences between the academic achievement and discipline outcomes, including suspensions, of students with disabilities in rural and urban schools. Therefore, we leveraged a statewide longitudinal data set to explore academic achievement and discipline outcomes for students with disabilities in rural schools and compared those outcomes to students with disabilities in urban schools. We then followed up with analyses to evaluate differences by disability category. The full data set of students in urban and rural schools included 1,306,134 observations from 366,529 unique students with disabilities across 11 consecutive years. We used a series of linear mixed-effects models to evaluate academic achievement for students in Grades 3 to 8 and generalized linear mixed-effects models to evaluate two discipline outcomes, in- and out-of-school suspensions. Overall, we found that students with disabilities in rural schools had lower reading scores, fewer in-school suspensions, and more out-of-school suspensions. Unique patterns across disability categories also emerged. [ABSTRACT FROM AUTHOR]

This study explored whether Year 1 school children exposed to a 12-week classroom-based gross motor program progressed differently than Year 1 children undertaking their regular school program in motor proficiency, mathematics, and reading outcomes. Fifty-five Australian Year 1 school children (25 boys, 30 girls, mean age 6.77 ± 0.40 years) were exposed to either (i) their normal school program (Class N) or (ii) a 12-week program comprised of gross motor circuits and physically active: a) reading lessons (Class R) or b) mathematics lessons (Class M). Motor proficiency and academic performance in mathematics and reading were assessed using the Bruininks–Oseretsky Test of Motor Proficiency (2nd Edition) and the Wechsler Individual Achievement Test—2nd Edition—Australian Standardised Edition, respectively. Differences in outcomes between classes following the 12-week program were assessed. Mean change scores for the mathematics composite were significantly greater for participants in Class R (9.61 ± 5.62, p =.001) and Class M (7.57 ± 5.79, p =.019) than for participants in Class N (0.76 ± 8.00). Mean change scores for reading (11.54 ± 7.51, p =.017) and total motor composites (6.12 ± 5.07, p =.034) were also significantly greater for participants in Class M than Class N (4.47 ± 3.50 and 0.82 ± 4.38 respectively). A 12-week classroom-based gross motor program may be beneficial for motor skill development and learning in Year 1 school children. This pilot evaluation may usefully inform future experimental studies to further investigate whether classroom-based motor skill programs have a beneficial effect on motor proficiency and academic outcomes in children in the early years of primary school. [ABSTRACT FROM AUTHOR]

Learning maths is challenging for many primary school students, and teachers must understand students' learning and emotional processes specific to learning maths. The current research, grounded in control-value theory, focused on achievement emotions regarding maths. Primary school students (N = 71) were studied with the primary objective of examining the longitudinal trajectories of achievement emotions of third graders over two years. The Portuguese Achievement Emotions Questionnaire for Elementary Students was administered biannually to assess enjoyment, anxiety, and boredom regarding maths. The results indicate that enjoyment decreased and boredom increased over time, revealing three emotional profiles: positive, negative and moderate. The positive profile showed the highest scores in maths achievement. Profile membership was moderately stable and became increasingly stable and structured. In examining the complexity of students' emotional profiles and processes, the importance of understanding them to enhance educational support, development, and learning was highlighted. [ABSTRACT FROM AUTHOR]

Copyright of Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education is the property of Balikesir University, Necatibey 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.)

Based on stereotype threat and stereotype lift theory, this study explores implicit stereotype threat effects of gender stereotypes on the performance of primary school children in mathematics. Moreover, effects of implicit gender stereotypical cues (gender-specific task material) on motivational aspects were explored, which have revealed mixed results in stereotype threat research in the past. N = 151 German primary school children (47.7% female; mean age: M = 9.81, SD = 0.60) calculated either stereotypical or neutral mathematical text problems before motivational aspects were assessed. Contradicting our expectations, results neither revealed a stereotype threat effect on girls' performance nor a lift effect on the boys. Instead, girls calculating stereotypical tasks outperformed girls in the control group, whereas boys' performance did not significantly differ compared to the control group. Regarding motivational aspects, only traditional gender differences emerged as girls reported significantly more pressure and tension calculating the mathematical tasks. The discussion focuses on the way in which stereotypes can affect children's cognitive performance and in turn, their mathematical performance. [ABSTRACT FROM AUTHOR]

Properties of arithmetic operations are important in mathematics and play a significant role in elementary school students' learning of mathematics. At the same time, it is quite challenging to help students learn arithmetic operational properties beyond memorization, so that they know when and how to use a specific arithmetic property. This paper reports a study containing two parts to explore students' learning of the Commutative Property of Addition (CPA) as related to the content presentation in textbooks. Part one is to assess selected students' performance on CPA at the end of Grade two, and part two is to explore possible contributions of textbooks to students' performance in Shanghai. Firstly, we evaluated the performance of 41 second-graders on CPA by collecting data through a paper-and-pencil test, which was followed up with individual interviews. Through analyzing how textbooks present and organize this topic, we sought to better understand from a curriculum standpoint how students' performance on CPA is impacted by textbooks. Results revealed that Shanghai textbooks make a positive contribution to students' learning performance. The findings from this study help to shed light on how those textbooks aid student learning, and provide an example for further reflection on student learning of arithmetic operational properties in different curricula. [ABSTRACT FROM AUTHOR]

This study examines the link between inhibitory control skills (the ability to plan and suppress an inappropriate action in favour of a goal-oriented reaction) and the sense of self-efficacy (both social and emotional), and mathematics achievements in students with learning disabilities. In this study, 60 sixth-grade students with learning disabilities who attended integrated classes in a general education setting were tested using three instruments: an inhibitory control questionnaire, a self-efficacy questionnaire, and a mathematics achievement test. Findings show that learning-disabled learners have better mathematics achievements and social self-efficacy the higher their inhibitory control skills are. Interestingly, no statistically significant association was found between inhibitory control and emotional self-efficacy. An examination of the pattern of associations between the study parameters pointed to a statistically significant absence of a mediating effect by self-efficacy on the link between inhibitory control and mathematics achievements. The two linked variables appear to be independent variables and the emotional component of self-efficacy is a predictor of achievement. In addition to this, self-efficacy was found to facilitate better inhibitory control. [ABSTRACT FROM AUTHOR]

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement. [ABSTRACT FROM AUTHOR]

Morphemes, the smallest meaning-bearing units of language, recur in many words. Therefore, morphological knowledge can facilitate the comprehension of novel words. This study tested the effectiveness of a morphological training program on children's learning and retention of exposed words and morphologically related unexposed words compared with an active control condition. Norwegian second graders (N = 717) unselected for ability were individually randomized to either a morphological (n = 366) or a mathematical training program (n = 351). Both programs lasted for 8 weeks and were delivered as self-contained apps in a classroom setting. The morphological training built on the principle that frequency of target elements together with variation of nontarget elements can support implicit learning. Treatment-blind examiners assessed participants' meaning-based knowledge (word comprehension and definitions) and code-based knowledge (word reading fluency and spelling) at pretraining, immediately post training, and at follow-up 6 months later. An intention-to-treat analysis showed lasting effects of the morphological training on meaning-based knowledge of exposed words (posttest: d =.37; follow-up: d =.31) and unexposed words containing trained morphemes (posttest: d =.27; follow-up: d =.27) and code-based knowledge of exposed words (posttest: d =.22; follow-up: d =.13). For code-based knowledge of unexposed words, there were significant training effects at the posttest (d =.12) but not follow-up (d =.05). There were no significant effects on a far-transfer measure of general vocabulary. These results demonstrate that a brief morphological training program can produce lasting and educationally meaningful gains in students' word knowledge. Educational Impact and Implications Statement: Words can consist of several meaningful parts, or morphemes, such as -ist in guitarist and re- in reuse. Understanding common morphemes helps children infer the meanings of new words. In this study, we tested the effects of working with an educational application (app) focusing on morphemes. Children completed app exercises such as sorting words or pictures according to their meaning, combining morphemes to build words, or identifying the correct word or morpheme to fit a sentence or picture context. We found that the app was effective in improving Norwegian second graders' ability to explain, understand, read, and spell words, including words which were not shown in the app, but which contained trained morphemes. The brief low-cost training produced long-term effects with a minimal burden on teachers. [ABSTRACT FROM AUTHOR]

One of the most fundamental subjects of primary school mathematics, the concept of fraction plays a key role in students' educational background. Students experience difficulties and misconceptions regarding this concept. Therefore, it is of great importance to understand this subject well and to use different teaching methods and techniques. Various methods can be used in learning mathematics, such as invention method, computer-assisted teaching, problem solving, creative drama and discussion. Argumentation method is a scientific discussion of a claim on a subject by providing data, warrant and backing, and by revealing the rebuttal and the invalidity of the claim. Students gain more skills by interacting with teachers or collaborating with their peers, and that they possess skills that have not been obtained before or that are too difficult to achieve on their own. Therefore, the argumentation method was chosen for its effect on the development of primary school students’ fraction calculation strategies. Having a case study design, this study was conducted with 28 primary school fourth-grade students and 10 open-ended questions prepared by the researchers were used during interviews. The results suggested that primary school students were able to develop fraction calculation strategies through the argumentation method. In general, inventing strategies, using representations, number sense, addition and subtraction, using unit fractions and proportional reasoning were used as fraction calculation strategies. It recommended to use the argumentation method in other critical subjects of mathematics as well. [ABSTRACT FROM AUTHOR]

It is well accepted that the home learning environment impacts school performance; however, much of the previous research has focused on preschool children. This exploratory study used an online, Qualtrics survey to ask parents (n = 177) of elementary students about the home learning environment. Our research questions addressed (1) the amount of time children spend on mathematics, reading, written language, and science at home, and differences by subject and/or grade; (2) parental beliefs about the importance of engaging in home learning activities in each of the four subjects; (3) parental confidence in supporting each of the four academic subjects; (4) parental and child enjoyment of the four academic subjects; and (5) who (parents, child, or teacher) initiated home learning activities in the different subject areas. The results indicated that elementary school-age children were engaged in reading, mathematics, science, and written language activities at home; however, the most time was spent on reading activities. Parents reported viewing engagement and assistance with academically related activities at home as important; however, they were more confident assisting with reading and written language than mathematics or science. Strong associations were noted between parental enjoyment of a subject and their confidence in assisting their child. Overall, teachers initiated more activities for older children and were more likely to initiate mathematics activities. When children initiated an activity, it was typically reading related. [ABSTRACT FROM AUTHOR]

This qualitative study explores the potential for metaphor, movement, gesture, and vocalization in helping learners notice mathematically important features of graphs, and in making mathematics more accessible for learners with visual impairment. Two elementary school students with visual impairment were introduced to several multimodal activities related to the graphs of mathematical functions, using a pre-/post-assessment methodology. Video recordings of the session were coded for qualitative changes in engagement with graphs through multimodal representations. After the activity intervention, both students showed improvements in their ability to voice, gesture, and describe details of mathematical graphs with accuracy and understanding. The findings demonstrate the potential of multimodal methods for teaching mathematics and enhancing other skill areas through movement, metaphor, voice, and gesture. The findings suggest that full-bodied experience with graphs can provide foundational support for learners with visual impairment to work with print or tactile graphics. We propose that purposeful selection of materials and collaboration between teachers of students with visual impairment, mathematics educators, and teachers of dance and physical education can enhance the design and implementation of effective lessons using multimodal means. [ABSTRACT FROM AUTHOR]

• Number line accuracy and estimation patterns were studied in children at risk of MLD. • Number line accuracy predicted growth in numerical operations and math reasoning. • Number line accuracy predicted intercept but not growth (slope) in math fluency. • Children best fit by the linear outperformed those best fit by the logarithmic model. • Math skills did not differ based on models from the proportion judgment perspective. Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; M age = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns. [ABSTRACT FROM AUTHOR]

The present study aimed to examine the mediating role of parental involvement in the association between parental attitudes toward their own mathematics and reading abilities and children's learning interests in the Chinese context. Participants included 395 Chinese elementary students whose ages ranged from 6.53 to 12.82 years (mean = 9.68 years) and their caregivers. The results showed that parental attitudes toward their own mathematics and reading not only had a domain-specific effect on parent-reported children's learning interests in these subjects but also had a cross-domain effect on other subjects. Furthermore, parental home- and school-based involvement mediated the association between parental attitudes toward mathematics and reading and parent-reported children's learning interests in these subjects. At the domain-specific level, parental home-based involvement, rather than school-based involvement, mediated the relation between parental attitudes and children's learning interests in mathematics and reading. At the cross-domain level, both home- and school-based involvement mediated the association between parental attitudes toward their own reading and children's mathematics interests. The findings underline the relevance of parental attitudes toward their own mathematics and reading and parental home- and school-based involvement in the development of Chinese elementary school students' learning interests. • Parental attitudes toward math and reading had domain-specific and cross-domain effects on children's learning interests. • Parental home- and school-based involvement mediated the link between parental attitudes and children's learning interests. [ABSTRACT FROM AUTHOR]

• Corrective feedback influenced children's in-the-moment math problem solving. • Feedback with verification reduced persistence relative to the correct answer alone. • Feedback with verification enhanced reliance on entrenched incorrect strategies. • Feedback from a person reduced accuracy relative to computer feedback alone. The current study examined how different features of corrective feedback influenced children's performance and motivational outcomes on a mathematics task. Elementary school-aged children from the United States (N = 130; M age = 7.61 years; 35% female; 60% White) participated in a Zoom session with a trained researcher. During the learning activity, children solved a series of mathematical equivalence problems and were assigned to different feedback conditions that varied in feedback content (correct answer alone vs. correct answer with verification) and feedback source (computer alone vs. computer with person). In terms of content, feedback with verification cues led to decreased persistence, decreased strategy variability, and higher reliance on entrenched strategies relative to feedback that contained the correct answer alone. In terms of source, feedback from the computer alone enhanced children's accuracy; however, the most resilient children received feedback from the computer and a person. Findings are discussed in light of existing feedback theories. [ABSTRACT FROM AUTHOR]

The article discusses an adaptation of a secondary school mathematics comics-based instructional package for primary school mathematics classroom, and the teachers' and students' perceptions about the use of comics in the classroom. Further suggestions by the teachers on fine-tuning the package are also discussed. It reports on the use of a comics-based teaching package for instruction in the Singapore secondary mathematics classrooms and the positive responses from both students and teacher.

This article estimates the effect of school closures in the spring of 2020 on the math skills of primary school children in Italy, which was the first Western country hit by the COVID-19 pandemic, responding with a strict lockdown and total school closures through the end of the school year. Leveraging unique longitudinal data collected in the province of Torino, a large metropolitan area in northern Italy, we analyse the learning outcomes of two adjacent cohorts of pupils, the pre-Covid and the Covid cohort. The pandemic had a large mean negative impact on pupils' performance in mathematics (−0.19 standard deviations). Learning loss was greater for girls and for high-achieving children of low-educated parents. Net of individual characteristics, the impact was harshest in schools with a disadvantaged social composition. [ABSTRACT FROM AUTHOR]

Background: Developmental research provides considerable evidence of a strong relationship between verbal and visuospatial working memory (WM) and mathematics ability across age groups. However, little is known about how components of WM (i.e., short‐term storage, processing speed, the central executive) might relate to mathematics sub‐categories and how these change as children develop. Aims: This study aimed to identify developmental changes in relationships between components of verbal and visuospatial WM and specific mathematics abilities. Sample: Children (n = 117) were recruited from four UK schools across three age groups (7–8 years; 9–10 years; and 14–15 years). Methods: Children's verbal and visuospatial short‐term storage, processing speed, and central executive abilities were assessed. Age‐based changes in the contributions from these abilities to performance on mathematics sub‐categories were examined. Results: When WM was examined both as an amalgamation of its component parts, and individually, relationships with mathematics were more evident in younger children compared to the middle and older age groups. However, when unique variance was examined for each WM predictor (controlling for the other components), many of those relationships disappeared. Relationships with processing speed and the central executive were found to be more evident in the older age groups. Conclusions: The WM‐mathematics relationship changes dependent on age and mathematical sub‐component. Overlap in individual WM abilities in younger children, compared to reliance on the central executive and processing speed in older children, suggests a set of fluid resources important in mathematics learning in younger children but separating out as children grow older. [ABSTRACT FROM AUTHOR]

The teaching of mathematics is a topic of concern in the fields of pedagogy, psychology and neuroscience. Many primary and secondary school students show little interest in studying mathematics, which is accompanied by poor marks, low school success rates and learning disabilities. It is possible to think that these difficulties are general throughout the population and not related only to pathological developmental conditions and disabilities. Within psychology, the cultural-historical approach and activity theory allow us to analyse and characterize the content of educational methods. This study analyses three proposals for teaching mathematics in the third year of preschool education in Mexico according to type of orientation, the concepts taught, the actions the teacher does with the students and the classroom communication. It discusses the need to reconsider the content of educational work in preschool institutions in order to guarantee children's optimal level of preparation for the conceptual learning of mathematics in primary school. [ABSTRACT FROM AUTHOR]

Although important for the acquisition of later math skills, fractions are notoriously difficult. Previous studies have shown that higher math anxiety (MA) is associated with lower performance in symbolic fraction tasks in adults and have suggested that MA may negatively impact the acquisition of fractions in children. However, the effects of MA on fraction skills in school‐aged children remain underexplored. We, therefore, investigated the impact of MA on the performance of younger (second and third graders) and older (fifth and sixth graders) children in math fluency (MF), written calculation, fraction knowledge (FK), and symbolic fraction and nonsymbolic ratio processing. On the basis of our prior work suggesting a perceptual foundation for fraction processing, we predicted that symbolic, but not nonsymbolic, math skills (especially fractions) would be impaired by MA. As predicted, higher MA was associated with lower performance in general mathematics achievement and symbolic fraction tasks, but nonsymbolic ratio processing was not affected by MA in either age group. Furthermore, working memory capacity partially mediated the effects of MA on general mathematics achievement, FK, and symbolic fraction processing. These results suggest that understanding the bidirectional interactions between MA and fractions may be important for helping children acquire these critical skills. [ABSTRACT FROM AUTHOR]

Math word problems can be solved with a good understanding of language, correct translation, and use of proper operations. However, elementary school students will only get the correct answer if the result is done correctly. Then a numeracy competency detection system is needed through the answer of math story questions. This study aims to build a system of checking student answers in stages. The main contribution is the technique for comparing the trees from two multimodal input and assess student answer automatically. System extracted operand from math story sentences and classified operator using random forest to generate the key then convert it to the tree. We use OCR library to extract text from student's answer image and identify operand, operator, and result to build student's answer tree. A tree matching is applied to compare the similarity of trees for automatic assessment. The dataset used in this research is 500 questions, 300 data for training, and 200 data for testing. There are two categories of questions, single and mixed operator, with five class namely addition, subtraction, multiplication, division, and mixed. Based on the experiment, the accuracy of classification for mixed operator is 68.8%, whether for single operator is 84.31%. For tree matching, we achieved 78.12% accuracy with the error occurs due to the limitations of processing student's answer image. [ABSTRACT FROM AUTHOR]