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This study aims to explore the perceptions of elementary mathematics teachers regarding assessment for learning (AfL). The participants of this study included three elementary mathematics teachers, each with over 5 years of teaching experience at Sukkur IBA community colleges and schools in Sindh, Pakistan. These participants were selected using purposive sampling techniques. A qualitative exploratory case study research approach was used, with data collected through semi-structured interviews and observations. To ensure the trustworthiness of the study, the interview guide and observation checklist were reviewed by experts. The data were analyzed using thematic analysis. The findings of this study revealed that teachers had a limited understanding of the concept of assessment for learning. Based on these results, the study recommends several measures: the initiation of an assessment literacy program, an increase in class time, reducing the number of students per class, using moveable chairs to enhance classroom flexibility, and making amendments to the assessment policy. [ABSTRACT FROM AUTHOR]

Traditionally, learning among young students has taken place within structured, physical classroom settings. However, the emergence of distance learning has introduced a diverse range of learning methods, including online, hybrid, and blended approaches. When the COVID-19 pandemic led to extended delays in in-person instruction, use of educational technologies such as asynchronous videos and online platforms were deployed to deliver mathematics curricula aligned with the Common Core State Standards (CCSS), though best practices for teaching mathematics asynchronously are not well studied. This study focuses on exploring the effectiveness of a math course on proportional reasoning that was co-designed, developed, and deployed in 5th and 6th grade Orange County classrooms. Examining the learning experience design (LXD) paradigm, this research focuses on discerning its influence on (n = 303) children's engagement during their involvement in an online, video-based math course. LXD is implemented by combining evidence-based pedagogical instructional design with human-centered user experience (UX) design. The study utilized a structural equation model to analyze the relationships between learners' user experiences, situational interest, mind-wandering, and online engagement. The results demonstrated significant direct effects between students' situational interest, user experience, and their level of online engagement. Findings also indicate that students' situational interest and mind-wandering significantly mediate the relationship between their user experiences and online engagement. These results have important theoretical and practical implications for researchers, designers, and instructors. By combining evidenced-based pedagogical learning design with human-centered user experience design, LX designers can promote situational interest, reduce mind-wandering, and increase engagement in elementary mathematics courses conducted in asynchronous online settings. [ABSTRACT FROM AUTHOR]

This study aims to explore the perceptions of elementary mathematics teachers regarding assessment for learning (AfL). The participants of this study included three elementary mathematics teachers, each with over 5  years of teaching experience at Sukkur IBA community colleges and schools in Sindh, Pakistan. These participants were selected using purposive sampling techniques. A qualitative exploratory case study research approach was used, with data collected through semi-structured interviews and observations. To ensure the trustworthiness of the study, the interview guide and observation checklist were reviewed by experts. The data were analyzed using thematic analysis. The findings of this study revealed that teachers had a limited understanding of the concept of assessment for learning. Based on these results, the study recommends several measures: the initiation of an assessment literacy program, an increase in class time, reducing the number of students per class, using moveable chairs to enhance classroom flexibility, and making amendments to the assessment policy. [ABSTRACT FROM AUTHOR]

In the United States, teachers are often expected to use student assessment data to inform their instructional decisions. This study explores how teachers' collective reflections on students' mathematical thinking are influenced by the specific contexts of their classroom, school, and current events like the COVID-19 pandemic. The study uses audio recordings of a group of elementary teachers' reflections on student thinking through Cognitive Interview Reports. The results highlight how teachers' reflections on student data are heavily influenced by the shifting contexts of what is important in the world of teaching due to the COVID-19 pandemic. This ultimately shaped what the teachers were able to pay attention to in student data and what they identified as possible in their future practice. [ABSTRACT FROM AUTHOR]

The implementation of the Mother Tongue-Based Multilingual Education (MTB-MLE) policy in the Philippine basic education has gained traction among educators. Skepticism as to its effectiveness is evident especially in mathematics class where English is the universally recognised medium. This study explored how elementary teachers from a rural school in the Philippines appropriate the MTB-MLE policy in a mathematics classroom. Their attitudes toward the policy and the challenges met in the implementation were examined. An instrumental case study was conducted with documentary analysis, non-participant observation, in-depth interview, and focus group discussion as methods of data collection. Five Grades 1–3 teachers served as participants. Results showed that teachers do not fully observe the policy. They code-switch during discussion and do not religiously use the prescribed teaching guide. Fidelity to the policy is only apparent in the presence of authority. Teachers generally have negative attitudes towards the policy which is due to their colonial thinking, perceived complexity, and non-utilitarian view of the local language. Mismatch in the students' language and the language of instruction, lack of equivalent local terms for some mathematics terms, and haphazardly done teaching and learning materials are the challenges that impede teachers' effective implementation of the policy. [ABSTRACT FROM AUTHOR]

Background and Objectives: The purpose of the present study was the pathology of the elementary school math curriculum with emphasis on the main elements of the curriculum of purpose, content, implementation, evaluation and materials Methods: The present study is an applied and quantitative (descriptive survey (and qualitative) interview in terms of purpose and method. Statistical population in both qualitative and quantitative sections includes all teachers of Chaldoran, Shawat cities. And chaiparah in the academic year 2015-2016, in which 260 students were selected in the quantitative section by proportional stratified sampling method, and in the qualitative section, by purposeful sampling, with 20 teachers to theoretical data saturation. The tools used in this study were 46 researcher-made questionnaire based on Likert scale and interview to assess validity of questionnaire and interview validity. The reliability of the questionnaire was determined by Cronbach's alpha coefficient (0.94) and the data were analyzed by SPSS software. Findings: The results showed that the program Elementary National Mathematics Curriculum has various disadvantages in each of the five components of purpose, content, implementation, evaluation and materials and resources. Conclusion:: Although the educational system has tried to make a difference in the curriculum But this change, despite the centralized education system, the inadequacy of goals, the bulk of the content, the failure to properly implement and evaluate, and the inadequate provision of schools with tools Ray first period of mathematics education based on problem solving model has not been successful. [ABSTRACT FROM AUTHOR]

In this study, we examine two U.S. elementary teachers' use of worked examples, representations, and deep questions in elementary mathematics lessons both before and after a project intervention designed to promote teaching improvement. This intervention was guided by a cognitive construct containing these three aspects, which were demonstrated via cross-cultural video lessons of both U.S. and Chinese teachers. We specifically analyze two teachers (Ann and Bea) who taught first-grade lessons on the topic of inverse relations. Although their lessons were rated similarly in year 1, the rating of their lessons in year 4, post-intervention, demonstrated different patterns of change. While Ann's use of worked examples and representations underwent no significant improvement, Bea spent more time unpacking a single worked example with a representational sequence fading from concrete to abstract (also called "concreteness fading"). Neither teacher showed improvement in asking deep questions. An analysis of the teachers' responses to the project intervention revealed that their video noticing skills and personal takeaways were related to the areas of teaching where they improved. Other factors such as teachers' prior knowledge, beliefs, and textbook resources, also played a role in teaching changes. These findings shed light on a recent endeavor called the "science of improvement" in mathematics teaching, which seeks to document teaching changes and the underlying mechanisms that might induce these changes. Implications for both research and practice are discussed. [ABSTRACT FROM AUTHOR]

The aim of this study is to determine the mistakes and misconceptions experienced by the teachers on the basis of the definitions and examples of geometry subjects in the error and misconception detection test prepared for elementary school mathematics teachers in secondary school geometry subjects. Errors and misconceptions experienced by teachers will open the door to mistakes and misconceptions that students will experience during the lesson. For this reason, by identifying the errors and misconceptions experienced by primary school mathematics teachers in geometry subjects, producing solutions will ensure the prevention of misconceptions. The study group of the research consists of 20 primary school mathematics teachers working in secondary schools in the center of Kars in the 2021-2022 academic year. Since the teachers who could be reached while forming the study group were included in the research, the appropriate sampling method was used. In the research, the "Error and Misconception Identification Test", which was developed by the researcher and determined by taking expert opinion, was applied. In the results of the research, it was determined that primary school mathematics teachers mostly experienced errors and misconceptions about basic geometric concepts, quadrilaterals and prisms. It was determined that the teachers did not experience the misconception that they only made mistakes in some questions. [ABSTRACT FROM AUTHOR]

Curricula enhanced through the use of digital games can benefit students in their interest and learning of Science, Technology, Engineering, and Mathematics (STEM) concepts. Elementary teachers' likelihood to embrace and use game-enhanced instructional approaches with integrity in mathematics has not been extensively studied. In this study, a sequential mixed methods design was employed to investigate the feasibility of a game-enhanced supplemental fraction curriculum in elementary classrooms, including how teachers implemented the curriculum, their perspectives and experiences as they used it, and their students' resulting fraction learning and STEM interest. Teachers implemented the supplemental curriculum with varying adherence but had common experiences throughout their implementation. Teachers expressed experiences related to (1) time, (2) curriculum being too different, and (3) too difficult for students. Their strategies to handle those phenomena varied. Teachers that demonstrated higher adherence to the game-enhanced supplemental fraction curriculum had students that displayed higher STEM interest and fraction learning. While this study helps to better understand elementary teachers' experiences with game-enhanced mathematics curricula, implications for further research and program development are also discussed. [ABSTRACT FROM AUTHOR]

The U.S. Nation's Report Card reveals that lower performing students exhibited greater achievement decline than their average/high performing peers based on 2022 long-term trend mathematics assessments for age 9 students. Technology, including computer-assisted instruction, plays an important role in today's dynamic learning environments. Currently, there is a lack of computer-assisted intervention programs that systematically teach generalized word problem-solving skills that are driven by mathematical models. Model-based problem solving (MBPS) is one of the essential emphases in the Common Core mathematical practice standards. This study investigated the effects of a web-based computer tutor, MBPS, on enhancing word problem-solving performance of elementary students who are struggling in mathematics. The MBPS tutor incorporates best practices that are identified by the Institute of Educational Sciences' (IES) latest practice guide, including providing systematic instruction, visual and verbal supports, and teaching of precise mathematical language. Findings indicate that the MBPS tutor boosted participants' performance above and beyond the business-as-usual comparison group. [ABSTRACT FROM AUTHOR]

The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessions of kindergarten students' (N = 36) mathematical and programming activities. Students worked in small groups (4–5 students) with robot coding toys on the floor in their classrooms, solving tasks that involved programming these toys to move to various locations on a grid. Drawing on a semiotic mediation perspective, we analyzed video data to identify the mathematics concepts and skills students demonstrated and the overlapping mathematics-programming knowledge exhibited by the students during these programming tasks. We found that kindergarten children used spatial, measurement, and number knowledge, and the design of the tasks, affordances of the robots, and types of programming knowledge influenced how the students engaged with mathematics. The paper concludes with a discussion about the intersections of mathematics and programming knowledge in early childhood, and how programming robot toys elicited opportunities for students to engage with mathematics in dynamic and interconnected ways, thus creating an entry point to reassert mathematics beyond the traditional school content and curriculum. [ABSTRACT FROM AUTHOR]

Elementary students demonstrate conflicts when measuring with rulers as well as measuring with discrete units. Their conflicts often lie in their focus on counting tick marks or focusing on the endpoint of objects on rulers or ignoring spaces with discrete units. In this study, we also investigated another area of conflict: students' conceptions on where measurements should start on a ruler. Across two time points, 32 first graders and 37 third graders responded to a series of measurement tasks in the form of incorrect worked examples meant to expose students to these common conflicts of where the measurement starts and how to determine the overall length. Although students often said the objects should start at one, they were more likely to indicate that the object should be aligned with zero the closer the object was positioned to zero. However, many students said starting at the edge of the ruler (before zero) was okay, effectively equating the edge with either zero or one. Interestingly, on two related worked examples, their continuous and discrete measurements were not associated with each other. The incorrect worked examples helped illustrate important areas for further instruction, especially around their conceptions of rulers' edges and the impact of spaces with discrete units. [ABSTRACT FROM AUTHOR]

Diagnosing students' mistakes in solving word problems using Newman's Error Analysis (NEA) is time-consuming. To address this limitation, NEA was incorporated in the Cognitive Diagnostic Assessment (CDA) with Ordered Multiple Choice (OMC) word problem testlets developed in this study for assessing students' attribute mastery level in solving word problems involving 'Time'. The assessment instrument was developed based on the principled assessment design which comprised four building blocks: (i) construct map, (ii) item design, (iii) outcome space, and (iv) measurement model. The construct map was adapted from NEA for guiding the development of the assessment instrument. The assessment instrument was administered to a sample of 90 Year Four students in three elementary schools. The results indicated that the instrument showed appropriate difficulty level and discrimination power, satisfactory model-data fit, and high reliability. Thus, the CDA with OMC word problem testlets developed could be a valuable instrument for pinpointing students' mistakes and their mastery level of word-problem-solving attributes involving 'Time'. [ABSTRACT FROM AUTHOR]

Digital game-based learning builds on the general characteristics of games. The incentive system (points, scores, stars, levels, and performance feedback) integrates design elements to keep a learner engaged. In the work described here, we investigated which elements of the incentive system design—rewards, penalties, or feedback—have the potential to trigger students' motivation to play the game. We used eye tracking of eight primary school children, aged 8–11 years, as they interacted with the incentive system of a mathematics game-based item and its specific design, followed by a semi-structured interview. Eye-tracking results show that students paid minimal visual attention to the incentive system during the game, regardless of their level of performance in the game or their age group. The feedback at the end of the game attracted more of their visual attention and provided a good opportunity to inform them about their performance. The semi-structured interviews revealed a high level of self-reported excitement about playing the game, mainly related to the design of the incentive system. Elements of the incentive system triggered students' wish for student-to-student competition, which has been shown in the literature on traditional tangible rewards to stifle intrinsic motivation under certain conditions. The results of this study show that the design of the incentive system has the potential to promote extrinsic motivation with the game through rewards and penalties, and open the reflection on its possible spillover effect on intrinsic motivation in digital game-based learning. [ABSTRACT FROM AUTHOR]

This study analyzed the effect of online flipped learning model (OFLM) on university students' online learning environment engagement. In addition, students' views about experiences in flipped teaching implementation were examined. The participants consisted of 34 students who were in the 2nd year of a primary school mathematics teaching program at a state university in Türkiye and who enrolled in the Approaches to Learning and Teaching Mathematics course taught online during the COVID-19 pandemic period. Quantitative and qualitative methods were simultaneously used to capture a holistic perspective. The quantitative data were obtained from the student engagement scale, and the qualitative data from the reflective diaries written by the students. The results revealed that OFLM had a positive and significant effect on students' learning environment engagement when compared before and after the implementation process. Considering the factors of engagement scale, a significant increase was identified across the students' behavioral and emotional engagement. However, no significant increase was noted across their cognitive engagement. The positive effect of OFLM on students' engagement was also observed in reflective diaries written by the students during the implementation process. In this regard, the majority of the students reported that OFLM provided effective and active teaching, they had a lot of fun during the process, and their interest increased in the lesson. The qualitative results confirmed those of quantitative and revealed the reasons for the significant increase in students' engagement. The results of the present study yield strong evidence for the flipped learning to improve student engagement. This study harmonizes that flipped learning can be applied effectively in online education, and thus increasing students' learning environment engagement. [ABSTRACT FROM AUTHOR]

Educators must balance the needs of students who start the school year behind grade level with their obligation to teach grade-appropriate content to all students. Educational software could help educators strike this balance by targeting content to students' differing levels of mastery. Using a regression discontinuity design and detailed software log and administrative data, we compare two versions of an online mathematics program used by students in three education agencies. We find that although students assigned the modified curriculum did progress through content objectives more quickly than students assigned the default curriculum, they did not perform better on pre- and post-objective quizzes embedded in the software, and most never progressed far enough to reach the grade-level content. Furthermore, there was no statistically significant effect of the modified curriculum on formative test scores. These findings suggest policymakers and practitioners should exercise caution when assigning exclusively remedial content to students who start the school year behind grade level, even though this is a common feature of many math educational software programs. [ABSTRACT FROM AUTHOR]

This study aims to explore teacher noticing differences of the sampled US and Chinese elementary teachers from cross-cultural mathematics videos. A total of 34 expert teachers commented on 25 video clips online. We coded what and how teachers noticed from the videos both quantitatively and qualitatively. Findings reveal teachers' strong interests and profound reflections, especially in the teaching domain including representations, communication, and teacher questioning/guide. Cross-cultural differences in teacher noticing were identified, which were discussed based on possible cultural influences. Implications in research and practice, teacher support, and methodology are discussed. [ABSTRACT FROM AUTHOR]

Mathematics specialists tasked with the responsibility of supporting teacher learning face both the opportunity and the challenge of transforming the organization of the school workplace to support educators' collective, ongoing learning, which is not the norm in most school settings. In this study, we examine a coaching routine called Teacher Time Out (TTO), which was organically developed by a school-based mathematics coach and the teachers with whom she worked. Through the routine, coaches and teachers work through complex, in-the-moment pedagogical decision making while collectively facilitating mathematics discussions among students. The routine thus opens opportunities for educators to learn about ambitious teaching alongside their colleagues. We report findings from an analysis of 360 TTOs that occurred over three years of one coach's work supporting a school-wide, multi-year instructional reform effort in mathematics teaching and learning. We found that the coaching routine fostered teachers' collective inquiry into practice, as they engaged with the unpredictability of teaching during real-time instruction with students. We discuss the potential of this routine to support coaching as a lever for organizational reform, reshaping mathematics teaching across many classrooms. [ABSTRACT FROM AUTHOR]

Teachers' attitudes and beliefs play an important role in their integration of digital games in the classroom thus the transformative potential of game-based learning. In this study, we adapt the Technology Acceptance Model to examine elementary teachers' acceptance of a digital mathematics game and investigate antecedents to their intention to use the game to teach mathematics. The hypothesized extension of Technology Acceptance Model includes redefined factors in the context of game use during mathematics instructions (perceived ease of use, attitude towards game use, perceived usefulness for mathematical learning), a social factor (environmental support), and specified outcome factors depending on orientations (game-driven intention, mathematics-driven intention). Using survey data from 304 elementary teachers in the USA, the findings confirm associations within the adapted model, including direct links from attitudes and environmental support towards intentions to use the digital game and indirect links from perceived ease of use and usefulness. Implications for acceptance theories and teaching practices to use digital games are discussed. [ABSTRACT FROM AUTHOR]

This study aims to reveal the nature of the relationship between elementary school mathematics teachers' TPACK (Technological Pedagogical Content Knowledge) competencies and their use of ICTs.The convergent mixed method was used, and 185 elementary school mathematics teachers participated in the sampling of the quantitative phase of the study. 30 elementary school mathematics teachers voluntarily formed the study group of the qualitative phase. Technological pedagogical content knowledge competencies scale, information, and communication technologies (ICT) competence perception scale for preservice teachers, and semi-structured interview form were used as the data collection tools. The quantitative data obtained from the research were analyzed with arithmetic mean, standard deviation, frequency, percentage, t-test, one-way analysis of variance and Tukey test. The content analysis technique was used in the analysis of the qualitative data, the quantitative data were modeled by applying the SPSS program, and the qualitative data were modeled by using the N-Vivo program. The findings show that elementary school mathematics teachers feel self-competent in TPACK. Similarly, elementary school mathematics teachers were also found to feel efficacious in using their ICT skills. Elementary school mathematics teachers' perceptions of competency in TPACK were found to differ significantly by the variables of gender, computer education status, level of computer knowledge and daily use of the computer. In addition, was determined that elementary school mathematics teachers' efficacy perceptions for the use of ICTs differ significantly by the variables of gender, computer education status, level of computer knowledge, and daily use of the computer. It was further revealed that elementary school mathematics teachers mostly use the computer for tasks related to their lessons and for research purposes. [ABSTRACT FROM AUTHOR]

After researching how elementary teachers address social and emotional learning in their classrooms, a teacher educator and a preservice teacher demonstrate one method for integrating social and emotional learning into a fourth-grade mathematics lesson. [ABSTRACT FROM AUTHOR]

Solving word problems involving 'Time' is an important skill but poor mastery of the skill among elementary students has often been reported in the literature. In addition, the available diagnostic tools in the literature might be less efficient for identifying the various errors made by many students in solving word problems. Thus, an online problem solving Cognitive Diagnostic Assessment (CDA) with Ordered Multiple-Choice (OMC) items was developed as a web application with automated scoring features to increase the efficiency in assessing Grade Five students' mastery level of word problem-solving attributes involving the topic of Time. The online problem-solving CDA with OMC items was developed based on the principled assessment design which comprised four building blocks: (i) construct map, (ii) item design, (iii) outcome space, and (iv) measurement model. Newman's Error Analysis was adapted to specify the construct map required for the development of OMC items. In this article, we documented the empirical evidence regarding item quality, the validity of the cognitive models, the reliability of the instrument, and the diagnostic analysis of students' responses. This study involved 128 Grade Five students in three elementary schools. The results indicated that the instrument showed appropriate difficulty level and discrimination power, satisfactory model-data fit, and high reliability, but most of the students were not at the highest mastery level of the word problem-solving attributes. The findings of the study suggested that the web application could be a valid and reliable diagnostic tool for pinpointing students' errors made in solving word problems. Besides, the findings also highlight the need for intervention to enhance the students' mastery of word problem-solving attributes. [ABSTRACT FROM AUTHOR]

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

This study explores peer feedback in a combined fifth and sixth-grade classroom. Drawing on Hattie and Timperley's (2007) model for feedback, we analyzed 334 peer feedback comments gathered during six mathematics lessons. Our analysis revealed evidence of peer feedback being beneficial to the students who provide it as well as those who receive it. Specifically, we share examples of how peer feedback can support opportunities for providers of feedback to 1) self-regulate by choosing mathematics strategies, 2) make connections between their own mathematical ideas and those of their peers, and 3) engage in ongoing back-and-forth conversations. Findings from our study point to recommendations for teachers to be more purposeful in their prompts to students about the types of feedback they might provide one another. [ABSTRACT FROM AUTHOR]

Multi-tiered System of Supports (MTSS) is a framework in which educators intensify intervention and instructional supports in response to student data. Response to Intervention (RTI), is one of the most prevalent forms of MTSS utilized in schools and is commonly used to identify students with disabilities, including culturally and linguistically diverse learners who are often disproportionately represented in special education. Culturally and linguistically relevant RTI holds promise for promoting equitable outcomes for diverse students, including Dual Language Learners (DLL). A case study design was used to explore the actions and beliefs of an elementary mathematics teacher as she sought to meet the needs of a diverse group of learners. Findings illustrate examples of individual and collective teacher efficacy, understanding student progress, valuing student voice and discourse, believing in her CLD students' ability to succeed, and working towards a larger shared vision at the school. Implications for culturally and linguistically relevant tiered mathematics instruction are discussed. [ABSTRACT FROM AUTHOR]

Popularly used in marketing and business, gamification has been gaining interest in educational contexts for its potential to invigorate otherwise mundane or difficult processes. A gamified environment transfers motivational elements of games to learning activities thereby engaging learners in the learning task thus transforming dull classroom environments to smart ones. This paper presents the design process of a gamification intervention in geometry at elementary level, based upon Huang and Soman (Gamification of education. Research report series: behavioural economics in action, 29. Rothman School of Management, University of Toronto, Toronto, 2013) model. We describe how insights from various sources helped us to refine an intervention previously used in one school. The design focuses on gamifying the tangram, an unplugged resource, through incorporating game-based elements of leader boards, points/stars and challenge levels to motivate young learners individually and in teams. Cognitive and motivational scaffolding undergird five challenge levels to bring affordances to self and social elements for learner participation in increasingly complex geometry tasks. There are limited theoretical models to guide educational researchers, especially ones that do not require digital resources. This paper presents our insights and recommendations to support scaffolded learning in student-centred gamified learning environments. [ABSTRACT FROM AUTHOR]

Popularly used in marketing and business, gamification has been gaining interest in educational contexts for its potential to invigorate otherwise mundane or difficult processes. A gamified environment transfers motivational elements of games to learning activities thereby engaging learners in the learning task thus transforming dull classroom environments to smart ones. This paper presents the design process of a gamification intervention in geometry at elementary level, based upon Huang and Soman (Gamification of education. Research report series: behavioural economics in action, 29. Rothman School of Management, University of Toronto, Toronto, 2013) model. We describe how insights from various sources helped us to refine an intervention previously used in one school. The design focuses on gamifying the tangram, an unplugged resource, through incorporating game-based elements of leader boards, points/stars and challenge levels to motivate young learners individually and in teams. Cognitive and motivational scaffolding undergird five challenge levels to bring affordances to self and social elements for learner participation in increasingly complex geometry tasks. There are limited theoretical models to guide educational researchers, especially ones that do not require digital resources. This paper presents our insights and recommendations to support scaffolded learning in student-centred gamified learning environments. [ABSTRACT FROM AUTHOR]

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors' beliefs associated with teaching philosophies influence both the content that prospective teachers have the opportunity to learn (what) and the nature of the prospective teachers' opportunities to learn (how). Through analytic induction, three assertions were developed to understand and explicate: similarities in opportunities to learn, differences in opportunities to learn, and perceptions about the purpose of the methods courses across the three cases. Specifically, the first assertion examines how all three methods instructors focused on developing conceptual understanding and combating mathematical misconceptions for which prospective teachers most often experience opportunities to learn through representations and approximations. The second and third assertions place more emphasis on differences across the cases based upon observed instructor actions and their beliefs. This study is significant because it helps us gain a deeper understanding about prospective teachers' opportunities to learn within one teacher education program, and therefore, may point toward what can be done in the future to better prepare teachers in elementary mathematics education and the development of ambitious instruction. Additionally, this study unpacks how prospective teachers in the same teacher education program may have varying experiences and thus varied access to opportunities to learn. [ABSTRACT FROM AUTHOR]

Chinese word segmentation is an important research direction in related research on elementary mathematics knowledge extraction. The speed of segmentation directly affects subsequent applications, and the accuracy of segmentation directly affects corresponding research in the next step. In the machine learning methods for extracting basic mathematical knowledge points, the Conditional Random Field (CRF) model implements new word discovery well, and is increasingly used in knowledge extraction of basic mathematics. This article first introduces the traditional CRF process of named entity recognition. Then, an improved algorithm CRF++for conditional field model is proposed. Since the recognition rate of named entities based on traditional machine learning methods is not high, a post-processing method for entity recognition that automatically generates a dictionary is proposed. After identifying mathematical entities, a pruning strategy combining Viterbi algorithm and rules is proposed to achieve a higher recognition rate of elementary mathematical entities. Finally, several methods of disambiguation after entity recognition are introduced. [ABSTRACT FROM AUTHOR]

Black parents are often presumed to be uninvolved in their children's education, especially in mathematics. These stereotypes are arguably sustained by White, middle-class expectations for parent engagement. This qualitative study challenges the dominant narrative by exploring the ways eight Black parents support their elementary-aged children's mathematical identities. Although many scholars have examined the relationship between mathematics identity and academic outcomes, few have explored the role parents play in this identity development. Drawing on Martin's (2000) mathematics identity framework and McCarthy Foubert's (2019) Racial Realist Parent Engagement framework, the author argues that Black parents' experiential knowledge of race and racism in mathematical spaces positions them to teach their children about the everyday importance and usefulness of mathematics. Using parent interviews and family observations, the author's findings suggest the parents supported their children's mathematics identities using four approaches: 1) pragmatic (emphasizing financial literacy and basic life skills), 2) aspirational (promoting math-intensive careers), 3) affirmational (sharing words of encouragement), and 4) race-conscious (applying mathematical concepts to lessons in Black history, culture, and anti-Blackness). Implications for educators are discussed, as parent identity support strategies may be useful for reform-oriented teachers seeking to foster positive mathematical identities in Black children. [ABSTRACT FROM AUTHOR]

Mathematics teacher educators can use video clips of children solving mathematics problems to help teacher candidates attend to nuanced aspects of teaching and learning mathematics. However, the process of selecting and using video clips to support teacher candidates' learning to teach mathematics is underexplored as are the ways in which mathematics teacher educators can use self-study to examine these processes. In this article, we present the Playlist Process – a method we developed, using the metaphor of a playlist, to examine our practice – and the three insights that emerged during our multi-year, multi-institutional collaborative self-study: (1) use explicit scaffolds to support the development of teacher candidates' awareness; (2) incorporate Torres' Rights of the Learner as a tool for supporting teacher candidates' learning about equitable practices; and (3) increase attention to grain size and progressions of children's solution strategies. The article concludes by considering how the Playlist Process can support other teacher educators as they engage in self-studies of their practice and collaborate across institutions. Implications for future practice and research are included. [ABSTRACT FROM AUTHOR]

Several teaching moves have been suggested to support young children's simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, Big Fish Story, with dyads of 3 to 4-year-old students. As part of the implementation, the teacher-researchers used these teaching moves to support young children's in-the-moment answers to simple addition and subtraction problems. We use session-level data (n = 94 sessions) nested in dyads to examine and compare the frequency with which the use of these teaching moves are associated with two types of student responses, in order to preliminarily identify teaching moves that may support young children's performance on simple arithmetic tasks. We conclude with implications for the field and early childhood practitioners. [ABSTRACT FROM AUTHOR]

Imperative of time when technology is developing with a huge drive momentum is also teaching developments according requirements of time. The process of teaching mathematics in the lower cycle requires teachers to follow the experiences of developed countries, who have put technology at the service of teachers and students in order to increase the results of both students and teachers. Teachers knowledge of the content of the material that is explained is not sufficient for the teaching profession, but these must be supplemented with methodological knowledge of the subject and the use of adequate tools during teaching. This paper deals with challenges faced by teachers of the primary school in the subject of mathematics. The challenges of a teacher's daily life are both teaching content of the subject, as well as the insufficient teaching tools, the organization and management of the classes. The instrument used in this research is the questionnaire, completed by 104 primary school teachers from several cities of R.N.M. Results obtained after the processing of the questionnaires show that the teachers are sufficiently prepared both in the mathematical content and in the methodological aspect of the subject of mathematics. This paper also confirms the hypothesis, according which the preparation of teachers in the methodological aspect of the subject of mathematics depends on the preparation of teachers in terms of mathematical content (0.687 Pearson correlation coefficient) [ABSTRACT FROM AUTHOR]

This observational study used data from 270 second‐grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm, (b) invented, (c) mixed, and (d) unclassified. We used two‐level hierarchical linear regression to investigate the association between students' strategy use and their performance on a standardized test in mathematics. Results indicated that students in the mixed strategy groups had significantly higher mathematics achievement than those in the standard algorithm and the unclassified groups. [ABSTRACT FROM AUTHOR]

This paper presents findings from a two-year qualitative study examining integration of computer science (CS) and computational thinking (CT) into elementary mathematics instruction. Integrated units were developed by elementary teachers and CS/CT coaches with support from university faculty with expertise in CS/CT and elementary mathematics. CS/CT instruction primarily relied on the Scratch environment, although some lessons made use of Code.org materials. This research primarily relied on two theories of integration (i.e. Kiray, 2012. A new model for the integration of science and mathematics: The balance model. Energy Education Science and Technology Part B: Social and Educational Studies, 4(3), 1181–1196) that provided insight into the level of interconnection between the disciplines and the relative amount of instructional time spent within each discipline. Findings revealed that cross-grade CS/CT concepts included sequencing, looping, and conditional logic. Within each category: (a) concepts were taught with increasing complexity across the grades, (b) the mathematics was dominant and CS/CT was important but secondary, and (c) three types of lessons emerged: No integration, partial integration, and full integration. Lastly, lessons generally included a transition from less integrated to more integrated activities with an initial focus on discipline-specific conceptual understanding prior to integrated activities. [ABSTRACT FROM AUTHOR]

Copyright of Revista Latinoamericana de Etnomatemática is the property of Universidad de Narino and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A critical role of mathematics teacher education is to equip teachers with understandings and ambitious practices that support effective mathematics teaching for students from diverse backgrounds, specifically connecting to children's mathematical thinking (CMT) and children's linguistic, cultural, and family funds of knowledge (CFoK). Drawing on data from a larger research project, TEACH Math, this longitudinal case study uses the lens of authority to examine one teacher's, Sena's, understandings and practices related to CMT and CFoK over a 4-year period, i.e., through mathematics methods, student teaching, and early career teaching. Findings identify changes made in understandings and practices related to CMT and CFoK, with a focus on the development of recognition and realization rules. Emphasis is placed on how authority was shared in the classroom and how this may have impacted one teacher's development of two very different learning-to-teach trajectories for connecting to CMT and CFoK. Implications for teacher educators focused on supporting novice teachers in developing ambitious mathematics teaching practices are discussed. [ABSTRACT FROM AUTHOR]

Informed by a constructivist-based, student-adaptive pedagogical approach, this study explores the benefits of teacher–learner discourse moves for the mathematics learning of students with learning disabilities (LD). During a constructivist teaching experiment for nurturing the multiplicative reasoning and problem solving of five third-grade students with school-identified LD, we analyzed the global trends and detailed dynamics of teacher–student interactions with statistical discourse analysis. We found that the teacher's discourse moves to support each individual student's problem solving helped engage them in mathematical reasoning, which improved their problem-solving performance. Thus, this study contributes to knowledge in the field of special education by (a) specifying ways in which discourse-oriented mathematics instruction can help each student with LD and (b) showcasing a novel statistical analysis of teacher–student discourse. [ABSTRACT FROM AUTHOR]

As teacher education shifts to focus on teaching beginners to do the work of teaching, assessments need to shift to focus on assessing practice. We focus on one teaching practice, eliciting student thinking, in the context of elementary mathematics. We describe assessments in two contexts (field and simulation). For each assessment, we describe the eliciting of three prospective teachers what could be seen about the skills of group of prospective teachers (N = 44). We report on how three prospective teachers had differing opportunities to demonstrate their skills in the context of the field assessment, but similar opportunities in the context of the simulation assessment. Although both contexts make important contributions, in each case, contributions are counterbalanced are by significant challenges. Although the authors do not argue for one assessment context over the other, they offer insights into the affordances and challenges of each so that teacher educators can make responsible decisions. [ABSTRACT FROM AUTHOR]

Copyright of Dilemas Contemporáneos: Educación, Política y Valores is the property of Dilemas Contemporaneos: Educacion, Politica y Valores and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner. We compared the impact of three PLE formats on the early algebra knowledge and teaching practices of elementary mathematics teachers: (1) a facilitated summer workshop, (2) a multimedia course completed on teachers' own time, and (3) learning resources provided in the algebra curriculum unit that teachers used individually. Our findings suggest that all three formats can be mapped against a set of principles for quality professional learning. Analysis of pre- and post-treatment measures indicate that participating teachers' knowledge of algebra content and best practices significantly increased, regardless of the PLE format with which they engaged. Interviews with a subset of the teachers from the three groups point to the key features of each of the formats that can be capitalized on by designers of PLEs. [ABSTRACT FROM AUTHOR]

The mathematics education field recognizes the importance of noticing children's mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers' knowledge of children's mathematical thinking and participants' problem posing in response to children's mathematical thinking, we developed the Responding Rubric, which measures four elements of responding to children's mathematical thinking (group or individual responses, consideration of children's existing strategies, anticipation of children's future strategies, and a responsive problem). Using the Responding Rubric, we were able to illustrate elements of teachers' responding skills. Following our presentation of findings, we discuss how our results further our understanding around teachers' noticing skills and provide directions for future research. [ABSTRACT FROM AUTHOR]

Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children's multiple mathematical knowledge bases (MMKB), including children's mathematical thinking and children's home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children's MMKB in instruction may be to scaffold teachers' noticing of potential spaces in elementary mathematics curriculum materials for connecting to children's MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children's MMKB. [ABSTRACT FROM AUTHOR]

Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity models during mathematics instruction. Based on an examination of 64 videotaped lessons on inverse relations, we identified 110 "diagram episodes." An analysis of these episodes reveals that linear quantity models, especially tape diagrams, were used more frequently in US classrooms than in Chinese classrooms. However, Chinese lessons used these models for the sole purpose of modeling the underlying quantitative relationships, whereas US lessons mainly used them to aid in computation. In addition, while US teachers rarely involved students in discussion of linear quantity models, Chinese teachers spent significant time engaging students in co-constructing, comparing, and explaining these models. [ABSTRACT FROM AUTHOR]

Copyright of Cumhuriyet International Journal of Education is the property of Cumhuriyet University, Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Developing students' number sense is a critical area of research in mathematics education because of the role number sense plays in early mathematics learning. In particular, cognitive psychology research has pinpointed verbal counting as a number sense construct that is critical in later mathematics achievement. This study explored variations in 7- and 8-year-old students' number sense outcomes as they engaged in a countingfocused instructional treatment for differing durations. Sixty students in three elementary classrooms in the United States participated in the counting-focused instructional treatment. A generalized estimating equations (GEE) analysis showed an associated average increase in test scores for students participating in 9 weeks of the counting-focused instructional treatment as compared to students participating in 3 weeks of the instructional treatment. This study provides preliminary results about an instructional practice, based in numerical cognition theory, for elementary mathematics teachers to facilitate opportunities for students to develop their number sense. [ABSTRACT FROM AUTHOR]

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers', and especially early career teachers' (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students' mathematical vocabulary use and development. Yet, there was variability in ECTs' focus on how to teach mathematical vocabulary, expectations for students' precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students' language development in the mathematics classroom. [ABSTRACT FROM AUTHOR]

Drawing on a larger, cross-institutional study that examines equitable elementary mathematics education, this article reports initial findings related to tensions that emerged for preservice teachers (PSTs) related to trusting students with open-ended, challenging mathematics tasks. Data composed of 194 PSTs' written responses to a survey question. Using methods of qualitative analysis, findings indicate two prominent tensions that emerged for PSTs related to trusting students with open-ended challenging tasks: productive struggle versus unproductive failure and teacher control versus student control. These findings suggest that reform efforts that encourage teachers to implement open-ended, challenging tasks may not come to fruition if underlying issues of (mis)trust teachers may have related to students are not unpacked and addressed. [ABSTRACT FROM AUTHOR]

The purpose of this research is to combine multimedia elements and mathematics learning material to a mathematic learning interactive application. Research and design methodology that used is Game Development Life Cycle (GDLC) which consist of initiation, pre-production, production, testing and release. Content inside the game is made using gamification and expert system concept. The result of this research is an interactive learning game to support student to understand mathematic materials. The purpose of this application is to help student to learn mathematic in an interactive and interesting way, to deliver mathematic material easily. [ABSTRACT FROM AUTHOR]