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Metacognitive awareness (MA) and critical thinking (CT) are crucial higher-order thinking skills in mathematics education. MA and CT skills of pre-service teachers are considered important predictors of their future teaching practices in the teaching and learning of mathematics. In this context, the study examines the potential effects of socio-demographic (e.g., gender) and academic variables (e.g., academic year and academic achievement) on MA and CT skills of pre-service mathematics teachers (PSTs). Additionally, the aim of this study is to explore the relationship between the MA and CT skills of PSTs. Employing a quantitative research methodology, the study was structured around a correlational model. It involved 218 PSTs, using the "MA Inventory" and "CT Standards Scale" for data collection. The data were analyzed through independent sample t-test, one-way analysis of variance, correlation analysis, and simple linear regression analysis. The findings indicate that PSTs possess a high level of MA and CT skills. Significant differences in MAs of PSTs were observed with respect to academic year and academic achievement, while the CT skills of PSTs showed significant differences concerning gender and academic achievement. A strong, positive, and significant correlation was found between MA and CT skills of PSTs. Furthermore, the MAs of PSTs were identified as a significant predictor of their CT skills, explaining 38% of the variance in CT skills. [ABSTRACT FROM AUTHOR]

In this article, we explore the transformative impact of advanced, parameter-rich Large Language Models (LLMs) on the production of instructional materials in higher education, with a focus on the automated generation of both formative and summative assessments for learners in the field of mathematics. We introduce a novel LLM-driven process and application, called ItemForge, tailored specifically for the automatic generation of e-assessment items in mathematics. The approach is thoroughly aligned with the levels and hierarchy of cognitive learning objectives as developed by Anderson and Krathwohl, and takes specific mathematical concepts from the considered courses into consideration. The quality of the generated free-text items, along with their corresponding answers (sample solutions), as well as their appropriateness to the designated cognitive level and subject matter, were evaluated in a small-scale study. In this study, three mathematical experts reviewed a total of 240 generated items, providing a comprehensive analysis of their effectiveness and relevance. Our findings demonstrate that the tool is proficient in producing high-quality items that align with the chosen concepts and targeted cognitive levels, indicating its potential suitability for educational purposes. However, it was observed that the provided answers (sample solutions) occasionally exhibited inaccuracies or were not entirely complete, signalling a necessity for additional refinement of the tool's processes. [ABSTRACT FROM AUTHOR]

In this article, we explore the transformative impact of advanced, parameter-rich Large Language Models (LLMs) on the production of instructional materials in higher education, with a focus on the automated generation of both formative and summative assessments for learners in the field of mathematics. We introduce a novel LLM-driven process and application, called ItemForge, tailored specifically for the automatic generation of e-assessment items in mathematics. The approach is thoroughly aligned with the levels and hierarchy of cognitive learning objectives as developed by Anderson and Krathwohl, and takes specific mathematical concepts from the considered courses into consideration. The quality of the generated free-text items, along with their corresponding answers (sample solutions), as well as their appropriateness to the designated cognitive level and subject matter, were evaluated in a small-scale study. In this study, three mathematical experts reviewed a total of 240 generated items, providing a comprehensive analysis of their effectiveness and relevance. Our findings demonstrate that the tool is proficient in producing high-quality items that align with the chosen concepts and targeted cognitive levels, indicating its potential suitability for educational purposes. However, it was observed that the provided answers (sample solutions) occasionally exhibited inaccuracies or were not entirely complete, signalling a necessity for additional refinement of the tool's processes. [ABSTRACT FROM AUTHOR]

Robotics offers innovative possibilities at all levels of education, which should be considered when planning the teaching process for certain engineering mathematics topics in higher education. This paper introduces a new teaching–learning technique that utilizes STEAM-based methods to explore cycloidal curves for Computer Science Engineering BSc students. Traditional frontal teaching has been enhanced with methods addressing the generational needs of students, including problem-based learning, STEAM integration, and project-based learning. We developed a methodological model that merges traditional teaching advantages with practical modern approaches suitable for Generation Z. The four-stage model for learning cycloidal curves employs various didactical approaches, utilizing different learning techniques at each stage to create an engaging and effective learning experience. A vital component of this model is the use of Desmos dynamic geometry software to create animations alongside educational robotics to aid visualization. We conducted quantitative studies with 98 first-year Computer Science Engineering students using a quasi-experimental research design to evaluate the new teaching technique's effectiveness. Results from the Mann–Whitney U test indicated that the experimental group significantly outperformed the control group. Additionally, the Kruskal–Wallis test confirmed that the four-stage model for learning cycloidal curves enhances learning achievement for all students, regardless of their prior knowledge. [ABSTRACT FROM AUTHOR]

This case study reports on an intervention that took place within a second-year mathematics module at a higher education institution in the United Kingdom. Prior to completing an essay, students were supported to understand the potential benefits and risks of using Generative AI to aid their process. Students were allowed unpenalised use of Generative AI to complete this assessment. They were interviewed to gain an understanding of how they used this technology, and their perceptions of it. A small sample (n=3) allowed for in-depth exploration. All participating students reported using Generative AI in ways which developed their critical awareness of the technology, and the authors believe that the overall value of the assessment to students was enhanced. The case study ends with recommendations for integrating Generative AI into assessment, and directions for further study in this rapidly developing field. [ABSTRACT FROM AUTHOR]

A good physics education depends on a good, transferable mathematics education. A concept for a cross-modular blended learning math course developed for the first two semesters of our physics teacher trainee study program is introduced. The course covers the important new mathematics required for the development of the conceptual understanding of the classical experimental physicsmechanics and electrodynamics. It is based on three pillars: parallelism of the math topics to the physics lectures, spiral-curricularity to prior knowledge and high quality digitally available interactive materials such as interactive videos, formative tests and exercises to foster a self-regulated learning of the students in online as well as face-to-face learning environments. The blended learning math course and its face-to-face math seminars are integrated into the experimental physics modules. Results of surveys among the first two cohorts of course participants indicate that the design of the math course is well accepted and the interactive videos are very well received by the students. Initial tests on the learning effectiveness indicate a sufficient development of long term knowledge by the students. [ABSTRACT FROM AUTHOR]

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

This study assessed the impact of a cognitive apprenticeship model (CAM)-based stratified teaching module on the mathematical proficiency of high school students. The stratified cognitive apprenticeship model teaching module (SCTM) first involves grouping students based on their mathematical abilities. Students with higher performance are placed in one class, while those with lower scores are placed in another. Instruction for each group is then conducted using the cognitive apprenticeship model, tailoring the teaching approach to align with the specific needs and abilities of each group. A quasi-experimental design was adopted and 150 students were recruited. This study compared the outcomes of a control group, which was instructed using conventional teaching methods (CI), with those of two experimental groups—one instructed using a stratified cognitive teaching method (SCTM)-based on the CAM—and another instructed using the CAM alone. Students' performance was evaluated based on a mathematics test including the following dimensions: knowing and understanding, investigating, communication, and application (of mathematical knowledge to real-life problems). The data were analyzed using an analysis of covariance (ANCOVA). The results indicated that students instructed using the SCTM outperformed their peers in mathematical achievement, thereby validating SCTM's effectiveness as a comprehensive educational strategy for mathematics education at the senior high school level. [ABSTRACT FROM AUTHOR]

Copyright of Educação Matemática Pesquisa is the property of Pontificia Universidade Catolica de Sao Paulo, Programa de Estudos Pos-Grad. em Educacao Matematica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we describe an idea for mathematics lectures that involves using digital tools for first-year university students. Materials in the Moodle course include live broadcasts, lecture recordings, Moodle tests, sample solutions and videos. The aim of the paper is to find out from students' feedback which digital tools help them understand the material better. We focus also on the tools used in the Desmos environment slides. Students' feedback showed that using Desmos slides during the lecture helped them understand the theory better and try the tasks immediately. Graphical Desmos tools were the most appreciated because they helped to visualize the studied topic. [ABSTRACT FROM AUTHOR]

In this paper we deal with a geometric machine that has gone somewhat unnoticed in mathematics education: the Perfect Compass. It allows conics to be drawn using a special two-aperture compass, based on Apollonius' conic sections. Proposed in the 1 Oth century, it seems that was never built in medieval times -at least no archaeological remains from the medieval period have been found- and later constructions have operational limitations. This machine has been reengineered by us to make it fully functional and thus become a suitable instrument for education. We have built it using Digital Manufacturing technology, such as 3D printing and laser cutting, so that it can be widely available in the service of mathematics education. We also show how its operation results in a machine where its manipulation allows direct knowledge of the method and concepts used. [ABSTRACT FROM AUTHOR]

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely the kinds of contexts that experienced provers used to establish combinatorial proofs of binomial identities. Our findings show that overall, our participants used a variety of contexts in their work; we also demonstrate ways in which previous experiences influenced the contexts they chose, and we offer some instances in which features of a context supported their combinatorial proof production. We offer some theoretical implications of our work, and we conclude with a discussion of limitations and avenues for future work. [ABSTRACT FROM AUTHOR]

Many students who take a mathematics course as part of their post-secondary education are not enrolled in a mathematically-intensive degree program. This poses a challenge to mathematics departments that, for example, value and privilege more traditional mathematics curriculum: should students in such courses be taught differently than those in more traditional mathematics courses? What should constitute the curricula of these courses and who should teach them? How might the local institutional context influence the courses that are ultimately offered? This paper sketches a theory intended to help frame responses to these questions. We then present an example of this theory in action, in the form of a general education mathematics course for first-year, underprepared students. The ongoing design, teaching, and evaluation of this course might inspire further revisions to general education in mathematics at the undergraduate level. We present the motivation for the design of the course, a summary of what was ultimately enacted, and our reflections of this ongoing event. Our intention here is not to present our course and an evaluation of its 'success' – however that might be conceptualised – but rather to display a rigorous vision for post-secondary general education mathematics. [ABSTRACT FROM AUTHOR]

Technical skills related to basic mathematics in higher education have been a key foundation for further allied courses across primary programmes. While the traditional learning strategies appear to be inadequate to enhance the basic mathematics skills of university students, digital mathematical games pose the potential to improve such a set of skills by means of mobile learning. This work focuses on investigating the influence of digital mathematical games on students' basic mathematics skills under four various academic programmes. To illustrate the proposed scheme, a case study is conducted in a state university in the Philippines across undergraduate programmes in information technology, hospitality management, industrial engineering, and education. It was found that the use of digital games can improve the skills of students in basic mathematics. Thus, the educational system may be redesigned along with the positive effects of digital games on traditional skill enhancement initiatives. [ABSTRACT FROM AUTHOR]

The article explores the relationship between mathematics education and humanity, with a focus on the efforts of the International Commission on Mathematical Instruction (ICMI). The ICMI recognizes the significance of mathematics education in addressing societal challenges and promoting sustainable development. The article provides evidence of this relationship through various initiatives, such as the International Congress on Mathematical Education, ICMI Study 27, and the Felix Klein Medals awarded to Professors Ubiratan D'Ambrosio and Alan Bishop. Additionally, the article mentions the International Mathematics Union's interest in mathematics for humanity and sustainable development. The ICMI's work aligns with the goal of inclusive mathematics education for all learners, considering social, cultural, and historical contexts. The text also highlights the Capacity and Network Project (CANP), which supports the enhancement of mathematics education in developing regions while respecting local knowledge and experiences. [Extracted from the article]

Purpose: This study aims to describe and examine the effectiveness of the mathematics-based learning method, called Accountamatics (Accounting from Mathematics perspective). The Accountamatics method is rooted in the principles of double-entry bookkeeping and the rules of debits and credits, which were initially documented by Luca Pacioli, a Mathematics Professor, in a mathematics book. Design/methodology/approach: This study uses a quasi-experimental design, spanning a duration of one semester, to examine its research objectives. The participants included 230 students from the Faculty of Economics and Business in Indonesia, who were accredited by AACSB. Control variables, including gender, majors and study backgrounds, were taken into consideration. The data was analyzed using a linear regression test, followed by a comparative t-test. Findings: The study findings show a significant positive impact of the Accountamatics method on student performance when compared to traditional learning approaches. Furthermore, the analysis indicates that the control variables examined in the study did not have a significant effect on student performance. Thus, it can be inferred that the implementation of the Accountamatics method has a beneficial effect on the academic performance of college students. Practical implications: The study findings provide valuable insights for faculty members in higher education institutions, highlighting the potential benefits of incorporating mathematics-based teaching in accounting as an alternative approach for business students. These findings contribute to the existing knowledge on innovative teaching methods that can enhance the study of accounting within the business curriculum. Originality/value: Over the span of around 25 years, extensive research has been conducted to compare traditional teaching methods with innovative approaches. However, the results have not consistently shown that the innovative methods outperform their traditional counterparts. In response to this, the Accountamatics method has been developed, building upon the fundamental knowledge in accounting that has been used since 1494. Despite its historical significance, this method is sometimes regarded as limited to technical knowledge in the modern era. [ABSTRACT FROM AUTHOR]

Higher vocational mathematics education is advanced and related to real-time applications providing vast knowledge. Teaching and training peculiar mathematical problems improve their educational and career-focused performance. Therefore optimal performance assessment methods are required for reducing the lack of knowledge in mathematics learning. This article hence introduces an Articulated Performance Assessment Model (APAM) for consenting mathematics assessment. In this model, fuzzy optimization is used for consenting different factors such as understandability, problem-solving, and replication. The understandability is identified using similar problem progression by the students, whereas replication is the application of problem-solving skills for articulated mathematical models. From perspectives, problem-solving and solution extraction is the theme that has to be met by the student. The assessments hence generate a perplexed outcome due to which the fuzzy optimization for high and low-level understandability is evaluated. The optimization recommends the change in varying steps in problem explanation and iterated replication for leveraging the students' performance. This process swings between irrelevant and crisp inputs during fuzzification. In this process, the crisp inputs are the maximum replications produced by the students for better understanding. Therefore, the proposed model is evaluated using efficiency, maximum replication, fuzzification rate, and analytical time. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has posed one of the most challenging situations for the academicians as well as the students all around the world. Students being the biggest stake holders of the education process, their challenges during this pandemic become even more pivotal. These challenges vary in intensity and type depending on multiple items. In this paper, we analyse and document the challenges particular to the courses of mathematics and statistics in higher education. A survey was carried out for students, who have taken mathematics/statistics courses at universities mainly in UAE, to analyse various items affecting the learning process during the COVID-19 pandemic. The results of the survey showed that a significant portion of students are satisfied with distance education. [ABSTRACT FROM AUTHOR]

One of my last assignments at the university of Gothenburg was to teach a sequence of three seminars in programming for prospective teachers (n=37). The three seminars are given in the introduction of this manuscript. Since this was a course for prospective upper secondary teacher of mathematics, it was decided that it should be a course in programming for learning mathematics. This manuscript is a research article but also a manuscript about programming in GeoGebra, Python, and Wolfram Alpha. The examples I shared with my students led me to write a book about programming. See the reference list. [ABSTRACT FROM AUTHOR]

The purpose of this study is to comprehensively describe the results of the analysis of the ability to understand concepts and misconceptions in terms of differences in learning styles, as well as gender differences. The data to be collected in this study is in the form of primary data and secondary data. The primary data is obtained from primary sources and secondary data is obtained from secondary sources. The primary source in this study is informants, namely students, and the secondary source is documentation of student test scores as an illustration of student abilities. The instruments in this study are student learning style tests and auxiliary instruments in the form of misconception diagnostic tests. Learning style test in the form of a questionnaire. This instrument is used to uncover visual, auditorial, and kinesthetic learning style variables. Misconception diagnostic tests use the Certainty of Response Index (CRI). The results of the CRI analysis based on student answer criteria are: (a) 5.83% of student problem solving do not know the concept (lucky guess); (c) 22.30% of the student problem solvers did not know the concept; (b) 50.18% of student problem solving mastered the concept well; and (d) 21.69% of student problem solving occurred misconceptions. [ABSTRACT FROM AUTHOR]

Copyright of Revista Didasc@lia: Didáctica y Educación is the property of Universitaria de Las Tunas, Centro de Estudios de Didactica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Assessment is often used to promote learning, but the mechanisms of how assessment relates to epistemology – knowledge and knowing – have been scarcely studied and theorised. In this study, we examine students' epistemic resources in relation assessment in the context of university mathematics education. We draw on the theoretical framework of epistemic injustice in order to understand how assessment produces knowledge and knowers. Using reflexive thematic analysis, we analyse 77 students' essays about their experiences and ideals of assessment practices. We discuss how the students contributed to co-constructing the dominant status of exams in mathematics - exams were deemed fit to assess mathematical knowledge. At the same time, experiences of alternative assessment practices enabled students to re-define what constitutes valid knowledge and how such knowledge can be demonstrated and assessed. We conclude by noting that developing student-centred assessment practices not only fosters students' learning but also promotes their epistemic resources. [ABSTRACT FROM AUTHOR]

The training of non-specialists, particularly engineers, in mathematics requires designing specific didactic proposals that make the importance of mathematics evident. One approach to creating such proposals consists in analyzing the mathematics used in authentic contexts of engineering research and then effectuating a didactic transposition to mathematics teaching. To this end, in this research, we use elements of the anthropological theory of the didactic and the methodology of didactic engineering. Initially, we analyze the blind source separation method, a case of inverse modeling widely used in numerous engineering contexts (e.g., telecommunications, acoustics, geophysics, biosignal analysis). More specifically, we examine the algorithm based on the A x = b matrix model and its use in a signal processing context. Based on this analysis, we designed a didactic device that focuses the study on a simulated signal mixture of pure tones and implemented it in two first-year university mathematics courses in the virtual modality. This article reports the results of the students' first approximation to mathematical modeling activity in a setting of authentic research in engineering using a blind source separation method. [ABSTRACT FROM AUTHOR]

It is generally accepted that teachers' beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors, classroom video from three units of instruction, and survey and interview data from students in the classes, this paper examines instructors' stated beliefs, ways these beliefs manifested in their teaching, and students' beliefs across the course. Both instructors made curricular choices clearly aligned with their stated views of the nature of mathematics, learning, and teaching. Day-to-day instructional choices reflected these stated beliefs as well, but the difficulty of material and tensions with other beliefs like the importance of interactivity manifested. Characterizations of the interactivity of classes and placement of the mathematical authority in class are provided through descriptive and quantitative measures. These characterizations of instruction provide nuanced portrayals of classroom norms and changes in those norms throughout the semester. Furthermore, subtle shifts in student beliefs about teaching and learning are noticeable, suggesting students' beliefs about teaching and learning mathematics can be influenced even by modest changes in instructional practice. [ABSTRACT FROM AUTHOR]

This study explored what Ghanaian student teachers value in college mathematics learning. A cross-sectional survey involving 180 student teachers from College of Education in Ghana was conducted using the What I Find Important (WIFI) in mathematics learning questionnaire. The study employed principal component analysis with Oblimin rotation and one-way multivariate analysis of variance in analyzing the data gathered. Among the findings, it was found that student teachers value exploration, connections, understanding, and fluency in their study of college mathematics. Also, the findings of the study revealed a statistically significant difference in what student teachers value in college mathematics learning across college class levels. To facilitate a clearer understanding of valuing in the colleges of education in Ghana, it is considered important to establish through research the values of teacher educators regarding college mathematics learning and teaching, and how these values reflect what student teachers value and those values espoused in the new 4-year Bachelor of Education (B.Ed.) curriculum in Ghana. [ABSTRACT FROM AUTHOR]

To cope with an unpredictable future, higher education in mathematics and science (MS) needs to educate a knowledgeable and skilled workforce. Co-operative learning (CL) is a teaching method associated with increased academic achievement and development of generic skills. Thus, the purposes of this scoping review are to assess the evidence base of CL in undergraduate MS education to inform teaching practices and to identify potential knowledge gaps to inform future research. The review covers 24 empirical studies conducted from 2010 to 2020 on the prevalence, uses, and outcomes of CL elements in undergraduate MS education. The results show that there are few such studies, and these are rarely conducted outside the US or in disciplines other than chemistry. The most frequently implemented CL elements in the included studies are heterogeneous group formation, the use of roles, and different CL structures. The most prevalent student outcome of implemented CL elements in the reviewed studies is enhanced academic success, followed by student attitudes, generic skills, and psychological health. The results have implications for future implementation of and research on CL in international MS higher education. [ABSTRACT FROM AUTHOR]

In this paper, we aim to contribute to the planning and implementation of education in higher mathematics education for students from non-mathematics study programs, specifically focusing on multivariable calculus, i.e., multiple integrals. Indeed, the outcomes of various empirical studies indicate that students from non-mathematical faculties struggle to grasp and comprehend multiple integrals and multivariable functions in general. The research presented in this paper aims to ascertain whether there is a significant correlation between students' achievements in multiple integrals and their achievements in applying knowledge and skills from analytical geometry (to define sets of points in the plane and space, determined by lines, curves, planes and surfaces). Additionally, the study investigates whether this correlation potentially varies based on the various instructional teaching approaches. The presented empirical research was conducted at the Faculty of Engineering, University of Kragujevac, with 72 second-year students, divided into two groups. The results indicate that the given linear correlation is statistically significant and positive. Moreover, the differences in correlation coefficients calculated for two groups of students who acquired knowledge in multiple integrals through different instructional approaches are not statistically significant. These findings underscore the need to devote substantial attention to the teaching of multiple integrals, especially in devising methods that enable students to visualize specific mathematical concepts in both plane and space. Additionally, a precise definition of integration domains, and an accurate specification of variable bounds, should be emphasized in the multiple integrals teaching and learning process. [ABSTRACT FROM AUTHOR]

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

Copyright of Educação Matemática Pesquisa is the property of Pontificia Universidade Catolica de Sao Paulo, Programa de Estudos Pos-Grad. em Educacao Matematica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Featured Application: This study can be further extended to determine the ability of artificial intelligence to classify professional skills and success in cognitive task solutions according to EEG data. A high level of mathematical education is often associated with high effectiveness in solving cognitive problems and professional success. It is known that cognitive processes are accompanied by specific bioelectric activity in the brain and success in mathematical education as a behavioral phenotype is also reflected in EEG both during mental activity and at rest. This study tested the potential to distinguish volunteers with an advanced level of education in mathematics (AM) from individuals with a basic level of education in mathematics (BM) based on the frequency parameters of the resting-state electroencephalogram (EEG) recorded before the start of cognitive tasks. Further, the volunteers were divided into two groups, highly successful and moderately successful, according to their task-solving performance. The Light Gradient Boosting Machine learning algorithm was used for cross-subject classification based on the power spectral density of seven EEG frequency bands. It most accurately recognized and differentiated EEG of highly successful from highly successful BM subjects. The results indicate that success in solving tasks in combination with a high level of education in mathematics can be reflected in or predicted by the specific rhythmic activity of the brain at rest. [ABSTRACT FROM AUTHOR]

In this concluding commentary, I embed the articles of the special issue "Transition from school into university mathematics: experiences across educational contexts" into the current landscape of research on secondary–tertiary transition, and discuss the advancement they made related to the synthesis published in 2008 by Gueudet. My aim is to elaborate a new synthesis across the topics of affect and the use of sociocultural perspectives that have framed the work of all contributions. For that, I focus on four major themes. First, I consider the complex relationship between affect and socio-cultural dimensions in the papers, which raises the need for theory networking in further research clarifying mutual roles of the two dimensions. Second, international diversity is only partially expressed in the collection of papers, thus should be a major topic of research in future that would provide a more comprehensive view on the transition from school to university mathematics. I thirdly discuss how the collection of papers deepens our understanding of the complexity and diversity related to the students' experience with the secondary–tertiary transition and its potential impact for teaching. Finally, I propose and justify the need for systematic design and evaluation of interventions targeting a change in students' affect related to the transition. In sum, the wide range of the significant findings in this special issue and their mutual relations add new perspectives to the research on secondary–tertiary transition and evidence a new spectrum of research directions. [ABSTRACT FROM AUTHOR]

Drawing on the commognitive framework, we construe the secondary-tertiary transition (STT) as a distinctive element in the pedagogical discourses of various communities. Our interest rests with university tutors in light of the emergent recognition of their impact on undergraduates' mathematics learning in many tertiary contexts worldwide. We aim to understand the roles of STT communication in tutors' reflections on incidents that took place in their tutorials. Our participants were undergraduate students in the advanced stages of their mathematics degrees in a large New Zealand university and who were enrolled in a mathematics education course. Throughout the semester, the participants led tutorial sessions for first-year students and wrote reflections on classroom incidents that drew their attention. Our data corpus consisted of 58 reflections from 38 tutors collected over four semesters. The analysis revealed that STT communication featured in tutors' descriptions of classroom incidents, assisted them in making sense of unexpected events, positioned their instructional actions as replications of what was familiar to them from their own STT experience, and contributed toward generating new pedagogical narratives. We situate these findings in the literature concerning undergraduate tutoring and teachers' perspectives on STT. [ABSTRACT FROM AUTHOR]

The transition from school to university mathematics is a challenging process for many students. This phenomenon is reflected by high dropout rates from mathematics programs especially during the first year at university that may be related to the development of students' mathematical interest and self-concept. Taking a learning psychological perspective, it is a relevant question if all students have similar development patterns of these variables or if students who are at risk to drop out show an unfavorable development. Moreover, for didactical issues, it is of particular relevance which factors influence this development. Within a longitudinal study, 556 first-semester students stated their interest and self-concept at the beginning and the middle of the first semester; dropout was measured at the beginning of the second year. By using regression analyses, we found that the development of students' interest and self-concept is related to dropout. It seems that interest in university mathematics and mathematical self-concept of students, who dropped out, decreased significantly in contrast to the characteristics of students who continued their studies. In an exploratory follow-up study, we identified factors which probably influenced the development of students' self-concept by asking 18 students in a first-semester mathematics course "linear algebra" about learning situations in which they experienced the emergence or the decline of self-concept. Using qualitative content analysis, we found that most of these situations occurred when students worked on mathematical homework tasks or got criterial feedback on their solutions. Based on the presented results, we discuss implications for teaching and learning of undergraduate mathematics. [ABSTRACT FROM AUTHOR]

This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students' sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of academic social norms in a large-lecture course represented by the acquisition model of learning in college, detached from communal and collaborative disciplinary practices. Findings provide insights into the local educational context of an East Asian country as a case study when exam-oriented mathematics is institutionalized as normalcy. [ABSTRACT FROM AUTHOR]

Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their figured worlds, identities, and mathematical knowledge constructed through those experiences. Our analysis revealed their contrasting experiences in these two contexts, adding to our understanding of the phenomenon of "double discontinuity" in terms of not only how it is relevant to Hong Kong but also how it may manifest in the specific cultural context. Moreover, we found coherency and continuity during the prospective teachers' secondary–tertiary transition; their learning experiences in both environments served as critical resources upon which they reflected to envision their future mathematics teaching. We conclude with implications and suggestions for mathematics teacher education to support prospective teachers' (and their future students') transitions between high school and university mathematics. [ABSTRACT FROM AUTHOR]

Investigating the transition between educational levels is one of the main themes for the future of mathematics education. In particular, the transition from secondary school to STEM degrees is problematic for the widespread students' difficulties and significant for the implications that it has on students' futures. Knowing and understanding the past is key to imagine the future of a research field. For this reason, this paper reports a systematic review of the literature on the secondary-tertiary transition in Mathematics Education from 2008 to 2021. We constructed two corpuses: one from the proceedings of three international conferences in mathematics education (PME, ICME, and INDRUM) and the other from peer reviewed research papers and book chapters returned by the databases ERIC and Google Scholar. A clear evolution in perspectives since 2008 emerges from the analysis of the two corpuses: the research focus changed from a purely cognitive to a more holistic one, including socio-cultural and — to a lesser extent — affective issues. To this end, a variety of research methods were used, and specific theoretical models were developed in the considered papers. The analysis also highlights a worrisome trend of underrepresentation: very little research comes from large geographical areas such as South America or Africa. We argue that this gap in representation is problematic as research on secondary tertiary transition concerns also consideration of socio-cultural and contextual factors. [ABSTRACT FROM AUTHOR]

This study explores the diversity of university mathematics teachers' perspectives and experiences in relation to the secondary-tertiary transition (STT). Data for this study consist of responses of 310 university mathematics teachers from 30 countries to a survey. The survey design and data analysis are informed by an adaptation of a theory of improvement for education and by four idealized approaches for improving STT as identified in the literature: jump-oriented, enculturation-oriented, diversity-oriented, and cross-community-oriented. We characterize the diversity of perspectives and experiences in the data and examine ideas for future projects in light of these four approaches. We conclude that while jump-oriented approaches for improving STT are still the most prevalent, in part due to a persistent perspective of STT as a "deficit," university mathematics teachers' discourse on STT is becoming more diverse and nuanced. We find it particularly promising that participants' suggestions for future action are aligned with the four approaches, and most notably, with the cross-community approach expressing the emergent need for greater communication between the secondary and tertiary mathematics education communities. [ABSTRACT FROM AUTHOR]

Understanding the secondary–tertiary transition is not only an educational matter, but also an inclusion and equality matter as mathematics qualifications lead to better employment and better earning for students. Research on what causes the crisis associated to this transition has so far focused on the impact of cognitive and epistemological changes in university mathematics. Recently, attention has been given to sociocultural and affective issues, which indicate the impact of diverse contexts on such event in the students' life. Here we present a study investigating the experiences of first-year mathematics students in three European countries. The study adopted the framework of transition as a rite of passage and to detect the changes in attitudes towards the mathematics which originated the crisis, the three-dimensional model for attitude towards mathematics (TMA) was used. Data consist in one questionnaire translated into three languages and administered to students in the first year of study. Most of the questions were open-ended, and the data were analysed first qualitatively and then quantitised. Results show that while the transition experiences of the students may seem on the surface uniform, some significant differences emerge for motivation to join mathematics degrees, motives for changes in perceived competence, and impact of university mathematics formalism. We hypothesise a link between these changes and the differences in educational environments in the three countries. We conclude with highlighting the need for more research of this kind to understand the secondary–tertiary transition in the educational context in which it happens. [ABSTRACT FROM AUTHOR]

In this study, performance data from students on a mathematics graduate programme from Spring 2019 to Spring 2020 were collected and analysed. The results showed that, if the right course delivery method was implemented, the impact of the coronavirus pandemic (COVID-19) on students' performance could be minimal. Based on the study, some recommendations are made on how to improve students' performances in graduate-level mathematics courses. [ABSTRACT FROM AUTHOR]

This study examines how collective argumentation in the integration of the ACODESA method (collaborative learning, scientific debate and self-reflection) and GeoGebra can help students understand parametric equations. The participants of the study consist of 24 university students enrolled in a mathematics education programme at a state university in Turkey. Data were collected through students' written productions, screen recorder software, and transcriptions of the students' argumentations for selected groups. The collected data were analysed based on Toulmin's model. Results of the study indicate the use of GeoGebra in ACODESA method triggered a sense of understanding of parametric equations. It became apparent that the participants constructed parametric equations from existing knowledge of trigonometric identities, definition of function, and general form of the equation of a circle by making connections between algebraic and geometric representations. The integration of GeoGebra into ACODESA method also fostered some process aspects of mathematical reasoning (generalizing, conjecturing, and justifying) on parametric equations. [ABSTRACT FROM AUTHOR]

The effectiveness of technology-enhanced resources in mathematics in higher education is far from clear, nor is student engagement with such resources. In this review article, we investigate the existing literature in three interrelated areas: student engagement with technology in higher education and mathematics; what works and what does not in technology in education and in mathematics in higher education; evaluating the use of technology in higher education and mathematics; and the use of frameworks and models. Over 300 research articles were identified for this purpose and the results are reported in this review. We found a dearth of studies in undergraduate mathematics education that specifically focus on student engagement with technology. In addition, there is no overarching framework that describes both the pedagogical aspects and the educational context of technology integration in mathematics. [ABSTRACT FROM AUTHOR]

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

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

Research suggests that high school students often have negative experiences with mathematics. To address this challenge, this paper shares findings of a design-based research project in which researchers and teachers developed and used a narrative approach to lesson planning in order to design lesson experiences that provide opportunities for high school students to become captivated with mathematical content ("CMLs"). The goal of this approach is to provide students positive aesthetic opportunities, such as inspiring student curiosity, while maintaining cognitive demand and coherence. Overall, students reported more positive, varied aesthetic experiences (e.g., suspense, surprise) in CMLs than in other lessons with the same teacher and students. These findings provide evidence that designing lessons as mathematical stories shows promise and can offer students more positive aesthetic experiences in mathematics. [ABSTRACT FROM AUTHOR]

Challenges to the quality of basic mathematics education, especially in under-resourced countries, are well documented. It is in response to these challenges that the International Commission of Mathematical Instruction (ICMI) launched its programme of Capacity and Networking Project (CANP). This programme aims to create and sustain effective regional networks in low-income and lower-middle-income countries and develop the educational capacity of those responsible for mathematics teachers. This paper reports on the deliberations among the representatives of CANP, ICMI and the International Mathematical Union in working towards the common goal of making high quality mathematics education available to all. [ABSTRACT FROM AUTHOR]