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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]

A multiple-baseline across participants design was used to investigate the effect of the Cover-Copy-Compare (CCC) intervention on multiplication-fact fluency for students with emotional and behavioral disorders (EBD). Although CCC is a well-researched intervention for mathematics, limited research has been conducted with students with EBD even though these students often struggle academically. Results indicate that a functional relation was established between CCC and an improved number of digits correct per minute for multiplication problems for only one of three elementary-age boys with EBD. Tau-U effect sizes ranged from no effect for one participant to a large effect for another participant. The length of the intervention and the initial level of a student's skills may be related to the effectiveness of CCC for students with EBD and should be explored in future studies. [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]

The goal of this development is introducing a reader the solution of one class comprising trigonometric equations in the Teaching Course of Mathematics by using trigonometric form of the complex numbers. An exemplary approach to solving these equations, suitable for students from 11th to 12th grade, as well as for pupils participating in mathematical camps, olympiads, mathematical competitions, computer mathematics olympiads is considered. [ABSTRACT FROM AUTHOR]

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction measures for predicting which students would not meet state standards on the state mathematics test in fourth grade (n = 411), fifth grade (n = 362), and sixth grade (n = 304). A combined measure consisting primarily of fraction number line estimation items and general fraction concept items was the most accurate screener of risk status in fourth, fifth, and sixth grades (area under the curve [AUC] =.84,.81, and.85, respectively). To maximize efficiency for classroom use, the length of the combined screener was reduced using best subset automatic linear modeling. The study highlights the importance of fraction knowledge for predicting mathematics achievement more generally and validates an effective and practical screening tool for the intermediate grades. [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]

• Solving the incongruent perimeter-comparison task relies on an inhibition ability. • School-age children and adults performed a negative priming paradigm. • We found significant negative-priming effects in both children and adults. • This novel study compared inhibitory control between high/low achieving students. • High-achieving students were more efficient at inhibiting a misleading intuition. Many people apply the "larger area–larger perimeter" rule to solve the perimeter comparison problems, even in situations where this intuitive rule is misleading. To investigate whether inhibitory control is needed in the perimeter comparison reasoning and whether the efficiency of inhibitory control varies with students' ages and achievements, we designed a negative priming paradigm and conducted two experiments. In Experiment 1, a negative priming effect was observed in both Chinese primary school students (n = 123) and college students (n = 42) when they were solving a perimeter comparison task. In Experiment 2 (N = 86), we found that the negative priming effect existed in both high-achieving and low-achieving primary school students, but the magnitude of this effect appeared to be smaller in high-achieving students. These results imply that success in solving geometry quantitative problems requires the ability to inhibit the larger area–larger perimeter intuition in some situations and also that high-achieving students are more capable of doing so. [ABSTRACT FROM AUTHOR]

When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general. Lay Description: What is already known about this topic: Students must be instilled with conceptual understanding to achieve mastery of mathematical understanding and be able to properly solve complex or novel problems.Students would likely exhibit misconceptions if they do not have sufficient conceptual understanding.Students' conceptual understanding can be examined by evaluating their confidence levels in solving a problem. What this paper adds: A three‐tier diagnostic test (question and answer, reasoning, and confidence) can be used to examine students' conceptual understanding.Students performed unsatisfactorily on number sense because they lack conceptual understanding of topics related to number sense.Students held significant misconceptions on understanding the basic meaning of numbers and operations, recognizing the number size, using multiple representations of numbers and operation, recognizing the relative effect of operations on numbers, and judging the reasonableness of a computational result. Implications for practice and/or policy: Conceptual understanding of related topics reflecting number sense should be prioritized over procedural knowledge and mathematical rules.Lack of conceptual understanding of relevant topics and relying on mathematical rules and formulas are the main root causes of students' unsatisfactory performance.The deliberate use of estimation questions, multiple presentations, and judging the reasonableness of a result can help learners develop their conceptual understanding of number sense. [ABSTRACT FROM AUTHOR]

Many students fall below benchmarks in the area of fractions computation, particularly students with disabilities. Self-regulated strategy development (SRSD) is one strategy with proven effectiveness for improving outcomes for students with disabilities, although very few studies have applied SRSD to the area of mathematics. In this study, we used SRSD Fractions to teach adding and subtracting fractions with unlike denominators, simplifying fractions, and converting fractions to mixed numbers using the mnemonics FILMS, CUT, and EDIT. A researcher provided instruction in small groups to fifth-grade students at risk for disabilities. The results from use of a multiple-baseline-across-groups design suggest a functional relationship between SRSD Fractions and 8 fifth-grade students' digits correct on timed fraction probes. Results from treatment fidelity, social validity, and academic engagement during the intervention are also reported. We also discuss limitations and directions for future researchers. [ABSTRACT FROM AUTHOR]

Students with early indicators of behavior risk have predictable, negative outcomes, and those with co-existing academic problems have significantly more negative outcomes. Identifying academic subclasses of students with behavior risk can inform integrated interventions and school-based problem-solving teams. In addition, identifying academic strengths among a population of children typically only differentiated by severity of maladaptive behaviors may offer insight into academic resiliency. Using a sample of 676 elementary school students identified as behaviorally at risk, latent class analysis of reading and math indicators was conducted. Results indicated a three-class structure was the best fit for these data, with Class 1 (25%) having the least academic risk, Class 2 (37%) as below average reading and math, and Class 3 (38%) with significant academic deficits. Class membership was found to significantly predict end of year statewide assessment performance. While those behaviorally at-risk students with co-occurring academic deficits were very likely to fail the end of year assessments (Class 3; 88%–99% failure rates), those with stronger academic skills (Class 1) were increasingly more likely to pass (47%–56% pass rates). Practical implications, including intervention selection, and future directions are discussed. [ABSTRACT FROM AUTHOR]

• The perceived teacher support, mathematics learning engagement, and mathematics anxiety of 1796 Chinese children were investigated four times from the 3rd and 6th grades. • Bidirectional relations between perceived teacher support and learning mathematics anxiety emerged from grades 3 to 6. • The relations between perceived teacher support and mathematics evaluation anxiety were unidirectional (from mathematics evaluation anxiety to perceived teacher support). • Mathematics learning engagement mediated the relation between perceived teacher support and mathematics anxiety (including MEA and LMA). There has been growing interest in the relation among students' perceived teacher support, mathematics learning engagement, and mathematics anxiety in the last decade. Longitudinal models are needed to provide new insights into the role of engagement in mathematics learning. Based on the control-value theory and developmental dynamic bio-psycho-social model of mathematics anxiety, the present study followed 1796 students from Grades 3 to 6 to investigate the longitudinal associations among perceived teacher support and two conceptually distinct dimensions of mathematics anxiety (i.e., mathematics evaluation anxiety and learning mathematics anxiety). We further explored the potential mediator effects of mathematics learning engagement between perceived teacher support and mathematics anxiety. We found bidirectional longitudinal associations between teacher support and learning mathematics anxiety from grade 3 to grade 6, as well as unidirectional longitudinal associations between teacher support and mathematics evaluation anxiety (from mathematics evaluation anxiety to teacher support). Furthermore, mathematics learning engagement mediated the relation between perceived teacher support and mathematics anxiety (including learning mathematics anxiety and mathematics evaluation anxiety). These findings highlight the importance of understanding the dynamic interplay among perceived teacher support, mathematics learning engagement, and mathematics anxiety from a developmental perspective. [ABSTRACT FROM AUTHOR]

The present study investigated the nature and similarity of academic motivation profiles toward German and Math among German elementary school students while accounting for the dual global and specific nature of academic motivation proposed by self-determination theory. The determinants (self-concept, sex) and outcomes (anxiety, academic achievement, effort) were investigated. Latent Markov analyses revealed five profiles (Highly Extrinsic , Controlled , Moderately Extrinsic , Self-Determined , and Non-Motivated) characterized by differing levels of global and specific motivation. These profiles had similar properties (within-sample similarity) and had a similar membership (within-person similarity) across domains. Self-concept predicted membership into profiles with higher global self-determination, while girls were more likely to belong to the Highly Extrinsic profile. Most desirable outcomes were associated with the Self-Determined profile, then the Moderately Extrinsic profile, followed by the remaining three profiles. Students' engagement in their academic work is seldom driven by a single motive but rather seems to be motivated for a variety of reasons. The present study identified naturally occurring motivational combinations for Math and German classes among a sample of elementary school students. Five profiles, characterized by differing levels of global and specific motivation levels, were identified which were replicated and had a similar membership across Math and German domains. We showed that students' sex and academic self-concepts are drivers of their motivation profile memberships, and that these profiles differ from one another in terms of youth's performance and well-being. • Five profiles were identified with differing levels of global and specific motivation. • Profiles fully replicated across German and Math school subjects. • The profiles demonstrated high within-sample and moderate within-person similarity. • Self-concept and students' sex predicted profile membership. • Profiles differed from one another in terms of anxiety, effort and grades. [ABSTRACT FROM AUTHOR]

Interactive dialogue within feedback episodes is essential for developing primary school students' mathematical reasoning competence. Our goal was to better understand the nature of the associations between observed dialogue, teachers' formative feedback, and students' mathematical reasoning. We applied a two-step approach, first constructing a video-analysis instrument for assessing the quality of interactive dialogues and then combining the interaction data with student and teacher questionnaire data from 804 students in 44 fifth and sixth grade primary school classes. The quality of the observed dialogues predicted class differences in students' self-efficacy for explaining but not in their reasoning competence, which was predicted by perceived formative feedback. • Rasch analysis of video rating data on interactive dialogue within feedback episodes. • Relationship of interactive dialogue, formative feedback, and reasoning competence. • Mathematical reasoning was predicted indirectly by formative feedback. • Math self-efficacy on the class level was predicted by interactive dialogue. [ABSTRACT FROM AUTHOR]

Social disruption caused by natural disasters often interrupts educational opportunities for children. However, little is known about children's learning in the following years. This study examined change in academic scores for children variably exposed to a major bushfire in Australia. Comparisons were made between children attending high, medium, and low disaster-affected primary schools 2-4 years after the disaster (n = 24,642; 9-12 years). The results showed that in reading and numeracy expected gains from Year 3 to Year 5 scores were reduced in schools with higher levels of bushfire impact. The findings highlight the extended period of academic impact and identify important opportunities for intervention in the education system to enable children to achieve their academic potential. [ABSTRACT FROM AUTHOR]

Aerobic fitness and fundamental motor skills have both been related to children's academic achievement. Results of studies that have simultaneously related aerobic fitness and fundamental motor skills to academic achievement have provided inconsistent results, and the exact relations with achievement in distinct academic domains remain unknown. The current study examined unique relations between aerobic fitness, fundamental motor skills, and achievement in reading, mathematics and spelling. In total, 891 students (mean age = 9.17 years, SD = 0.66) from 22 primary schools participated. Two multilevel structural equation models were constructed, with relations between aerobic fitness (20m-shuttle run test), fundamental motor skills (tested with items of the Körperkoordinationstest für Kinder and Bruininks-Oseretsky Test for Motor Proficiency) and: (1) overall academic achievement, or; (2) achievement in the domains of reading, mathematics, and spelling (assessed with standardized academic achievement tests). Fundamental motor skills were more strongly related to overall academic achievement than aerobic fitness, but the exact relations differed by academic domain. Aerobic fitness predicted spelling achievement, whereas motor skills predicted reading achievement, and both were predictive of mathematics achievement. Although more research is needed to disentangle the exact way in which aerobic fitness, motor skills, and academic achievement are linked, the results suggest that children's academic achievement benefits most from engagement in various physical activities which target both aerobic fitness and gross motor skills. These findings emphasize the importance of providing children with opportunities to engage in a wide variety of sports and activities. • Motor skills are a stronger predictor of academic achievement than aerobic fitness. • Motor skills predict achievement in mathematics and spelling, but not reading. • Aerobic fitness predicts achievement in mathematics and reading, but not spelling. [ABSTRACT FROM AUTHOR]

The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering belief that intellectual and academic abilities can be developed) along with SR processes in which students set goals, self-monitor, and use strategies to engage motivationally, metacognitively, and behaviorally through challenging tasks. Students (n = 69) were randomly assigned to business-as-usual control and the two versions of fractions intervention. Multilevel models, accounting for the nested structure of the data, identified a moderation effect on fraction word problems: For students receiving fractions intervention with embedded SR, response to intervention was robust across the continuum of students' pretest word problem skill; by contrast, without SR, response to fractions intervention depended on students' pretest word problem skill. On the remaining outcomes, results reflected stronger outcomes when fractions intervention embedded SR instruction without moderation. [ABSTRACT FROM AUTHOR]

Background: Knowledge of urogenital schistosomiasis can empower individuals to limit surface water contact and participate in mass drug administration campaigns, but nothing is currently known about the schistosomiasis knowledge that schoolchildren have in Ghana. We developed and implemented a survey tool aiming to assess the knowledge of urogenital schistosomiasis (treatment, transmission, prevention, symptoms) among science teaches and primary and junior high school students in the Eastern Region of Ghana. Methods: We developed a 22-question knowledge survey tool and administered it to 875 primary and 938 junior high school students from 74 schools in 37 communities in the Eastern Region of Ghana. Teachers (n = 57) answered 20 questions matched to student questions. We compared knowledge scores (as percent of correct answers) across topics, gender, and class year and assessed associations with teacher’s knowledge scores using t-tests, chi-squared tests, univariate, and multivariate linear regression, respectively. Results: Students performed best when asked about symptoms (mean±SD: 76±21% correct) and prevention (mean±SD: 69±25% correct) compared with transmission (mean±SD: 50±15% correct) and treatment (mean±SD: 44±23% correct) (p<0.0005). Teachers performed best on prevention (mean±SD: 93±12% correct, p<0.0005) and poorest on treatment (mean±SD: 69±16% correct, p<0.001). When listing five facts about urogenital schistosomiasis, teachers averaged 2.9±1.2 correct. Multiple regression models suggest that gender, class year, teacher score, and town of residency explain ~27% of variability in student scores. On average, junior high school students outperformed primary school students by 10.2 percentage points (CI95%: 8.6–11.8); boys outperformed girls by 3.5 percentage points (CI95%: 2.3–4.7). Conclusions: Our survey parsed four components of student and teacher knowledge. We found strong knowledge in several realms, as well as knowledge gaps, especially on transmission and treatment. Addressing relevant gaps among students and science teachers in UGS-endemic areas may help high-risk groups recognize risky water contact activities, improve participation in mass drug administration, and spark interest in science by making it practical. [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]

English learners (ELs) experience difficulty with mathematical problem solving because word problems require complex processes beyond basic math skills, such as the use of linguistic information, identifying relevant information, and constructing the appropriate problem statement. This study used a combined multiple baseline design and criterion changing design to assess the effectiveness of a paraphrasing intervention on the problem-solving performance for nine third-grade students who are ELs and at risk of mathematical disabilities (MD). Although the magnitude of the Tau-U effect sizes was in the small range, the visual analysis indicated that all students displayed increasing trends in problem-solving accuracy as a function of the paraphrasing intervention. The results were discussed in terms of providing continual support toward maintaining intervention outcomes. [ABSTRACT FROM AUTHOR]

Abstract It is still unclear which cognitive factors stand at the base of mathematical creativity. One factor could be inhibition, but results are inconsistent. A possible explanation is that this relation is more complex than the direct relations tested, until now. In the current study, the hypothesis was tested that cognitive inhibition moderated the relationship between mathematical ability and mathematical creativity. The sample included 82 primary school students between 8 and 12 years of age. Mathematical creativity was measured with a multiple solution task and scored on fluency, flexibility, and originality. While there was a direct relation between mathematical ability and mathematical creativity, inhibition did not have a direct effect on mathematical creativity, but it positively moderated this relationship for flexibility and originality. These results indicate that reduced inhibition strengthens the relationship between mathematical ability and mathematical flexibility and between mathematical ability and mathematical originality, but not the relation between mathematical ability and mathematical fluency. These findings are discussed in relation to children with high and low mathematical abilities, measurement of inhibition, and the domain-general/domain-specific discussion of creativity. [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: Many developing countries are in a state of nutritional transition from prevalent under-nutrition to the emergent problem of over-nutrition (overweight and obesity), which is associated with increased morbidity and mortality, and whose complications can persist into adulthood with long-term consequences. However, data are limited on the risk factors for overweight and obesity (O&O) among primary school children, particularly those in rural and semi-urban areas in these countries. Aim and objectives: To determine the socio-demographic factors associated with overweight and obesity among primary school children in semi-urban areas. Subjects and methods: 1187 school pupils aged 6–11 years recruited from semi-urban areas using multistage sampling were interviewed for risk factors of overweight and obesity using a structured questionnaire. Nutritional status was assessed using body mass index and this was classified using a standard method. The proportions were compared using Pearson’s chi-squared. Multivariate logistic regression analysis was also carried out with overweight and obesity as the dependent variable and socio demographic factors as independent variables. The level of statistical significance was set at p <0.05 in all the statistical analyses. Results: Fifty-eight pupils (4.9%) had overweight and obesity while 1129 (95.1%) were either of normal nutritional status (1088, 91.6%) or were thin/severely thin (41, 3.5%). Among those with overweight and obesity, 41 (3.5%) were overweight and 17 (1.4%) obese. A higher prevalence of overweight and obesity was significantly associated (in unadjusted analysis) with female gender [unadjusted Odds Ratio, OR (95% CI) = 2.42 (1.37, 4.28)], attendance at private schools [OR (95% CI) = 3.34 (1.86, 6.00)], higher socio-economic status families [OR (95% CI) = 2.32 (1.65, 5.80)] and presence of a television in the pupil’s bedrooms [OR (95% CI) = 2.22 (1.02, 4.82)] on bivariate analyses. However, only gender, school type and family socioeconomic status were independently associated with overweight and obesity on multivariate logistic regression analysis. Conclusion: We conclude that overweight and obesity among primary school pupils in semi-urban areas is associated with female gender, attendance at private schools and higher socioeconomic status families. Preventive programmes should accordingly be more directed at children from affluent families; particularly those who are females and those attending private schools. [ABSTRACT FROM AUTHOR]

In this study, we analyzed the emotional and conative characteristics of fourth grade students of elementary school as follows: motivation for learning math, situational interest in learning mathematics during teaching, mathematics anxiety, self-esteem in relation to academic achievement and attributions of success and failure in mathematics. In a sample of 200 students and 20 teachers were analyzed emotional and conative characteristics capable of above-average and below average in math-age students. The study used the descriptive method, a questionnaire and a test. The research results are presented graphically and in tabular form with an explanation and discussion. In the conclusion are set the directions which should further improve this insufficiently studied area. [ABSTRACT FROM AUTHOR]

In the Arab region, several assessments are available to evaluate student skills in mathematical computations. However, none of them uses formative evaluation to guide universal screening of struggling learners or students with learning disability (LD). The current study aimed to develop mathematical computation curriculum-based measurement (MC-CBM) for Arab speaking fourth grade students, examine its psychometric properties, test its adequacy for use in an Arab context, namely Oman, determine an adequate time for its administration, and develop performance benchmarks. MC-CBM were administered to 528 fourth grade students. Results indicated that the developed measures were adequate for use in the Arab context. Received operation characteristic (ROC) curve indicated good specificity and sensitivity estimates for the MC-CBM. Performance benchmarks were obtained using the 25th and 75th percentiles. Implications are discussed from a contextual perspective. [ABSTRACT FROM AUTHOR]

Children with higher levels of executive function (EF) skills consistently demonstrate higher levels of academic achievement. Despite the consistency of these associations, fundamental questions remain about whether efforts to improve an individual child's EF skills result in corresponding improvements in his or her academic performance. In the absence of experimental evidence, developmentalists have used repeated measures designs to test the nature, magnitude, and direction of the associations between EF skills and academic achievement. In contrast to previous studies, this study described how between- and within-person associations between EF and achievement address different questions. Using data from a subsample of participants (N = 6,040) from the Early Childhood Longitudinal Study-Kindergarten, 2010-2011 (ECLS-K:2011) cohort, we estimated a series of latent growth curve models with structured residuals to test the between and within-person associations between 2 dimensions of EF (working memory, cognitive flexibility) and 2 domains of academic achievement (math, reading). Whereas between-person associations between EF and achievement were large (φ = .55-.91), the within-person associations were small (βs = -.10 -.25). Within-person effects of earlier reading achievement on later EF skills was the most consistent finding. Results were unchanged when analyses were repeated using the subset of children who were eligible for free and reduced-price lunch, a proxy for low socioeconomic households. Results are discussed with respect to interest in improving EF skills as a means for facilitating school outcomes. [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]

The effectiveness of a weighted blanket intervention and structured work boxes for improving engagement for a child with autism during math circle time in a general education kindergarten classroom were evaluated relative to baseline using an alternating treatments design. The structured work boxes resulted in higher levels of engagement, and the weighted blanket resulted in levels that were similar to or lower than baseline. Additional research is needed on sensory-based interventions; in the meantime, teachers should use evidence-based practices. [ABSTRACT FROM AUTHOR]

Data analysis inherently requires problem solving, yet it is the most understudied mathematical skill for individuals with extensive support needs. The current study taught elementary students with extensive support needs (i.e., autism and intellectual disability) to solve math word problems requiring analysis of scaled pictographs through modified schema-based instruction on an iPad. Results of the single-case multiple probe across participants design found a functional relation between the iPad-based math intervention and math problem solving, with a large effect size (Tau-U = .96) confirming visual analysis. In addition, participants were able to generalize problem-solving skills when they were presented with data analysis problems from grade-level social studies textbooks and visual supports were faded. Implications for practice and future research in teaching mathematics to learners with extensive support needs are discussed. [ABSTRACT FROM AUTHOR]

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities and the quality of explicit instruction served as treatment intensity metrics. A total of 465 kindergarten students with mathematics difficulties from 136 intervention groups participated. Results suggested comparable performances between the 2:1 and 5:1 intervention groups on six outcome measures. Observation data indicated that student practice differed by group size. Students in the 5:1 groups received more opportunities to practice with their peers, while students in the 2:1 groups participated in more frequent and higher quality individualized practice opportunities. Implications in terms of delivering Tier 2 interventions in small-group formats and engaging at-risk learners in meaningful practice opportunities are discussed. [ABSTRACT FROM AUTHOR]

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students' explanations of those comparisons, as well as the relation between those measures and scores on a criterion test: released fraction items from the National Assessment of Educational Progress. We also considered the extent to which reasoning and language contribute to the prediction. Results indicated a significant moderate correlation between accuracy and explanation quality. Commonality analyses indicated that explanation quality accounts for little variance in National Assessment of Educational Progress scores beyond what is accounted for by traditional measures of magnitude understanding. Implications for instruction and assessment are discussed. [ABSTRACT FROM AUTHOR]

Recent multiplication with regrouping research shows that the combination of the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) has been effective in several studies. More evidence is needed to demonstrate CRA-SIM's effectiveness across settings and students. Therefore, the purpose of this study was to replicate previous findings in which CRA-SIM led to improved performance of students receiving tertiary interventions. This study extended the research by including problemsolving application in order to align the intervention with current standards for mathematics. Three elementary students receiving tertiary interventions participated in the study. The researchers used a multiple baseline across students design to show a functional relation between CRA-SIM and student performance. In addition to mastery of multiplication with regrouping, students applied their knowledge, discriminating between different operations when solving word problems. The implications and program components that influenced these results will be 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]

IN THIS PAPER WE PRESENT THE IMPORTANCE OF MENTAL CALCULUS IN THE DEVELOPMENT OF CREATIVE THINKING IN PRIMARY SCHOOL STUDENTS. IN THE LAST PART WE PRESENT SOME PROCESSES OF MENTAL CALCULUS WITH MANY EXAMPLES. [ABSTRACT FROM AUTHOR]

Disorders of reading, math, and attention frequently co-occur in children. However, it is not yet clear which cognitive factors contribute to comorbidities among multiple disorders and which uniquely relate to one, especially because they have rarely been studied as a triad. Thus, the present study considers how reading, math, and attention relate to phonological awareness, numerosity, working memory, and processing speed, all implicated as either unique or shared correlates of these disorders. In response to findings that the attributes of all three disorders exist on a continuum rather than representing qualitatively different groups, this study employed a dimensional approach. Furthermore, we used both timed and untimed academic variables in addition to attention and activity level variables. The results supported the role of working memory and phonological awareness in the overlap among reading, math, and attention, with a limited role of processing speed. Numerosity was related to the comorbidity between math and attention. The results from timed variables and activity level were similar to those from untimed and attention variables, although activity level was less strongly related to cognitive and academic/attention variables. These findings have implications for understanding cognitive deficits that contribute to comorbid reading disability, math disability, and/or attention-deficit/hyperactivity disorder. [ABSTRACT FROM AUTHOR]

Abstract The aim of this study is to examine the development of two separable aspects of math anxiety, anxiety about math-related situations and anxiety about failure in math, and their cross-lagged relationship with arithmetic achievement. The mean level of anxiety about math-related situations decreased among second, third, and fourth graders, and the level of anxiety about failure in math declined among third, fourth, and fifth graders. The rank-order of individuals was more stable in arithmetic achievement than in either aspect of math anxiety. Arithmetic achievement predicted later anxiety about failure in math, but neither aspect of math anxiety predicted later achievement. The results underline the importance of paying attention to math anxiety because anxiety about math-related situations seems to be as stable in primary school as it is in secondary school students. It is important to provide sufficient educational support and take into account affective factors related to learning from the beginning of schooling. Highlights • Math anxiety and achievement of primary school students were examined during a year. • Anxiety about math-related situations decreased among second to fourth graders. • Anxiety about failure in math decreased among third to fifth graders. • Arithmetic achievement predicted later anxiety about failure in math. • Neither aspect of math anxiety predicted later achievement. [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]

Many previous studies have investigated developmental differences in numerical processing by manipulating numerical distance and physical size in a number sequence. While it has been theorized that children's maturity level in executive functioning affects their numerical processing, the interaction between numerical processing and executive functioning through development remains unclear. We divided 60 Japanese school children, aged 8-12 years, into three age-related groups (second graders, fourth graders, and sixth graders) and had them perform physical and numerical comparison Stroop tasks. In the physical comparison task, the numerical Stroop effect (i.e., automatic numerical processing) was evident in each group, but, in the numerical comparison task, the numerical distance effect (i.e., intentional numerical processing) was evident in each group. Also, in the numerical comparison task, the size congruity effect (an index of the attentional and inhibitory control mechanisms of executive functioning) was more salient among second graders than among fourth or sixth graders. These results suggest that numerical processing matures and then plateaus just before primary school, while executive functioning continues to develop. Thus, these data provide evidence of a developmental dissociation between numerical processing and executive functioning. [ABSTRACT FROM AUTHOR]

This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model. The system is designed to help average and low‐achieving second graders in mathematics with word‐based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem‐solving procedure into stages and the concentration on the stages that are problematic for students. Specifically, we compared mathematical word problem‐solving performance and computational skills of students who utilized the computer‐assisted system with students who employed general strategy instruction. Participants consisted of 52 second‐grade students randomly assigned to treatment conditions. Students were pretested and posttested with mathematical problem‐solving and computation tests, and repeated measures of their progress with respect to word problem solving were registered. The results showed there was a significant difference between the experimental and control groups in terms of the word problem‐solving progress measure, favouring the experimental group. This confirms that providing students with a computer‐assisted system offered the opportunity to explore all stages of the problem‐solving procedure as one possible way to enhance their problem‐solving skills. Lay Description: What is currently known about the subject matter Problem‐based learning is recognized as an instruction method that positively influence learning outcomes along with higher order thinking skills.The use of computers to implement findings from qualitative research related to problem‐solving teaching strategies can develop reasoning skills in mathematics and problem solving of elementary students with learning difficulties in mathematics.Polya's model helps students to solve mathematical word‐based problems. What the paper adds to this subject This paper suggests that efforts to improve word problem solving should focus on episodes students neglect when solving problems.This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model.This empirical study investigates whether providing students with computer‐based assistance at each stage of the problem‐solving process helps students to overcome their difficulties.This study explores whether students fail to solve the problem because they do not understand the specific relations among the three problem quantities, or in choosing a correct solution strategy, or in carrying out the solution strategy correctly. The implications of study findings for practitioners Combining Polya's model with computer assistance at each solving procedure stage enhances student's capabilities to solve mathematical word‐based problems.Students encountered problems when reviewing their solutions; this signifying that students did not recognize the variants of the problem. [ABSTRACT FROM AUTHOR]

Mathematical and spatial reasoning abilities during childhood predict later success in male-dominated science, technology, engineering, and math (STEM) disciplines, yet relatively little is known about the affective correlates of children's math and spatial performance or gender differences therein. In the present research, we assessed math and spatial anxiety in 394 elementary schoolchildren (ages 6 to 12 years) and investigated their relations to math achievement and spatial reasoning performance, respectively. In addition, we evaluated children's verbal anxiety and reading ability to determine the domain specificity of relations between anxiety and cognitive performance during childhood. At the zero-order level, math, spatial, and verbal anxiety were moderately correlated with one another and with children's performance in the corresponding cognitive domains. Importantly, however, all three forms of anxiety displayed some domain specificity in their relations to cognitive performance. Gender differences in math and spatial anxiety were also domain-specific, with girls reporting significantly greater math and spatial anxiety, but not verbal anxiety, across the age range tested. These results demonstrate that math and spatial anxiety represent unique constructs early in development, exhibiting specificity in their associations with gender and cognitive performance during the first years of formal schooling. [ABSTRACT FROM AUTHOR]

Early childhood trauma increases the risk of academic difficulties. The purpose of this study was to investigate the prevalence of early contact with child protection services (CPS) and to determine whether early exposure to maltreatment investigations was associated with important academic outcomes. The authors focused specifically on standardized test scores (math and reading), grade retention, and special education status in third grade. The sample was diverse and included all children born between 2000 and 2006 and enrolled in Michigan’s public schools (N = 732,838). By the time these students reached third grade, approximately 18% were associated with a formal CPS investigation. In some school districts, more than 50% of third graders were associated with an investigation. African American and poor students were more likely to be investigated for maltreatment. Children associated with maltreatment investigations scored significantly lower on standardized math and reading tests, were more likely to be identified as needing special education, and were more likely to be held back at least one grade. These findings indicate that involvement with CPS is not an infrequent event in the lives of young children and that within some school districts, maltreatment investigations are the norm. Child welfare and educational systems must collaborate so that the early academic struggles experienced by victims of maltreatment do not mature into more complicated difficulties later in life. [ABSTRACT FROM AUTHOR]

Abstract: The long‐standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10–11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking. [ABSTRACT FROM AUTHOR]

Integrated Science, Technology, Engineering and Mathematics (STEM) education is an emerging approach to improve students’ achievement and interest in STEM disciplines. However, the implementation of integrated STEM education depends strongly on teachers’ competence, which entails, among others, teachers’ attitudes. Nonetheless, not much is known about the factors that influence teachers’ attitudes toward teaching integrated STEM. Therefore this paper uses a survey method to get insight into the relationship between three groups of variables and teachers’ attitudes toward teaching integrated STEM: teacher background characteristics, personal attitudes and school context variables. The results of the multiple regression analyses reveal three variables that are positively linked with teachers’ attitudes: professional development, personal relevance of science and social context. Moreover two variables show a negative correlation: having more than 20 years of teaching experience and experience in mathematics. The results of this study provide valuable information about factors related to teachers’ attitudes toward teaching integrated STEM. Moreover, these results can be deployed by school administrators to guide them when implementing integrated STEM education in their school. [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]

Accumulating research has established explicit mathematics instruction as an evidence-based teaching practice. This study utilized observation data from a multi-year efficacy trial to examine the longitudinal effects of a core kindergarten mathematics program on the use of explicit mathematics instruction among two distinct groups of teachers: one group that used standard practices in Year 1 of the efficacy trial and the core program in Year 2, and a second group that used the core program in both years. Targeted teaching practices consisted of teacher models, student practice opportunities, and teacher-provided academic feedback. Implementation of the program in Year 2 was found to increase the mean rates of teaching practices of teachers who used standard teaching practices in Year 1. Effect sizes are also suggestive of a positive impact of a second year of implementation with the core program. Implications for designing explicit mathematics programs and investigating evidence-based practices in future research are discussed. [ABSTRACT FROM AUTHOR]

Is the development of number line estimation (NLE) similar across regions? Data from Canada (Quebec, n = 67, M age = 7.9 years; Manitoba, n = 177, M age = 7.8 years), Chile (n = 81, M age = 7.9 years), and Northern Ireland (n = 171, M age = 7.3 years) were analyzed. Twice, approximately one year apart, students completed a 0–1000 NLE task and other mathematical tasks. Using latent profile analysis, students' estimates were classified as belonging to either a uniform or variable profile. At Time 1, estimation accuracy differed across regions, but at Time 2, patterns of performance were similar. Regional variations in improvements were related to curricular demands. Moreover, mini meta-analyses of the associations between NLE and other mathematical tasks revealed medium effect sizes. Overall, the NLE task can provide insights into concurrent and longitudinal mathematics achievement, but educational experiences should be considered when comparing performance across regions. • We examined number line estimation (NLE) development for students in four regions. • Latent profile analysis of error patterns revealed a uniform and variable profile. • Development and performance were closely tied to students' educational experiences. • Mini meta-analyses revealed medium effect sizes between NLE and other math skills. • The number line task is a useful tool for comparisons across diverse groups. [ABSTRACT FROM AUTHOR]

Most research on this topic has focused on examining parent and teacher judgments separately. Therefore, information about the relationship between parent and teacher judgments and children's cognitive competence is relatively sparse. To bridge this research gap, this study aimed to examine the relationships between both parent and teacher judgments and children's mathematics and reading competencies. The present study used data from the Starting Cohort 2 of the German National Educational Panel Study, which primarily collected data on children, but also collected data on parents and educators. The results of multilevel regression models confirmed the significant contribution of both parent and teacher judgments in explaining the variance in mathematics and reading competencies. More importantly, the results indicated that the combined contribution of parent and teacher judgments to children's competencies is more meaningful than their independent judgments. This result highlights the role of family-school partnerships in promoting children's educational success. • Parent and teacher judgments correlate with children's mathematics and reading competencies. • The magnitudes of correlations are relatively similar across competence domains. • Combined parent and teacher judgments explain more variance than their independent judgments. • Parents and teachers have concordant judgments about mathematics and reading. [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]

The study examines associations between school-based teacher hiring and achievement inequality in mathematics and science. Using a nationally representative sample of 295,416 students from 34 OECD member countries who participated in the Program for International Student Assessment (PISA) 2012, the study finds that school-based hiring is associated with a larger gap in the distribution of teacher quality between advantaged and disadvantaged schools. This study also finds an association between school-based hiring and inequality of achievement based on socioeconomic status. This suggests that school-based hiring may contribute to exacerbating inequality in learning opportunities and increasing family background’s positive effect on achievement. [ABSTRACT FROM AUTHOR]