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Gender inequality is strongly linked with poor performance in science and mathematics for female students in secondary schools owing to socio-economic and cultural issues as well as learning strategies. According to the Certificate of Secondary Education Examination results of 2021 in Tanzania, the failure rate for female students was higher than that for male students, and such failure in chemistry was associated with inadequate knowledge about the tested concepts, failure to identify the requirements of the respective questions and lack of adequate mathematical skills. Real practical sessions are integral parts of chemistry to enhance the learning environments for both female and male students. However, the real laboratory practices especially for chemistry are challenged with the costs of the construction of physical laboratory infrastructure and reagents, and the time-consuming and physical demands on personnel during real practical sessions. Thus, this study explores gender-based effects of the chemistry virtual laboratory against a paper-based approach towards a real chemistry practical in Tanzanian secondary schools. The results indicate that the combined exposures of virtual laboratory and paper-based practicals improve real practical performance for both female and male students. Moreover, the performance of real practical practices progressively improved for female students when they were first exposed to the virtual laboratory and then the paper-based practical. Such improvements can be associated with the virtual laboratory providing interactive learning environments which support female students to connect and engage. [ABSTRACT FROM AUTHOR]

Tablet‐based technology has become a conduit for the administration of curriculum‐based measurement (CBM) tools. Using tablets to administer CBM probes has many advantages; however, little is known about how students perform on CBMs when administered via a tablet. The current investigation compared digits correct per minute obtained from 44 third‐grade students on CBM addition fluency probes administered via three different modalities. Students completed the probes using traditional paper and pencil, a tablet using their fingers to write the answer, or a tablet application using a keyboard to type the answer. A within‐subjects group design showed students performed significantly better on the tablet when using their finger to write the answer, even though most students (58%) indicated this was their least preferred modality. The discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. Practitioner points: Third‐grade students responded to math facts faster when writing with their fingers on an iPad, even compared to paper and pencil.The results are inconsistent with other studies that found students were faster when using paper and pencil.Finally, most third‐grade students preferred answering addition facts with a pencil on paper. [ABSTRACT FROM AUTHOR]

This study aimed to utilise linear and equipercentile equating procedures in establishing the equivalence of paper-based and computer-based Grade 7 Mathematics Achievement tests. The single group counter-balanced test equating design was used in the study. Paired t-tests results showed that the performance of the students in paper and computer-based tests were not the same. The respondents found the computer-based test more difficult than paper-based test. Also, this result was supported by the differential item functioning analysis where 27 out of 40 items were flagged for differential item bias. Based on this result, it is essential to implement equating procedure in interpreting the scores of computer-based and paper-based Mathematics Achievement tests. The linear and equipercentile equating procedures had similarities on the way scores are transformed based on the ability of the students. The transformed scores were used to interpret fairly whether the students took the paper-based or computer-based Mathematics Achievement tests. Findings showed that students with "beginning" and "developed" proficiency levels found the computer-based test more difficult than the paper-based test while students with "proficient" level had similar performances in both tests. Lastly, students with "advanced" proficiency level found paper-based test more difficult than computer-based test. [ABSTRACT FROM AUTHOR]

The major focus of school education is the intellectual development of students and mathematics is a very effective subject in this regard, if taught and assessed properly. For this study, papers of SSC (Grade-10) for the years 2014 and 2015 set by the Board of Secondary Education, Karachi were scrutinized to know if the items of these papers had measured essential mathematical skills or not. These items were then compared with the items set by General Certificate of Education (GCE: O-Level), University of Cambridge Local Examinations Syndicate (UCLES) for mathematics papers, serving as a benchmark for this study to highlight the shortcomings. The results revealed that the items of SSC papers were highly biased towards 'Factual Knowledge' and 'Routine Procedures'. The study concluded that these items assess knowledge of facts and algorithms only and do not measure essential mathematical skills (involvement of higher levels of thinking processes) of students. The study recommends to improve the items of papers so that essential mathematical skills can be measured rather than the capacity of memorization because with this practice, thinking habits cannot be inculcated among students. [ABSTRACT FROM AUTHOR]

This study aimed to compare and examine the effectiveness of interactive STEM learning and paper-and-pencil STEM learning in terms of mathematical literacy skills of elementary school students. This research is of a quasi-experimental type with a non-equivalent pretest-posttest control group design. Sampling was carried out on the elementary school populations in Bengkulu and South Sumatra Provinces in two stages. In the first stage, schools in rural and urban areas were selected, and in the second, classes in each school were randomly selected. The selected sample consisted of fifth-grade students of the Public Elementary School of Terawas, Musi Rawas, with an experimental class A (n = 20) and an experimental class B (n = 19), as well as fifth-grade students of the Public Elementary School of Bengkulu City, with an experimental class A (n = 25) and an experimental class B (n = 22). Data collection was conducted using mathematical literacy skills tests in reference to the PISA and Minimum Competency Assessment (level 1-3). Data analysis was performed using descriptive and inferential statistics; it employed an independent t-test for the comparative testing and an N-gain test for testing the effectiveness of STEM learning. The results showed that there were differences in math literacy skills between interactive STEM and paper-and-pencil STEM for students in urban schools, but not significantly different for students in rural schools. General STEM learning was effective in increasing the literacy of elementary school students, and interactive STEM in particular demonstrated the highest level of effectiveness in the urban school. [ABSTRACT FROM AUTHOR]

As an increasing number of British universities are now requiring/encouraging mathematics applicants to have taken ‘extension papers’ such as the Mathematics Admissions Test (MAT), Advanced Extension Award (AEA) and Sixth Term Examination Paper (STEP), current students were asked how useful they were in preparation for their degree. The MAT was most commonly described as good preparation for undergraduate mathematics, whilst most participants who had taken the AEA were indifferent regarding its usefulness. Participants were positive about STEP, commending its similarity to undergraduate-style assessment and its challenging questions. The students’ views suggested that those wishing to be well prepared for tertiary mathematics should take one of these papers, preferably STEP. However, whilst universities may not necessarily wish to require applicants to pass extension papers, it may be beneficial for universities to recommend students to take them in order to improve their mathematical thinking and expectations of undergraduate mathematics study. [ABSTRACT FROM AUTHOR]

This paper presents an example of how paper folding can be used in a geometry class to support conceptual understanding. Specifically, it explains an activity that constructs a rhombus and explores its attributes by using paper folding. The steps of constructing a rhombus are described and some discussion questions are given to consolidate understanding. [ABSTRACT FROM AUTHOR]

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations. [ABSTRACT FROM AUTHOR]

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods:WeBWorK, an open-source system for web-based homework, or traditional paper-and-pencil homework. We assessed learning for 439 students in 19 college algebra classes at a large public university in the United States. Twelve classes usedWeBWorKand seven had traditional paper-and-pencil homework. Analysis of covariance revealed no significant differences in algebra performance or achievement gain by homework group, ethnicity or gender when statistically controlling for previous mathematics achievement. Results support the conjecture thatWeBWorKis at least as effective as traditionally graded paper-and-pencil homework for students learning college algebra in moderately sized lecture-based classes. [ABSTRACT FROM AUTHOR]

In this introduction, we set the stage for a collection of papers from the Co-constructing Mathematics Motivation in Primary Education–A Longitudinal Study in Six European Countries Project (MATHMot for short), an international study aiming to identify the factors that shape the development of motivation in mathematics from a comparative perspective in primary education. Students' motivation, performance, academic emotions, and subject-related identity and agency are observed across six countries: Norway, Sweden, Finland, Estonia, Portugal, and Serbia. MATHMot builds on the belief that one of the main goals of mathematics teaching should be children's long-term motivation for learning the subject, which in turn supports students in striving for exemplary achievement in mathematics. This special section attempts to observe students' mathematics motivation in early grades and how different contributions from the classroom, home or the student's individual characteristics shed light on its development and adjacent concepts like academic emotions and math-related identity and agency. [ABSTRACT FROM AUTHOR]

By providing students with a highly interactive and hands-on learning experience, robotics promises to inspire a new generation of mathematical learning. This paper aims to review the empirical evidence on the application of robotics in mathematics education and to define future research perspectives of robot-assisted mathematics education. After a systematic search in online database via keyword search and snowballing approach, we analyzed 20 empirical studies on how to teach and learn mathematical knowledge through robotics. The results indicate that (1) most studies were conducted with a small sample size, the largest research groups were elementary school students and secondary school students, most studies used LEGO robots, robots were primarily applied to teach and/or learn graphics, geometry, and algebra, and almost half of the studies taught mathematics by engaging students in game-like interactions with robots; (2) half of the studies adopted a non-experimental research design, and most studies evaluated student performance through observation, test/examination, questionnaires, or verbal interviews; and (3) instructional implications proposed in the 20 papers can be clustered into four themes: human-robot interaction, connections between mathematics and real life, pedagogical suggestions, and facility conditions. The 20 papers suggest that robotics generally plays an active role in mathematics education; however, there are indeed situations in which no significant improvement was found in students' mathematical learning. In view of this, we prospect the future research perspectives of robot-assisted mathematics education and propose that more rigorous intervention studies could be conducted to further explore the integration of robotics and mathematics education. [ABSTRACT FROM AUTHOR]

In Victoria, Australia, senior secondary mathematics students are expected to use technology and thus need to make decisions about using pen-and-paper (P&P) or technology when solving mathematics problems. The predominant technology is a Computer Algebra System (CAS). This study investigated the beliefs about CAS held by twelve Year 11 students as they learnt to use CAS and whether these beliefs were stable over time. These students held a range of beliefs related to the usefulness of CAS, speed of CAS compared to P&P, whether CAS is proper mathematics, choice of CAS or P&P, ease of use, the correctness of answers and solving problems in Mathematical Methods (i.e. the mathematics subject studied). Beliefs are often described as being stable (e.g. McLeod, 1992), but some researchers stress stability needs to be determined empirically rather than being seen as a characteristic of beliefs (e.g. Liljedahl et al., 2012). For this sample of students, stability (rather than instability) is a feature of students' beliefs about CAS. [ABSTRACT FROM AUTHOR]

Structural equation modeling (SEM) is well-known in statistics due to its flexibility and accessibility. In the Scopus database alone, there were more than 1,500 search results related to SEM in mathematics education. However, there is a lack of scientific reviews of mathematics education that use SEM. The purpose of this study was to investigate research trends related to SEM in mathematics education. The researcher used Biblioshiny and VOSviewer to conduct bibliometric analysis on 1,017 papers that have been published in the Scopus database. The result showed that the number of publications in the research area has continuously grown over the last few decades. The US was the most prolific country in terms of publication and international collaboration. Professor Herbert W. Marsh had the most publications and citations, while the most productive journal was Frontiers in Psychology. The most current keywords include STEM, technology acceptance model, control-value theory, and computational thinking. Hence, these findings may serve as a guide for future researchers to conduct relevant research using SEM. [ABSTRACT FROM AUTHOR]

The peer tutoring approach is a student-cantered teaching method in which students learn in pairs with teacher supervision. The study discussed in this paper is a systematic literature review related to the effectiveness of peer tutoring approaches which has been published within the last 5 years. A complete text analysis was conducted using 20 research papers stating the impact of the peer mentoring approach for this writing. Among the things obtained from previous studies are the variety of ways to implement peer tutoring approach, the impact on 3 aspects in students which are mathematical achievement, social skills and cognitive skills and the teaching theories used. The findings of the study indicate that most past studies used quantitative research methods with the concept of age peer approach. Then, constructivism theory was the most frequently applied with a sample of high school students. In conclusion, this systematic literature review shows that the peer tutoring approach in mathematics education has many benefits in various aspects and needs to be extended to improve the quality of education. [ABSTRACT FROM AUTHOR]

In this article, I will discuss a collective research project that I designed for my History of Mathematics course. My students, who are by and large pre-service teachers, explored online, digital versions of 18th-century British almanacs that contained question-and-answer sections for mathematics. In a multi-stage research process, they explored the primary sources, investigated selected mathematical problems from the almanacs, conducted prosopographies of the contributors to the almanacs, and finally surveyed secondary sources. They then presented their results in pairs to their classmates. Through these presentations, as well as the prosopographies and notes they shared on our online classroom management system, the working pairs of students wrote research papers that placed their findings within the context of the research of the whole class. This collective research project allowed my students to begin focused and purposeful research within the first week of classes. Moreover, this project encouraged them to become highly engaged with their primary sources and enabled them to work as a team. This collective research project framework could be applied to a variety of groups of primary sources from the history of mathematics (such as textbooks and journals), now widely available online, to a variety of mathematics courses. [ABSTRACT FROM PUBLISHER]

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both courses culminated in a final project in which students created and investigated solutions to their own modeling tasks. In this paper, we describe how our courses (1) centered justice as pedagogy, (2) were environments for student agency and exploration, and (3) explicitly demonstrated how mathematics and social justice are intertwined. Drawing on frameworks of mathematical modeling for social justice, we present and analyze student-created tasks to showcase how they utilized mathematics as a tool to question and critique the world around them. [ABSTRACT FROM AUTHOR]

This paper explores a recent move towards project-based learning for a first-year undergraduate statistics module at the University of the West of England, Bristol. The course is aimed at students specialising in Mathematics and Statistics. A classroom-based end of module project week was developed with the focus on project-based learning, supported by Dewis-R data generation and e-Assessments. Simulation of a practice-based environment with a dedicated working area and daily deadlines is incorporated to enhance the activity. Students are faced with a highly relevant statistical analysis task, that is large and has not had the prior data screening or cleansing that they may be accustomed to in basic didactic teaching. Indications are that the project-based learning approach, assessed during a project week with supplementary e-Assessments and a final report, is well received and leads to improved student outcomes. [ABSTRACT FROM AUTHOR]

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students' geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the Euclidean geometry context. For this, we designed and implemented two mathematical tasks with 52 secondary education students (15–16 years old, 10th grade) during the COVID-19 emergency lockdown period in Italy. The tasks involved four phases: constructing, exploring, conjecturing, and proving. This article presents an epistemic analysis of the tasks and a cognitive analysis of the answers given by one of the students. The theoretical tools of the onto-semiotic approach supported these analyses. Cognitive analysis allows us to confront the intended meanings of the task and the meanings actually employed by a student, thus drawing specific conclusions about the roles of such artifacts in written arguments and give an interpretation of their combined use in mathematics education. [ABSTRACT FROM AUTHOR]

Based on the expectancy-value perspective on identity and identity formation, this paper explores the relationship between math identity (MI) and the dimensions of motivation (i.e. intrinsic value, attainment value, utility value and perceived competence) and math achievement in primary school. An additional aim of our research was to explore these relationships in different cultural contexts and investigate potential gender and grade differences concerning MI. The participants were 11,782 primary school students from Norway, Sweden, Estonia, Finland, Portugal and Serbia. All predictors from the motivation spectrum were significant for students' MI across the examined countries and had a stronger association with MI than math achievement. Among the motivational dimensions, intrinsic value had the strongest association with students' MI. Boys had significantly more positive math identities than girls in Estonia, Finland, Norway and Portugal. The results showed that the grade 4 students perceived themselves less as "math persons" than their grade 3 peers in all countries. [ABSTRACT FROM AUTHOR]

Given the increasing prevalence of web technology, web-based mathematics environments have been increasingly widely used in mathematics education for the past two decades. The COVID-19 pandemic has led to an urgent transition from traditional mathematics instruction (TMI) to web-based mathematics instruction (WBMI) at all levels of mathematics education. At this point, it is crucial to scrutinize the effects of WBMI on K-16 students' mathematics learning comprehensively. This meta-analysis research contained a total of 63 studies with 115 effect sizes, which aimed to investigate the effectiveness of WBMI on K-16 students' mathematics learning by incorporating potential moderators, namely mathematics topics, mathematical content standards, feedback status, type of instructional features, age (i.e., grade level), and assessment methods. Based on findings, WBMI has a significantly strong effect on K-16 students' mathematics learning (g = 1.10, p = 0.01, 95% CI [0.95, 1.27]). Moderator analyses reveal that the effect sizes of WBMI on K-16 students' mathematics learning varied significantly depending on all these potential moderators. Additionally, higher-level mathematical concepts, statistics and probability, WBMI with providing feedback, tutorial systems, undergraduate students, and traditional paper-pencil assessment are the strongest moderators in their context. The most notable results of this research are that WBMI is significantly more effective on students' mathematics learning than TMI, while even in the context of WBMI, traditional paper-pencil assessment is significantly more effective than online assessment. This meta-analytic research provides a comprehensive and up-to-date perspective on the effectiveness of WBMI on K-16 students' mathematics learning. [ABSTRACT FROM AUTHOR]

Begun in the niid-90s, computers have long been a staple in teaching mathematics to engineering sttidents. In recent years. with the effects of the Covid-19 pandemic and the arrival of Generation Z in tertiary education, the role of blended learning has increased. This paper highlights some of the greater challenges and successes of the transition from traditional teaching techniques to the creation of blended learning environments through three case studies. First, the translation of pen-and-paper education to a computerissed form in everyday online and face -to-face practice classes. Second, the reimagination of correspondence courses as blended learning courses. Finally, setting thefinal exams in a compliterised environment: what types of questions are appropriate to measure students' eflective understanding of engineering mathematics. [ABSTRACT FROM AUTHOR]

Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this activity and the construction by students of knowledge, such as mathematical concepts and theorems, that is new to them. This issue is significant to seeking a better integration of mathematical practice and content, emphasised in curricula in several countries. In this paper, we address this issue by exploring how students generate mathematical knowledge through discovering and handling refutations. We first explicate a model depicting the generation of mathematical knowledge through heuristic refutation (revising conjectures/proofs through discovering and addressing counterexamples) and draw on a model representing different types of abductive reasoning. We employed both models, together with the literature on the teachers' role in orchestrating whole-class discussion, to analyse a series of classroom lessons involving secondary school students (aged 14–15 years, Grade 9). Our analysis uncovers the process by which the students discovered a counterexample invalidating their proof and then worked via creative abduction where a certain theorem was produced to cope with the counterexample. The paper highlights the roles played by the teacher in supporting the students' work and the importance of careful task design. One implication is better insight into the form of activity in which students learn mathematical content while engaging in mathematical practice. [ABSTRACT FROM AUTHOR]

This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model set-up and revision for these different scenarios and approaches as well as contemporary science approaches. Changes in student ranking of biology and math as well as student feedback are included. This paper may be of interest to any faculty member designing or revising a similar course or inserting modules on these topics into any related course. [ABSTRACT FROM AUTHOR]

Mathematics is not just the queen of the sciences; it permeates through art, commerce, and in fact, every aspect of modern life. However, while we as mathematicians see beauty in the mathematical way of thinking and problem-solving, our students tend to think of mathematics as a set of rules and abstract computations. Our pleasure of doing mathematics usually does not transfer over to our students. In this paper, we describe two liberal arts general education courses which seek to develop a broad appreciation of mathematics for students who may not require any technical mathematics course for their academic major or chosen career path. We present mathematics as it relates to everyday life, with the goal of improving student appreciation of mathematics. [ABSTRACT FROM AUTHOR]

Research investigating teachers' knowledge and practices aimed to improve student participation, engagement and achievement in mathematics and science has often used qualitative methods involving observation and analysis of lesson videos. Some researchers have used excerpts of videos in various ways to gather data about their participants' anticipated actions in the moment. In the current study, we aimed to track primary teachers' developing adaptive expertise when teaching interdisciplinary mathematics and science lessons over a two-year period. In this paper, we describe the processes followed to design a questionnaire that used episodes from videos of interdisciplinary mathematics and science lessons to construct multiple choice items. The adaptive expertise scoring for the items was reliable but this improved when including an open-ended question for participants to explain their selection of an action for the classroom moment captured in the video episode. [ABSTRACT FROM AUTHOR]

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a mathematics teacher attempting to share authority as well as applying several moves recognized as supporting meaningful student learning. Data has been collected in a fourth-grade Norwegian classroom and is analyzed by means of open coding, inspired by literature. We identify the moves used by the teacher, and we rank these moves along two dimensions: (1) their potential to support mathematical reasoning and (2) their potential for sharing authority. From this, we uncover how a teacher's work of orchestrating mathematical discussions involves moves in all four quadrants, and we discuss how the interplay of moves affects the authority structures and the collaborative reasoning in the classroom. [ABSTRACT FROM AUTHOR]

The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience. [ABSTRACT FROM AUTHOR]

This is a fairy tale taking place in Chessland, located in the Bermuda triangle. The chess pieces survey their land and trap enemy pieces. Behind the story, there is fascinating mathematics on how to optimize surveying and trapping. The tale is written by the students in the PRIMES STEP junior group, who were in grades 6 through 9. The paper has a conclusion, written by the group's mentor, Tanya Khovanova, explaining the students' results in terms of graph theory. [ABSTRACT FROM AUTHOR]

This paper examines the extent to which teacher factors of the dynamic model of educational effectiveness can explain variation in student achievement in mathematics. It also searches for the extent to which any of these factors matters more for academically resilient students than for all the other low-socioeconomic-status students. Participants were all teachers (N = 66) of 14 schools in socioeconomically disadvantaged areas who teach mathematics to students of Grades 4–6 (N = 904). Teacher factors were measured through a student questionnaire, whereas mathematics achievement at the beginning and the end of the school year was measured through written tests. Student background characteristics were measured through a student questionnaire. Information on parents' occupational status was also collected. Multilevel modelling analysis revealed that all teacher factors explain variation in mathematics achievement. Differential effects for all factors but modelling and assessment were identified. Implications of findings are discussed. [ABSTRACT FROM AUTHOR]

With this paper, we share an activity for the undergraduate mathematics classroom called The Harp Project that leverages the aesthetic nature of both the mathematical and the musical arts. This project was conceived as a STEAM/PBL project with the added feature that it was carried out in pieces by an entire class. Anecdotal evidence suggests that the uncommonly high level of students' interest and engagement in the experience and the communal feel of their participation can be attributed to this collective quality of the project's design. For this reason, we invite others to consider this curricular experience as it appears viable for supporting efforts to cultivate a broader population of students with an affinity for mathematics. [ABSTRACT FROM AUTHOR]

This paper shows how one mathematics teacher, in a government secondary school in rural Rwanda, re-contextualises learner centred education (LCE) and English medium instruction (EMI) policies in classroom practice. Data are drawn from an ethnographic, critical case study and include lesson transcripts and teacher and student perspectives. The study indicates the importance of including non-verbal language in investigations of classroom interaction, and problematises the tendency to equate LCE with student talk in groups. In these lessons, whole-class interactions are managed by the teacher and student verbal participation is limited. Nevertheless, students co-construct and participate in activities and communicate mathematical meanings. The teacher observes and responds to students and enables students to access the English and mathematics they need for examinations. EMI limits student verbal participation and access to the textbook. The study indicates the importance of learning from and responding to classroom realties rather than pedagogical and linguistic ideologies. [ABSTRACT FROM AUTHOR]

Objective - This paper explores the mathematical proficiency espoused by Kilpatrick et al. to improve teacher and learner mathematics performance in South Africa. A mixed-method approach involving interviews and questionnaires was used. Methodology/Technique - The sample included 7 principals or deputy principals, 7 departmental heads who supervised mathematics, 1 mathematics teacher who taught mathematics in grades 10 to 12, 1 mathematics teacher who taught Mathematics, and 1 learner from each grade 8 to 12 was included in the sample. Each participant was interviewed and had to complete a questionnaire. Finding - Kilpatrick et al. (Kilpatrick, Swafford, & Findell, 2001), who viewed Mathematical Proficiency as a fivestranded process involving conceptual understanding, productive disposition, procedural fluency, strategic competence, and adaptive reasoning, were used as a lens through which this study was conducted. We discovered several systemic, societal, and pedagogical challenges that teachers and students faced, all of which had an impact on their Mathematics teaching and learning. Our findings were in line with what was found in the literature review. The researchers concluded that there were always intervention strategies that could help to reduce or eliminate the challenges that Mathematics teachers and students face. Novelty -The researchers concluded there were always intervention strategies that could assist in minimizing or eradicating the challenges faced by the teachers and learners of mathematics, thus improving their socio-economic standing. [ABSTRACT FROM AUTHOR]

Mathematics is often taught by explaining an idea, then giving students practice in applying it. Tutoring systems can increase the effectiveness of this method by monitoring the students' practice and giving feedback. However, math can also be taught by having students work collaboratively on problems that lead them to discover the idea. Here, teachers spend the bulk of their time orchestrating collaborations and supporting students in building productively on each other's contributions. Our research question is: Can tutoring technology somehow make teaching-by-eliciting more effective? Using tutoring technology, we developed an intelligent orchestration system named FACT. While students solve problems in small groups, it makes recommendations to the teacher about which groups to visit and what to say. Data from over 50 iterative development trials (study 1) suggest that FACT increased neither the collaboration nor productivity of the students' struggle compared to paper-based classes. However, the data also suggest that when there is just one teacher in the classroom, then only a few of the groups that need a visit can get one. We modified FACT to directly send students the provocative questions that it formerly sent only to teachers. A pilot test (study 2) suggests that this version may increase productive struggle, but increasing collaboration remains an unsolved problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss about just-non-CLT groups and we give a characterization of solvable just-non-CLT groups which have no subgroup of index p, where p is the smallest prime dividing |G|. [ABSTRACT FROM AUTHOR]

The purpose of the research presented in this paper was to study the role of concrete and table representations created by students in learning how to solve an optimization problem called the transportation problem. This topic was learned in collaborative groups using table representations suggested by teachers in 2021. In 2022, the researchers decided to enrich the students' learning environment with concrete objects and urged the students to use them to present the problem to be solved. The students did it successfully and, to be able to record it in their notebooks, they constructed a table representation by themselves without any help from their teacher. After that, they managed to solve the problem by manipulating the objects. At the same time, each step in the solution was presented with changes in the table. The students were assessed before (pre-test) and after collaborative learning (test) in both academic years. The pre-test results were similar, but the test results were better in 2022. Therefore, it can be concluded that using concrete and table representations constructed by students in learning how to solve transportation problems makes collaborative learning more constructivist and more effective than when they use only table representations suggested by their teachers. [ABSTRACT FROM AUTHOR]

The paper discusses an example of an educational project in modern mathematics in which school students create mathematics that is new to them. The mathematical results produced by the students in the theory of definability also have an "absolute" novelty, i.e., are the basis for professional publications. The described course was based on recent results of this article's authors in the theory of definability. The new results were obtained by a group of 10 schoolchildren from different regions of Russia. [ABSTRACT FROM AUTHOR]

This paper considers an approach to mathematical education adequate to the task of developing mathematics and its applications in the 21th century. This approach is based on improving the efficiency of the educational process by maintaining the motivation of students of various categories. The basis for the formation of motivation is, on the one hand, independent design; invention of mathematical objects, methods of action, and models of the world around us; and the discovery of facts of mathematical reality and, on the other hand, solving of new, unexpected, and feasible tasks for the student. The student's work is similar to the work of a mathematician–researcher and programmer. The possibilities of research work in educational mathematics are significantly expanded due to computer-based intramathematic experiments. Debugging a computer program is a special kind of mathematical experiment. [ABSTRACT FROM AUTHOR]

More than 35 years have passed since Shulman introduced the term "pedagogical content knowledge" [PCK] to the field of teacher education. As is the case with any new construct in a field, Shulman's advocacy for PCK in the mid-1980s was almost certainly a reaction to the priorities of the field at that time. A primary goal of this paper is to refresh our collective memories of the origins of and development of PCK as a research domain, with a particular focus on what may have prompted scholars such as Shulman to propose the construct of PCK in 1986. With this historical lens as background, I also seek to consider what might be fruitful future directions in the field's thinking about teaching and teacher knowledge. [ABSTRACT FROM AUTHOR]

This issue is the first of a specialPRIMUStwo-part issue collecting articles from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. It is inspired by the “Regional Faculty Workshop on REU Issues” in 2013 and the Joint Mathematics Meeting 2015 Mathematical Association of America’s “Themed Session on Perspectives and Experiences on Mentoring Undergraduate Students in Research.” This issue consists of seven papers focusing on the larger issues involved in creating, running, and sustaining an undergraduate research program in mathematics. [ABSTRACT FROM AUTHOR]

Every new generation of students have difficulties with learning mathematical subjects. The success in Mathematics is getting lower and lower, not only in Macedonia but also on global level. Mathematical materials that contain only problems with solutions without their visual representation are hardly acceptable for many students. So, visualization plays an important role in the process of teaching mathematics subjects. In this paper, we will present the solution of examples of plane equation and, by using free software, visualization of that solution is made. For solving several examples, we are going to use the Computer Algebra System (CAS) in GeoGebra. [ABSTRACT FROM AUTHOR]

This paper presents results of a systematic review of papers published at the LUMAT journal on the current issues positively and negatively affecting teaching and learning in mathematics, in concurrence with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The analysis also offers insight into the most studied topics in mathematics education research, including key demographic and methodological characteristics such as year of publication, participants, education level, research methodologies, and research focus. Data was gathered from the studies published in the LUMAT: International Journal on Math, Science and Technology Education, starting from its first volume in 2013. So far, 225 articles were published in this journal, with 133 studies written in English and 51 studies related to mathematics. Although earlier studies support the notion that mathematics education is mostly traditional, this review suggests current research has thorough and positive outcomes, such that mathematics educators are likely to implement non-traditional approaches, encouraging student engagement, peer collaboration, and mathematical discourse. Certainly, in such learning environments, students tend to feel more motivated and less anxious about learning mathematics. They may also be more active and responsible in their learning, collaborate with peers, and get into mathematical discussions. Yet, there are also a number of difficulties and obstacles highlighted both in teaching and learning of mathematics. The findings might inspire several instructional implications for mathematics educators, curriculum developers, and researchers. Recommendations are given to add into what the existing literature claims and offer greater empirical evidence to support the verdicts. [ABSTRACT FROM AUTHOR]

In this paper a part of the data from a larger study, the Enactment Project, is explored. The exploration is guided by two research questions. The first is specific to the instructional core of teacher practice while the second is related to student perceptions of how they learn mathematics. The project adopted the Complementary Accounts Methodology. Micro-analysis of how three teachers enacted their instructional objectives, using qualitative data analysis methods, led to the identification of three components of an instructional core, namely, Development of concepts and skills [D], Student work [S] and Review of student work [R] that pervade the lessons of the three teachers. They enacted their instructional objectives through instructional cycles comprising combinations of D, S, and R. A lesson was found to comprise one or more instructional cycles. The post-lesson video-stimulated student interview data, showed that teachers helped their students learn mathematics in their lessons specifically in the S and R activity segments. This paper also dispels the myth about stereotypical mathematics instruction in Asian classrooms whilst contributing to this issue of ZDM in memory of David Clarke. It was his work related to the Complementary Accounts Methodology that provided colleagues in Singapore with a tool to illuminate mathematics instruction in their schools. [ABSTRACT FROM AUTHOR]

In this commentary, I draw exclusively on the ten papers in this issue of ZDM focused on Mathematical Tasks and the Student. These papers represent various cultural and theoretical stances and when reading them I was looking for common themes across some or all the papers. Based on my readings, I argue that (a) each task has the potential to promote domain-specific as well as domain-transcendent goals potentially communicating a more coherent and connected picture of mathematics, (b) tasks cannot be considered independently from their enactment and prior enactments should inform future implementations, and (c) the context of the implementation of a task (i.e., the teacher, classroom norms, and student agency) is essential and needs to be considered in the design phase. [ABSTRACT FROM AUTHOR]

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]

Assessment of students' mathematics knowledge within higher education (HE) has normally taken a very traditional approach. Closed-book assessments have long been the favoured mode of assessment (Iannone & Simpson, 2011) which often requires students to recall facts, formulae, and methods. One could argue that this type of assessment is limited in its ability to effectively assess how well a student's ability to authentically use mathematics has developed. Due to the recent pandemic, many institutions were forced to rethink their assessment methods so that they could be delivered online and remotely. As such, there has been a renewed sense of need for more 'authentic' assessments for mathematics-based programmes. In this paper, we will discuss our journey of creating more authentic assessments for apprentices enrolled on a new Data Science Degree Apprenticeship, particularly in mathematics/statistics. We will compare two years of delivery of the course; the first year of delivery which comprised of traditional assessment methods (coursework/exam) and the second year of delivery that used more authentic assessment methods. We will discuss the pros and cons of each model by reflecting on our practice and drawing on apprentices' feedback. [ABSTRACT FROM AUTHOR]

Elements of the Individualized Education Programs (IEP) for culturally and linguistically diverse students with mathematics learning disabilities (CLD-MD) have long been inadequate at capturing the cultural, linguistic, and learning needs of this subset of students. Efforts to address the knowledge gap of understanding of culturally and linguistically diverse (CLD) students within the mathematics community, specifically those focused on mathematics learning disabilities, have typically focused on strategies for specific mathematics concepts and skills such as computation, word-problem solving, or fraction strategies. As the population of CLD students who are identified both as culturally and linguistically diverse and having a specific learning disability in the area of mathematics increases, there have been increased efforts to identify strategies that support the complexity that their identities bring to mathematics instruction. Much of this work is nascent in the field, and as such, this paper provides a variety of evidence-based strategies that provide appropriate whole-class instruction and intensive interventions for CLD-MD students. [ABSTRACT FROM AUTHOR]

This paper provides on-the-ground accounts of epistemic violence against Black immigrant children in mathematics classrooms. From a critical feminist perspective, we introduce Dotson's notion of silencing as an enactment of epistemic violence. According to Dotson, one way to enact epistemic violence is to damage a particular group's ability to speak and be heard. A successful act of communication depends on the audience's willingness and ability to "hear" the speaker. Therefore, denying this reciprocity in communication is a form of epistemic violence. Using this conceptualization, we conducted a secondary data analysis from a larger study aimed at enhancing teachers' knowledge and abilities to implement problem-solving teaching. We identify and characterize three practices of silencing Black immigrant students in Chilean mathematics classrooms that damage their agency as knowers and doers of mathematics. Beyond language issues, we show that silencing is a form of anti-Black onto-epistemic violence that prevents Black immigrant students from being recognized as legitimate subjects of knowledge in mathematics classrooms. [ABSTRACT FROM AUTHOR]

This study investigated the impact of visual cueing on attention guidance, deep-thinking promotion, and performance optimization in arithmetic word problem solving for students with mathematical learning difficulties (MLD). The participants included eight students with MLD and twenty students without MLD who attempted to solve mathematical word problems with and without visual cueing. Eye movements were recorded during the tasks. A repeated-measure design and nonparametric tests were applied to enhance the statistical power of the study. The data analysis results indicated that visual cueing effectively guided and sustained the attention of students with MLD, reducing their off-task duration. However, it showed limited influence in facilitating deep thinking and performance improvement for these students. There were no significant attention-guidance or performance-improvement effects observed in the problem-solving processes of students without MLD, who initially demonstrated better concentration levels and performance. The potential explanations for these findings are further discussed in this paper. [ABSTRACT FROM AUTHOR]

Growth in fully online mathematics education has been steady for decades. This is where essentially all interactions associated with the teaching and learning process are mediated via the online medium. Initially spurred on by technological innovation and a variety of socio-cultural forces, growth has more recently rapidly accelerated due to pandemic restrictions. Many suggest we are on the precipice of profound transformation in mathematics education, the outlines of which remain unknown. In leveraging online education possibilities and advancing online mathematics education, this paper considers aesthetic experiences associated with learning mathematics fully online. First, three assumptions are made to highlight the importance of these experiences. Second, three challenges are identified regarding the current state of fully online mathematics education. Finally, specific instructional design and online teaching strategies are outlined that potentiate experiences of wonder and beauty often associated with mathematical discovery. As its central theme, the paper seeks to answer how we may take advantage of this technology in delivering quality mathematics education without allowing it to diminish our human essence. [ABSTRACT FROM AUTHOR]