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Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

In this paper we discuss the types of knowledge used by six middle school students as they engaged with a debugging task designed to integrate ideas from computer science, mathematics and science. Our findings show that the computational thinking practice of debugging is a rich source of opportunities to integrate these different disciplines. The analysis illustrates how the types of knowledge the students did and did not use at each step of the debugging process were related to their ability to succeed at each step. Our work contributes to theory and practice by uncovering implications for studying debugging through two refined frameworks and for designing debugging tasks to support transdisciplinary learning.

This paper provides evidence on the effect of local prescription opioid use on academic achievement of 3rd-8th graders between 2009 and 2018. Using county fixed effects models, I find that when counties have higher levels of prescription opioid use, students score lower on standardized assessments two to three years later, with variation by student subgroups and magnitudes comparable to effective interventions. I find the largest magnitudes in counties with higher poverty rates and states with below-median state education spending. As test score effects predict adult outcomes, these findings point to economic and public health challenges when affected children become adults.

This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and Vinner's theoretical framework to analyze the students' errors that were rooted in mathematical and in real-life contexts.

This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in probability. It is particularly focused on the reality of mathematical work performed by students and teachers. For this research, classroom sessions were developed in an in-service teacher training course designed (and adapted) according to the Japanese Lesson Study model. Through the combined use of the Theory of Didactical Situations (TDS) and the Theory of Mathematical Working Spaces (ThMWS), a coding of the sessions observed was developed. Based on this coding, different patterns emerged which gave each session a specific rhythm and identity from which it was possible to recognize and characterize different strongly didactic contracts. The study highlights the difference between the potential contracts intended by the teachers and those observed in practice. The tools, and especially the coding, developed for the study could be used for future research on instructional situations or in-service teacher training.

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

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

The present paper aims at investigating the relationship between students' attitudes toward online homework use and mathematics anxiety among secondary school students. In this study, a model has been proposed by integrating the technology acceptance model (TAM) with mathematics anxiety theory. Three hundred and forty-five secondary school students participated in the instrument of the study that included 20-item based on a 5-point Likert scale. The subsequent analysis using Partial Least Squares Structural Equation Modeling (PLS-SEM) supported the negative relationship between attitude toward an online homework (OHW) tool and mathematics anxiety. The results revealed that perceived usefulness and perceived ease of use are predictors of attitude toward the use of OHW. This study maximized the capability of acceptance of the OHW tool in mathematics learning. The findings provided by the study will encourage mathematics educators to implement mathematics OHW tools in the learning process.

Purpose: This paper defines and assesses student learning patterns under the influence of problem-based learning (PBL) and their classification into a reasonable minimum number of classes. Study utilizes PBL implemented in an undergraduate Statistics and Operations Research course for techno-management students at a private university in India. Design/methodology/approach: Study employs an in situ experiment using a conceptual model based on learning theory. The participant's end-of-semester GPA is Performance Indicator. Integrating PBL with classroom teaching is unique instructional approach to this study. An unsupervised and supervised data mining approach to analyse PBL impact establishes research conclusions. Findings: The administration of PBL results in improved learning patterns (above-average) for students with medium attendance. PBL, Gender, Math background, Board and discipline are contributing factors to students' performance in the decision tree. PBL benefits a student of any gender with lower attendance. Research limitations/implications: This study is limited to course students from one institute and does not consider external factors. Practical implications: Researchers can apply learning patterns obtained in this paper highlighting PBL impact to study effect of every innovative pedagogical study. Classification of students based on learning behaviours can help facilitators plan remedial actions. Originality/value: 1. Clustering is used to extract student learning patterns considering dynamics of student performances over time. Then decision tree is utilized to elicit a simple process of classifying students. 2. Data mining approach overcomes limitations of statistical techniques to provide knowledge impact in presence of demographic characteristics and student attendance.

In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I present design recommendations and metaphorizing activities for educators building their undergraduate cryptology course.

What do ethical relations look like in the context of the many injustices that pervade mathematics education? In this paper, I argue, first, that violence is the relation that characterizes much of contemporary mathematics education and, second, that understanding ethical relations requires considering mathematics as an equal actor in creating possible relations rather than simply treating it as a context for human relations. I examine how literature in care theory, emancipatory pedagogies, and mathematics education have framed ethical relationality and suggest that the feminist new materialist conceptualization of response-ability offers several contributions for rethinking agency, justice, and praxis for mathematics teachers concerned with addressing mathematical violence.

Educational communities have expanded 3D printing in education, emphasizing the educational value of "creation" to develop the competencies required in the future. This study was conducted for the purpose of identifying the effect size by synthesizing prior studies on the effect of 3D printing in education. To achieve the goal, 26 research papers on 3D printing in education conducted in South Korea from 2014 to 2021 were selected and meta-analysis was performed. The results of meta-analysis are as follows. First, the overall effect size of 3D printing in education was 0.759, which was found to be a medium effect size. Second, the effect sizes for each categorical variable are as follows: both the affective domain and the cognitive domain showed medium effect sizes for the learning effects. Middle school showed a large effect size, and elementary school and high school had a medium effect size. Gifted students had a large effect size, and general students had a medium effect size. In terms of the concentrated subjects, mathematics showed a large effect size and science and technology showed a medium effect size. Single subject showed a large effect size and convergence education had a medium effect size. Both offline classes and blended classes showed increased effect sizes. Both the team activity and the individual activity showed a median effect size. The out-of-school program showed a large effect size, and the school program showed a medium effect size. 3D pens showed a large effect size, and 3D printers showed medium effect size. In terms of the modeling type, unstructured modeling showed a large effect size, as did semi-structured modeling, while semi-structured modeling showed a medium effect size. This study has implications for instructional design that can increase the effect of 3D printing in education.

Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their expertise results in new, hybrid meanings and understandings that can benefit practice. This paper aims to help researchers from these communities come together by presenting a novel methodology for collaborative inquiry and qualitative data analysis--"dialogical inquiry"--based on Mikhail Bakhtin's theory of dialogism. In this framework, "truth" is conceived as never finalised but always coevolving through dialogue that involves participants with different "voices" and "languages". We describe the three principles that underpin "dialogical inquiry": motivation, power balance and a process for solving disagreements. These three principles interact together to create a space where critically productive dialogue allows for meanings to coevolve and new, hybrid understandings to emerge. We illustrate our operationalisation of these principles (i.e., the methods of "dialogical inquiry") in two areas: understanding solutions to linear ordinary differential equations and making meaning of the Bakhtinian concept of superaddressee. We reflect on our use of this methodology in Mathematics Education research and invite the readers to create their own dialogic spaces of collaboration.

Understanding children's attitudes towards mathematics provides insights into their lived mathematical experience and engagement. Despite the considerable amount of research into students' attitudes toward mathematics, limited research has been conducted into "young children's" attitudes toward mathematics (YCATM). Within this limited research, investigating YCATM has certain challenges. From a methodological perspective, limitations exist regarding the type of research techniques that can be employed to study the nuances of the issue. The foci of this paper are to present and evaluate a methodological approach that used children's drawings (N = 106) and interview responses as the primary sources of data. Findings indicate that the strategy of "Draw yourself doing mathematics", when used with other research methods, generated rich attitudinal data in the form of personal stories about YCATM.

Formal teacher leader programs that develop, position, and reward teachers to work with peers to improve instruction are a growing reform effort in the United States, yet there are few published studies of their efficacy. In this paper, we examine the impacts of one district's teacher leadership program on students' annual state test performance. The program placed full-time instructional coaches and partly released English language arts (ELA) and mathematics content specialists in each of 11 district schools. To assess the program's impact, we examined five years of student-level state test data; two years before the adoption of the intervention and three years afterwards. Using an interrupted time series design, we examined trends in performance before and after the adoption of the intervention. Overall, there were no significant effects in ELA, and a small negative effect in mathematics. By contrast, in the stable sub-sample of students who were in the district for the five years examined in the study, there was a large significant positive effect in mathematics and large but non-significant positive effect in ELA. We conclude with a discussion the implications of these findings for research and policy.

This study aims to examine adaptability for educational games in terms of adaptation elements, components used in creating user profiles, and decision algorithms used for adaptation. For this purpose, articles and full-text papers in Web of Science, Google Scholar, and Eric databases between 2000-2021 were searched using the keywords "educational games", "serious games", "game-based learning", "adapt*", "player modeling", "user modeling". After applying the inclusion and exclusion procedures of studies accessed in the search, 26 studies were included in the study. The studies were analyzed in line with the themes determined for the components used in the adaptation of educational games. According to the results, adaptive educational game design was made for a wide variety of fields such as programming teaching, physics, mathematics, computational thinking, and logic. As for adaptive factors; It was determined that adaptations were made for the game, educational content, interface, and non-player character (NPC) behaviors. It is understood that pre-game adaptation and in-game adaptation methods are used as adaptation types. Finally, it is seen that Bayesian networks, artificial neural networks, fuzzy logic, deep learning, item response theory, and decision tree methods are preferred as decision systems in the adaptation process. The findings of this literature review can facilitate the design process by providing a roadmap for researchers interested in adaptive educational game design.

This paper reports on a transdisciplinary approach to science with a Year 4/5 class incorporating citizen science through the Birds in Backyards project. This transdisciplinary approach created opportunities for student engagement through science, mathematics, design and technology, humanities and social sciences (HASS), arts and English, while also creating meaningful connections to nature and the local environment.

This study focuses on a case study that highlights the mathematical discourse developed by two pairs of students when dealing with a specific transition task, i.e., an activity leading to the construction of a graph of a function based on the exploration of another representation of the same function. Such a task was designed to work on the "transition beyond" that involves moving from the graph of a function in a dynamic geometry environment to the Cartesian graph of the same function in the paper-and-pencil environment. In this case study, I analyze in fine-grained detail the discourse developed by two pairs of high-school students (ages 15-16) and describe how they translate the dynamism of the proposed representation into the paper-based context. The analysis aims at investigating the potentialities of transition tasks for supporting the building of bridges between multiple representations of the same function. The analysis also showcased the important role dragging routines played for making the transition.

Numerous preservice primary school teachers begin their training with a negative attitude towards mathematics: this phenomenon can have important consequences for their training path and for their future teaching. How teachers' training programs could affect preservice teachers' attitudes is one of the main issues in research on future teachers in the field of mathematics education. However, longitudinal studies developed during specific teacher development programs are still rare in the research field of teacher development. In this frame, this paper reports on the results of a longitudinal 2-year study carried out within the initial training of 35 preservice primary school teachers. According to the three-dimensional model of attitude towards mathematics, we developed the analysis of future teachers' emotional disposition towards mathematics, vision of mathematics, and perceived competence in mathematics, at the beginning of the training path and after 2 years. We found two main results on two different levels. First, a positive change in future teachers' attitude towards mathematics, generalized over all the three dimensions, occurred during the training period, and this result opens the issue of the relationship between formative choices and change in attitude. Second, our data confirm the strong relationship between the three dimensions of attitudes: every change in one dimension affects the other two dimensions.

The research on which we report in this paper was framed within the socioepistemological theory and dealt with the fundamental role of variational practices in the understanding of COVID-19 pandemic graphs. Given the proliferation of mathematical graphs related to the pandemic in the media, we proposed to analyse the variational practices in use in the interpretation of graphs of exponential behaviour that a Chilean newscast of high rating used to inform the population about the pandemic in Chile. For this purpose, a thematic analysis intertwined with documentary analysis techniques was carried out, in order to describe the types of graphs shown in the newscast, and a variational reference system was studied to analyse the use of variational practices. To obtain our results, the types of graphs most frequently shown in the newscast at the beginning of the pandemic were identified and the use of the variational practices of "comparison," "seriation" and "prediction" in such graphs was analysed. In conclusion, the need is discussed for the conceptual evolution of the exponential function to be accompanied by a pragmatic evolution in school that favours the use and development of variational practices in the student body.

This paper examines preservice teachers' experiences when they engage with tasks using dynamic technological applets to analyse data pertaining to societal issues. We examine two vignettes that discuss preservice teachers' interaction with dynamic visual representations of data related to plastic pollution and food supply. We analyse this data with an eye toward the relationship between the affordances of the technology and the emergence of participants' curiosity. We adopt the Embodied Curiosity theoretical lens to show how the foundational construct, relational-curiosity, provides opportunities for curiosity to be visible and recognized as a tool for meaning-making. This research provides insights into how preservice teachers can mitigate the challenges and tensions they face when navigating connections between mathematics and social justice issues.

This paper aims to investigate the reasons some female mathematicians give to justify their choice to not work in academia after finishing their doctoral studies. Nine female mathematicians who finished a PhD in Sweden answered a written questionnaire. Through collective narrative analysis, two main tracks were identified. One narrative described the struggle with self-identity in a gendered structure which included implicit power, while the other was more positive about exposure to discrimination, and highlighted the desire to work with applied mathematics. Through deductive thematic analysis, the results show that the main obstacle raised was the difficulty of getting a job in academia after their doctoral studies, especially permanent positions, without support. Compared to previous research, the lack of family-oriented political policies was not considered a main problem. Instead, the reasons provided by the respondents are structural problems, such as access to post-doc positions, and the stress of having to get research grants, as well as cultural aspects within the structure, including implicit and explicit use of power.

Background: The coronavirus pandemic has caused a shift in how many teaching, learning and research activities are conducted internationally. Lockdowns compelled all education sectors, including higher education (HE), to adopt a variety of online learning practices at short notice. As these changes in practice have implications beyond the pandemic, more needs to be understood about settings across the globe where the move to online may pose particular challenges. This study brings a focus to how lecturers in a college of education in Nigeria responded to the professional demands of lockdowns and developed strategies for managing educational activities that have relevance during and beyond the pandemic itself. Purpose: The aim of the study reported in this paper was to examine lecturers' perceptions of the management of teaching, learning and research activities during a lockdown, drawing out longer term implications. Methods: Data were collected through in-depth, one-to-one interviews with six lecturers from a college of education in Nigeria. Interview data were analysed qualitatively. Findings: Detailed analysis indicated that lecturers' strategies included encouraging students to engage in self-directed learning, as they uploaded learning materials on messaging groups and the college's e-learning platform. However, lecturers felt that the quality of teaching and assessment was compromised by factors including: irregular power supply, poor internet connection, high data costs and some students' limited digital skills. A particular concern was students' lack of interaction on the online platforms, which lecturers perceived to result in a more passive teaching and learning process. Lecturers also experienced difficulties undertaking research activities. A range of strategies and implications for the ongoing management of educational activities was discussed. Conclusions: The study offers insights into how some of the challenges encountered could be addressed to support sustainable online and blended teaching and learning in the longer term, in settings internationally where there are barriers to accessing online teaching and learning. Crucial aspects include strengthening educational technology training for lecturers and students, enhancing e-learning platforms for teaching practical courses, and enabling lecturers to develop beneficial and valuable online resources.

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with problem-based learning (PBL) which builds on such authentic real-life problems. How can the learning of pure mathematics benefit from these education approaches? We present a taxonomy to classify types of problems encountered discussing the notion of the problem context -- it can be internal or external to mathematics, or both.

In this paper the author looks at the letters of two renowned women mathematicians and scientists of the Victorian period, Mary Somerville and Ada Lovelace, while also considering the imperceptibility of Sophie Germain, an important French mathematician and philosopher in their epistolary exchanges and philosophical writings. Drawing on the importance of mathematical correspondences and epistolary education in the creation, circulation and dissemination of knowledge, as well as in processes of formal and informal learning, the author argues that Lovelace's and Somerville's letters leave traces of a remarkable genealogical line of women's mentorship and personal relations in the nineteenth century world of British mathematics in the backdrop of contradictory discourses around gender, mathematics, and science education.

Computational Thinking (CT) has emerged in recent years as a thematic trend in education in many countries and several initiatives have been developed for its inclusion in school curricula. There are many pedagogical strategies to promote the development of elementary school students' CT skills and knowledge. Unplugged learning tasks, block-based programming projects, and educational robotics are 3 of the most used strategies. This paper aimed to analyze the effect of Scratch-based activities, developed during one scholar year, on the computational thinking skills developed and concepts achieved by 4th-grade students. The study involved 189 students from two school clusters organized into an experimental group and a control group. To assess students' computational knowledge, the Beginners Computational Thinking Test developed by Several Zapata-Cáceres "et al." (2020) was used. The results indicate statistically significant differences between the groups, in which students in the experimental group (who performed activities with scratch) scored higher on the test than students in the control group (who did not use Scratch).

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when evaluating the proofs that they read. First, mathematicians' evaluations of identical arguments were sensitive to researchers' manipulation of authorship, with most accepting arguments purportedly produced by a colleague while taking a more critical view of that same argument if produced by an undergraduate student. Our thematic analysis of interview responses led to three context-based factors influencing mathematicians' responses when evaluating student-produced texts: "course goals, instructors' expectations, and assessment type." In the final section, we consider implications for researchers focused on understanding common practice amongst mathematicians as well as the pedagogic consequences of our findings for practice in the classroom.

Teachers' and students' values influenced the teaching and learning process in the mathematics classroom. Few studies were conducted to compare teachers' and students' value in mathematics learning. This paper explores Malaysian mathematics teachers' and students' values in mathematics learning. Fifty-three mathematics teachers and 354 secondary school students participated in the online survey. This study reports ten semantic differential items and an open-ended question related to mathematics learning. An independent t-test was conducted on the semantic differential items. Thematic coding analysis was performed to code the open-ended questions based on the framework of three intersecting values: mathematical values (the discipline), mathematics educational values (the pedagogy), and general educational values (the ethical and moral principles). The findings showed significant mean differences in mathematics educational values between teachers and students. No significant difference was found in mathematical values between teachers and students. Moreover, the qualitative data confirmed the similarities in mathematical values and differences in mathematics educational values between teachers and students. The current study also discusses possible reasons for the differences in teachers' and students' values. The findings imply that teachers' and students' values are crucial in enhancing teaching and learning in the mathematics classroom.

When embarking on our journey of learning in mathematics, we may envision a linear path of modules for acquiring mathematical knowledge and understanding to reach a predetermined outcome. However, this is a partial representation since the outcome and path are developing and adapting and our learning is continuously emerging. In this paper, our journey of learning in mathematics is re-envisioned as a complex adaptive system with agents, internal diversity, internal redundancy, decentralised control, sources of disruption and sources of coherence. As will be illustrated through the adaptive cycle of a complex adaptive system, learning may emerge between phases of destabilisation and development. For this emergence there needs to be openness to embrace a disruption, reflection to interpret the disruption, connection to respond to the disruption and inspiration to grow and adapt in response to the disruption. There also needs to be a balance between individual and collective learning. Through navigating these cycles along our journey of learning there may be emergence of learning experiences within and beyond mathematics.

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.

Mathematics was considered to be a universal language that God used to write the book of nature. Many of the greatest mathematicians (such as Descartes, Leibniz, Euler, Cantor) saw their mathematical work as a way to have a clearer insight into the existence of God and His infinity, as well as to glorify His name. This paper explores the mathematics-theology relation in the works of some of the greatest mathematicians from the fifteenth century to the present day. It also discusses how this information could be used to introduce the investigation of the reality of mathematics as divine language in the mathematics curricula of Catholic universities and colleges. At advanced levels, students need to understand Mathematics not only as a secular subject of technical utility, but also as a rich culture in which ideas of transcendence can be explored.

This paper outlines the development of a comparative research framework in subject didactics and applies this in the process of analysing the transformations from academic disciplines across different school subjects. The theoretical framework builds on the concepts of 'powerful knowledge' and 'transformation' and 'epistemic quality' within which transformation processes from the classroom to the societal level are considered as 'trajectories of powerful knowledge and epistemic quality'. The framework is used to analyse the findings from recent empirical studies across school subjects that have been reported on in publications arising from the Knowledge and Quality across School Subjects and Teacher Education (KOSS) network. The paper then focuses on analysing the transformations from disciplines across school subjects, given that the first boundary in defining powerful knowledge concerns knowledge that is specialized in both how it is produced and transmitted. To analyse this boundary, the findings from the empirical studies are grouped into broad subject categories. These are then compared with the corresponding disciplines by using the widely cited Biglan classification scheme of academic disciplines in higher education. Finally, we consider the implications for curriculum planning and teacher education policy and reflect on the concept of subject-specific educational content knowledge (SSECK).

Purpose: The case study is inspired in Interpretative Phenomenological Analysis (IPA) to make sense of a Relational Model within Artistic Creation (RMAC) developed by the author a long time in their artistic and research practices. Design/methodology/approach: An Interpretative Phenomenological Analysis (IPA) is considered within a case study where the author is simultaneously researcher and participant, using old unsolicited diaries for more than a decade as raw material. Findings: RMAC was previously presented as a tool for creating (maker) as well as a tool for research (researcher) in specific solo performance art projects, being the first time that it is approached through an Interpretative Phenomenological Analysis, bringing new insights into artistic practice and research within their intersections. Originality/value: This paper brings them the use of IPA in a case study with a researcher-participant to make sense of how RMAC, a model already presented formally and developed for many years, appeared and changed the author's professional and personal life. Also, it is given a new study using diaries as material within IPA.

Problem-solving and enquiry-based learning are integral in the Mathematics and Science curriculum in South Africa through online-based assessment. Online assessment has rapidly gained recognition because of technology. In this paper, the authors explored the views of online baseline assessment among Senior Phase First-year Mathematics Student Teachers. The researchers adopted a qualitative research method. Data was collected from the participants using an online Google form developed into a questionnaire. The participants in this study were first-year students enrolled for the Bachelor of Education in Mathematics at a university in a rural province of South Africa. The first-year student teachers were exposed to the senior phase baseline assessments through the licensed online Computer Aided Mathematics Instruction (CAMI) tool. One hundred and sixteen (116) senior-phase student teachers completed the online questionnaire. This study used convenience sampling since it was the most appropriate method to conveniently invite the participant. The findings revealed that first-year student teachers were enthusiastic and motivated to write the baseline assessment on computers for the first time. The result also showed that several first-year student teachers experienced difficulties solving mathematics problems using computers. This study recommends more intensive research on student teachers' views on online assessment regarding gender and time.

The advantages and disadvantages of ability grouping for student achievement are strongly contested, with studies presenting different results. However, much of this research has focused on class-level or subject-level ability grouping. Relatively less research has focused on school-level ability grouping. More importantly, the role of teacher support has often been neglected in the ability grouping literature. The aim of this study was to shed light on the under-investigated area of school-level ability grouping, with teacher support examined as a crucial theoretical mechanism. We examined whether teacher support plays a mediating and/or moderating role in terms of how school-level ability grouping is related to student achievement in English and mathematics. The participants were 554 Hong Kong secondary students from the high- (Band 1), medium- (Band 2), and low- (Band 3) ability groups. The results indicate that students from high-ability groups enjoyed greater levels of teacher support, which partly explains their higher levels of achievement. This finding supports a mediation mechanism. Moreover, the results also provide support for a moderation mechanism. When students in low-ability groups received high levels of teacher support, they were able to achieve as much as students in the high-ability groups, in English but not for math.

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to both teachers and learners. The study used the qualitative case study design to investigate Grade 11 mathematics learners' errors and misconceptions under hyperbolic functions at a rural high school in the Limpopo province of South Africa. Informed by the constructivist APOS theory conception levels, learners' errors were detected from their written responses in a diagnostic test. The learners were then individually interviewed during task-based interviews to infer on the misconceptions underlying their errors. Qualitative analysis of the data revealed the following categories of misconceptions: algebraic, conceptual, asymptotic, graphical, and notational misconceptions. The study established that errors, if diagnosed and corrected, are springboards and milestones to the formulation and construction of proper mathematical ideas. To resolve learners' misconceptions, this study recommends that teachers should use explorative and discovery pedagogical strategies to enable learners realize their own misconceptions and self-correct. Based on the findings of this study, the integration of Information and Communication Technologies (ICTs) in teaching functions as an intervention strategy will be explored.

Implementing an equity agenda in the classroom is both necessary and challenging for classes containing pre-service teachers. For this intervention, we chose to begin our History of Mathematics course for preservice middle school teachers with a cultural simulation training exercise: Bafa Bafa. After participating in the exercise, pre-service teachers were asked to write a reflection paper and were later interviewed about their experiences in the course. Although participants found Bafa Bafa an uncomfortable experience, it was not an unsafe one, and the preservice teachers agreed that this exercise helped them better understand, articulate, and notice experiences with microaggressions.

This special issue introduces recent research on mathematics in interdisciplinary STEM education. STEM education is widely promoted by governments around the world as a way of boosting students' interest and achievement in science, technology, engineering, and mathematics and preparing STEM-qualified workers for twenty-first century careers. However, the role of mathematics in STEM education often appears to be marginal, and we do not understand well enough how mathematics contributes to STEM-based problem-solving or how STEM education experiences enhance students' learning of mathematics. In this survey paper, we present a narrative review of empirical and conceptual research literature, published between 2017 and 2022. These literature sources are organised by a framework comprising five thematic clusters: (1) interdisciplinary curriculum models and approaches; (2) student outcomes and experiences; (3) teacher preparation and professional development; (4) classroom implementation and task design; and (5) policy, structures, and leadership. We use the framework to provide an overview of the papers in this issue and to propose directions for future research. These include: investigating methods and rationales for connecting the constituent STEM disciplines so as to preserve the disciplinary integrity of mathematics; clarifying what is meant by student "success" in interdisciplinary STEM programs, projects, and other educational approaches; moving beyond classroom practices that position mathematics as just a tool for solving problems in other disciplines; understanding what makes a STEM task mathematically rich; and asking how STEM education research can productively shape STEM education policy.

In this paper, we explore beliefs about teaching and learning held by 27 Namibian 11th graders (ages 16 to 18) experiencing difficulties in learning mathematics. Namibia's education system and its people's access to mathematics has suffered throughout years of colonization and apartheid. Namibia has made significant strides to create access and improve learning experiences. Its complex history provides a powerful context for exploring the beliefs and experiences of learners who persist despite experiencing difficulties. This research focuses specifically on learners experiencing mathematical difficulties, as the equity concerns of mathematics for these students are exacerbated through their experienced difficulties. While research on beliefs in mathematics education has been steadily growing, scant research has been conducted on the beliefs of learners experiencing persistent mathematics difficulties. Mathematics is recognized as a barrier to accessing higher education opportunities, and this research makes an important contribution to understanding the beliefs and resilience of Namibian learners experiencing mathematics difficulties. Understanding the beliefs and experiences of learners who continue to persist through their experienced difficulties can provide important insight into how to help and support all learners. The participants in this study shared their beliefs regarding experiences that would help them persist in their mathematics learning and their beliefs regarding systemic aspects of the Namibian schooling system.

The inclusion of games in mathematics programmes is widely believed to foster the enjoyment of mathematics. The focus of this paper is on fluctuations in emotional climate during the playing of whole-class mathematics games. A multimethod approach drawing on the sociology of emotions was employed to explore changes in the classroom emotional climate that were associated with game playing. The event-oriented inquiry was conducted with two teachers and a class of 10- to 13-year-olds in a New Zealand classroom during mathematics sessions. Over a series of eight mathematics lessons, there were three noticeable fluctuations in emotional climate, all of which occurred during whole-class games. Our analysis of these three events identified a successful interaction with dramatic emotional energy associated with a positive emotional climate, a successful interaction with undramatic emotional energy associated with positive emotional climate, and an unsuccessful interaction associated with negative emotional climate with interactional repair. The third event also illustrated how the incomplete nature of a game's rules can provide an opportunity for a negative emotional climate to be associated with game playing. The taken-for-granted wisdom that whole-class mathematics games can enhance emotional aspects of a classroom learning environment is supported by some of our evidence.

In this paper, we review algorithmic bias in education, discussing the causes of that bias and reviewing the empirical literature on the specific ways that algorithmic bias is known to have manifested in education. While other recent work has reviewed mathematical definitions of fairness and expanded algorithmic approaches to reducing bias, our review focuses instead on solidifying the current understanding of the concrete impacts of algorithmic bias in education--which groups are known to be impacted and which stages and agents in the development and deployment of educational algorithms are implicated. We discuss theoretical and formal perspectives on algorithmic bias, connect those perspectives to the machine learning pipeline, and review metrics for assessing bias. Next, we review the evidence around algorithmic bias in education, beginning with the most heavily-studied categories of race/ethnicity, gender, and nationality, and moving to the available evidence of bias for less-studied categories, such as socioeconomic status, disability, and military-connected status. Acknowledging the gaps in what has been studied, we propose a framework for moving from unknown bias to known bias and from fairness to equity. We discuss obstacles to addressing these challenges and propose four areas of effort for mitigating and resolving the problems of algorithmic bias in AIED systems and other educational technology.

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854-1912), Felix Klein (1849-1925), and Hans Freudenthal (1905-1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears without any further account of their viewpoints. In the paper, we seek to dig more deeply, asking the questions of what these three mathematicians' views on history in mathematics education were, how they themselves expressed these, and what the similarities and differences might be. Our departure point was the known texts by the three mathematicians in which they touch upon aspects of the history of mathematics in relation to teaching and learning, or mathematics education in general. When possible, these written works were accompanied by secondary accounts. Finally, we draw perspectives concerning the issue of how the views of these three mathematicians may or may not align with some of the trends in modern day HPM research.

The aim of this paper is to gain a better understanding of the role and scope of historical knowledge in work on using history of mathematics in education. This work can come from three types of actors, namely, teachers, teacher trainers, and educational researchers. The texts written by these actors show that their objectives and practices can be different, as is the historical knowledge they deploy. We can read writings of teachers who seek to 'give meaning' to school knowledge, by integrating original texts into their teaching progression. We also can read writings of educational researchers who prepare 'history capsules' for teachers, which can be introduced into teaching from time to time. To carry out this research, I focus on analyzing the complex relationships between the following three poles: objectives, pedagogical practices, and historical knowledge. To this end, I use the notion of ideal types introduced and developed by the sociologist Max Weber. Section 1 is devoted to the construction of ideal types corresponding to my aim. Based on these ideal types, in Sect. 2, I elaborate on the role and scope of historical knowledge in concrete situations where the history of mathematics is used; specifically, on the one hand during the reading of original texts in an educational context, and on the other hand, in the particular context of teachers education. Some further comments are made in the third and last section.

It is commonly known that the letter M in the two acronyms HPM and STEM stands for mathematics, and it is natural to regard mathematics as playing a significant role in science education. However, it seems that appropriate attention is not usually accorded to the role of M in the area of STEM where mathematics tends to be marginalized. In fact, throughout history one witnesses STEM at work so that the discussion of HPM and STEM in parallel will be beneficial to both. In both the historical and pedagogical aspects, it may be worthwhile to note that history of mathematics affords some means to mirror several different mathematical worlds in the context of HPM in a pluralistic way in order to offer a fuller view of the subject. In this paper I examine this issue through sampling many examples gleaned from the history of mathematics, particularly the role of M in the world of science and technology.