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This article aims to identify the mutual relationship between the awareness of the importance of mathematical competencies for the acquisition of work-related skills and the perceived importance of the latter for performance in future work and successful participation in the labor market. How these issues relate to math anxiety is also explored. The above is examined on a sample of university students in the selected education institution (HEI) N =297 in the Czech Republic in 2022. Subsequently, a series of semi-structured interviews were conducted with the students in 2023. It was found that by improving work-related skills for a future career, math anxiety increases. A crucial finding is up to 47 % of the perceived importance of competencies for future job performance can be explained by understanding the importance of mathematics for their acquisition. The findings of this study have the potential to contribute to the improvement of mathematics education and the development of a more skilled and capable workforce, which can ultimately lead to greater economic growth and social progress. In addition, this article contains practical recommendations on how to use these findings in the practice of mathematics education not only in the selected higher education institution.

Textbooks are one of the main resources for teaching and learning mathematics. This study examines the presentation of angle topics in 4th-grade mathematics textbooks in Indonesia and Singapore. The analysis focused on the general characteristics of the textbook and the nature of the mathematical tasks presented. The results showed that Indonesian mathematics textbooks are more likely to provide a more ample opportunity to learn than Singaporean textbooks based on the number and description of task activities. However, the distribution of items in each task activity in Singapore mathematics textbooks is more proportionate than in Indonesian mathematics textbooks. Concerning mathematical tasks, the findings show that the form of representation in Indonesian mathematics textbooks contains a more purely mathematical form, while Singapore's mathematics textbooks are dominated by visual form. Regarding contextual features, mathematical tasks in Indonesian and Singaporean mathematics textbooks are dominated by non-application forms. Closed tasks also dominate the response type of task for both textbooks. The implications of this finding can be applied to classroom teaching activities, as highlighted in the discussion section.

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the schema development in general and the system of linear equations was used as an example. A case study of an undergraduate class doing a linear algebra course in 2020 was considered in this study, where fifteen students participated in the study whereby they responded to a task with three question on solving a system of linear equations. The findings revealed that albeit minor manipulation errors, students were able to solve given systems of linear equations using the Cramer's rule and Gaussian elimination. However, students could not adequately go beyond the algorithmic computations to attain appropriate mathematical reasoning and establish underlying relations required to solve systems of linear equations, as no-one attained the trans-stage of conceptualization. It follows from this study that the identifications of the challenges that students encounter when solving systems of linear equations empowers course instructors on how to overcome the challenges.

This study aimed to interpret and describe students' mathematical thinking processes of non-routine mathematical problems that were solved based on didactic situation theory. This study uses a qualitative method, a phenomenological hermeneutics study for grade 8 students at a junior high school in Banda Aceh in the 2021-2022 academic year. Research data obtained through data were collected using instruments, namely written tests based on the didactic mathematical situation theory framework, structured observation, documentation, and clinical interviews carried out after the action. The results of the study show that the students' mathematical thinking processes in the critical reflection category can reach the convincing stage with algebraic arguments in validation situations. Subjects in the explicit reflection category can reach the convincing stage by providing arithmetic arguments in validation situations. Meanwhile, the category of students who cannot solve problems and can only specialize by giving examples of what is being asked. Students in this category have difficulty identifying relevant patterns and formulating the mathematical models needed to solve the problems. To support students in developing the level of mathematical thinking, the teacher can present contextual problems that are in accordance with the level of student thinking, can predict possible responses or ways of thinking of students to the problems given and present problems according to the structure of the concept sequence and the functional order of students' thinking. To support students in algebraic thinking category, teachers can start learning by presenting contextual problems that are easily recognized by students, then expand that context in symbolic form.

This study aims to investigate pre-service teachers' integration of technology and how the integration of technology influences the level of cognitive demands of the mathematics tasks in their mathematics technology activities. The purpose of this study was to investigate the various levels of cognitive demands of mathematical tasks created or modified by pre-service mathematics teachers for technology activities. This study presents case studies of pre-service teachers chosen from a group of participants, and these PSTs come from a variety of backgrounds. Showcase Portfolios and lesson plans were gathered in order to comprehend the selection/creation of mathematical tasks and how they were intended to be implemented in the classroom by PSTs. This study offers suggestions for teacher preparation to integrate technology into mathematics instruction in ways that support students' learning through a review of results, the cognitive demands of mathematical tasks in PSTs' technology activities.

The present study falls into the efforts to improve practices for addressing errors produced by learners in various situations involving the calculation of integrals. We attempt to clarify as precisely as possible the types of errors that secondary school students produce when using integrals in algebraic and graphical frames. Based on the synthesis of several works dealing with errors specific to integral calculus, we have been able to outline a typology of possible errors that can be produced by students in secondary school. We determine some subcategories for the three known categories of errors: conceptual, procedural, and technical. After administering a test to a random sample of secondary school students and conducting a principal component analysis, we were able to deduce that in the algebraic frame, certain conceptual and procedural subcategories dominate, with a notable advance for errors due to failure to recognize the integrand function. In the graphical frame, errors related to technical subcategories represent a major source of the erroneous productions of the students tested.

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

Gaming the system is a persistent problem in Computer-Based Learning Platforms. While substantial progress has been made in identifying and understanding such behaviors, effective interventions remain scarce. This study uses a method of causal moderation known as Fully Latent Principal Stratification to explore the impact of two types of interventions--gamification and manipulation of assistance access on the learning outcomes of students who tend to game the system. The results indicate that gamification does not consistently mitigate these negative behaviors. One gamified condition had a consistently positive effect on learning regardless of students' propensity to game the system, whereas the other had a negative effect on gamers. However, delaying access to hints and feedback may have a positive effect on the learning outcomes of those gaming the system. This paper also illustrates the potential for integrating detection and causal methodologies within educational data mining to evaluate effective responses to detected behaviors.

This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected between students and the teacher, and experiments and class discussions were filmed. The analysis consisted of identifying the development from informal strategies associated with the context of the problem to formal procedures. The results show that the process brings meanings to mathematical ideas such as variation, variables, and the relationship between variables, allows coordination and transition between representations and contributes to the learning of functions as a representation of the variation of physical phenomena.

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and practice of mathematics in both students and teachers. This perspective is relevant for understanding the complexities of teaching multivariate calculus. Traditional approaches to this subject have been lecture-based, but with the evolution of educational paradigms, active pedagogies have emerged as vital. These include among others inquiry-based learning, collaborative learning, the flipped classroom approach, technology-enhanced active learning, and project-based learning. The challenges students face in multivariate calculus range from conceptual complexities to visualization challenges and over-reliance on memorization. In this work, we propose a holistic approach for defining class activities in multivariate calculus with emphasis in integrating visualization techniques, real-world applications, collaborative activities, and feedback mechanisms. Accordingly, four class activities, grounded in the principles of ATD and tailored to address challenges in multivariate calculus, are proposed. These activities aim to foster significant understanding, relevance, and engagement in students.

This study compared the problem-solving abilities of ChatGPT and 58 pre-service teachers (PSTs) in solving a mathematical word problem using various strategies. PSTs were asked to solve a problem individually. Data was collected from PSTs' submitted assignments, and their problem-solving strategies were analyzed. ChatGPT was also given the same problem to solve with various prompts, and the correctness of its solutions and problem-solving strategies were assessed alongside those of PSTs. The results indicated that PSTs used diverse strategies and achieved accurate solutions, but not always relevant strategies to children's level of understanding. ChatGPT employed similar strategies to PSTs but mostly produced incorrect solutions, and its performance needed to be contextualized in the primary school context. The study highlights the potential of ChatGPT in mathematics teaching and informs teacher education programs about the possibility of using it in teaching problem-solving strategies.

This study examines language demands in undergraduate university mathematics classes with a view to better preparing and supporting international and other culturally and linguistically diverse (CLD) students in the United States universities. We observed and analyzed the language demands of 13 entry-level mathematics classes across two large universities. Findings showed that mathematics instruction required extensive and varied listening skills requiring students to listen to long and uninterrupted stretches of sometimes fast paced speech. Technical vocabulary contributed to the language demands, but instructors used both academic and colloquial varieties of language in instruction, interweaving mathematical nouns with phrasal verbs to explain mathematical processes. We suggest a greater focus on development of academic listening skills in English language classes as well as potential collaboration with mathematics campus resources and faculty for additional student support for preparing CLD students for potential future discourse practices.

This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of knowledge. Specifically, an interpretation of its application in the teaching of mathematics is under investigation, specifically in the process of formation and development of concepts in the field of Euclidean geometry. However, the elements that are derived are essential for the treatment of concepts in any sub-branch of mathematics. The analysis of this process and the factors that influence the development show some fundamental elements to consider in the research activity in the field of mathematics education.

The effectiveness of group problem-solving in mathematics depends on the extent to which meaningful participation is distributed across all group members. One way to explore how participation is distributed within groups is by examining how students are positioned within group interactions. In this study, we explore the social instructional factors that cause elementary students to move in and out of positions that support cognitive engagement during collaborative problem-solving in mathematics. Using a case study analysis of three elementary students working in a group, we found five social instructional factors that caused students to move in and out of cognitive-oriented positions during group work in mathematics: (1) building an ally through common language, (2) physical access to the chalkboard and resources, (3) tone of voice, (4) teacher intervention, and (5) contestation from peers. The findings promote implications for effectively facilitating group work in mathematics.

This case study examined teachers' perceptions and use of adaptive diagnostic assessment for improving teaching and learning of elementary-level mathematics. The purpose was to understand how the teaching and learning of mathematics occurred in the classroom and changes that transpired due to the implementation of diagnostic assessments. Findings illustrate that diagnostic assessment can be a critical tool for improving pedagogical practice by enhancing mathematics teaching and learning by creating groups of students, planning lesson time, focused pedagogy, giving student feedback, communicating with stakeholders, and improving teacher efficiency. Participants demonstrated satisfaction with the benefits offered by diagnostic assessment for improving mathematics teaching and learning. Participants described challenges that hindered their effective use of diagnostic assessment tools. The findings of this study support a case for the adoption of diagnostic assessments to improve pedagogical practice and promote mathematics learning among elementary-level students.

This article presents a case study and ideas to flip classical dialogic learning method. Some possibilities of using ChatGPT to stimulate the active role of the student in the dialogic teaching method are shown. Data from observations of students training to be teachers of mathematics and informatics in their work with artificial intelligence (AI) are presented. A model for the application of the flipped dialogue in the education of students is proposed. An example of dialogue is given. The study concludes that that the main advantages of using flipped dialog learning with AI are easy access to the platforms, the lack of stress and stimulating the research qualities of students when searching for specific information or stimulating the system to make mistakes. The ability to ask the right leading questions and to detect the gaps of the "interlocutor" are important competencies applicable in dealing with life's problems.

In this research, we aimed to determine whether students' math achievements improved using ChatGPT, one of the chatbot tools, to prepare lesson plans in primary school math courses. The research was conducted with a pretest-posttest control group experimental design. The study comprises 39 third-grade students (experimental group = 24, control group = 15). The implementation process lasted five weeks and 25 lesson hours. In the experimental group, lessons were taught according to plans prepared using ChatGPT, while in the control group, existing lesson plans were used. Students' academic achievement was measured with a multiple-choice achievement test of 25 questions with two separate questions for each learning objective. According to the results, students' academic achievement increased significantly (d = 1.268) in math lessons taught according to lesson plans prepared using the ChatGPT. Although there was a difference between the posttest scores of the experimental group and the control group in favor of the experimental group, it was determined that this difference was not significant. These results show that teaching primary school math according to lesson plans prepared using ChatGPT is effective in academic achievement. Teachers should consider ChatGPT and their plans, combining them and benefiting from both in the implementation process.

Student's attitude towards 21st-century mathematics teaching is affected by factors such as content knowledge, knowledge of teaching and learning activities, attitude towards mathematics and technology knowledge. The aim of this study was to construct structural equation models for investigating 21st-century mathematics teaching and learning among secondary mathematics students in the Secondary Educational Service Area Office Lopburi (SEAOL). Quantitative research used the 21st-century TPACK framework. The research sample consisted of 400 SEAOL students from the 1/2022 semester using multi-stage sampling. A questionnaire was used to assess 21st-century secondary school mathematics teaching and learning with a 0.934 confidence of. The data was analyzed using the appropriate software and revealed key components and their relationships. The results show that teaching and learning, fundamental technology capability, content knowledge, specialized technology use, and mathematical content implementation all affected mathematics teaching in the 21st-century for SEAOL students. Influence was 0.89, 0.70, 0.63, 0.25, and 0.21. School technology support has a 0.59 effect on students' basic technological skills. Technology's role in learning influenced students' technology use by 0.21. This research shows how each aspect affects 21st-century mathematics education at the SEAOL, and math overload had the least effect. Teachers and stakeholders should investigate and innovate to improve the use of specialized technology in teaching to help students acquire higher-level mathematical content and apply it in their daily lives.

This research aims to analyze the results of studies conducted in Turkey on reasoning skills in mathematics teaching and to reveal what kind of trend there is in this field. Within the scope of this study, databases were searched with the keywords "reasoning"(muhakeme, akil yürütme) and "reasoning skill" (Muhakeme becerisi, akil yürütme becerisi), and the results were examined in accordance with the inclusion criteria regarding mathematics teaching. One hundred sixty-three studies were included. Each of the studies included in the meta-synthesis study was analyzed descriptively according to type, year, method, sample type and size, data collection tools, statistical analysis, learning field, keywords, reasoning type and purpose. In addition, the studies' results were content analyzed and tabulated by coding the differences and similarities between them with a holistic approach. It has been determined that studies on the learning fields in the mathematics curriculum are mostly carried out in the field of learning numbers and operations in the secondary school mathematics curriculum. When evaluated in terms of reasoning types, almost half of the studies were conducted on mathematical reasoning. It has been observed that after mathematical reasoning, the most focus is on proportional reasoning. When the aims of the studies included in the research were examined, it was determined that the most focused ones were "examining the factors affecting reasoning skills", "measurement of reasoning skills" and "the effect of teaching practices on reasoning skills". In the studies examined, it was seen that there were 33 teaching practices whose effects on reasoning skills were examined.

The fact that the mathematics course is abstract, that it is not possible to associate it with daily life, and that it is impossible to concretize abstract expressions causes a prejudice against the this course and leads to a decrease in the academic achievements of students. It is seen that throughout history, various studies have been carried out taking this situation into consideration. A group of these studies is on realistic mathematics education. Realistic mathematics education is an approach that aims to concretize the abstract concepts of mathematics by relating them to real-life situations. The purpose is to make mathematics more understandable by concretizing it. In the study, the subject of calculating the surface area of prisms with the use of realistic mathematics education was taught, and the purpose of the study was to examine the effects of this application. The study group consisted of 20 5th grade students. While determining this group, maximum variety sampling strategy was preferred. In the study, action research, one of the qualitative research methods, was used, and the data were interpreted with the help of descriptive analysis and content analysis. The data collection tools in the study included semi-structured interview forms, video recordings, photos and activity sheets prepared by the students under the guidance of the researcher in accordance with the realistic mathematics education approach. When the findings were examined, it was seen that the students showed a positive development in the meaning and visualization processes; that they could reach mathematical inferences on their own; that they enjoyed the mathematics lesson; and that the realistic mathematics education approach gave positive results on learning. Based on these results, it was suggested that not only the application of the realistic mathematics education approach for different acquisitions but also the inclusion of these activities in the textbooks in accordance with the curriculum will result in improvements in favor of learning.

Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.

In the 21st century, the demand for proficiency in mathematics has escalated, as it underpins critical thinking, problem-solving, and innovation in various fields. Recognizing the significance of mathematics education, after-school programs have emerged as potent supplementary platforms to enhance students' mathematical skills and achievement. This study aimed to determine the impact of the after-school program on fostering mathematics in the 21st century. The study was conducted at Chaparral Middle School of Alamogordo Public Schools District in New Mexico, USA to middle school students enrolled for the school year 2023-2024. The research method is experimental. The after-school program students were exposed to the mathematics resources in the 21st century such as Khan Academy, ALEKS, Peer-Assisted Learning Strategies, Illustrative Math, and the like. Evidence-based resources were used to foster students' mathematics achievement. A standardized test that measures mathematics achievement was the main instrument used in the study. The mean, standard deviation, and t-test were used to analyze the data collected. The analysis with a t-value of 7.889 and probability value of 0.000 revealed that students exposed to the after-school program performed significantly in terms of mathematics achievement. Researchers recommend that teachers may use the after-school program to foster mathematics achievement. Teachers might also incorporate activities into their Mathematics teaching that demand students to engage resource materials to foster students' mathematics potential in the 21st century.

Background: The STEM education system has garnered significant interest due to its innovative approach in creating a multidisciplinary and integrated knowledge structure that connects science, technology, engineering, and mathematics, and allows students to apply scientific knowledge in a comprehensive and holistic manner. Consequently, evaluating the teaching methods of teachers in accordance with STEM standards is critical. This assessment should take into account various educational objectives, including cognitive, skill-based, and emotional aspects. Purpose: This study aimed to evaluate the creative teaching practices of mathematics teachers for gifted students according to STEM standards. Method: The study applied the descriptive analytical method and developed a rating scale for evaluating creative teaching practices based on STEM standards, verifying the psychometric properties in several ways. The study sample consisted of 64 teachers of mathematics for gifted students. Results: The results showed that the degree of application of creative teaching practices by the teachers of gifted students according to STEM standards was at the moderate level in three domains: planning, implementation, and assessment. Conclusions: Despite the importance of achieving integration for STEM, the actual teaching practices of teachers of the gifted according to these standards were generally average and did not reach acceptable and ambitious levels.

Background/purpose: The purpose of this qualitative study was to identify strengths and deficits of alternative teacher certification programs, with particular emphasis on approaches to strengthening mathematical content knowledge and pedagogy. Materials/methods: Six participants included both teacher candidates enrolled in internship in the alternative master's elementary or early childhood program and recent graduates of the programs at a university in the southeast United States. Data were collected through semi-structured interviews conducted via an online focus group to elicit conversation among the participants of their combined perceptions of program-level recommendations to better prepare them to teach elementary mathematics. Using inductive, open coding of the transcribed data, the researchers identified and ultimately agreed upon the emerging themes related to perceptions of preparation program components. Results: Related to research question one, participants shared meaningful experiences related to the instructor modeling effective mathematics teaching practices that have impacted their own teaching. Related to research question two, five common themes, including recommendations for improvement, were revealed: Need for more preservice mathematics methods instruction and theory into practice; Preparedness for accommodating diverse needs; Analyzing student data to inform practice; Utilizing and securing available resources; and navigating curricular changes/district mandates. Conclusion: Based on the results of the study, teacher candidates in the elementary and early childhood alternative master's programs are in need additional content, pedagogy, and resources to effectively teach elementary mathematics.

High school math projects center on solving real-world examples in a wide variety of situations that require a creative skill set. Creativity in high school mathematics takes place in a subtle form. In contrast, creativity presents itself conspicuously in art. Therefore, this paper will explore the utilization of polynomial equations in drawing various figures as part of algebra class projects. Additionally, these projects incorporate integrated digital tools in mathematics. The paper will analyze three algebraic projects: the first project involves drawing a bird, the second project focuses on drawing a butterfly, and the third project entails drawing a bat using polynomial equations with the technological tool Desmos. All three projects are products of student work that encompass figures requiring up to forty polynomial equations. The students' impressive work demonstrates the power of mathematics in pushing the boundaries of other subjects. As digital technology becomes increasingly integral, mathematical tools are positioned as universal tools for the future and are poised to rival artists in producing visual art. This raises the intriguing question: can a mathematician create better art with mathematical equations through digital technology than an artist?

This study investigates school-age children's arithmetic operations performance while solving larger-size problems which produces interferences in memory. Complex problems can trigger competing responses in working memory, which are irrelevant to a task goal and increase the likelihood of interference from previously learned problems (De Visscher et al., 2018). Interference control in working memory is required to be able to manage and suppress irrelevant information while performing cognitive tasks such as arithmetic problem-solving (Unsworth, 2010). The present study explores potential cognitive processes while performing arithmetic tasks and emphasizes the important role of interference control for better performance in such tasks. This study applied a mixed-effect model experimental design. Forty-four primary school children were involved in the study. The results showed that children's performance in terms of correct responses was similar for both small-size and large-size problems. However, their response speed was significantly lower in larger-size problems, which created more interference in working memory.

This study examines the effects of a working memory (WM) sensitive math intervention in students with learning disabilities (LD). The intervention aims to improve early mathematical competencies while accounting for weak cognitive resources through a reduced instructional design. These principles are considered to be effective for learning. Ten students with mild to moderate intelligence impairment participated in our study. We applied an AB single-case intervention study across participants to evaluate the effects of the intervention. The students take part in at least 10 30-minute intervention sessions. Non-overlap indices, as well as regression analysis, support positive effects on students' mathematical competencies. Nevertheless, there are still students for whom the effects were unstable or failed to materialize. Besides the effectiveness of the WM-sensitive math intervention, the results support the assumption that the mathematical learning of students with LD is similar to that of students without LD but delayed.

The researchers conducted a qualitative case study on a learning community comprising special education and psychology majors. This community was strategically organized to foster interdisciplinary learning among its members and to design interventions for students struggling with mathematics anxiety, specifically in classes like Algebra 1. Working alongside a university faculty member and a graduate student, the undergraduates applied mental health principles from psychology research to real-world situations. Their efforts included teaching Algebra 1 to a student grappling with both a learning disability in mathematics and mathematics anxiety. In their approach, the group utilized mindfulness principles to tailor conversations to the high school student's interests, effectively incorporating mindfulness techniques into the mathematics tutoring sessions. This approach proved successful, particularly when the student was experiencing high levels of anxiety, enabling significant progress in his Algebra 1 work. The collaborative efforts also provided substantial benefits to the college students, who learned about each other's fields of study. They effectively combined this knowledge in practical ways and applied it in real-world settings. The findings of this study offer important insights for the training of pre-service special education teachers and college students in related fields.

Understanding how marginalized students experience and perceive mathematics is critical to achieving the goal of inclusive and equitable math pedagogy. We report on 67 focus groups with 251 predominantly Black high schoolers experiencing economic marginalization in the Southern United States and attended to their achievement level and race-gender identities. Students often shared concerns about their teacher's math knowledge for teaching and effectiveness in supporting academic success. Their self-perceptions of math identities varied, and students often did not value advanced math even when they expressed career interests that require advanced math. We discuss practical implications for supporting the math development of marginalized high schoolers, including centering the needs and strengths of Black girls, and propose an expanded inclusive and equitable pedagogical framework.

Attention to the disconnection between culture and mathematics has been addressed then and now (Wilder (in: Graves et al., Proceedings of the international congress of mathematicians, American Mathematical Society, 1950; Liu in Taiwan Journal of Mathematics Education, 8:79-88, 2021b). Recently, studies, workshops, and contests about an approach to relating culture and mathematics, such as incorporating mathematics history or mathematics writings in class, have emerged. However, although the effectiveness of such an approach was proved, employing it as instruction was still significantly ignored, not to mention the approach to creating mathematics literary writings--the goal that the Mathematics-Literature Contest aimed to achieve. Additionally, no empirical studies have systematically assessed the contest, especially from the cultural perspective. Through teachers' and students' perceptions, this qualitative case study aims to examine the impact of mathematics literary writings on the development of mathematics teaching/learning and the mathematics culture represented in the contest. Ten teachers and 20 students were interviewed. Data were analyzed by following Yin's five phases (2016). The study visualizes an evolutionary model of the contest, signifying the development of mathematics culture simultaneously. Results demonstrated that the contest caused teachers and students, who constituted the internal force, to consolidate the mathematics culture, which was enriched by the external force--to reinterpret the connection between mathematics as well as culture and the reform of general education. The developed mathematics culture included elements other than mathematics, such as the Chinese writings and their interactions with mathematics and life experiences. The findings hold implications for mathematics and general education: An interdisciplinary curriculum design can help cultivate teachers' and students' intellectual acumen; higher education communities worldwide must follow the trend.

This study examined how and to what extent a prekindergarten teacher's perceptions of ready children and diversity--which are influenced by broader societal culture--influence their abilities and ways of incorporating children's funds of knowledge into their practice. The methodology used was based on a descriptive case study of a teacher, Linda, who participated in a two-year professional development (PD) program that focused on using funds of knowledge in culturally and developmentally responsive early mathematics pedagogy. How Linda incorporated children's funds of knowledge when teaching mathematics was closely linked with her notions of the prototypical ready children and her essentialized understanding of culture and diversity. Findings suggest the importance of asset-oriented perspectives of each child and family and attention to cultural practices when learning funds of knowledge to raise teachers' sensitivity toward and use of children's funds of knowledge to enrich children's learning.

Is children's literature only beneficial to children? Or do the benefits of children's literature also extend to the knowledge and mathematical skills of the teachers who employ it and reflect on it? This study seeks to investigate the role of picturebooks on the mathematical knowledge of preschool teacher candidates. For this purpose, in-depth examinations of how picturebooks can be used in teaching preschool mathematics and children's literature. As well as the changes in the content knowledge of the teacher candidates, were done by conducting focus group interviews with teacher candidates. This is a qualitative case study consisting of focus group discussions in which high-level knowledge sharing and production can be achieved through interaction and associations. In the research, 11 picturebooks were discussed, and 8 teacher candidates participated in 6 focus group interviews lasting a total of 338 min throughout a 7 week period. The study's findings have demonstrated that through children's literature, teacher candidates' misconceptions about measuring length can be revealed and eliminated without the need for another source, with discussions based on consciously and systematically selected picturebooks. Thus, it can be said that picturebooks act as a catalyst for the studies that aim to enhance the mathematical content knowledge of teacher candidates. The study has also observed that picturebooks can comprehensively address the fundamental concepts of length measurement.

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary pre-service teachers (PSTs) and 13 elementary PSTs drew upon when solving a comparison proportional reasoning problem. Data from written work and videos of PSTs' explanations were analyzed using the robust understanding of proportional reasoning for teaching framework. Both elementary and secondary PSTs ubiquitously drew upon the same four knowledge resources (comparison of quantities, ratios, proportional situation, and ratio as measure). Elementary PSTs were more apt to counterproductively draw upon the knowledge resource ratios ? fractions, while secondary PSTs more often counterproductively drew upon equivalence. Mathematics educators can leverage the knowledge resources afforded by this task and strategically highlight productive and counterproductive resources to tailor instruction that develops PSTs' robust understanding of proportional reasoning.

Previous studies have found positive effects of Game-Based Learning for mathematics. While most studies assume that this effect is explained by the presence of flow/immersion during games, this has not yet been established. The aim of the current study is to verify if immersion indeed is associated with mathematical skills improvement when using a Game-Based Learning intervention. This was tested among 59 Greek high school students, using authentic design. After having received a traditional education module, the students were tested and then engaged for four weeks in a desktop-based 3D Virtual Learning Environment where they could play mathematic minigames. They were subsequently re-tested to verify if they showed a significant increase in mathematical skills. The students showed an improvement in their mathematical skills (Cohen's d = 1.26), with significant results for functions, geometry, and thinking skills and methods. On the individual level, about half of the students showed a 10% increase in one of the domains (numbers & calculations, functions, geometry, thinking skills and methods, and algorithms and number theory). Immersion was found to be reflected by engagement and presence, but neither one of these aspects was associated with mathematical achievement after the intervention. It is concluded that Game-Based Learning is an effective approach to increasing mathematical skills, yet the underlying mechanisms are not yet understood. The authors discuss several alternative mechanisms based on the literature that can be verified in future studies.

Mathematical problem solving remains a struggle for many students today (Celebioglu et al., 2010; Englard, 2010; Gavaz et al., 2021; N. H. Lee et al., 2014; Yeo, 2011). Though intervention studies have reported measured impact on improving students' problem-solving abilities (Gavaz et al., 2021; Gidalevich & Kramarski, 2019; N. H. Lee et al., 2014), few studies examine how learners would approach a non-routine problem without learning problem-solving strategies in school (Celebioglu et al., 2010; Saygili, 2017; Yazgan, 2015; Yeo, 2011). The latter would complement instruction related to strategies by making known the entry point of young problem solvers. In this study, 10 Grade Two students in a neighborhood primary school in Singapore were individually engaged in solving a non-routine problem with access to manipulatives. Based on their mathematics instructional history in school, the students have not been introduced to the relevant problem-solving strategies related to the task. The study examines how the students approach and solve the problem. Findings revealed that all the ten students were able to solve the problem with eight of them using manipulatives to help them. The study recommends that prior to classroom teaching, teachers can invite students to share their problem-solving methods and demonstrate how formal notations can capture these mathematically. Appropriate manipulatives should also be made accessible during problem-solving lessons.

In this qualitative study, we examined how prospective mathematics teachers' instructional visions align with their instructional practices through an approximation of practice opportunity. Namely, we employed scripting tasks to understand how prospective teachers complete a scripting task and respond to students' misconceptions, and we compared their instructional visions with their responding practices. The 81 prospective mathematics teachers who were taking the "Misconceptions in Mathematics Teaching" course at two different state universities comprised the participants. Data was obtained from the instructional vision questionnaire and two scripting tasks in fractions. We analyzed the data using the content analysis technique. Our findings indicate that the majority of the participants' instructional visions were aligned with ambitious instruction, while their responding practices were mostly inconsistent with their visions. Our findings suggest that while their instructional visions were highly reform based, prospective mathematics teachers still need to be oriented in an ambitious instructional direction in their practices.

Behavior and academic outcomes in school are interrelated; students who struggle with academics are likelier to exhibit troublesome behavior and students who struggle with behavior tend to fall behind academically. Multitiered systems of support (MTSS) offer frameworks for providing increasingly intensive support for students with academic and behavioral difficulties, but it can be challenging to efficiently integrate academic and behavioral supports rather than implementing separate resource-intensive systems. This article describes how behavior support can be integrated within Tier-2 interventions for reading and mathematics. A strategy that included four evidence-based elements--teaching expectations, self-monitoring, self-evaluation, and mystery match--was embedded within academic intervention lessons to target students' academic engagement, respectful behavior, and effort. In this article, we describe our approach as one way that academic and behavioral supports might be integrated within a tiered intervention system.

The home math environment is vital for early math development. Yet, there is limited understanding of how parents translated their attitudes towards helping children learn math (HCLM) into actions to influence their young children's math-related outcomes. Thus, the present study examined whether parents' perceived competence, value, and pressure about HCLM contributed to young children's math competence through parents' interest in HCLM, home math activities, and children's interest in math. One hundred forty-seven parents were surveyed about their attitudes, practices, and their children's math interest. Meanwhile, their children were individually tested on applied math problem solving. Results showed that parents' perceived competence and value about HCLM predicted their interest in HCLM, while parents' pressure about HCLM predicted children's math interest. Parents' interest in HCLM is positively linked to children's applied math problem solving via children's math interest. This study shed light on the importance of promoting parents' positive attitudes towards HCLM.

Early detection of and relevant information on children's mathematical difficulties is important to initiate targeted teaching and intervention. This study investigated the extent to which strategy use in single-digit addition provides additional predictive information about 61 grade one children's (6-year-old) mathematical achievement 3 years later that is not available from a standardised mathematics achievement test. Four predictors available in year one (arithmetic strategy use, mathematical achievement, non-verbal reasoning skills and sex) explained 54% of the variation in grade four mathematics achievement. Arithmetic strategy use was the most important single predictor of year four mathematics achievement (R[superscript 2] = 30%) and explained an additional 12% variation if added to a model comprised by the three other year one predictors. This result suggests that systematically obtained measures of how young children solve single-digit arithmetic problems might provide useful information about their foundational number knowledge, which in turn may reveal how well they achieve later in school.

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms' mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy execution when solving multi-step subtraction problems with three EFs (i.e., updating, inhibition, and shifting). With a choice/no-choice design, 150 fifth-graders' (M[subscript age] = 10 years, 11 months) direct subtraction (DS; e.g., 712 - 346 = ?; 712 - 300 = 412, 412 - 40 = 372, and 372 - 6 = 366) and subtraction by addition (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) use to solve multi-step subtractions was examined. Participants were offered ten subtractions in one choice condition (free choice between DS and SBA), based on which we obtained data about task proficiency and strategy selection, and in two no-choice conditions (mandatory use of either DS or SBA), which were used to examine strategy execution. The results showed that task proficiency in the choice condition was associated with updating and inhibition but not with shifting. Furthermore, strategy selection was associated with updating but not with inhibition and shifting. Strategy execution was associated with updating but not with inhibition and shifting. The inclusion of separate strategy selection and execution parameters helped to unravel how arithmetic performance and EFs are associated.

Empirical studies on effects of formative assessment (FA) on motivational outcomes and underlying mechanisms are scarce. The core elements of FA, feedback and adaptive teaching behavior, might be helpful in promoting the experience of competence, which in turn is a prerequisite for promoting intrinsic motivation. However, instructional impact also depends on the students' perception of teacher behavior. Therefore, this study (N = 27 teachers and 613 students) aimed to test whether FA has a positive effect on intrinsic motivation mediated by students' perceived competence support (PCS). In a three-group design, two versions of FA were compared with a control group. In both versions of FA, teachers used a tool for learning progress assessment (LPA), while in one version, teachers received a combination of LPA and additional support consisting of materials for feedback and adaptive instruction (LPA+). A path model for half-longitudinal designs was estimated. Results support the motivational effect of FA. LPA and LPA+ both positively influence students' PCS which is in turn associated with higher intrinsic motivation. A small indirect effect on intrinsic motivation mediated by PCS was shown for both intervention groups, which was only significant for LPA. For LPA+, higher-performing students particularly benefitted from the intervention. Teachers' use of FA practices can foster students' PCS which seems to be a promising way in motivation-enhancing teaching.

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed a series of tasks designed to elicit shortcut strategies. First, students solved each task by means of their preferred strategy; those using shortcut strategies were construed as adaptive for that task. Second, students solved the same tasks by means of whatever alternative strategies they had available; those offering at least two strategies were construed as flexible for that task. Third, for each task, students were asked to indicate which of their strategies they believed was optimal. Across all grades, students were more flexible than adaptive. Overall, sixth graders exhibited higher levels of flexibility than third graders and marginally lower levels than eighth graders. Sixth graders exhibited higher levels of adaptivity than those in either grade three or grade eight. Students' accuracy, which improved with maturation, was influenced positively by both adaptivity and flexibility, with flexibility having the greatest influence in grade three and adaptivity in grade six. The findings raise further questions concerning, inter alia, culture's influence on students' strategy choices and the interaction of adaptivity, flexibility and maturity on accuracy.

The latest content and practice standards for mathematics have promoted the use of academic language and discourse in this content area. As such, the WIDA Consortium has evolved its guidelines to deepen teachers' conceptual understanding of language in their content areas, and thus, enable them to provide more effective instruction to multilingual learners. Karen L. Terrell explores one of the primary "key language uses" in mathematics -- the narrative genre. She also considers how visuals can be powerful scaffolds and means of expression for multilingual learners and discusses how visuals can be used for students to both receive and express knowledge. The use of narrative and visuals can make mathematics more accessible to all students.

Scholars suggest that culturally responsive instructional supervision (CRIS) is an important component of equitable teaching practices in schools. This fictional case study details the experiences of a fifth-grade team who, along with their principal and their instructional coach, perform a discourse analysis of their own mathematics lessons to diagnose the equity gaps in their teaching and make necessary adjustments. The case narrative highlights the need for equitable teaching practices in the mathematics classroom and the potential needs of school leaders as they work to create more equitable learning environments in their schools through the use of CRIS.

We examined the characteristics of video annotations frequently discussed during debriefing conversations as part of video-assisted coaching cycles. We also analyzed how mathematics coaches used written annotations to inject ideas into debriefing conversations when supporting teachers to reflect on important classroom events. Coaches and teachers asynchronously created the annotations based on what they noticed while watching video of an implemented lesson. Findings revealed annotations that were coach-created, focused on the teacher, contained content about goals and discourse, or contained connections were most frequently taken up during the debriefing conversation. In addition, we identified four unique ways coaches used annotation references to inject new ideas into the conversations. We present a rationale for continued research on the relationship between noticing artifacts from a lesson (i.e., video annotations) and subsequent reflective conversation between a coach and teacher.

This study investigated the added value of real-time adaptive feedback on seventh graders' performances in tablet-based geometry learning. To isolate the effects of the medium (ie, tablet) from those of the feedback, three groups were compared: paper-and-pencil, pen-based tablet without feedback and pen-based tablet with feedback. The feedback was provided by a tutoring system based on an artificial intelligence that automatically interpreted students' pen strokes on the screen. A total of 85 French students drew three geometric shapes, either on paper or on a tablet, and then performed a transfer task on paper. Results showed that using a tablet without feedback did not improve learning but seemed to enhance interest in the task compared to the paper-and-pencil group. Students in the tablet with feedback group performed significantly better than the other two groups on learning, as well as on transfer. This study was the first to combine media comparison and added-value approaches to test the effects on students' geometry performances of using a new educational app on a pen-based tablet in a naturalistic classroom environment. Results showed that it was not the medium used but the intelligent tutoring system-based feedback that improved students' performance. Our data therefore indicate that artificial intelligence is a promising way of providing learners with real-time adaptive feedback in order to improve their performances.