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The adequate preparation of future teachers of mathematics is critical, requiring sufficient opportunities to develop both pedagogical skill and content knowledge. Yet, despite new recommendations for mathematics teacher preparation, we know little about the landscape of course-based learning opportunities in US elementary teacher education programs. To what extent do US elementary teacher education programs meet the Standards for Preparing Teachers of Mathematics outlined by the Association of Mathematics Teacher Educators (AMTE) for mathematics content and methods courses? Based on an a priori power analysis, we gathered a random sample of 291 higher education institutions. Within these institutions, we analyzed 736 programs, including Bachelor's, Master's, and Credential programs. We found that overwhelmingly US elementary teacher education programs do not meet the aspirations outlined in the AMTE standards, with Master's and Credential programs and those covering all elementary grades particularly falling short. Potential explanations for these challenges and implications for teacher education program design are discussed. [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]

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]

Building on previous findings that preschool children develop an awareness of base-ten structure from informal exposure to multidigit numbers, we tested whether kindergarten children would benefit from formal place value instruction, using this informal foundation as a starting point. A total of 124 U.S. kindergarten students participated in a school-based study that used a pretest-training-posttest design. One group of students completed 20 brief lessons focused on the relational structure of base-ten symbols, using activities informed by cognitive science research on relational learning. A second group of students completed 20 practice sessions on single-digit addition and subtraction problems. Both groups showed growth in place value understanding, but students in the experimental curriculum showed greater growth than children in the control group on measures that required precise understanding of base-ten syntax (i.e., counts of base-ten units). Educational Impact and Implications Statement: Previous studies have shown that preschool children develop partial understanding of multidigit number meanings outside of school, likely through learning mechanisms that support comparisons and making connections. In this study, we asked whether having this informal foundation enables kindergarteners to learn from formal instruction in place value earlier than previously believed, and furthermore, whether this accelerated learning is evident on place value activities that can be performed with rough estimates of place value meaning, place value activities that require precise understandings base-ten notation, or both. We designed 20 short lessons that scaffolded children's comparisons to help them discover symbol meanings through repeated exposures. Growth in place value understanding was observed in children who received these lessons, as well as those who received business-as-usual single-digit calculation practice and background informal learning; however, students who received place value instruction made greater gains than the control group in their precise understanding of base-ten units. [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]

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]

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]

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.

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]

AbstractPrior short-term studies have shown the effectiveness of worked examples and self-explanation prompts in improving elementary students’ mathematics knowledge. However, year-long classroom-based interventions have been tested only with older students. The purpose of the current study was to explore the effectiveness of a year-long classroom intervention, MathByExample, which paired worked examples and self-explanation prompts with practice problems. We utilized a classroom-based experimental design where 5th-grade classrooms were randomly assigned to one of two conditions. Findings illustrate that intervention dosage impacts the effectiveness of the intervention in improving 5th graders’ grade-level mathematics knowledge. In addition, prior knowledge impacted the effectiveness of the intervention for two of the four outcome variables. This study expands the literature on the use of worked examples and self-explanation prompts in several ways. It provides evidence that this tool has the potential to improve elementary students’ learning. It included four different measures of math knowledge, which provides stronger support for the effectiveness of the intervention. Finally, it adds to the literature that shows the benefits of studying and explaining both correct and incorrect worked examples. [ABSTRACT FROM AUTHOR]

Background or Context: Teachers knowing their students is consequential for students' participation and learning. Evidence in mathematics education points to the ways that knowing the details of students' mathematical thinking supports teacher and student learning. What it means to know students and what teachers learn about their students are situated in the everyday practices of schooling. Purpose, Objective, Research Question, or Focus of Study: This study investigates how teachers characterized their students mathematically and how they considered meeting students' needs in math class. Research Design: This qualitative study focused on interviews conducted over four years with 61 teachers of kindergarten through second grade across two school districts. Conclusions or Recommendations: This study found that rather than describing what they knew about the details of their students' mathematical thinking or detailing specific tasks, tools, or teacher moves that supported their students, many teachers characterized students in ways that were in line with practices that organize districts, schools, and classrooms. Our data raise questions about the ways in which the structures and common practices of schools are shaping teachers' descriptions of their students in mathematics, and the corresponding classroom practices then engaged. [ABSTRACT FROM AUTHOR]

Background: Educational games are increasingly recognized as effective teaching tools, especially in elementary education. This study focuses on the application of a treasure hunt game in teaching mathematics, specifically time measurement concepts, to second-grade students at SD Islam PB Soedirman, Cijantung, East Jakarta. Aim: The primary aim of this research was to assess the impact of the treasure hunt game on the improvement of mathematical learning outcomes among the students. Method: This research adopted a quantitative experimental approach with a Post-test Only Control Group design. The sample consisted of 50 second-grade students divided into two groups: an experimental group (2D) and a control group (2G), each with 25 students. The experimental group was taught using the treasure hunt game, while the control group did not receive any special intervention. Data collection was conducted through observation and objective testing with 13 multiple-choice questions that had been validated. Data analysis was performed using SPSS for testing validity and reliability, as well as for prerequisite and hypothesis testing. Results: The prerequisite test results indicated that the data were homogenous and valid. The hypothesis testing, conducted using a paired t-test, showed a significant value of 0.003 (p < 0.05), indicating a significant difference between the experimental and control groups. Conclusion: Based on the findings, it can be concluded that the treasure hunt game significantly influences the improvement of mathematical learning outcomes in time measurement for second-grade students. This suggests the effectiveness of game-based learning methods in the context of elementary mathematics education.

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.

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]

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]

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 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]

This cross-cultural study examines how elementary mathematics teachers in Finland and the United States shifted their instructional systems during the period of Emergency Remote Teaching (ERT) in the spring of 2020. Using Ruthven's (2009) framework of Structural Features of Classroom Practice, researchers analysed 15 teachers’ descriptions of their mathematics teaching during ERT in contrast to their typical practice. Exploring how teachers in both contexts navigated challenges of ERT through a cross-cultural lens allowed researchers to identify similarities and differences in teaching practices and use of activity formats, synthesized in composite models of teachers’ instructional systems. The differences in the systems can be traced to underlying cultural assumptions about the nature of elementary mathematics education and the roles of teachers, students, and curriculum resources within each system.

This article introduces a social justice problem-solving task designed for grades K-2 that explores place value and food insecurities. The intentions and instructional design of the task are shared, including how the task recognizes students' identities, leverages problem solving and use of multiple strategies, and purposefully integrates mathematical goals with interdisciplinary ELA connections through a social justice lens. Sample student work from the task and lessons learned from the instructors are shared to inspire others wishing to design and implement similar tasks in their elementary mathematics settings. [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]

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]

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]

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]

The results of the PISA test which measures students' Mathematics skills place Indonesian students in the bottom 5th position, 73rd out of 79 participating countries with an achievement score of 379 which is certainly below the OECD average of 489. Students still think of Mathematics as a subject lesson that are quite difficult. This assumption arises due to experiences that have been obtained before in the process of learning mathematics which is less fun for students. The learning process is largely determined by the learning theory mastered by educators. As a professional, educators must have knowledge of various ways so that learning objectives can be achieved. The basic knowledge that must be possessed is related to learning theory. One of the learning theories that educators can use is the humanistic learning theory. The purpose of this study is to describe the implementation of humanistic learning theory in an open-ended approach to the mathematics learning process in elementary schools. Using the library research method, it was found that open ended research utilizes humanistic learning theory in its development, which is illustrated in the four steps of the open-ended approach

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]

This research examines the relationship between high school, namely, high school profiles, and students’ success during an elementary mathematics course at university. For the analysis of this relationship, a mixed methods case study was chosen as the research design. The instruments for collecting the data were a questionnaire and a semi-structured interview that provided answers to the research questions. The sample consisted of 81 students (N = 81) from the University of Applied Sciences in Ferizaj, Kosovo, who participated in the questionnaire, and 12 out of the 81 students were also interviewed. The research results indicated that a positive, not strong, correlation exists between high school and university success. Moreover, students expressed that knowledge gained in high school made them feel sufficiently prepared during the lectures on elementary mathematics. The high school profile makes a difference in the students’ success in the elementary mathematics course at the university.

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]

In this interactional ethnographic investigation, one third grade elementary mathematics classroom served as a lens to develop an interactional understanding of authority negotiations between two students. Through a discursive analysis of one telling case, we demonstrate how students navigated classroom interactions by maintaining a relationship close to their teacher's positionings and through adhering to the co-constructed storylines of the classroom cultures in the making. Findings elucidate the ways students use the authority of the teacher in assigning mathematical competence during collaborative work. Future directions for research on understanding shared authority in mathematics education are considered. [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.

Background: Current efforts to promote reasoning, problem solving, and discussion are often framed as advancing equity, but scholarship suggests individual students' opportunities to learn can vary considerably in classrooms that attempt to take up these approaches to teaching mathematics. Noticing students' mathematical strengths and positioning their contributions as competent is among aspects of instruction associated with more equitable learning outcomes for students from marginalized groups, but research has yet to comprehensively examine the range and nuance of this aspect of teachers' practice in classrooms that feature broad distributions of participation. Purpose: The purpose of this study was to examine teachers' instructional practice with respect to assigning competence in two mathematics classrooms that demonstrated high levels of student participation. We investigated the kinds of situations in which teachers positioned students as competent, and the ways assigning competence opened opportunities to participate. Setting: Data were collected at a public elementary school in a culturally, linguistically, and economically diverse neighborhood in southern California. Participants: Participants included two teachers and 45 students from two third-grade classrooms. Teachers had participated in ongoing professional development focused on leveraging children's mathematical thinking in instruction. Research Design: We drew from qualitative methods for analyzing video to investigate classroom interactions from 12 mathematics lessons. Data sources included video recordings, transcripts, and student work. We used Studiocode software to parse each lesson into phases and episodes. Drawing from previous studies, we identified a subset of episodes in which teachers explicitly positioned a student's contribution as competent. An iterative process of coding and discussion was used to analyze patterns with respect to student participation, teacher support, and the unfolding of rights and obligations related to participating in mathematical activity. Findings: Analyses revealed different kinds of situations in which students participated in mathematically substantive ways (in terms of providing detailed explanations of their ideas or engaging with the details of a peer's idea) and teachers positioned their contributions as competent. These situations included highlighting, clarifying, and amplifying contributions; supporting the specificity of student contributions; recognizing emergent ideas; and validating unprompted attention to mathematical details. Assignments of competence emerged in ways that were integrated into teachers' ongoing efforts to surface and make explicit the details of their mathematical ideas, while also broadening the kinds of contributions students could make to joint mathematical work. Conclusions: Helping students to know what it could look and sound like to participate in the moment while recognizing a wide range of contributions as competent created openings for students who in many classrooms might be excluded or relegated to the periphery of conversations. Making competence explicit was a contingent, relational practice that required teachers to find specific ways of leveraging student strengths to support their participation. Recommendations for advancing mathematics teaching must attend to the nuances with which particular practices unfold to open or constrain individual students' opportunities to learn. [ABSTRACT FROM AUTHOR]

In the United States, national and state standardized assessments have become a metric for measuring student learning and high-quality learning environments. As the COVID-19 pandemic offered a multitude of learning modalities (e.g., hybrid, socially distanced face-to-face instruction, virtual environment), it becomes critical to examine how this learning disruption influenced elementary mathematic performance. This study tested for differences in mathematics performance on fourth grade standardized tests before and during COVID-19 in a case study of a rural Ohio school district using the Measure of Academic Progress (MAP) mathematics test. A two-way ANOVA showed that fourthgrade MAP mathematics scores were statistically similar for the 2019 pre-COVID cohort (n = 31) and 2020 COVID-19 cohort (n = 82), and by gender group, between Fall 2019 and Fall 2020. Implications for rural students' academic performance in virtual learning environments are discussed. [ABSTRACT FROM AUTHOR]

Abstract 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.

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]

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.

We aimed to investigate the responsive teaching practice of preservice teachers (PSTs) using an artificial intelligence-based chatbot designed to serve the dual roles of a virtual student and a virtual mentor. We identified four unique profiles of PST's questioning patterns using latent profile analysis. We examined the changes in PSTs' questioning patterns after receiving feedback from a virtual mentor and investigated the differences in their self-assessments regarding interaction effectiveness by profile. PSTs' tendency to adjust their questions varied. There was no statistical difference in the effectiveness of interactions among profiles. We include theoretical and empirical implications for teacher education. • AI-based chatbots can be useful for examining the responsive teaching practices of preservice teachers. • Chatbots can create optimal simulated environments for preservice teachers by presenting virtual students and mentors. • Four distinct patterns of responsive teaching questioning practices were identified among preservice teachers. • Feedback from the virtual mentor may influence the questioning practices of preservice teachers. • Preservice teachers' self-assessments of questioning effectiveness did differ from their observed questioning quality. [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]

Context: The island of Malta is a former British colony, and to this day, education continues to be accessed bilingually. For mathematics education, Maltese and English are used for verbal interaction, with subject-specific words tending to be retained in English. Written mathematics texts are in English, including textbooks, worksheets, digital texts, and examinations. Thus, the "academic" language of mathematics is generally considered—and accepted—to be English. Objective of Research: It is important for Maltese students to gain access to the academic (English) mathematics language to access the discourse of power and still use Maltese in the process. The focus of this study is language as part of the discourse of fractions. The research question was: How can Maltese bilingual children be supported in accessing the discourse of fractions? Participants: The author assumed the dual role of teacher and researcher. The students were 16 nine-year-old children attending a fourth-grade class. Six of these children also participated in two interviews each. Intervention: The author adopted a teacher/researcher role and taught the topic Fractions (five lessons). The topic was chosen at the request of the class teacher. The class teacher stated that although her students had previously mastered fractions of a region (e.g., 1/3 of a circle), they had not understood fractions of quantities (e.g., 1/3 of a set of 12 books). During her teaching, the author focused on language explicitly; she started discussions on fractions with the students using Maltese and English, and gently prompted them toward increased use of mathematical English. The aim of this more detailed articulation of mathematical ideas was for the children to express a better understanding of fractions of quantities. Research Design: This qualitative case study centered its analysis on the classroom interaction and interview data. The theoretical framework drew from Anna Sfard's definition of mathematical discourse, namely, that a discourse consists of words, endorsed narratives, routines, and visual mediators. "Understanding of fractions" was considered in terms of participation in, or engagement with, in the discourse of fractions. Conclusions: The initial use of translanguaging enabled new discourse elements related to endorsed narratives, routines, and visual mediators. These three elements then supported lengthier and varied contributions in the academic language, and thus, I argue that the endorsed narratives, routines, and visual mediators served as "anchors" to support new language practices (new words of the discourse). Ultimately, the children's engagement with the four discourse elements indicated that by the end of the five lessons, they had a better understanding of fractions of quantities. [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.

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]

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]

Student struggles with fractions are well documented, and due to fractions’ importance to later mathematics achievement, identification of the errors students make when solving fraction problems is an area of interest for both researchers and teachers. Within this study, we examine data on student fraction problem errors in pre- and post-quizzes in a digital mathematics environment. Students (n = 1,431) were grouped by prevalence of error types using latent class analysis. Three different classes of error profiles were identified in the pre-quiz data. A latent transition analysis was then used to determine if class membership and class structure changed from pre- to post-quiz. In both pre- and post-quiz, there was a class of students who appeared to be guessing and a class of students who performed well. One class structure was consistent with the idea that early fraction learners rely heavily on whole number principles. Identification of co-occurrence of and changes to fraction errors has implications for curricular design and pedagogical decisions, especially in light of movements toward personalized learning systems.