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This study assessed the effectiveness of a program aimed at improving the early numeracy skills of students with moderate intellectual disability. The persistence of the acquired skills and the program's impact on learning were monitored. Feedback from the students and their mothers was also gathered. Using a multiple-probe design across subjects, the results were visually presented through graphical analysis. Three male students aged 8–9 years participated. After obtaining high-reliability findings from reliability analyses, results showed the program effectively increased students' number skills with a high effect size. These skills persisted post-intervention, and both students and mothers expressed positive views of the intervention. [ABSTRACT FROM AUTHOR]

Teachers are key users of classroom assessment data; however, their needs and preferences are often overlooked in the design and development of the assessments themselves. We used principles of Human-Centered Design (HCD) to systematically solicit, study, and integrate teachers' needs in the design and development of a classroom-based early mathematics assessment. We recruited 18 teachers to participate in a series of research activities that align with HCD methodology. Data informed the articulation of the use case and test specifications, thereby elevating teachers' voices to improve test-development decisions that consider the end users from the start. [ABSTRACT FROM AUTHOR]

Background Objective Methods Results and Conclusions Implications A resurgence in teaching coding in primary school classrooms has led to a pedagogical swing towards using physical computing and coding to develop students' use of algorithms, computational thinking, and problem‐solving skills. Two obstacles impede the optimal development of these objectives: the availability of a suitable pedagogy and an instructional sequencing model for primary school teachers to effectively present coding and computational thinking concepts and skills to students in alignment with their developmental stage.This study aims to address both obstacles by introducing the 3C Model, a newly developed instructional sequence grounded in established pedagogies and designed to effectively teach coding and computational thinking skills to primary school students based on their developmental stage.The qualitative study employed two data sources to triangulate findings, using: (1) semi‐structured interviews and thematic analysis to investigate 11 primary school students' perceptions of their learning experiences with the 3C Model, and (2) researcher observations along with reflections of the students' developed and demonstrated learning through the method of knowing‐in‐action, reflection‐in‐action, and reflection‐on‐action.The findings of this study fill a gap in the existing literature by demonstrating that the pedagogical and sequential approach embedded in the 3C Model not only enhanced students' engagement levels but also resulted in improved curriculum learning outcomes. The 3C Model provides teachers with a coherent and age‐appropriate instructional structure. It uses physical computing devices and digital coding platforms to introduce coding concepts, furthering the development of computational thinking skills in primary school students beyond mere procedural and rote learning.The study holds important implications for practical applications, as it addresses an absence in the literature of an established pedagogy and instructional sequencing model for effectively teaching coding and computational thinking concepts and skills to primary school students. Drawing on established pedagogical and developmental learning theories, the 3C Model provides primary school teachers with an engaging, age‐appropriate instructional method that avoids decontextualised teaching and surface‐based learning. Instead, it encourages collaborative student work and contextualised learning, steering away from isolated and generic approaches. [ABSTRACT FROM AUTHOR]

Interest in teachers' moves to classroom discourse has started to increase since how teachers respond to students' thinking influences students' learning. The purpose of this study was to investigate the moves used by one sixth grade mathematics teacher at a public middle school in Turkey to support student reasoning in mathematics instruction and their influence on classroom discourse. Six 80‐min lessons were analyzed with particular attention to how the teacher elicits, responds to, facilitates, and extends student reasoning. The results revealed that teacher moves mainly included low‐potential moves in all categories. The teacher mainly tried to elicit student answers in the lessons and aimed to facilitate their understanding through questioning. He also tended to confirm students' answers and re‐represent their thoughts to the class, occasionally adding further information. However, the results showed that the teacher had a dominant role in classroom interactions. Besides, from time to time, the teacher did not focus on student responses and postpone the student reactions. However, the teacher moves that limit student contribution, such as ignoring students' answers and insisting on their own points of view, reduce the depth of classroom interactions and student understanding. In general, the teacher's ability to support student reasoning and facilitate productive classroom discourse was not sufficient. Practitioner points: Teacher plays a prominent role in classroom interactions.Teacher moves tend to be in low potential as eliciting, responding, facilitating, and extending.The capacity of the teacher to promote meaningful classroom discourse and assist student reasoning is limited. [ABSTRACT FROM AUTHOR]

Two groups of mathematics faculty, one from a four-year college and one from a two-year college, redesigned their respective introductory college mathematics courses following presentation of observational data regarding how faculty had been teaching the courses. This presentation emphasised how infrequently faculty teaching introductory college mathematics employed recommended pedagogical practices. This work was part of a multi-year federal grant project designed to increase the numbers of underrepresented students majoring in STEM disciplines. While the two teams developed very different redesigned course activities, in both instances the primary motivation for initiating the work was the information provided to faculty in a professional development workshop regarding how they had previously been observed teaching the mathematics content and how infrequently they utilised the pedagogical practices recommended by STEM education experts. The paper also highlights faculty resistance to curricular reform and enumerates some ways of addressing this resistance. The paper also discusses why faculty from two-year and four-year institutions resisted working together on course redesign and provides recommendations for future efforts addressing course redesign. [ABSTRACT FROM AUTHOR]

• Preschool teachers use different types of picture books for mathematics instruction. • Most teachers use these books monthly or weekly for mathematics instruction. • General features are rated more important than domain-specific features. • Teachers prefer picture books with basic mathematical content. • Teachers' rating of picture book features is influenced by preschool year taught to. Preschool teachers' selection and use of instructional materials play an important role in their provision of qualitative mathematics instruction. Picture books were recently shown effective for supporting early mathematical competencies. Picture book features further contributed to their effectiveness. The current study aimed to investigate teachers' selection and use of picture books for mathematics instruction with special attention for their evaluation of picture book features. We also analyzed the contribution of teachers' beliefs and children's age to teachers' picture book selection and use. Sixty-six preschool teachers participated in an online interview about (a) their picture book use for (mathematics) instruction and (b) the domain-specific (i.e., numeracy) and general features they rate important when selecting a picture book for mathematics instruction. Teachers also filled in a questionnaire regarding their beliefs about mathematics and learning and teaching mathematics. Results showed that more than 90 % of the teachers used picture books for mathematics instruction. About 40 % used them at least once and maximum four times a week and 6 % used them on a daily basis. When selecting picture books for mathematics instruction, teachers rated general features more important than domain-specific features and features related to basic mathematical content more important than features related to complex mathematical content. Teachers' instruction and scheme and formalism beliefs contributed to their preference for Arabic numerals and comparisons between quantities. Children's age was positively related to teachers' preference for complex mathematical content. The limited focus on mathematical content when selecting and using picture books points to the importance of teacher professional development on the selection and use of picture books for enhancing early mathematical competencies. [ABSTRACT FROM AUTHOR]

Background/Context: Kindergarten mathematics instruction is critical for students' future academic success. The nature and quality of this instruction may vary depending on classroom characteristics. However, little empirical work has examined how mathematics instruction in kindergarten might differ based on classroom performance levels. Purpose, Objective, Research Question, or Focus of Study: This study focuses on whether kindergarten teachers' mathematics instructional practices differ based on reported performance levels of students in the classroom. In particular, we focused on whether mathematics instructional time, as well as the extent to which teachers use traditional versus ambitious mathematics practices, differed based on teaching a higher proportion of children performing below grade level. Research Design: This study used a nationally representative dataset of approximately 2,900 kindergarten teachers from the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11. With these data, the study utilized a model that compared teachers to each other within the same school (i.e., school fixed effects). Conclusions or Recommendations: This study found that mathematics instructional time did not differ based on the proportion of children reported to be below grade level in the classroom. However, how teachers taught mathematics differed: teachers who reported having a greater percentage of students performing below grade level used ambitious practices less frequently. These findings were not moderated by measures of teacher background or teachers' reported expectations of their students. [ABSTRACT FROM AUTHOR]

We examine the effects of a year-long national-scale professional development (PD) program on mathematics instructional quality. In contrast to previous studies examining the effects of this program on instruction by comparing before and after participation or participants and non-participants, we examine whether instructional quality changed during the program. More specifically, we conduct an analysis of 174 video-recorded mathematics lessons given by 52 teachers during their year of participation. Contrary to previous studies, the results demonstrate that the instructional quality did not improve over the course of the PD. We suggest that the explanations for the diverging results concern how, when, and to what extent instructional quality changes in PD programs. Specifically, we discuss how the explanations may illuminate the significance of PD duration for PD effects, and how these effects may be mediated by features concerning the PD content and the scale at which the program is implemented. [ABSTRACT FROM AUTHOR]

The present study examined whether the number of manipulatives used in arithmetic strategy instruction influences learning. First graders were randomly assigned to one of the following conditions for learning a decomposition strategy to solve arithmetic problems: intervention with a single manipulative, intervention with multiple manipulatives, and a business-as-usual control condition. Both intervention conditions produced a greater increase in the use of decomposition for mental calculation than the control condition. The pattern of results across the intervention conditions varied as a function of the outcome examined. In terms of children's mastery of strategy execution with the manipulatives, there was no difference between these conditions. In terms of generalization, children whose instruction involved two complementary manipulatives tended to generalize the base-10 strategy to mental calculation to a greater extent than children whose instruction involved a single manipulative. Most noteworthy was that the findings indicated path-dependent transfer: children who mastered decomposition in the multiple-manipulatives condition were more likely to generalize this knowledge to mental calculation than those who achieved mastery via practice with a single manipulative. The implications of these findings for better understanding the conditions under which manipulatives are likely to affect learning for different outcomes is discussed. [ABSTRACT FROM AUTHOR]

This study explores how elementary and secondary school students solve multiplicative structure problems (multiplication, partitive division, and measurement division). A questionnaire was used with nine problems involving natural numbers and fractions, and the research examined both the level of success of students and the strategies employed for each type of problem (by grade level). The results show a lower level of success in problems with fractions than with natural numbers, with students having difficulty recognizing that the structure of the problems was the same. Algorithms were the most commonly used strategy, but other strategies also emerged, depending on the type of number involved (natural numbers or fractions). [ABSTRACT FROM AUTHOR]

During the past 20 years, numerous studies examining the use of problem posing in mathematics instruction have documented positive outcomes in terms of students' problem-solving skills, creativity, and attitudes and beliefs regarding the study of mathematics. However, despite these promising results, problem posing in mathematics instruction has rarely been studied in the population of students with learning disabilities (LD). This study describes a problem-posing intervention that draws on an existing Conceptual Model–based Problem-Solving program (COMPS, Xin) into the problem posing task. The COMPS-based problem posing intervention is designed to teach word problem posing skills to students with LDs under structured posing situations. The study used a multiple baseline across participants design and found the intervention was effective in improving students' problem solving and posing skills. It provided implications for future research and teaching regarding the use of problem posing interventions in mathematics for students with LDs. [ABSTRACT FROM AUTHOR]

Students with exceptionalities who do not make adequate progress with core instruction in mathematics require more intensive research-based interventions such as explicit instruction or video modeling to address instructional needs. This study examined the effects of combining point-of-view video modeling, explicit instruction, and augmented reality to teach mathematics to students with disabilities. The researchers employed a multiple baseline across skills, single-subject research design to evaluate the effects of the intervention on student performance across four mathematics skills. Two eighth grade students identified as having a disability impacting mathematics, one with autism spectrum disorder and one with a specific learning disability, participated in the study. Visual analysis determined a functional relationship between the dependent and independent variables. Tau-U result for the intervention phase was 1.0 across all four skills for each participant. Participants demonstrated high levels of maintenance, and with one exception, students were able to apply the skills to word problems without additional training. Limitations and implications for future research and practice are discussed. [ABSTRACT FROM AUTHOR]

Inclusive opportunities for students with extensive support needs are a predictor of both in school and post-school outcomes; however, successful inclusion must consider how student learning needs and evidence-based practices are incorporated. Potential exists to align evidence-based instruction for students with extensive support needs utilizing the Multi-tiered System of Support (MTSS) framework for all students within the inclusive math classroom across tier 2 and tier 3. Findings of this single-case, multiple probe, across student research study suggest that embedded instruction is an effective and feasible instructional practice to support specially designed instruction in early numeracy within a tiered support model for students with extensive support needs in the inclusive math classroom. Based upon our findings, we sought to develop a model of practice for specially designed instruction (SDI) within tiered systems of support for students with extensive support needs that educational teams, school administrators, and policymakers can use to design math instruction within inclusive settings. [ABSTRACT FROM AUTHOR]

This systematic review investigates the characteristics of effective mathematics interventions for students with intellectual disabilities (ID) age 5 to 12, focusing on early numeracy, arithmetic, and arithmetical problem solving skills. Twenty studies from 2008–2020 were reviewed: 17 had a single-subject design and three a group-comparison design. The studies included a total of 135 students with ID. Consistent with previous studies, the analysis showed that interventions with systematic and explicit instruction with feedback and the use of manipulatives are effective instructional approaches and strategies for students with ID. This study reveals that effective interventions are well-structured, high intensity learning sequences adapted to the students' achievement level. The intensity of an intervention requires careful consideration of the number of intervention sessions per week and their duration. Further studies should investigate which instructional strategy is most effective for each type of skill and the optimum intensity of interventions. [ABSTRACT FROM AUTHOR]

By examining the effects of a national-scale teacher professional development (PD) program on instructional practices and student mathematics achievement, we contribute to calls for empirical studies investigating the impacts of such programs conducted at scale. The program corresponds well with core critical features of high-quality teacher PD and mathematics instruction identified in the literature, and the results indicate that it has had a small but statistical significant impact on teachers' instructional practices. However, no effect was found for student achievement. These results raise questions as to the importance of the critical features and how programs incorporating all of them affect instructional practices and student achievement. [ABSTRACT FROM AUTHOR]

Several universities are witnessing an increase in students' enrolment in mathematics-intensive programmes over the last decades. This increase has come with the price of high failure rates in foundational mathematics courses, which poses challenges to mathematics teaching and learning in higher education. It is therefore inevitable, for some universities, to transform the teaching and learning of mathematics to more student-centred approaches that engage the students mathematically and enhance their success rates. We approach this transformative effort by investigating students' perception of teaching, feedback, and assessment as a first step in reforming the teaching of a first-year mathematics course at a Norwegian university. The results of both quantitative and qualitative analyses of the data generated using a questionnaire from 107 (80 men) engineering students show that the status quo of teachings offers little support for learning. The teaching is dominated by teacher-led instruction, note-taking, and large pieces of proof which make learning difficult for students during class activities. The results also show that the current structure of the course offers limited formative feedback to students and that the assessment tasks require restructuring to capture students' time and effort. We discuss the implications of these findings and make some recommendations for improvement. [ABSTRACT FROM AUTHOR]

A steward of the discipline was originally defined as an individual to whom "we can entrust the vigor, quality, and integrity of the field", and more specifically, as "someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application" [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper we apply this construct to the context of mathematics and argue that even for those early in their training in mathematics, stewardly practice of mathematics can be introduced and practiced. Postsecondary and tertiary education in mathematics -- for future mathematicians as well as those who will use math at work -- can include curriculum-spanning training, and documented achievement in stewardship. Even before a formal ethical practice standard for mathematics is developed and deployed to help inculcate math students with a "tacit responsibility for the quality and integrity of their own work", higher education can begin to shape student attitudes towards stewardly professional identities. Learning objectives to accomplish this are described, to assist math instructors in facilitating the recognition and acceptance of responsibility for the quality and integrity of their own work and that of colleagues in the practice of mathematics. [ABSTRACT FROM AUTHOR]

Developing both conceptual and procedural knowledge is important for students’ mathematics competence. This study examined whether Grade 9 general education mathematics teachers’ self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders’ algebra achievement after 2.5 years, depending on students’ mathematics difficulty (MD) status. Data for this study were drawn from the High School Longitudinal Study for the years 2009–2010 and 2011–2012 (N = 19,104). Multiple regression analyses indicated that students with MD who participated in Grade 9 mathematics classrooms where teachers self-reported the use of less CFI and more PFI were more positively associated with having higher algebra achievement after 2.5 years. Conversely, students without MD in classrooms where mathematics teachers self-reported the use of more CFI and less PFI were positively associated with having higher algebra achievement after 2.5 years. However, this study’s findings do not suggest that teachers should disregard CFI and provide only PFI when teaching students with MD. Because the data set did not include any variable to discover whether teachers provided sufficient support (i.e., evidence-based practices) for students with MD, who have more constraints in their cognitive skills compared to students without MD, to benefit from CFI, the findings of this study should be interpreted cautiously. Directions for future research and practical implications are discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to examine current mathematics interventions designed for students in kindergarten through eighth grade to determine how often they incorporated the five strands of mathematical proficiency identified by the National Research Council (2001). The five strands are conceptual understanding, procedural knowledge, strategic competence, adaptive reasoning, and productive disposition. A systematic review of the literature resulted in 13 meta‐analyses of that studied a total of 19 unique interventions. The five strands of mathematical proficiency were then compared to each intervention to determine with which strand(s) the intervention aligned. None of the 19 interventions contained all five strands, but interventions could be combined to enhance math proficiency. The strands of mathematics proficiency could provide a framework with which to meaningfully combine intervention components. HIGHLIGHTS: A review of 19 math interventions found that none of them addressed all five strands of proficiency, and it would require combinations of them to do so. The strands of math proficiency could provide a framework for intervention decisions in math. [ABSTRACT FROM AUTHOR]

As teachers are faced with increasing demands to meet the needs of diverse learners, such as the growing number of students with ASD, the need to accommodate each learner and provide opportunities for individualized learning becomes critical. Therefore, the aim of this A-B single-case study was to explore a variety of support strategies (e.g., video modeling, concrete manipulatives, guided practice, self-monitoring checklists, and error correction) to see which aspects of the multicomponent instruction were helpful in improving the fraction problem-solving accuracy for three students with ASD. Our analysis examined patterns in skill improvement and support levels required. All students improved their accuracy of solving fraction problems, although one student required more guidance. Using both quantitative and observational findings, we further examined each student's individual experience with the intervention and discuss future directions and implications. [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]

This study focused on academic and social correlates of collaborator preferences of African American and White sixth-graders in mathematics classrooms in fall and spring. Students' appraisals of emotional risk were examined as a moderator. Nomination procedures identified collaborator preferences, group affiliations, and social centrality; students self-reported engagement and emotional risk; school records provided achievement scores. Results indicated students preferred group affiliates, but not exclusively, as collaborators. Students with greater centrality, achievement, and engagement received more nominations. In the fall, high achievers received more nominations when appraisals of risk were high; whereas, engaged students whose appraisals of risk were low received more nominations. Results are interpreted in relation to coordinating social and academic factors in peer collaboration. [ABSTRACT FROM AUTHOR]

Access to high-quality resources is integral for educators to provide research-aligned mathematics instruction. Identifying the supplemental resources educators use to plan mathematics instruction can inform the ways researchers and organizations disseminate research-based practices. The goal of this study was to identify the frequency in which early childhood educators (i.e., pre-Kindergarten through third grade) reported using various resources to plan for mathematics instruction. Furthermore, we investigated whether differences were observed based on teacher factors (i.e., general or special education, route to certification, years of experience) and locale (i.e., rural, urban, suburban). We retained data from 917 teachers for data analysis. The three most frequently reported resources by educators were colleagues, Teachers Pay Teachers, and Google/Yahoo. The three least frequently reported resources were the typical outlets researchers use to reach teachers: What Works Clearinghouse, Teaching Exceptional Children, and Teaching Children Mathematics. General and special education teachers differed on their self-reported usage of five resources: colleagues, Google/Yahoo, teaching blogs, Teaching Exceptional Children, and the What Works Clearinghouse. Rural educators self-reported that they were less likely than suburban educators to use colleagues or specialists at the district to plan instruction. Implications for future research and practice are discussed. [ABSTRACT FROM AUTHOR]

New understandings and methods have proliferated as technology continues to root itself more deeply in an increasing number of areas within the field of education, causing, naturally, the technology-based tools to find a wider application in assessing students' knowledge and progress. With the resulting rapid development of Web applications, Web 2.0 tools have found a niche in a great many steps of the instruction process and have emerged as an integral part of educational technology. Indeed, those studying to become teachers are, quite naturally, one of the most important factors in ensuring that further improvements in this type of technology will be incorporated in mathematics instruction. Accordingly, this study aims to examine what preservice teachers thought of a class during making up part of their teacher training in which they used Web 2.0 tools (e.g., Plickers, Kahoot, Edmodo, ZipGrade) to design activities and lesson plans that they implemented in real classroom settings, which were then discussed in together as a class. The research is conducted with the case study method and the participants consisted of 24 senior preservice teachers of primary school mathematics education in a state university in Turkey. The study's data were collected using written interview forms and subsequently analyzed using content analysis. At the end of the study, it was found that Web 2.0 tools contribute to professional development, instruction and student-teacher-parent interaction dimensions for teachers; on the other hand, it was revealed that it contributes to affective characteristics, learning and skills dimensions in terms of students. Concerning limitations, preservice teachers stated that the need for the Internet and technological devices in order to use Web 2.0 tools were significant obstacles to their use. Based on the conclusions, it is recommended that future studies investigate the effects of different Web 2.0 tools on different content areas as part of preservice teacher training. [ABSTRACT FROM AUTHOR]

Summary: Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., person‐presentation). However, there are indicators that person‐presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked examples during extended classroom instruction, the current study compared the impact of person‐presentation to strategy labels on students' posttest accuracy and ratings of strategy generalizability. Five algebra teachers and their 168 students used worked examples either presented using fictitious students or with a strategy label during a multiweek unit on equation solving, with teachers randomly assigned to condition. All students compared and discussed the worked examples. In this context, we found no effect of condition on student accuracy at posttest, nor on their ratings of the generalizability of the presented strategies. We discuss why previously found negative effects of person‐presentation may not have extended to this context. [ABSTRACT FROM AUTHOR]

This paper reports changes of the quality of instruction and students' attitudes towards mathematics at one high school during 3 years while teachers participated in a teacher community. The setting for this research was a small-sized high school in South Korea with 154 students and three mathematics teachers. I analyzed the teachers' mathematics classes based on types of interaction, types of questions, and mathematical quality in instruction. Their students' responses for the National Assessment of Educational Achievement study about attitudes towards mathematics were also analyzed. The findings show that this school, over all, improved the mathematical quality and changed the types of questions and the types of interactions towards students' participation in discussing, exploring, and probing mathematical meanings. The students' attitudes towards mathematics became more positive throughout the 3-year period. However, the changes in each teacher's mathematics instruction were different. This study discusses the challenges of having an effective teacher community and researching teachers as learners. [ABSTRACT FROM AUTHOR]

With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching primarily nonacademic skills to students with ASD, this article offers practical tips for implementing a unique and innovative approach to providing mathematics instruction to students with ASD across a variety of instructional contexts. Guidelines to develop and implement the concrete-representational-abstract (CRA) sequencing instruction with video-based instruction (VBI) in teaching mathematics to students with ASD are provided. [ABSTRACT FROM AUTHOR]

Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students' emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts. [ABSTRACT FROM AUTHOR]

Student-centered instruction is featured in reforms that aim to improve excellence and equity in mathematics education. Although research on stereotype threat suggests that student-centered instruction may have differential effects on racial minority students, the relationship between student-centered mathematics instruction and student engagement remains understudied. This study examined the relationship between student-centered mathematics instruction and adolescents' behavioral, cognitive, emotional, and social engagement in mathematics and whether the relationship differed by ethnicity. The authors used a multilevel path analysis with data from 3,883 sixth- to 12th-grade students (52.1% girls, 38.2% eligible for free/reduced lunch, 66.1% Caucasian, 23.8% African American, 7.2% multiracial, and 2.9% Asian American). The results showed that student-centered instruction was positively related to all dimensions of mathematics engagement. However, the positive association between student-centered mathematics instruction and student engagement was weaker for African American students. This study provides empirical evidence for the benefits of student-centered instruction while suggesting differential effects based on students' ethnicity. [ABSTRACT FROM AUTHOR]

Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task before instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The authors systematically contrasted teaching with challenging tasks using a task-first lesson structure with that of a discussion-first lesson structure to three composite classes of first- and second-grade students (n = 73). Subsequent assessments of mathematical performance revealed that the discussion-first lesson structure was somewhat more efficacious in improving fluency performance but both structures similarly improved problem-solving performance. The findings suggest there is more than one way of incorporating challenging tasks into mathematics lessons to produce sizeable learning gains. [ABSTRACT FROM AUTHOR]

Quality of mathematics education has gained significant attention in educational politics and among educators as mathematics advances the foundations of analytical thinking necessary to excel in today's knowledge-based economy. Recent research on instructional quality has focused on students' development of competencies. Competency-based instruction is believed to be an effective approach to instruction as it is closely aligned to educational standards. We use data from the National Assessment Study 2012 in Germany and apply the theory of planned behavior to determine what motivates mathematics teachers (n = 1660) to take a competency-based approach to instruction. Results indicate that competencies outlined in the educational standards are a tangible element of current mathematics instruction. Within the framework of this study, we identified teachers' perceived behavior control as the strongest determinant of taking a competency-based approach to instruction. We conclude that advancement of competency-based instruction depends on teachers' beliefs about their professional resources. [ABSTRACT FROM AUTHOR]

This study sought to determine the effect of a virtual forum, as a mediation strategy, on learning differential calculus content associated with limits and continuity of functions among first-semester computer engineering students in a Venezuelan university. The research was quantitative and used a pretest-posttest quasi-experimental design with an experimental and a control group. An intra-group analysis based on a Student's t-test found that the forum strategy had an effect on the experimental group's learning, while the traditional strategy based on face-to-face activities had no effect on the control group's learning. However, the intra-group analysis found no significant differences between both groups' posttests, suggesting a need to review the way the forum is implemented to improve learning outcomes in mathematics in the future. [ABSTRACT FROM AUTHOR]

Play-based preschool pedagogy usually relies on informal teaching while policy trends and some research call for increased formalisation of the pedagogy. Using Bernstein’s concepts of classification and framing, this article characterises mechanisms that link evaluation of preschool to the push towards the formalisation of teaching in preschool. Moreover, it is suggested how preschool teaching of mathematics can be conceptualised in a way that widens the pedagogical responsibilities of the teachers to include a broader range of social activities than typically expected. These responsibilities concern how teachers are involved in pedagogical situations, if situations are planned and if the mathematics is a pedagogical goal in the situation or instrumental in some other activity. It is argued that a practice built on these principles could both honour well-developed play-based preschool practices and provide a structure for teaching preschool mathematics in which using traditional child-teacher interaction is only one of many options. [ABSTRACT FROM AUTHOR]

The study explores how teachers perceive and go about students’ thinking in connection to particular mathematical content and how they frame the notion of applied mathematics in their own classrooms. Teachers’ narratives are built around two released PISA 2012 mathematics items, the ‘Drip rate’ and ‘Climbing Mount Fuji’ (will be referred to as the Fuji item). Teachers show concordance as to the reasons that could make either of the items difficult for students and are able to provide more examples justifying their reasoning for the ‘Fuji’ item. Suggestions linked to making the items more familiar to the students mostly relate to de-contextualization of the items’ content towards a more formal mathematical record. The teachers agree that students need only basic mathematical knowledge, at a level learned during elementary school, in order to solve these problems. Yet, at the same time, many teachers have difficulty clearly verbalising which procedures students are expected to follow to be able to solve the tasks. Disagreement among the teachers is noticeable when labelling the most difficult part(s) of each of the selected items. Mathematics teachers show openness for learning on how to create math problems we examined in this study, but question the purpose and meaning in incorporating more such problems in their own teaching. [ABSTRACT FROM AUTHOR]

In response to the COVID-19 pandemic, schools transitioned to Emergency Remote Teaching (ERT). In May 2020, as part of an existing study of flipped Algebra instruction, we interviewed eleven Missouri teachers to understand how their instruction changed as they moved to ERT. Drawing on practical rationality, we found the pandemic led to a breach of norms (assigning grades, synchronous meeting times, delivering new content, and students' completion of work). Findings highlight the interconnected nature of norms and reveal differences in teachers' responses to the breach of norms. We found administrative policies, particularly around grading, significantly impact teachers' decisions during ERT. [Display omitted] • District and building policies, or lack thereof, were a significant cause of norm breaches • Grading, meeting synchronously, delivering new content, and students completing work were pre-pandemic norms breached • Breaches to normal grading practices were commonly interconnected with the other norm breaches • Teachers primarily adhered to individual and institutional obligations when making instructional decisions • Differences between flipped and non-flipped teachers' responses concerned preparing content and student access [ABSTRACT FROM AUTHOR]

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b) guided practice, (c) independent practice, and (d) formative assessment. Currently, students are struggling to subtract two- and three-digit numbers requiring regrouping. The co-teacher, Ms. Snyder, suggests that the students need more visuals and concrete examples during instruction.Mrs. Zampelli teaches third grade in a general education classroom. She has support from the special education teacher and a paraeducator who provide consultation and instructional coaching. Of the 18 students in her class, nine have Individual Education Programs. The special education teacher, Mr. Ortiz, provides great suggestions to make learning “hands-on.” However, the concept of fractions and specifically comparing fractions with like numerators or denominators causes problems every year. Both teachers emphasize multiple representations (e.g., fraction cubes, fraction circles, fraction bars, number lines) of the concepts. Students are able to solve problems when working with manipulatives but struggle to solve problems in the abstract. Leading teammates suggest a more structured framework for incorporating manipulatives and representations. [ABSTRACT FROM AUTHOR]

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using ‘induction’, ‘polynomial identities’ nor ‘generating functions’, and will give a proof of the ‘Vandermonde Identity’ using elementary notions of probability. [ABSTRACT FROM AUTHOR]

Purpose: This study examines the content and efficacy of instructional leaders’ expectations and feedback (press) in relation to the improvement of middle school mathematics teachers’ instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in four large urban school districts across the United States. We used transcripts of interview data, surveys, and video recordings of instruction of 271 cases, over 4 years, to determine the content of administrator press, as reported by teachers, and the relationship between the content and change (if any) in instruction. To do so we used qualitative coding of interview transcripts, and ran a series of statistical models to examine the nature of the variance in and impact of administrative press. Findings: Most of the administrators’ press, as reported by teachers, was not targeted toward specific teachers’ mathematics instruction in ways that would likely lead toward improvement in those practices. Rather, the press focused on content-neutral instructional practices or classroom management and organization. Implications for Research and Practice: The instructional leadership practice of administrator observation and feedback is widespread, yet understudied as it relates to changes in teacher practice. Our findings indicate that current policies that mandate principals to spend substantial time in classrooms are unlikely to result in significant improvements in the quality of instruction unless meaningful resources are invested to support administrator learning. [ABSTRACT FROM AUTHOR]

The poor state of mathematics education in South Africa is well documented. Few learners are graduating from the school with high quality passes in mathematics in order to enter university. There has been intervention in mathematics education system in an attempt to improve it. Yet, more than ten years after the first democratic election, South Africa is still grappling with poor performance in mathematics and how to change this situation. Much has been done about this inadequacy. South Africa has developed models to update teacher skills as an attempt to intervene. One of such professional development models is a lesson study. In this study, the researcher employed qualitative case study design to explore mathematics teachers' views on lesson study as a professional development model for improving their instruction. Based on the data collected, lesson study is one of the professional development models that teachers would be happy to enlist in as they (teachers) believe that the lesson study provides opportunity for collaboration hence assisting in the improvement of their mathematics instruction. [ABSTRACT FROM AUTHOR]

In this article, Amanda Jansen, Dawn Berk, and Erin Meikle investigate the impact of mathematics teacher education on teaching practices. In their study they interviewed six first-year teachers who graduated from the same elementary teacher education program and who were oriented toward teaching mathematics conceptually. They observed each teacher teaching two lessons: one on a mathematics topic that was developed in their teacher education program (target topic) and one on a mathematics topic that was not addressed in their program (control topic). Based on their observations, the authors identified four instructional practices for teaching mathematics conceptually that the participants used in their classroom practice and found that these teachers were more likely to enact two of these instructional practices when teaching target topics: use of mathematical language to support students' sense making and use of visual representations. They also found that the teachers enacted two other instructional practices-use of story problems and pressing students for mathematical explanations-in both target and control topic lessons but did so with limitations in control topic lessons. For teacher education to influence teaching, the authors assert, it is important to develop content knowledge for teaching and pedagogical knowledge in tandem with developing beliefs. [ABSTRACT FROM AUTHOR]

Teachers need more clarity about effective teaching practices as they strive to help their low-achieving students understand mathematics. Our study describes the instructional practices used by two teachers who, by value-added metrics, would be considered "highly effective teachers" in classrooms with a majority of students who were English learners. We used quantitative data to select two fifth-grade classrooms where students, on average, made large gains on a mathematics achievement test, and then examined teaching practices and contextual factors present in each classroom. Participants included two teachers from a mid-Atlantic district and their students who were 67% English learners and 68% economically disadvantaged. We found that the use of multiple representations of mathematics concepts, attention to vocabulary building, individual and group checks for understanding and error analysis were prevalent practices in both high gains classrooms. Also, class sizes ranged from 12-19 students. Discussion focuses on whether observed practices are aligned with recommended teaching practices for English learner students. [ABSTRACT FROM AUTHOR]

Research findings support the use of computer-assisted instruction (CAI) as a curriculum supplement for improving math skills, including math fact fluency. There are a number of websites and mobile applications (i.e., apps) designed to build students’ math fact fluency, but the options can become overwhelming. This article provides implementation guidelines to help teachers plan for CAI, including criteria for selecting a program and recommendations for monitoring student progress. In addition, free resources for CAI are discussed. [ABSTRACT FROM AUTHOR]

Background Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims This study evaluated the effect of instruction on a math concept and procedure within the same lesson relative to a comparable amount of instruction on the concept alone. Direct instruction was provided before or after solving problems to evaluate whether the type of instruction interacted with the timing of instruction within a lesson. Sample We worked with 180 second-grade children in the United States. Methods In a randomized experiment, children received a classroom lesson on mathematical equivalence in one of four conditions that varied in instruction type (conceptual or combined conceptual and procedural) and in instruction order (instruction before or after solving problems). Results Children who received two iterations of conceptual instruction had better retention of conceptual and procedural knowledge than children who received both conceptual and procedural instruction in the same lesson. Order of instruction did not impact outcomes. Conclusions Findings suggest that within a single lesson, spending more time on conceptual instruction may be more beneficial than time spent teaching a procedure when the goal is to promote more robust understanding of target concepts and procedures. [ABSTRACT FROM AUTHOR]

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving. [ABSTRACT FROM AUTHOR]

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This study explores the feasibility of algebra instruction for adults with IDD through an experimental curriculum. Ten individuals with IDD participated in a 6-week course framing mathematics concepts within the context of everyday challenges in handling money. The article explores classroom techniques, discusses student strategies, and proposes possible avenues for future research analyzing mathematics instructional design strategies for individuals with IDD. [ABSTRACT FROM AUTHOR]

A common practice in textbooks is to introduce concepts or strategies in association with specific people. This practice aligns with research suggesting that using "real-world" contexts in textbooks increases students' motivation and engagement. However, other research suggests this practice may interfere with transfer by distracting students or leading them to tie new knowledge too closely to the original learning context. The current study investigates the effects on learning and transfer of connecting mathematics strategies to specific people. A total of 180 college students were presented with an example of a problem-solving strategy that was either linked with a specific person (e.g., "Juan's strategy") or presented without a person. Students who saw the example without a person were more likely to correctly transfer the novel strategy to new problems than students who saw the example presented with a person. These findings are the first evidence that using people to present new strategies is harmful for learning and transfer. [ABSTRACT FROM AUTHOR]

It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed. [ABSTRACT FROM AUTHOR]

Because recent initiatives highlight the need to better support preschool-aged children's math and science learning, the present study investigated the impact of professional development in these domains for early childhood educators. Sixty-five educators were randomly assigned to experience 10.5 days (64 hr) of training on math and science or on an alternative topic. Educators' provision of math and science learning opportunities were documented, as were the fall-to-spring math and science learning gains of children (n = 385) enrolled in their classrooms. Professional development significantly impacted provision of science, but not math, learning opportunities. Professional development did not directly impact children's math or science learning, although science learning was indirectly affected via the increase in science learning opportunities. Both math and science learning opportunities were positively associated with children's learning. Results suggest that substantive efforts are necessary to ensure that children have opportunities to learn math and science from a young age. [ABSTRACT FROM AUTHOR]

This paper summarizes results from a math intervention implemented in a high-poverty urban community. Over 7,300 students from kindergarten to 4th grade in 1 low-socioeconomic-status school district participated in the study. Students from 13 different schools (36 different classroom) participated in the treatment. Comparisons were made to purposely selected control-group schools and all other students in the district. The aim of the intervention was to help early elementary-age students living in poverty learn essential math facts and master basic computational skills as a foundation for improving their math ability. The study used a pre-test/post-test quasi-experimental design with control and treatment groups. Achievement for both groups was compared to that of the school district as a whole, with analysis disaggregated by poverty status. The results found positive gains in the treatment group's math achievement at every grade level, transcending differences in socioeconomic status. [ABSTRACT FROM AUTHOR]