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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]

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]

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.

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.

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.

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]

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]

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 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.

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 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.

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.

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]

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.

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]

Background and Objective: One of the most sensitive parts of the education system in every person's life is elementary school. A period that plays a very important role in the life of each person; and the success or failure in this period will have very serious effects on the future of the individual. Meanwhile, the role and importance of mathematics is felt more than other subject matters as many students are weak in this course. For this reason, the teaching of this course should be changed from a strict and inflexible subject matter that is limited to lecturing to various approaches in accordance with mathematics education and active teaching methods along with new educational technologies. Educational technology and e-learning are some of the concepts that were introduced and attracted a lot of attention in the field of education with the growth and development of information and communication technologies (ICTs). Recently, Wanser proposed a theory of educational humor processing, a theory that has evolved from the basic models of persuasion and incompatibility theories to explain the role of educational humor in facilitating learning. This research conducted with the aim of evaluating the effectiveness of the electronic humorous content on the learning and retention of students' mathematics. Methods: The present study was a semi-experimental research using pre-test-post-test design with experimental and control groups. The population consisted of all 5th grade students (N=2200) in elementary schools at Birjand in 2018. The statistical population of the study consisted of 58 people who were selected with convenience sampling. The study sample included a class as the experimental group and another class as the control group selected out of four classes, each consisting of 29 people. For data collection, Teacher-made test used in pre-test and post-test. In addition to, descriptive analysis, covariance test used to analyze the data. Findings: There is a significant difference between the mean scores of the experimental and control groups' mathematical learning variable. Regarding ETA, we can say that using humorous content, explains 15.4% of the variance of post-test scores ( = 15.4%،p < .05). There was no significant difference between the mean scores of pre-test and post-test of retention in the experimental group compared to the control group. The findings of this study showed that the effect of humorous electronic mathematical content on learning was significant (15%), but the effect of humorous electronic content on retention was not significant. Conclusion: The use of e-content is a step forward toward the effectiveness of the teaching and learning process. The application of this research results for pedagogues is that in order to improve mathematics learning, we should pay attention to the role and function of humorous education and electronic content; and by combining these two direct mathematical teaching methods to create interest in this subject matter. Combining the process of teaching mathematics with humorous e-content will increase students' attention and motivation, improve their mathematical learning, and foster their creative power. The findings of several studies suggest that providing opportunities for collaborative, moderated, and competitive learning in schools can help reduce anxiety and improve students' math performance. This requires a systematic and purposeful effort on the part of the education system to bring about a change in math textbooks and teaching methods. For this reason, it is necessary to take essential measures to make the e-content as effective as possible. This requires that professionals, teachers, and all educators collaborate effectively and efficiently to successfully design and produce e-content. ===================================================================================== COPYRIGHTS ©2020 The author(s). This is an open access article distributed under the terms of the Creative Commons Attribution (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, as long as the original authors and source are cited. No permission is required from the authors or the publishers. =====================================================================================

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: Fifty-two low performing schools were randomly assigned to receive Spatial-Temporal (ST) Math, a supplemental mathematics software and instructional program, in second/third or fourth/fifth grades or to a business-as-usual control. Analyses reveal a negligible effect of ST Math on mathematics scores, which did not differ significantly across subgroups defined by prior math proficiency and English Language Learner status. Two years of program treatment produced a nonsignificant effect. Publication of evaluation results from large-scale real-world supplemental mathematics instructional implementations such as this one can provide a realistic view of the possibilities, costs, and limitations of this and other computer aided instruction supplemental interventions.

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.

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]

Across the United States, there are many elementary aged students whose parents or themselves are from Mexico, Guatemala, and Central America having Mayan heritage. In alignment with instructional concepts that build a positive classroom culture encouraging higher level learning for all students, the authors designed and implemented a curriculum that supported students who need multi-leveled and authentic instruction promoting collaboration and social interaction. Positive relationships were built between students who have varying abilities, including those with physical, cognitive, and language challenges, in order to scaffold learning through cultural awareness connected to mathematics concepts. In the 2015-2016 school year, this school's student population included 74% Hispanic students, most of whom identified with the Mayan culture. The study of ancient civilizations, such as the Maya, can employ historical contexts to introduce elementary level students to the evolution and logic of today's mathematics. As a practitioner focused article, the purpose is to describe an educational experience that was designed to connect students to their culture through interdisciplinary learning with mathematics, visual art, and technology. The goal of the featured lesson is to provide elementary educators with effective teaching strategies that support all students;' learning in mathematics and to engage students to demonstrate their understanding through multiple avenues of expression, including visual arts and through technology. The authors' impressions of how students responded to this interdisciplinary lesson are discussed along with future directions for integrating curriculum that assist teachers in designing culturally connected curriculum. [ABSTRACT FROM AUTHOR]

Supporting growth in problem solving is key to capacity development for both teachers and students. When teachers engage in rich academic conversations that inquire deeply into content and pedagogy, they have an opportunity to cultivate student capacity to engage in rich academic discourse, problem solving and mathematical learning. In this study, we examined an intensive professional development training intervention in which teacher participants learned to use and understand the Teaching Learning Community (TLC) approach, design and connect standards-based lessons, and nurture a mindset of learning and thinking like a problem solver among students and teachers alike. We further examined whether there were any differences in students' MAP test scores over time among students whose teachers participated in the intervention and students whose teachers did not participate. Findings from the Analysis of Variance of students' MAP test scores indicated that students whose teachers participated in the intervention demonstrated more growth in mathematical proficiency, particularly in Grade 3. Thus, implementing an intervention like the one described herein that provides the appropriate resources to teachers, education in the form of high-quality professional development, and an opportunity to collaborate with peers and experts can result in direct improvement to student achievement in math.

Reciprocal peer tutoring in mathematics was conducted with 487, ten to twelve year-old students from 20 elementary schools in three different school districts. The peer tutoring technique, a form of paired mathematics, placed specific emphasis on mediation through strategic metacognition between tutor and tutee. Student mathematics attainment significantly increased using this technique (Effect Size=+0.43). Student perception of the social status of their tutoring partner influenced attainment outcomes. Greatest mathematics attainment gains were predicted by having a higher opinion of the cognitive ability of students’ mathematics tutoring partner and by having a mathematics tutoring partner that you believed was less popular. After peer tutoring, students showed increased social relationships in and out of school. Gains in social relationships were indicative of a more inclusive classroom being developed. The implications for theory, policy, practice and future research are discussed.

This study aims to determine differences in learning outcomes of Mathematics of primary school students using problem based learning model. The type of research used is the meta-analysis of research that has been done before. This research uses quantitative synthesis method. The purpose of this study is to determine the effect of using problem based learning model on elementary mathematics subjects. Data collection in this research is done by searching journal through google scholar. Keywords used for journal search are: improving the results of elementary mathematics learning, problem based learning. From the model of problem based learning selected 10 research results to be analyzed further in% form. Based on the results of the analysis of 10 research results, it can be concluded that the learning with Problem based learning model (PBL) can improve the learning outcomes of learners learner. Increased learning outcomes from the lowest 5% to the highest 40%, with an average of 22.9%.

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]

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The integration of virtual manipulatives in classroom practices facilitates student learning processes. For this, the teacher must understand how to support students in establishing mathematical connections between the manipulation and their interpretations of the representations. We present a learning scenario that integrates the use of virtual manipulatives in mathematical modelling tasks. It was designed and implemented during initial teacher training, with the aim of helping a group of first-year elementary school students to overcome difficulties identified in their comprehension of the meaning of subtraction. The research, following the principles of design-based research, included three distinct moments: an individual written pre-test, an intervention phase with six micro-cycles, and an individual written post-test. The analysis of the collected data—audio, screen recordings, and written productions—allowed us to identify the most influential structural characteristics of the learning scenario: mathematical communication, collaborative learning, self-regulation, and co-regulation of learning. Our results suggest that differentiated instruction, minimal guidance, and scaffolding played an important role in the support provided by the pre-service teacher to students in the mathematical modelling activities that integrated virtual manipulatives.

This descriptive study examines the elements of mathematical knowledge for teaching (MKT) that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.

The steepest descent (or ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development workshop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-min introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

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]

An increasing body of work provides evidence of the importance of bodily experience for cognition and the learning of mathematics. Sensor-based technologies have potential for guiding sensori-motor engagement with challenging mathematical ideas in new ways. Yet, designing environments that promote an appropriate sensori-motoric interaction that effectively supports salient foundations of mathematical concepts is challenging and requires understanding of opportunities and challenges that bodily interaction offers. This study aimed to better understand how young children can, and do, use their bodies to explore geometrical concepts of angle and shape, and what contribution the different sensori-motor experiences make to the comprehension of mathematical ideas. Twenty-nine students aged 6-10 years participated in an exploratory study, with paired and group activities designed to elicit intuitive bodily enactment of angles and shape. Our analysis, focusing on moment-by-moment bodily interactions, attended to gesture, action, facial expression, body posture and talk, illustrated the 'realms of possibilities' of bodily interaction, and highlighted challenges around 'felt' experience and egocentric vs. allocentric perception of the body during collaborative bodily enactment. These findings inform digital designs for sensory interaction to foreground salient geometric features and effectively support relevant forms of enactment to enhance the learning experience, supporting challenging aspects of interaction and exploiting the opportunities of the body. [ABSTRACT FROM AUTHOR]

In the United States, teacher preparation programs are under increased pressure to demonstrate their effectiveness in producing graduates with knowledge, abilities, and competencies to be quality teachers. However, very little research shows this kind of evidence. In a rare exception, Hiebert, Miller, and Berk (2017) found significant positive results of the influences of an elementary teacher education program on graduates' knowledge. Due to the rarity of these kinds of findings, we replicated their analyses with a different cohort of graduates from the same preparation program. Graduates completed a video analysis task correlated with high quality mathematics teaching for topics taught during their program and topics not taught during their program. Our results corroborate theirs, showing that graduates performed better on topics taught during their program versus topics not taught. These findings suggest that teacher education programs can have a significant positive and lasting effect on graduates' knowledge several years after graduation. [ABSTRACT FROM AUTHOR]

This study examined how Black students responded to the utilization of culturally responsive stories in their mathematics class. All students in the two classes participated in mathematics lessons that began with an African American story (culturally responsive to this population), followed by mathematical discussion and concluded with solving problems that correlated to the story. The researcher observed and recorded responses by students during each part of these lessons with protocols. Students independently reflected weekly by answering five questions to share their perspective on the African American stories. The teacher reflected on each lesson as well, describing thoughts on how these students responded to the story in each lesson. This paper examines the analyzed data from the target audience: Black students. Results revealed that Black students responded to the use of African American stories with high self-rated levels of engagement and enjoyment and that the stories helped them think about mathematics to varying degrees. Since students who are engaged and are thinking about mathematics are more likely to achieve mathematical understanding, the researcher concludes that this strategy should continue to be tested in diverse classrooms with an emphasis on student reflection to determine if the outcomes are transferable and generalizable. [ABSTRACT FROM AUTHOR]