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The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students' conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized controlled trial design, students were divided into either an intervention group (n = 64) or a control group (n = 56). Students in the intervention condition received a series of seven 35-minute lessons. Students in the control condition received "treatment as usual". Both post-test and delayed post-test results revealed that students in the intervention group performed significantly better than those in the control group on fraction concepts, with a stronger effect in measurement aspects compared to part–whole aspects. The intervention group also outperformed the control group on fraction arithmetic on both post-tests, while no significant difference was observed on fraction word problems. [ABSTRACT FROM AUTHOR]

School mathematics is not universal. It produces and is produced by social norms. What is considered as normatively appropriate school mathematics may vary when immigrant students (re)produce school mathematics in transitions between school mathematical practices at home and at school. In this study, one group of primary school students and two groups of secondary school students were interviewed to investigate their experiences with school mathematics in transitions. In contrast to some previous studies, the present study reveals instances where students positioned their parents as mathematically knowledgeable. To some students, it was important to know mathematical concepts in the mother tongue to be positioned as knowledgeable in mathematical conversations at home. This suggests that pedagogical practices should not only facilitate the transition of students’ everyday experiences into mathematics classrooms but also explore how school mathematics can be transitioned out of school, particularly considering transnationalities where ways of knowing transcend national boundaries. [ABSTRACT FROM AUTHOR]

The application of STEM (Science, Technology, Engineering, and Math) education in solving real-world problems is challenging. To tackle this challenge, a project-based learning approach that integrates robots with cost-effective self-made toys to problem-solving was adopted to assist rural primary school students to apply STEM skills. The purpose of this study was to evaluate the effects of the project-based learning approach which includes lecturing and hands-on activities on primary school students' STEM learning outcomes and attitudes. An experiment was conducted with 25 primary school students who voluntarily participated in a STEM summer-camp programme. Students were asked to assemble a paper house equipped with an IoT control module and LED light switches, and write and edit robot scripts to produce a robot-based storytelling narrative using the paper house they made as a context. The results show that the project-based learning approach was an effective approach for cultivating primary school students' STEM knowledge and skills as evidenced from the post-written test. The relationships between the students' STEM learning outcomes and attitudes were also confirmed by a clustering analysis. Students who had higher learning attitudes also achieved higher STEM learning outcomes; the findings are also supported by the feedback from the open-ended questionnaire items. This study suggests that integrating low-cost self-made toys and robots in project-based learning activities is an effective and practical approach to enhance primary school students' learning outcomes and learning attitudes in STEM education. [ABSTRACT FROM AUTHOR]

Participating in classroom mathematics conversations, particularly engaging with the opinions of others, can improve learners' mathematical comprehension. Teachers can use a variety of invitation and follow-up moves to encourage student engagement. The study aimed to explore teacher follow-up on learners' initial responses to teacher questions and building on learner ideas in Grade 9 mathematics classrooms. A qualitative approach and descriptive case study design were utilised. Data were collected from three schools in the same circuit in South Africa through classroom lesson observations, face-to-face teacher interviews and researchers' field notes. Three Grade 9 mathematics teachers, one from each school, were purposively selected, and the selected teachers' already established Grade 9 classes, with a maximum of 30 learners each (owing to the COVID-19 health protocol), were automatically involved. Cognitively guided instruction, a learner-centred approach that uses social constructivism as a research paradigm, guided this study. The exploration was supplemented by Brodie's conceptual framework on teacher follow-up moves. The findings revealed that the three teachers followed up on learner contributions and used different follow-up moves, namely insert, elicit, press, maintain and confirm. The study showed hybrid teacher moves. Although more teacher moves were skewed towards elicit and insert, which are closer to traditional practices, there is an indication of moving towards the press, maintain and confirm, which are reform-oriented moves. In addition to these moves identified by Brodie, acknowledging or praising the learner for responding was another move that emerged in this study. [ABSTRACT FROM AUTHOR]

The present study investigated direct as well as indirect relations between children's emotion regulation (anger- and avoidant-oriented strategies), behavior regulation, and mathematics achievement in a longitudinal study during the transition from primary to secondary school in Germany. Participants were 76 primary school students attending grade four at Time 1, of whom 51 participated again as secondary school students attending grade five at Time 2, as well as children's mothers and teachers. Anger- and avoidant-oriented emotion regulation strategies at Time 1 were negatively associated to behavior regulation at Time 2. Behavior regulation at Time 2 was positively related to mathematics achievement at Time 2. There were no direct relations between emotion regulation (anger- and avoidant-oriented strategies) at Time 1 and mathematics achievement at Time 2. However, we found significant indirect negative effects between emotion regulation (anger- and avoidant-oriented strategies) at Time 1 and mathematics achievement at Time 2 via behavior regulation at Time 1. Thus, anger- and avoidant-oriented emotion regulation at Time 1 indirectly affected mathematics achievement negatively at Time 2 via behavior regulation at Time 2. This study confirms the complex structure of self-regulatory processes and underlines the importance of specific emotion regulation strategies for mathematics achievement. [ABSTRACT FROM AUTHOR]

Research Findings: Children are increasingly using touchscreen technologies at home, which has become a recurring feature within their classroom too. Research has investigated the potential effect of using computer-based tests to assess pupils' performance rather than traditional paper tests. An agreement has still not been formed about the impact of the mode of assessment on pupils' mathematical test scores. A mixed methods design was employed to explore the impact of the testing on young children's mathematical test scores. Thirty-seven children 4-7-years old were recruited from a primary school in England with their parents. A mathematical test on paper and an iPad was administered to each participant which was accompanied by an interview. Data regarding the use of touchscreens at home were explored with an on-line parental questionnaire. The results showed that gender and test type impact mathematical test scores, with females performing the best on the iPad test. The findings also suggested that as tablet usage increased at home, iPad mathematical test scores decreased. The interviews revealed that children rely on different strategies when resolving mathematical problems. Practice or Policy: Digital testing may enable a better investigation of mathematical skills in the first years of schooling and of differences between males and females' responses to solving mathematical questions, which then could be used to tailor the curriculum. [ABSTRACT FROM AUTHOR]

In undergraduate mathematics education, students' collaborations have gained a reputation as a 'good' learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. In this study, I take a close look at a twenty-minute-long interaction between two first-year students who engaged in a sequence of routine problems about dot products presented in a computer-based learning-support system. The commognitive analysis of the interaction revealed an asymmetrical structure: one student led the mathematizing, while his partner followed and invested considerable efforts to avoid making a mathematical contribution. The leader's attempts to switch positions and inquiry into the follower's recurrent refusals to mathematize entailed loaded exchanges that took a toll on both students in terms of identity and affect. I compare these findings to previous studies with school students to discuss possible sources of ineffective communication in situations where students are expected to learn through collaborations. [ABSTRACT FROM AUTHOR]

In this study, a learning study was used to enhance prospective teachers' learning about how to teach a specific topic in mathematics or natural science to 4th-6th graders. It has been argued that participating in learning study can direct prospective teachers (PTs) towards the object of learning, and what needs to be enacted in teaching to make it possible for the learners to learn what is intended. However, less is known about what capabilities PTs develop from planning lessons in collaboration with peers and a teacher educator in learning studies. Our research question concerns what opportunities PTs have to develop pedagogical content knowledge (PCK) when participating in learning studies. We analyzed three groups' lesson planning on two occasions, once when planning without a teacher educator, and once when planning with a teacher educator in a learning study using theory-informed questions. The software NVivo was used as a tool to code their discussions concerning PCK. For the three groups studied, there were significant differences regarding possibilities for developing PCK under the two conditions. [ABSTRACT FROM AUTHOR]

Meaningful and enjoyable experiences are important in the education of children. In this qualitative case study, the garden program (incl. market garden shop, garden care, Kid's Kitchen, and chicken coop) in one Australian primary school was explored to determine its impact on the mathematical learning of children. Data were collected using focus groups (four student, three parent and three volunteer groups), three teacher interviews, weekly garden journal entries and, when possible, through observation. This program provided opportunities for enriched mathematical learning facilitated by: early exposure to mathematical applications through mixed-age groups at different stations; an authentic, real-life setting to apply mathematical learning; and the consolidation of mathematical experiences through weekly engagement. These program features were found to positively impact the mathematical readiness, attitudes and competence of students. [ABSTRACT FROM AUTHOR]

Cooperative learning is a teaching method that makes students achieve common goals through joint efforts. This study explores the influence of cooperative learning on learners through a quasi-experimental design, employing a pre-test–post-test data collection method. The Student Team-Achievement Division (Slavin, R. E. 1978. Using Student Team Learning. Baltimore, MD: Johns Hopkins University, Center for Social Organization of Schools) was used to apply cooperative learning with a one-month intervention. A total of 93 students from two sixth-grade classes participated in the study, who were taught by the same mathematics teacher at a school in Shenzhen, China. This study used a mixed-method approach adopting both qualitative and quantitative methods for data collection and analysis. For quantitative design, questionnaires were used. The data were analysed by SPSS 25.0. Then a descriptive analysis, one-way ANOVA analysis, and ANCOVA analysis were conducted. For qualitative design, data collection included interviews and observation. The qualitative data were transcribed and coded (Edwards, J. A., and M. D. Lampert. 2014. Talking Data: Transcription and Coding in Discourse Research. New York: Psychology Press), by open, axial, and selected coding. [ABSTRACT FROM AUTHOR]

Exploiting quasi-experimental variation in levels of capital funding, we provide new evidence on the asymmetric effects of investments in educational facilities on academic achievement. We merge data from 4 million 3rd–8th graders in Texas with school bond outcomes and school openings. We find meaningful differences in the impact across the top and bottom quintiles of the pre-treatment achievement distribution, a result supported by the peer effects literature and a "reshuffling" of higher performing students into new schools. The mean impact of bond passage on reading and math scores is positive—at roughly 1/10th of a standard deviation. However, the effect on the lowest scoring students is four times as large, while the effect reverses in direction for the highest performing students. [ABSTRACT FROM AUTHOR]

Museum-based mathematics exhibitions are increasingly prominent but under-theorized learning environments. In this study, we analyse the curriculum of United States mathematics exhibitions developed in the early 21st century in terms of their complex suggestions about the nature of mathematics and mathematical sense-making. We apply Rancière's notions of politics and aesthetics to explore what we describe as dissensus present in the texts, images, and multi-sensory exhibits of several major mathematics exhibitions. Our analysis characterizes this dissensus as a paradoxical mix of alternative and familiar mathematical aesthetics. On the one hand, we identify an alternative aesthetic emphasizing everyday ubiquity, sensuality, and informal sense-making. At the same time, we identify a countervailing emphasis on dominant notions of mathematics as esoteric, immaterial, and formal-symbolic. Museum mathematics efforts sometimes describe themselves as expanding how the public views and defines mathematics. A close examination of the exhibitions in this study reveals a complex picture, in which dominant and alternative forms of mathematics are co-present. The analysis suggests that museum-based mathematics researchers and practitioners view their work as containing political and aesthetic dimensions that can disrupt or reify what society counts as mathematics. [ABSTRACT FROM AUTHOR]

Solving word problems in mathematics presents difficulties for many English learners (ELs), including those who use Spanish as a home language. In the early stage of learning to solve mathematics word problems, some children, including ELs, experience difficulties. By English status, EL refers to those children whose home language was Spanish while in the process of developing English at school. Math difficulties (MD) refers to those children with low normative mathematical problem-solving scores in both English and Spanish. The purpose of this study was to determine those measures that increase the odds of identifying EL children with emergent MD. Elementary school children (grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, working memory [WM]) in both Spanish (L1) and English (L2) in Year 1 and again one year later. Multilevel growth modeling compared MD children identified one year later who manifested MD to children who were average math achievers or poor math achievers across the two testing waves (year 1 and year 2). The results indicated that significant growth parameters (i.e., measures of estimation, WM) increased the odds of identifying emergent MD relative to children with Persistent math deficits and average achievers. The results were discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the odds of identifying later math difficulties. [ABSTRACT FROM AUTHOR]

Studies have shown that failure experiences play a role in pre-service teachers' development. Given that autobiographical experiences are a foundation of learning and that failure is a wide-spread experience, particularly in mathematics, we need further insight into what kind of experience failure actually is. This paper draws on 59 pre-service teachers' written experiences of failure in order to map them out and provide insight into what counts as failure from the perspective of the future teachers of mathematics, that is, pre-service mathematics and pre-service elementary school teachers. The findings, alongside the earlier research on negative experiences, form a basis for conceptualising failure in mathematics as an autobiographical experience and distinguishing it from a negative experience. A theoretical insight into the nature of failure is gained; the failure experiences seem to be less relational than anticipated. The paper also discusses the relevance of failure experiences for teacher education. [ABSTRACT FROM AUTHOR]

This study was designed to assess the efficiency of a French version of GraphoGame (GG) against an equally engaging math intervention (Fiete Math, FM) in a large school sample of children from socioeconomically disadvantaged neighborhoods in grade 1 (N = 921). The intervention was implemented in two different cohorts who used GG or FM for about four months four times a week for 30 minutes. Gains in reading and mathematics were assessed before and after intervention. Given the nested nature of the data, results were analyzed using hierarchical linear mixed effect models with intervention and initial pretest level as fixed effects and individuals and classes as random effects. We found positive intervention effects of GG on phoneme awareness (effect size, ES = 0.23), orthographic choice (ES = 0.27) and word reading fluency (ES = 0.18). FM had a significant effect on math achievement (ES = 0.28) but not number comparison. Correlations between intervention gains and game variables (overall accuracy, number of levels played) suggest that the effects of GG were specific. Positive effects for focused digital reading and math interventions were found in a large school sample of children from socially disadvantaged neighborhoods. [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]

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]

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]

This study investigated pupil experiences and perceptions of two kinds of classroom-based physically active math lessons during the Moving Maths programme in a Finnish primary school context. Qualitative data were gathered in focus group interviews with 16 nine-year-old pupils. Pupils in the group with physically active breaks during math lessons expressed mixed experiences, while pupils in the group with physical activity (PA) integrated into math curriculum experienced increased positive emotional and cognitive engagement. It is concluded that integrating PA into mathematics lessons is a feasible pedagogical method, especially in the form of PA integrated into math curriculum goals. [ABSTRACT FROM AUTHOR]

Although feedback is recognized as one of the most relevant factors to improve learning, its effectivity is highly dependent on the specific setting. In particular, feedback in elementary school students has not been thoroughly studied. Within this scope, studying the effectiveness of different degrees and types of feedback for primary school students becomes relevant. The present study looks at two types of feedback designed for problem-solving in primary school: Knowledge of Results and Elaborated Feedback. A series of interactive problems was designed for tablets to cover a range of topics for fifth-grade mathematics. Through a quasi-experimental design, one group of students (n = 31) was provided with Elaborated Feedback, while another group (n = 33) was provided with Knowledge of Results. Feedback was given to the students as they worked on the interactive problems over 6 sessions. The effectiveness of both types of feedback was then measured using a pre- and post-test. Although Elaborated Feedback helped the students achieve better results during the sessions, the Knowledge of Results group scored higher on the post-test. The results add to the growing debate on the supposed benefits of providing increasing levels of information or guidance, in an area that shows scarce and contradicting evidence. [ABSTRACT FROM AUTHOR]

In order to address the problem of the underlying mechanism of mathematics learning disability (MLD), in the current research, we investigated the visual and auditory perceptions of elementary school children with visual and auditory MLD from the first to fourth grade. We found that children with visual mathematics learning disability (VMLD) and those with auditory mathematics learning disability (AMLD) all had problems in both visual and auditory perceptions. After further analysis, we found that children with VMLD suffered from more serious problems with visual perception than with auditory perception while it was the other way around for children with AMLD. Children with visual and auditory mathematics learning disability (V-AMLD) had both serious problems with visual and auditory perceptions. It thus can be seen that the visual Arabic code of number was more closely tied with the visual perception while the auditory-verbal code of number more closely associated with the auditory perception. The results shed light on the subtypes of MLD and contributed to the intervention. [ABSTRACT FROM AUTHOR]

Baroody, Lai & Mix [2006. The development of young childrens number and operation sense and its implications for early childhood education. In B. Spodek, & O. N. Saracho (Eds.), Handbook of research on the education of young children (2nd Ed., pp. 187–221). NJ: Lawrence Erlbaum.] differentiate between four different learning approaches: direct instruction, guided adult-initiated play, guided child-initiated play, and free play. The purpose of this article is to clarify which learning approach researchers in the field of mathematics recommend for mathematics learning in children younger than 6 years. We will do this by illustrating and comparing the theories of the four teaching approaches. The review of the theories shows that research supports a combination of guided adult-initiated and child-initiated approaches in mathematics learning, but that different approaches can have a positive effect in certain conditions. [ABSTRACT FROM AUTHOR]

The study examines the associations of specific self-reported internalizing and externalizing problems and performance in mathematics and reading in school-aged children across Europe. Data were drawn from 5,842 children between 6 and 13 years of age participating in the School Children Mental Health in Europe study and a large cross-sectional survey in France. Self-reported child mental health was assessed using the Dominic Interactive, academic performance was reported by teachers. Across Europe, controlling for key sociodemographic factors associated with achievement including maternal education, performance in mathematics was more often associated with the presence of externalizing and internalizing problems as compared to performance in reading. In addition, the findings point to significant sex differences in the associations of internalizing problems and academic achievement. Considering the impact of early academic difficulties in terms of later internalizing and externalizing problems and academic attainment, school-based interventions interrupting the cycle as early as possible are warranted. [ABSTRACT FROM AUTHOR]

The purpose of this study was to identify the different profiles and patterns of progress in numerical skills of 6- to 10-year-old elementary school students with mild or moderate intellectual disability (ID). A standardised test of numerical and arithmetic skills was administered to 57 students with ID at the beginning and at the end of a school year. A cluster analysis was conducted with the participants' numerical skills at Time 1 and Time 2. Four groups of children which exhibited significantly distinct profiles at the beginning of the school year were identified: (1) children with inconsistent basic numerical skills with numbers up to 10, (2) children with basic numerical skills with numbers up to 10, (3) children with numerical skills with numbers up to 20, (4) children with numerical skills with numbers up to 100 and arithmetic skills. The group of children with inconsistent basic numerical skills with numbers up to 10 did not progress significantly during the school year. In contrast, most children with the second, third and fourth profile extended their numerical skills to larger number domains (respectively up to 20, 100 or 1000) during the school year. The implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

The aim of this study was to better understand the gaps between policy and practice in inclusive education for the Republic of Serbia. The study compared the academic achievement in Mathematics of comparable students with mild intellectual disabilities (MID) in the fifth and sixth grade who attend typical elementary schools and special schools. A total of 249 students participated in the study. All students were either 11 or 12 years old at the time of the study and were matched by ability, based on local educational and psychological assessments. Results indicated that students with mild intellectual disabilities who attend special schools scored significantly higher on mathematics achievements in comparison to their peers with similar disabilities in regular schools. Although the aim of the Republic of Serbia's new education policy focuses on inclusion, preliminary research indicates that students may be integrated (not included) and that regular classroom practice may not be supporting students with disabilities. A closer look at strategies that appear successful in special schools (such as adapted teaching strategies, work in small groups of students, and continuous individualised support of teachers) may provide instructional insights for newly included students in Serbia. [ABSTRACT FROM AUTHOR]

We make a prima facie case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the Performance Indicators in Primary Schools (PIPS) Baseline assessment at the beginning and end of their first school year. Through a Rasch analysis of real and simulated data, we show that: (1) there appears to be a single, unidimensional pathway in learning to identify number symbols with discrete difficulty stages, (2) on examination of differential item functioning, this pathway is invariant across gender, country, socio-economic background, first language and across the first year of schooling and (3) almost all children make progress along the pathway during the year. A number identification scale may thus be a universal ruler by which all pupils could be assessed. [ABSTRACT FROM AUTHOR]

The aim of the present study is to advocate the use of a participatory action research programme, the Formative Scaffolding Programme (FSP), in mathematics. The FSP's main structure is presented as well as an implementation of a class intervention, with the aim of exploring the FSP test cycle's virtues in a social science class in a Swedish upper-secondary school. The motivations for the FSP's development were to enhance students' awareness of their mathematical proficiency, alter the level and strength of their self-efficacy, foster self-regulated learning (SRL), reduce and prevent mathematics-related anxiety, and visualise the learning process in mathematics. The primary findings of the study were there was a resemblance between the FSP setting and SRL phases, and that participation in the test cycle altered the level and strength of students' self-efficacy and fostered self-regulation in a mathematics test situation. The benefits of working in a formative scaffolding manner indicate that it is worth implementing the FSP on a larger scale. The study is an example of how students can engage in transforming classroom practice and be radical agents of change. [ABSTRACT FROM AUTHOR]

This cohort-sequential study explored the components of working memory that underlie math calculation in elementary school children who are monolingual (English) or English language learners (ELLs) whose first language is Spanish. To this end, children (N = 789) in grades 1, 2, and 3 at wave 1 were administered a battery of math, vocabulary, reading and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again one year and two years later to the same participants. Three important findings emerged. First, along with naming speed, the results suggest that growth in the executive component of WM was significantly related to growth in calculation performance. Second, performance on measures of reading, fluid intelligence, naming speed and executive processes in wave 1 were significantly related to wave 3 math calculation performance. Finally, the full latent growth model showed that monolingual and ELL children were statistically comparable in computation at wave 3. Thus, strong support was found for the notion that the executive component of WM was related to math computation but weak support for the notion ELL children experienced a math achievement gap. [ABSTRACT FROM AUTHOR]

This study examined Head Start's impact on fathers' school-based involvement and associations with Black children's cognitive, behavioral, and social-emotional skills. With a sample of 1,354 Black children, fathers' involvement was measured as attendance at school meetings, teacher conferences, school events, and/or volunteering at school events. Children's cognitive skills were literacy, language, and mathematics scores. Parents reported on the parent–child relationship, children's social skills, and behavioral concerns. Non-resident fathers in Head Start were more involved in Black children's schooling than not enrolled in Head Start. Unexpectedly, fathers' school-based involvement and Head Start enrollment were not related to children's developmental outcomes at kindergarten age. Head Start serving impoverished Black families should consider implementing targeted school-based father involvement initiatives that directly influence children. [ABSTRACT FROM AUTHOR]

Over three decades of research has shown that spatial reasoning and mathematics performance are highly correlated. Spatial visualization, in particular, has been found to predict mathematics performance in primary and middle school children. This research sought to determine the effectiveness of a spatial visualization intervention program on increasing student spatial reasoning and mathematics performance. Participants were 327 students from 17 classrooms across ten schools with nine experimental and eight control classes. The intervention program was delivered over a three-week period by classroom teachers, while the control classes received standard mathematics instruction. When compared to the control group, participants in the intervention group improved significantly on their spatial reasoning performance, and specifically on spatial visualization and spatial orientation. The intervention group also significantly improved on their mathematics test performance, with those in the intervention group outperforming their control group peers on geometry and word problems but not on mathematics questions requiring the decoding of graphics (non-geometry graphics tasks). These results add to evidence that a spatial reasoning enrichment program implemented by teachers in their own classrooms can enhance both spatial reasoning and mathematics performance. Moreover, the study provides new insights about the aspects of mathematics performance that are most affected by spatial visualization training. [ABSTRACT FROM AUTHOR]

This paper offers a new methodology for researching children's identifications in the early primary phase that makes visible the 'seeds' of academic dis-/identities, which typically flower later in adolescence. It focuses on the 'case' of mathematical identifications (MI) to exemplify how children come to dis/identify from the academic curriculum more broadly. MI is defined as any act where cultural representations of being mathematical are reflected back on to the child by others or the self, as they engage in mathematical activity. Data are presented concerning Bilal and Nico to show identifications in a hybrid home–school mathematics activity that contradict or 'align' with MI elicited in school-mathematical activity. It is argued that contradictions between these MIs indicate 'potential' development towards disengagement (the case of Nico). This contrasts with home–school alignment involving Bilal's 'schoolified' home activities, which (re)validate school-mathematical activity. It is further argued that this conceptual innovation offers potential for investigating identity in early childhood. [ABSTRACT FROM AUTHOR]

Using growth modeling, this study examined trajectories of 'switching on' (aspirations) and 'switching off' (disengagement) in mathematics across middle school and high school. In addition, guided by principles under expectancy-value theory, the study sought to determine the extent to which patterns of growth differed by motivation (self-efficacy and valuing) and socio-educational attributes (gender, language background, and achievement). The sample comprised 194 students from four schools who participated in three rounds of data collection across five academic years of their schooling, spanning middle school and high school. In the main, mathematics aspirations declined over time while mathematics disengagement increased. However, initial levels of aspirations and disengagement and their rates of change over time were impacted by motivational and socio-educational factors. Salient findings and their implications for educational assessment and practice are discussed. [ABSTRACT FROM AUTHOR]

Background: An emerging field of research indicates that the use of learning environments other than the classroom can improve pupils' academic achievement in several subjects, including their skills in mathematics. Purpose: The aim of this study was to investigate the association between Education Outside the Classroom (EOtC) and pupils' skills in mathematics. Methods: This explorative, quasi-experimental study involved schoolchildren (aged 9-13 years) from 15 Danish public schools who participated in EOtC over the course of a school year. The mathematical skills of pupils from 23 EOtC maths intervention classes (n=421) and 12 EOtC non-maths comparison classes (n=198) were measured at the start and end of the 2014-2015 school year. Results: Both groups showed improved maths skills; however, we found no significant difference between the EOtC maths and the comparison groups. Conclusion: The results indicate that, in this explorative study, moving maths teaching outside the classroom neither harmed nor improved pupils' mathematical skills. These results and implications for research are discussed. [ABSTRACT FROM AUTHOR]

This study investigated the interaction between self-efficacy and implicit beliefs of ability in their association with maladaptive learning in mathematics. The analysis was based on a large sample of 2538 Singapore Secondary 2 students (Mage = 13.75), who took measures of entity beliefs of ability, self-efficacy, and three maladaptive learning variables in mathematics: novelty avoidance, cheating, and anxiety. We conducted latent interaction analysis with gender and previous mathematics achievement controlled and found that higher self-efficacy did not buffer, but enhanced the positive association between entity beliefs of ability and the three maladaptive learning variables. When entity beliefs of ability were higher, the increase in the three maladaptive learning was larger for those with higher self-efficacy than those with lower self-efficacy. Findings suggest a revision of the moderation hypothesis in the literature: higher self-efficacy is more helpful in preventing maladaptive learning for incremental theorists than for entity theorists. [ABSTRACT FROM AUTHOR]

The benefit of homework (HW) has been the subject of ongoing debate among various stakeholders. Within this debate, and in relation to teacher development, prospective teachers' views of HW have received limited attention. In this study, we survey primary pre-service teachers' ('PSTs') views of HW use (n = 45 teaching grades 2-5; n = 39 teaching grades 6 and 7) in a single discipline (mathematics) at one large Australian university. The literature suggests students in upper primary and secondary grades will benefit from the use of mathematics HW. Results of the study, in contrast, suggest our PSTs teaching early primary grades planned to give proportionally (but not significantly) more mathematics HW than those teaching later grades. Reasons for this disparity are discussed. We argue there is a need in teacher development to equip PSTs with a better understanding of how classroom and home-based learning work together in the development of mathematical understanding. [ABSTRACT FROM AUTHOR]

Classroom disciplinary climate has emerged as a crucial factor with regard to student achievement. However, most previous studies have not explored potential gender differences in both students’ perceptions of the classroom disciplinary climate and the association between classroom disciplinary climate and student learning. Using data from the Organisation for Economic Co-operation and Development (OECD) Programme for International Student Assessment (PISA) 2012 for the Nordic countries, we found a significant association between the perceived classroom disciplinary climate of schools and students’ mathematics performance across countries. On the basis of an analysis of a pooled sample consisting of all 5 Nordic countries, we found that the correlation between classroom disciplinary climate of schools and maths achievement is significantly stronger for boys than for girls. Further analyses showed that this finding may partly be attributable to gender differences in the perception of the disciplinary climate of schools, whereby boys seemed to perceive the classroom disciplinary climate of schools more positively than girls. [ABSTRACT FROM AUTHOR]

The aim of this study is to compare students’ use of number sense strategies based on their mathematics success levels. Participants were 129 seventh graders from three elite secondary schools in Trabzon. Data were collected through a written examination with 10 problems and semi-structured interviews. Interview data were analyzed by considering students’ mathematics success and the differences and similarities among responses. Interviews were held with six students from two schools with different levels of mathematics success. The findings showed that students rarely used number sense strategies and mostly solved problems by using rules and algorithms. Even successful students seemed to have adopted the rule- and algorithm-based solution approach, making it necessary to investigate teacher criteria of mathematical competence. Another noteworthy finding from the interviews with students was teachers’ embrace of rule- and algorithm-based solutions when solving problems. The study finishes with an evaluation of the inclusion of number sense dimensions in secondary school mathematics textbooks in Turkey and recommendations for improving students’ number sense. [ABSTRACT FROM AUTHOR]

The goal of this study was to add to the existing literature by examining the effect of 1:1 iPad integration on the achievement of Canadian Grade 7 students. The school board we worked with provided an iPad to each Grade 7 student in the district to keep for the remainder of their time in the district. We examined the impact of the iPads on achievement with three cohorts of Grade 7 students, totaling 1,400 students. Achievement was assessed using students' report cards in language arts, mathematics, and learning skills. In language and mathematics, most of the analyses demonstrated statistically significant but small effects of iPad status on achievement. The effects were mixed in that the impact was sometimes positive, sometimes negative, sometimes negative and then positive, and sometimes neutral. There were no significant effects on students' learning skills, as reported on report cards. The implications of these findings are discussed in the manuscript. [ABSTRACT FROM AUTHOR]

Students must leave elementary school with a firm understanding of fractions and decimals in order to make satisfactory progress in advanced mathematics. Firm understanding includes manipulation of rational numbers using different models of representation such as area and length. Research has demonstrated that a graduated sequence such as concrete-representational-abstract (CRA) instruction is effective in teaching fraction conceptual understanding. The purpose of this study was to investigate the effects of a CRA tier two fraction intervention that presented fraction concepts using the area and length model. Seventeen fifth-grade students participated in small-group tier two interventions addressing fourth-grade fraction standards. The researchers measured student performance using curriculum-based pretests and posttests and found that students made significant progress. Results and implications are discussed. [ABSTRACT FROM AUTHOR]

Purpose: This study investigated the academic achievement and physical activity differences between types of activity breaks implemented in elementary school classrooms. This study evaluated whether there was a difference between the impact of purely aerobic-based movement breaks and the impact of academic-based breaks on children's academic achievement outcomes.Method: Participants included 460 children in 3rd grade through 5th grade at 4 elementary schools. There were 176 children in the schools that engaged in academic-based breaks and 284 in the schools that engaged in aerobic-only breaks. Schools were randomly assigned at the school level to implement either aerobic movement breaks with academic content infused within the breaks ("academic-based breaks") or aerobic-only movement breaks without the addition of academic material ("aerobic-only breaks") for approximately 10 min of activity per day. Math and reading achievement as well as children's step counts were measured before and after the intervention. A mixed-effects (multilevel-growth) model, in which the repeated measures of individuals nested within a classroom are analyzed, was used to answer all posited research questions.Results: Small to moderate effect sizes (ES) indicating gains in reading achievement (ES = .13) and steps (ES = .33) were found for classrooms that used aerobic-only movement breaks compared with those that used academic-based breaks.Conclusions: The type of movement breaks that are implemented in classrooms may have differential outcomes for children's achievement and activity levels. Results from the present study indicate that children who were given aerobic-only movement breaks had slightly larger gains in reading achievement and physical activity levels than children who were given academic-based breaks. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the interplay between test anxiety and working memory (WM) on mathematics performance in younger children. A sample of 624 grade 3 students completed a test battery consisting of a test anxiety scale, WM tasks and the Swedish national examination in mathematics for grade 3. The main effects of test anxiety and WM, and the two-way interaction between test anxiety and WM on mathematics performance, were modelled with structural equation modelling techniques. Additionally, the effects were also tested separately on tasks with high WM demands (mathematical problem-solving) versus low WM demands (basic arithmetic). As expected, WM positively predicted mathematics performance in all three models (overall mathematics performance, problem-solving tasks, and basic arithmetic). Test anxiety had a negative effect on problem-solving on the whole sample level but concerning basic arithmetic only students with lower WM were affected by the negative effects of test anxiety on performance. Thus, students with low WM are more vulnerable to the negative effects of test anxiety in low WM tasks like basic arithmetic. The results are discussed in relation to the early identification of test anxiety. [ABSTRACT FROM AUTHOR]

Is it possible to compare the results in assessments of mathematics across countries with different curricula, traditions and age of starting school? As part of the iPIPS project, a Russian version of the iPIPS baseline assessment was developed and trial data were available from about 300 Russian children at the start and end of their first year at school. These were matched with parallel data from representative samples of equal numbers of children from England and Scotland. The equating of the scales was explored using Rasch measurement. A unified scale was easiest to create for England and Scotland at the start and end of their first year at school when children only differ by a half a year in age, and live in adjacent countries with a common language. Although fewer items showed invariance across the three countries, it was possible to link iPIPS scores in mathematics from the start and end of the first year at school across Scotland, England and Russia. The findings of this study suggest that, despite the apparent difficulties, meaningful comparisons of mathematics attainment and development can be made. These will allow for substantive interpretations with policy implications. [ABSTRACT FROM AUTHOR]

This study is integrated in the field of Dance in Education, focusing on the instrumentalist aspect of art. We focused on creative dance as a catalyst to learn Mathematics’ contents. This interdisciplinary work can enhance the learning, as far as the understanding of Mathematics’ concepts is achieved through the body and revealed by expressive and creative movement. The main purpose of the investigation, quasi-experimental, was to analyze the impact of creative dance in the learning of Mathematics’ concepts in children (7/8 year old) in primary education, in two Portuguese schools. The sample included 8 classes, 117 children in total, of both genders. The intervention has taken place in two groups (experimental group and control group), with four sessions of creative dance in the experimental group. Both groups were assessed on three different occasions (pre-test, post-test and retest). The statistical techniques used for processing the data were the analysis of variance of mixed plans and the Student’s t test for paired samples. The conclusions showed that the students who consolidated the knowledge in the creative dance classes, exhibited significant differences in their learning gains in Mathematics, as compared to the control group. [ABSTRACT FROM AUTHOR]

To sort pupils at the end of primary school, some early-tracking systems apply a mechanism that unwittingly divides classes into two groups: students preparing for exams to enter better schools and everyone else, who decide not to compete for selective schools. Utilizing TIMSS data and a follow-up study in the Czech Republic, we show that this environment has a detrimental effect on pupils’ self-confidence in mathematics, particularly among girls, who do not apply for selective schools but have peers in their classroom who do apply. Our results imply that gender gaps in self-confidence can result from school competitive environments. [ABSTRACT FROM PUBLISHER]

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study was to investigate the effects of an explicit mathematics intervention using concrete-representational-abstract sequence to teach students to count in flexible ways and use skip counting as a strategy for multiplication for students with mathematics difficulties. Students were able to learn skip counting and improved in their multiplication abilities. Implications are also discussed. [ABSTRACT FROM PUBLISHER]

In the educational sciences, many discussions on the use of computer games occur. Most of the scientists believe that traditional computer games are time-consuming software and that game-playing activities negatively affect students’ academic performance. In this study, the accuracy of this general opinion was examined by focusing on the real game-playing scores of an elementary school students in Turkey. First, researchers selected a single-player strategy game. Second, the selected game was given to 105 fifth-grade students, who had not played it before, so that they could play it over a 30-minute period. The most successful student of the group finished the 23rd level of the game and collected 8152 points in total. In order to investigate the correlation between strategy game performance and academic performance, researchers derived the students’ average exam scores for six different courses (mathematics, physical science, science and technology, visual arts, music, and social sciences) from official documents. At the end of the study, it was found that participants’ mathematical or physical science skills were positively correlated with game success; however, a negative relationship was not exists between an individual's computer game success and academic performance. [ABSTRACT FROM AUTHOR]

This study investigates young students’ writing in connection to mathematical problem solving. Students’ written communication has traditionally been used by mathematics teachers in the assessment of students’ mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of resources. In order to help students develop their writing, teachers need to have a thorough knowledge of mathematical writing and its distinctive features. The study aims to add to the body of knowledge about writing in school mathematics by investigating young students’ mathematical writing from a communicational, rather than mathematical, perspective. A basic inventory of the communicational choices, that are identifiable across a sample of 519 mathematical texts, produced by 9–12 year old students, is created. The texts have been analysed with multimodal discourse analysis, and the findings suggest diversity in students’ use of images, words, numerals, symbols and layout to organize their texts and to represent their problem-solving process along with an answer to the problem. The inventory and the indication that students have different ideas on how, what, for whom and why they should be writing, can be used by teachers to initiate discussions of what may constitute good communication. [ABSTRACT FROM PUBLISHER]