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This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit instruction and showed rational number concepts related to fractions and decimals using fraction blocks, number lines, base 10 blocks, and coins. Students learned about unit fractions, fraction magnitude, fraction equivalence, addition of fractions with unlike denominators, equivalent decimals, and notation of fractions as decimals. The researchers used a multiple probe across behaviors design and demonstrated a functional relation between CRA-I and three behaviors: decreased fraction estimation error, accuracy in adding fractions with unlike denominators, and accuracy writing fractions as decimals. [ABSTRACT FROM AUTHOR]

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated instructional sequence featuring concrete, representational, and abstract stages of learning. In contrast, research on representational sequences featuring virtual manipulatives is less robust. Thus, this study evaluated an instructional strategy with virtual manipulatives, static representational drawings, and abstract algorithms to teach multiplication to three U.S. elementary students with mathematics difficulty. A functional relation was established via a single-subject multiple probe design between the treatment and students' accuracy performance. Baseline-corrected Tau estimates confirmed a medium effect size for all three students, while student performance on measures assessing the number of errors committed and the duration of sessions also returned favorable findings. [ABSTRACT FROM AUTHOR]

Background: The existing research on dialogue‐based learning and teaching predominantly highlights its capacity to yield productive educational outcomes, yet it often overlooks the pivotal factor of participation equity, which is fundamental to ensuring the efficacy of dialogic teaching and learning. Objectives: In this study, participation equity refers to a condition in which participation itself and opportunities to participate are fairly distributed among participants and all participants are equally listened to and respected. We designed a technology‐enhanced participatory visual learning analytical approach to promote equitable participation in dialogic collaborative problem solving from four dimensions: participation (i.e., ensuring equal contributions from all participants), opportunity (i.e., promoting equal engagement with others), responsiveness (i.e., encouraging equal attentiveness and responsiveness to others' input), and respect (i.e., cultivating a respectful communication style). Methods: The intervention class of fourth‐grade students (n = 59) interacted with a participatory visual learning analytical tool to reflect on their participation equity and learn productive peer talk moves to address equity issues concerning the four dimensions, while a comparison class (n = 59) only received simple feedback on participation and respect. Results: The results indicated that equal participation rates among group members were insufficient to secure participation equity. The intervention was effective in helping students realize and address equity‐related issues. Intervention students were more equitable regarding responsiveness and participation opportunity than the comparison students. Conclusions: The proposed multidimensional participation equity framework has the potential to deepen the understanding of equity and promote equitable learning interactions. Lay Description: What is currently known: Peer discussion has the potential to bring productive educational gains.Participation equity is essential in productive collaborative discussion.Participation equity currently mainly concerns the equality of participation. What we add: We use technology to help children analyse, visualize and reflect on participation equity.We use technology to teach students how to talk in an equitable approach.We define equity in four dimensions: participation, opportunity, responsiveness and respect. The implications for practitioners: Students should be guided to participate equally and respectfully in a group.Students should also be guided to equally listen to other group members' voices.Students should also be guided to equally address other group members. [ABSTRACT FROM AUTHOR]

This study extends prior research by manipulating both intervention and skill difficulty using a multiple baseline across participants design with changing phases in a virtual tutoring environment. Participants were four U.S. students from third and fifth grades for whom appropriate and challenging instructional targets were selected following diagnostic assessment using curriculum-based measurement. Instructional strategies were selected to align or misalign with those instructional targets. The multiple baseline design was used to determine the functional relationship between the instructional strategies (acquisition or fluency-building) with appropriate and challenging skills. Results suggested that indicated intervention strategies aligned with students' skill proficiency resulted in improvements but that contraindicated intervention strategies that were misaligned with students' skill proficiency did not. Furthermore, most students rated the contraindicated intervention strategies as less acceptable or reported higher levels of math anxiety. [ABSTRACT FROM AUTHOR]

Educational robotics (ER) is a constructivist approach to education that promotes experiential learning through actual activities for teaching and learning science, technology, engineering, and mathematics (STEM) subjects. Empirical findings have indicated that primary school students have limited interest in learning mathematics due to the inability to rationalize real-world applications without practical application. Therefore, this study aims to determine the implications of using ER to evaluate their effect on primary school students' mathematics learning achievement, interest, and attitude. A total of 40 respondents from year five participated in this quasi-experimental study that explored the difference between using ER and PowerPoint hands-on methods as instructional approaches to complement teaching and learning. The findings indicated that ER improved mathematics learning achievement and perceived interest with a high effect size, and students also indicated a positive attitude toward using ER to aid in learning mathematics. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effects of the concrete-representational-abstract–integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The intervention involved explicit use of fraction blocks, coins, base ten blocks, number lines, pictures, and abstract symbols to teach unit fractions, fraction and decimal equivalence, addition of fractions with unlike denominators, and writing fractions as decimals. The researchers demonstrated a functional relation between CRA-I and three different behaviors related to fraction concepts: decreased error in estimating fraction magnitude, addition of unlike fractions, and writing fractions as decimals. The findings show promise in the use of CRA-I for teaching fraction concepts to students with learning disabilities. [ABSTRACT FROM AUTHOR]

State standards include fluent use of standard computational algorithms. However, learning and using them require conceptual understanding of numbers and operations. Previous research using the concrete–representational–abstract (CRA) sequence has been effective in teaching computational algorithms to students at risk of and students with learning disabilities by emphasizing conceptual understanding. However, all the research was face-to-face and few captured the impact of the intervention on students' conceptual understanding. The current study occurred during the COVID-19 pandemic, so researchers modified CRA for remote instruction. This study investigated the effects of modified CRA on the fluency and accuracy of three sixth-grade students with learning disabilities. They also included an assessment of conceptual understanding. The researchers used a multiple probe across participants design, demonstrating a functional relation between CRA and students' fluency and accuracy. Researchers assessed conceptual understanding with informal measures that required application of their conceptual understanding. The results and implications are discussed. [ABSTRACT FROM AUTHOR]

The aim of this study is to determine whether Escape Rooms can be used as an active methodological approach for the purpose of teaching mathematics. The research adapted a quantitative approach via an experimental design. Two different study groups were established, the first of which comprised the control group who were taught using conventional training methods, and the second consisted of the experimental group, who were taught using a novel approach incorporating an Escape Room activity. The participants included 80 students who were all attending secondary school within the Kingdom of Saudi Arabia. The findings revealed how the activity involving the Escape Room led to a significant enhancement in the student's motivation, achievement and autonomy. The conclusion can be drawn that using an Escape Room in mathematics teaching can enhance learning achievement, anxiety, motivation and autonomy, with students' negative attitudes regarding mathematics learning considered as an important variable, particularly with respect to autonomy and motivation. Hence, Escape Rooms can potentially be more effective than conventional methods for teaching mathematics. [ABSTRACT FROM AUTHOR]

High-quality Tier 1 instruction is frequently conceptualized as the "foundation" for other tiers of intervention within multitiered systems of support (MTSS) models. However, the vast majority of Tier 2 intervention studies do not account for Tier 1 variables when examining intervention effectiveness. The purpose of this study was to examine Tier 1 predictors, or "quality indicators," of differential responsiveness to Tier 2 mathematics intervention. Data were drawn from a large-scale data set where all teachers taught the Early Learning in Mathematics (Tier 1) core program across the academic year, and a subset of students were selected for the ROOTS (Tier 2) mathematics intervention. We examined the following Tier 1 variables: (a) classroom-level mathematics gains, (b) Tier 1 fidelity of implementation, (c) Tier 1 classroom management and instructional support, and (d) class size. Response to Tier 2 intervention was not significantly predicted by any of the Tier 1 variables examined; however, the pattern of Hedges' g effect sizes suggested that students with higher quality of Tier 1 instruction tended to benefit less from the Tier 2 ROOTS intervention. Results are discussed in the context of implications for research and practice. [ABSTRACT FROM AUTHOR]

OBJECTIVES: Quantify the relationship between district policy permitting in-person instruction and educational outcomes during the 2020 to 2021 academic year for kindergarten through eighth grade students. METHODS: An ecological, repeated cross-sectional analysis of grade-level proficiency of students enrolled in public school districts in North Carolina (n = 115 school districts) was conducted. Univariate and multivariate analyses were performed to evaluate the association between the proportion of the school year a district spent in-person and 2020 to 2021 end-of-year student proficiency in the district. We then fit a multivariable linear regression model, weighted by district size, and adjusted for district-level 2018 to 2019 proficiency and district-level factors (rural or urban, area deprivation). RESULTS: Compared to 2018 to 2019, there was a 12.1% decrease (95% confidence interval [CI]: 16.8--19.3) in mathematics and an 18.1% decrease (95% CI: 10.8--13.4) in reading proficiency across the state at the end of 2020 to 2021. Compared to a district that remained entirely remote for the 2020 to 2021 school year, a district offering full in-person instruction had 12% (95% CI: 11%--12.9%) and 4.1% (95% CI: 3.5%--4.8%) more students achieve grade-level proficiency in mathematics and reading, respectively. In-person instruction was associated with greater increases in mathematics proficiency than reading, and greater increases in elementary-level students' proficiency than middle school--level. CONCLUSIONS: The proportion of students achieving grade-level proficiency in 2020 to 2021 fell below prepandemic levels at each evaluated time point in the academic year. Increased time spent in-person by a school district was associated with an increased proportion of students achieving grade-level end-of-grade proficiency in both mathematics and reading. [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]

This study used a multiple probe design to evaluate the effects of a teacher-implemented video-schedule intervention on the mathematical skills and untargeted challenging behaviors of five elementary-school students with autism. Results indicated that the intervention was effective in improving participants' academic performance, and a decrease in the level of challenging behaviors and stereotypy was observed for participants following the introduction of intervention. Additionally, academic gains generalized across academic problems and to a small group setting, suggesting that this technology-based intervention is an efficient use of instructional time. Future research targeting a variety of academic skills and examining intervention implementation by additional practitioners (e.g., teaching assistants) is warranted. [ABSTRACT FROM AUTHOR]

Fraction competence is essential for learning algebra and pursuing careers in science, technology, engineering, and mathematics. However, many children have difficulty using fractions, especially those struggling with mathematics. In this study, we examined the effect of a Tier 2 multicomponent fraction intervention for fifth graders, using a multiple-probe design across groups. The intervention included multiple instructional components: (a) explicit instruction; (b) multiple representations; (c) addressing misconceptions; (d) flexibility, reversibility, and generalizations; and (e) self-graphing. The intervention addressed fraction concepts and skills that need to be taught at Grade Levels 3 to 5 based on the Common Core State Standards for Mathematics content standards. The researcher provided the intervention in an intervention classroom at a U.S. charter school three times a week. The total session length ranged from 885 to 906 min across the groups. The results of this study indicated a functional relation between the fraction intervention, and all six students' percentages of correct answers obtained using fraction probes. The results from the fidelity of intervention and assessment and social validity during the intervention were also reported. Limitations and suggestions for future research and implications for practices are discussed. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

Tingir et al. (2017) concluded from their meta‐analysis that the subject areas taught through mobile devices had significantly higher achievement scores (d = 0.48) than the ones taught with traditional teaching methods. Given the relatively high positive effect of mobile devices on student achievement, we carefully analysed the selected research in this meta‐analysis. We reviewed Tingir et al.'s (2017) meta‐analysis based on analysis of the methodology of the selected research, while drawing on the work of Slavin (2003), Cheung and Slavin (2016), and Sung et al. (2019). Twelve of the 14 (86%) studies included in the meta‐analysis done by Tingir and his team (2017) present such major methodological flaws that they should not have been included. Our analysis leads us to believe that the conclusion of Tingir et al. (2017) is not justified. It is recognized that duration of experiment is negatively correlated with effect size: the shorter the duration, the higher the effect (Burston, 2015; Slavin & Lake, 2009). Although demanding more effort, the field of education must raise the bar if it is to have knowledge of acceptable value. Lay Description: What is already known about this topic?: Tingir et al. (2017) concluded from their meta‐analysis that: "the subject areas taught through mobile devices had significantly higher achievement scores than the ones taught with traditional teaching methods" (p. 366). What this paper adds?: We therefore reviewed the meta‐analysis by Tingir et al. (2017) and the underlying research. Our analysis leads us to believe that the conclusion of Tingir et al. (2017) is not justified.The data on reading used in the meta‐analysis by Tingir et al. (2017) do not make it possible to calculate a legitimate effect size for reading or to make a judgment about the effectiveness of mobile devices in the classroom.With respect to mathematics, the weakness and biases of the studies selected in the meta‐analysis by Tingir et al. (2017) should not have allowed them to calculate an effect size and do not provide a clear answer on the effectiveness of mobiles devices in the classroom.The studies in science selected by Tingir et al. (2017) demonstrate a set of methodological flaws that cannot provide a sound basis for determining a convincing effect of mobile device in the classroom on student achievement. Implications for practice and/or policy: Tingir and associates (2017) calculated an overall mean effect of 0.48 for mobiles devices on student achievement by combining research in reading (effect = 0.666; N = 3), mathematics (effect = 0.16; N = 3) and science (effect = 0.528; N = 8). The authors did not do a school‐level analysis (elementary, high school) in their school subject groupings due to the small number of studies, particularly in reading and mathematics.Twelve of the 14 (86%) studies included in the meta‐analysis done by Tingir and his team (2017) present such major methodological flaws that they should not have been included. As mentioned in the introduction, Slavin and his colleagues found different results in a related field. Slavin et al. (2009) found an effect size of 0.11 for the use of technology in the classroom, in computer‐assisted and computer‐based instruction, and an effect size of 0.05 for the use of digital tools 10 years later (Slavin, 2019). Given all the above, it is our opinion that the meta‐analysis by Tingir et al. (2017) cannot be used to justify the use of mobile devices in the classroom. [ABSTRACT FROM AUTHOR]

Data suggest students are not meeting grade-level expectations in mathematics. If high-quality instruction is not provided, the inequitable outcomes observed in schools will be maintained. The goal of this study was to identify the frequency in which rural special education teachers (SETs) serving students in prekindergarten through third grade self-report using practices during mathematics instruction. A secondary focus was to investigate whether rural SETs differed in their reported use of practices compared with (a) suburban and urban SETs and (b) rural general education teachers. Data from 901 teachers serving students in prekindergarten through third grade were retained. Of this sample, 150 teachers identified as SETs in rural (n = 55), suburban (n = 50), and urban (n = 45) schools. Results suggest teachers reported using research-based and unsubstantiated practices frequently. Rural SETs reported using research-based and unsubstantiated practices with similar frequency to urban SETs. Suburban SETs reported using explicit instruction more frequently than rural SETs. [ABSTRACT FROM AUTHOR]

Introduction: Developing graphicacy skills is important for students with visual impairments if they are to succeed in science, technology, engineering, and mathematics (STEM) content. Teachers of students with visual impairments report that they lack resources to use in teaching students graphicacy skills. Methods: Forty-one students with visual impairments in grades 5–10 completed a pretest, intervention, and posttest designed to evaluate their skills locating and interpreting graphical data. Videos of the pre- and posttests were scored using a researcher developed instrument. Results: Following intervention, there was a significant difference in students' ability to use descriptors and mathematical terms when exploring graphs and a map. Students answered significantly more questions correctly from pre- to posttest. Discussion: Students who receive direct instruction in how to locate and interpret data in graphs and maps can improve their level of independence in STEM classes. Use of an intervention that targets the development of graphicacy skills has been found to be effective. Implications for practitioners: More research is needed to determine effective hand strategies students should use when exploring different types of graphics. [ABSTRACT FROM AUTHOR]

Learning to compute with fractions is a major challenge for many students and especially for students with disabilities (SWD). Phase 1 of this study employed a randomized pretest–posttest comparison design to test the effects of two versions of formative assessment combined with an instructional program called Fractions at Work. In one condition, teachers used technology-assisted prompts to assess student performance and remediate errors. In the comparison condition, teachers gave students the same items for assessing progress but used their own methods of reteaching. Results indicated no difference between the two methods. However, pretest-to-posttest gain scores were significantly higher on all three measures regardless of type of formative assessment, and students maintained much of what they had learned. Phase 2 examined issues related to instructional dosage. Students who received additional weeks of instruction scored significantly higher than students who went back to their business-as-usual curriculum. [ABSTRACT FROM AUTHOR]

With facilitation of advanced technologies, design and application of smart become promising research issues in education. Although it is potential for students to learn geometric in authentic contexts, there were still lack of studies addressing smart learning issue in authentic context for geometry. This study aim to propose an app, called SmartUG, to support students smartly to consolidate geometry understanding and learning through enriching experience of exploring and applying related geometry surrounding. There were four smart mechanisms proposed in SmartUG (direction guidance, learning progress, object recognition and answer feedback) to guide students' measuring and applying geometry smartly and meaningfully in authentic contexts. A total of 83 fifth‐grade students participated in this experiment and were divided into three groups, an experimental group that learned with smart mechanisms, a control group that learned without smart mechanisms and a traditional control group that learning with traditional teaching approach. Basically, experimental group outperformed control group and traditional teaching group in term of geometry ability and estimation ability, which means students benefited from proposed SmartUG. Moreover, students showed positive attitude and high intention to use toward SmartUG. Students should be provided more chances to learn geometry smartly in authentic contexts with SmartUG. It is potential to future studies to implement more smart mechanisms to support students learning in authentic contexts. Moreover, the learning system can get smarter and smarter when the learning system gets more and more input data from students' use. Lay Description: What is already known about this topic: Geometry is important and strongly related to our surroundings.Students have few chances to learn Geometry through practicing in authentic contexts.Innovative technologies are potential to be utilized to facilitate smart learning. What this paper adds: Proposed a framework of smart mechanisms to support learning Geometry in authentic context.Utilized innovative technologies to facilitate smart learning in authentic context. Implications for practice and/or policy: Smart learning in authentic context helped improving students' motivation and achievements.The proposed smart mechanisms are effective to support smart learning.The smart mechanisms can be implemented not only for Geometry but also other subjects. [ABSTRACT FROM AUTHOR]

The present study explores the effect of two instructional methods for children with different levels of mathematical skills. One of these methods uses a conventional approach to learning multiplication and emphasizes the memorization of all arithmetic facts, whereas the other method is based on psychological principles and combines: a) the memorization of a small subset of problems aided by color cues and a portable time-table, with b) the use of single-step rules. One hundred and sixty second-grade children (aged 7-8) received instruction in one of these approaches – either the conventional method or the memory and rules method (M&R) – over the course of 6 months as part of their normal school education. Moderation analysis revealed that children with poor mathematical skills in the conventional group scored significantly better than their counterparts in the M&R group, whereas a significant advantage was observed in the M&R group for those children with strong mathematical skills. [ABSTRACT FROM AUTHOR]

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated risk for severe MD at kindergarten entry and examined whether these students improved from a category of high MD risk (i.e., <10th percentile) to a lower risk of MD (i.e., norm-referenced performance at or above the 10th, 20th, 30th, and 40th percentiles) between the fall and spring of kindergarten. Differential response to the program based on the classroom-level proportion of students with severe MD was also explored. A total of 795 kindergarteners with severe MD from 122 classrooms were included in the analyses. Results suggested students with severe MD in treatment classrooms improved from fall to spring at a greater rate than their control peers. Treatment students also demonstrated higher rates of improvement from below the 10th percentile to a performance at or above the 20th, 30th, and 40th percentiles across the school year. No evidence of differential efficacy of the program by the classroom-level proportion of students with severe MD was found. Implications for using explicit mathematics programs to thwart the onset of severe MD among academically vulnerable students are discussed. [ABSTRACT FROM AUTHOR]

Instructional interactions that occur between teachers and students around foundational mathematics topics are critical for supporting mathematical proficiency among students with mathematics learning disabilities (MLD). This study investigated whether the initial mathematics skill of 880 kindergarten students at risk of MLD predicted the quantity and quality of explicit instructional interactions (i.e., overt teacher modeling, student practice opportunities, and academic feedback) experienced during an empirically validated Tier 2 kindergarten mathematics intervention. It also examined whether the quantity and quality of such instructional interactions predicted gains in student mathematics achievement. Researchers conducted 740 direct observations of 255 intervention groups within a multiyear, randomized controlled trial. Results suggested that intervention groups with lower initial mathematics skill received higher rates of academic feedback and made more frequent errors. In addition, more frequent and higher quality academic feedback and group practice opportunities predicted increased mathematics achievement. Implications for investigating the active ingredients of mathematics interventions are discussed. [ABSTRACT FROM AUTHOR]

The purpose of this study was to determine the effects of an early numeracy Tier 2 intervention on the mathematics performance of second-grade students with persistent mathematics difficulties. Whole number content and instructional design features were used to boost performance in second-grade early numeracy concepts and skills. Researchers employed a pretest-posttest control group design with randomized assignment of 83 students to the treatment condition and 38 students to the comparison condition. The research team's mathematics interventionists delivered instruction four days per week for 20 weeks to small groups of second-grade students who were identified with persistent mathematics difficulties. Proximal and distal measures were used to determine the effects of the intervention. Findings showed that students in the treatment group outperformed students in the comparison group on the proximal measure of mathematics performance. There were no differences between groups on the problem-solving measures. [ABSTRACT FROM AUTHOR]

This investigation examined whether teacher practices, as measured by the Classroom Strategies Assessment System (CSAS), were associated with students' proficiency and gain scores, as measured by the Measure of Academic Progress (MAP), in 13 high-poverty charter schools in New Jersey. Results from two-level hierarchical linear models, fitted to a sample of 2,188 Kindergarteners through eighth-grade students in 110 classrooms, revealed that instructional and behavior management strategies on the CSAS were associated with (a) MAP gains in mathematics but not in reading and (b) MAP Rasch Unit (RIT) (proficiency) scores in mathematics and reading. The relationship between CSAS scores and student achievement did not differ across grade levels. In general, students in classrooms with higher quality use of classroom strategies exhibited higher gains in mathematics and proficiency scores in mathematics and reading. Implications for research and educational practices 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]

BACKGROUND: Despite increased interest in combining learning and physical activity (PA), the academic and PA benefits of active learning are uncertain. METHODS: A systematic search of 5 databases for studies combining learning math with PA in primary/elementary schools was conducted. Academic benefit was evaluated by pre‐post intervention math scores compared to a control group. Effect sizes (ES) were extracted/calculated when possible. Due to study heterogeneity, meta‐analysis was not conducted. RESULTS: Six randomized controlled trials and 5 quasi‐experimental studies evaluating 4082 participants (53% girls; mean age 7.5‐11.1 years) were eligible. Math scores were significantly better in the intervention group in 6 of 11 studies on at least 1 test (ES: 0.42‐4.7; p ≤.03). Other math tests either were not all statistically significant (2 studies) or the benefit varied across grades (1 study). No studies reported a decline in math scores. Of studies measuring PA with accelerometers, 4 of 5 reported significantly greater PA in the intervention group during the intervention (p <.05) or across the school day (p <.01). CONCLUSIONS: Undertaking PA while learning was largely equivocal for math scores but showed promising results for increasing daily PA, without detrimental effects on math performance. The need for more rigorous studies with comprehensive assessment of academic performance and PA is highlighted. [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]

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]

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]

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]

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]

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]

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]

Instructional choice is a low-intensity strategy that can improve academic engagement. In this study, we investigated the effects of within-activity choices offered during math by third-grade teachers to participating students with behavioral and academic needs. We utilized a professional development model to train teachers to implement instructional choice in the classroom while collecting direct observation data on student’s academic engagement. Teachers were able to implement practices with high levels of integrity and collect momentary time sampling data on one student with high levels of reliability. Using a withdrawal design, we found no clear functional relation between instructional choice and increases in student’s academic engagement. However, some students demonstrated an increase in level upon the introduction of the intervention. Both teachers and students rated the intervention goals, procedures, and outcomes as acceptable. Possible reasons for a lack of treatment effect on student academic engagement are discussed. [ABSTRACT FROM AUTHOR]

Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying pre-algebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their traditional literacy medium or an iPad app. Twenty percent of the mathematics problems included graphics such as maps, line graphs, and bar graphs. During each session, teachers of visually impaired students rated the amount of support they provided for students and the student motivation. Results: Students answered more mathematics problems correctly when using the iPad app and, overall, teachers reported that their students were more motivated with the app than with their traditional literacy medium. Students often used the hints provided in the app when they did not solve a problem correctly the first time. Discussion: Visually impaired students and their teachers found the app and graphics to be easy to use and motivating. The built-in Scratch pad was used by almost all students who were print users. Implications for practitioners: The study results contribute to the growing body of knowledge about the potential value of tablet-type devices for use by visually impaired students. [ABSTRACT FROM AUTHOR]

The primary focus of this study was to examine the effects of Shared Story Reading (SSR) during mathematics instruction on the behavioral outcomes of four elementary students with academic difficulty and challenging behaviors. In addition, the study examined the effect of implementing SSR during mathematics instruction on the teacher’s use of opportunities to respond (OTR). A multiple baseline design across participants was implemented to examine the effects of this curricular approach on increasing the teacher’s OTR, increasing student engagement, and reducing disruptive behavior. Results indicated there was an increase in OTR during the SSR lessons and suggest implementing SSR during mathematics instruction was effective for increasing engagement for students with academic difficulty and challenging behaviors. Results were not definitive regarding the effects of SSR decreasing disruptive behavior. [ABSTRACT FROM AUTHOR]

Mathematical reasoning is important in conceptual understanding and problem solving. In current reform-based, discourse-oriented mathematics classrooms, students with learning disabilities (LD) encounter challenges articulating or explaining their reasoning processes. Enlightened by the concept of conversational repair borrowed from the field of linguistics, this study designed an intervention program to facilitate mathematical reasoning of students with LD. Conversational repair, an ability to repair communicative breakdowns or inaccuracies, was designed in an implicit–explicit continuum to elicit self-explanation from students with LD in the context of mathematics word problem solving. Using a multiple-baseline across participants design, the study found that the intervention was effective for improving students’ mathematical reasoning and problem-solving ability measured by their self-explanation and word problem–solving performance. It provided implications for future studies concerning the use of conversational repair in mathematics classroom discourse for individuals with LD. [ABSTRACT FROM AUTHOR]

For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based instruction (SBI) and cognitive strategy instruction (CSI) delivered within an explicit instruction framework can be effective in teaching various math skills related to word problem solving. A multiple-baseline design replicated across groups was used to evaluate the effects of the intervention of bar model drawing on math problem-solving performance of students with MD. Student achievement was measured in terms of increased correct use of cognitive strategies and overall accuracy of math word problem solving. Results showed that bar modeling drawing is an effective strategy for increasing elementary students' accuracy in solving math word problems and their ability to use cognitive strategies to solve the problems. [ABSTRACT FROM AUTHOR]

The Common Core Mathematics Standards have raised expectations for schools and students in the United States. These standards demand much deeper content knowledge from teachers of mathematics and their students. Given the increasingly diverse student population in today’s classrooms and shortage of qualified special education teachers, computer-assisted instruction may provide supplementary support, in conjunction with the core mathematics instruction, for meeting the needs of students with different learning profiles. The purpose of this study was to explore the potential effects of the Please Go Bring Me-Conceptual Model-Based Problem Solving (PGBM-COMPS) intelligent tutor program on enhancing the multiplicative problem-solving skills of students with learning disabilities or difficulties in mathematics. [ABSTRACT FROM AUTHOR]

Researchers are increasingly interested in working memory (WM) training. However, it is unclear whether it strengthens comprehension in young children who are at risk for learning difficulties. We conducted a modest study of whether the training of verbal WM would improve verbal WM and passage listening comprehension and whether training effects differed between two approaches: training with and without strategy instruction. A total of 58 first-grade children were randomly assigned to three groups: WM training with a rehearsal strategy, WM training without strategy instruction, and controls. Each member of the two training groups received a one-to-one, 35-min session of verbal WM training on each of 10 consecutive school days, totaling 5.8 hr. Both training groups improved on trained verbal WM tasks, with the rehearsal group making greater gains. Without correction for multiple group comparisons, the rehearsal group made reliable improvements over controls on an untrained verbal WM task and on passage listening comprehension and listening retell measures. The no-strategy-instruction group outperformed controls on passage listening comprehension. When corrected for multiple contrasts, these group differences disappeared but were associated with moderate to large effect sizes. Findings suggest—however tentatively—that brief but intensive verbal WM training may strengthen the verbal WM and comprehension performance of young children at risk. Necessary caveats and possible implications for theory and future research are discussed. [ABSTRACT FROM AUTHOR]

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In addition, researchers compared the effects of concrete and virtual manipulatives within the treatment package. Results of the multiple probes across participants with an embedded alternating treatments design showed a functional relation between modified schema-based instruction and word problem solving. Two of three participants performed more steps in the virtual condition and one participant had equal performance in both concrete and virtual conditions. When given a choice between conditions upon skill mastery, all three participants preferred the virtual condition and maintained treatment effects. Implications for practice and future research are discussed. [ABSTRACT FROM AUTHOR]

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate ( N = 41, Experiment 1) and fifth- and sixth-grade students ( N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems. [ABSTRACT FROM AUTHOR]

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In addition, the effects of both interventions on students’ fact retrieval performance and generalization performance were also tested. To examine the effects of each intervention, the participants were divided into two groups and the order of the interventions was varied between the two groups. The results showed that, in general, students demonstrated a greater extent of strategy transformation and generalization after receiving the number sense intervention. However, the extensive practice intervention promoted students’ use of retrieval-based strategies to solve basic facts. Findings suggested that both interventions had positive impacts on students with MLD and should be used in tandem. [ABSTRACT FROM AUTHOR]

The RE4MUL8 Project involved the creation of an online/mobile resource for Intermediate Division (Grade 7 and 8) teachers of mathematics. This resource showcases video documentaries of seven key mathematics topic lessons (fractions, integers, proportional reasoning, composite shapes and solids, solving equations, and, patterning and algebraic thinking), as delivered by seven teachers in Ontario, Canada who were nominated by their respective District School Boards as being, or becoming, highly effective practitioners in the area of reform-based mathematics education. As part of a qualitative case study research design, these teachers, often along with their math coordinators, were then interviewed following the lesson, and shared reflections on the lesson itself and, more generally, on their ongoing journey towards reform-based mathematics teaching. This paper reports on three major themes that emerged from these discussions, namely, problem-based learning, the reality and necessity of ‘messy time’ transition to reform-based pedagogy, and, balancing instructional planning and practices. [ABSTRACT FROM PUBLISHER]

Systematically observing instruction for students with learning disabilities (LD) provides information regarding the quality of school-based interventions, allocation of instructional time, and other implementation variables associated with student outcomes. In this synthesis, observation studies of reading and mathematics instruction from 2000 to 2013 were identified through a systematic literature search. The purpose was to understand findings from observations of typical practice for students with LD during an era of increased exposure to evidence-based practices, educational policy reforms, and reports on reading and mathematics designed to influence instruction, and amid a period of increased academic expectations. Eleven studies focusing on academic instruction for students with LD were identified and reviewed. Cognitive strategy instruction, differentiated instruction, and opportunities for independent application (i.e., text reading, problem solving) were reported infrequently across the published observational research. However, findings provide some evidence of improved teacher use of effective instructional practices in several areas compared with earlier observation study syntheses. Implications for practice and areas for future research are discussed. [ABSTRACT FROM AUTHOR]

This study investigated the impact of cognitive strategy instruction (CSI) on mathematical word problem solving of students with mathematics disabilities. A sample of fourth-grade students in a Chinese primary school was divided into a treatment group (75 students) and a comparison group (75 students). The sample consisted of students with mathematics disabilities only, students with both mathematics and reading disabilities, as well as average- and high-achieving students. Results showed that students at all ability levels (except high-achieving students) in the treatment group outperformed significantly their counterparts in the comparison group; the intervention effect was stronger for students with mathematics disabilities only than for those with both mathematics and reading disabilities. The present study indicates that CSI is a contextually and pedagogically appropriate model that has a strong potential to improve mathematical word problem solving. [ABSTRACT FROM AUTHOR]