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Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students' successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement. [ABSTRACT FROM AUTHOR]

In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different Computer Algebra Systems (CAS), such as GeoGebra, Symbolab, Photomath and Wolfram Alpha among others. Difficulties and potentialities were observed in the mathematical work of the students. In the difficulties, it was observed that the students had problems interpreting the information from the CAS and the CAA feedback because their previous mathematical knowledge was not solid enough to do so. In the potentialities, it was observed that different characteristics of the task, together with the articulation of two or more artifacts allowed students to give meaning to the mathematical objects involved. [ABSTRACT FROM AUTHOR]

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students' creativity. Multiple solution tasks are mathematical tasks with an explicit requirement to be solved with different methods. For the purpose of the study, we used a textbook question which allows multiple solution pathways as our research instrument. This MST was administered to first-year mathematics students (18–20 years) along with additional questions related to their experience in school mathematics. The results of the study showed that students had difficulties complying with the demands of the task, but generally have a positive disposition toward MSTs. Moreover, the results underline the necessity of incorporating MSTs in mathematics classroom teaching to create a more coherent corpus of mathematical knowledge. The study also provides an example of how a regular textbook task can be used as an MST. [ABSTRACT FROM AUTHOR]

The increase in online education has implications for mathematics teacher educators who are tasked with teaching mathematics content and pedagogy to pre-service teachers (PSTs) who do not attend on-campus. Concerns about PSTs' content knowledge continues to be an ongoing issue, and ways to address this, especially in an online environment, require further investigation. While online courses offer accessibility and flexibility, it can be challenging to translate synchronous on campus teaching and experiences into the online environment. The importance of productive mathematical discourse has been identified as an appropriate pedagogy, yet the opportunity to engage in such discourse can be limited in the online environment. This paper provides the results from a case study of an online forum, which highlights how pre-service teachers can be engaged in productive online mathematical discussions, particularly when facilitated by the instructor's and other learners' interactions and presence. The findings indicated that social, cognitive, and teaching presence influenced the nature and frequency of online mathematical discourse. The study contributes to existing research through conceptualizing how productive mathematical conversations can occur outside of the classroom setting, with implications for mathematics teacher educators who are tasked with teaching content, pedagogy and practices to PSTs. [ABSTRACT FROM AUTHOR]

This paper set out to contribute to mathematics education research by elaborating on a methodology developed during a study, trying to understand, view and follow shifts in prospective teachers' discursive patterns. The methodology aims to illustrate and describe how prospective teachers adapt to the context of teaching through a flexible process. This flexible process is then described in the result as a narrative. It is argued that the methodology can be used in relation to different theoretical directions, such as research about beliefs, knowledge, or identity. Another contribution is that the methodology presented gives insights into bridging the gap between different analytical levels, micro and macro. With a theoretical foundation in 'Cultural Worlds' [Holland, D., Skinner, D., Lachicotte, W., & Cain, C. (1998). Identity and agency in cultural worlds. Harvard University Press.] the Social Semiotic approach of Systemic Functional Linguistics, SFL [Halliday, M., & Hasan, R. (1989). Language, context, and text: Aspects of language in a social-semiotic perspective (2nd ed.). Oxford University Press] is used as a methodological tool. SFL offers a toolkit that allows the analysis of meaning at the clause level to uncover how and why a speaker produces a particular wording rather than any other in a specific social practice. The paper aims to illustrate and describe how to go beyond findings in the micro-analysis and then present the result as a narrative case. [ABSTRACT FROM AUTHOR]

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women) out of 170 enrolled in College Algebra, Precalculus, and Calculus were analyzed using the categories of (1) confidence in mathematics ability, (2) value of mathematics, and (3) liking of mathematics. This paper provides context and theoretical depth to student reports of their attitudes in these categories. Statements at the intersections of both confidence and liking, and value and liking provide additional insights. First, students who perceive mathematics as valuable are more likely to like it. Second, the vast majority of students talk about confidence and liking together, and with a positive correlation. Further, these students tend to talk about liking or not liking mathematics because of their perceived ability in mathematics. Our study suggests the importance of proactive teaching strategies to improve students' perceptions of the value, liking of, and their confidence in, mathematics, and also suggests self-efficacy as a potential theoretical basis for this work. [ABSTRACT FROM AUTHOR]

The article offers information on the increasing interest in affect-related research in mathematics education, particularly within the MAVI community. The topics include the growing recognition of the role of affect in teaching and learning, the collaborative spirit of MAVI in promoting research on mathematical beliefs and education, and the contributions from different communities in a special issue of the International Journal of Mathematical Education in Science and Technology (IJMEST).

This paper reports on the development of the Teaching Mathematics for Social Justice beliefs (TMfSJ-B) scale and its psychometric properties. Preservice elementary education teachers enrolled in teacher education programmes at seven universities completed multiple surveys designed to understand the evolution of attitudes and beliefs about teaching mathematics. To our knowledge, the TMfSJ-B scale is the only survey specifically designed to measure pre- and in-service teachers' beliefs about teaching mathematics for social justice. Confirmatory factor analyses (n = 655) provided here indicate that the TMfSJ-B scale is a valid and reliable assessment of beliefs about social justice in mathematics teacher education, with three factors: (1) value of mathematics for all students; (2) integration of social justice into mathematics instruction; and (3) mathematics and its relation to inclusiveness. The purpose of this study was to validate measures produced by the TMfSJ-beliefs scale and discuss its potential use in teacher education programmes and research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Teacher practice is rife with tensions. Tensions around what and how best to teach, how to manage situations with students, and how to manage situations with colleagues, administrators, and parents. These tensions are often seen as pairs of opposing internal and external forces: this assessment is better, but it takes a lot of time. These forces are inescapable, and teachers have to learn to either manage them or resolve them. In this paper we look closely at tensions through the lens of opposing forces and, more interestingly, how teachers either learn to live with them or work to resolve them. And, in particular, we look at how this work differs if the tension exists between internal forces, external forces, or a tension between an internal and external force. Drawing on case studies of seven different participants we dive deep into the murky world of the lived experiences of teachers to understand better the way that tensions contribute to their beliefs, decisions, and actions. [ABSTRACT FROM AUTHOR]

International literature is increasingly disclosing the relevance of cultural aspects within the processes of teaching and learning mathematics. Knowledge is inextricably linked to the activities in which the subjects engage, and must be considered in relation to the socio-cultural context wherein the activity takes place. Literature reveals the relationship between the background culture (e.g. language, nationality, etc.) of prospective elementary teachers and their beliefs about mathematics and its teaching. In this paper, we define culture with reference to the wider discussion from cross-cultural psychology literature about cultural values, and we investigate if and how differences in individuals' cultural values are related to prospective teachers' beliefs about being successful in mathematics and in its teaching. We adopt a questionnaire from the studies by Schwartz to measure participants' values. We assign each prospective teacher of our sample to a cluster of beliefs and we analyse how the beliefs of prospective teachers are related to their values. Results show that cultural values and beliefs about mathematics are related, while this is not the case for beliefs about the teaching of this subject. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the learning experiences, beliefs and motivations of students in classes where the mathematics teachers have received support for using inquiry-based learning activities. Data were collected from 248 students in the age-range 11–16 using electronic questionnaires. Our results show that key features of inquiry-based mathematics were only moderately reflected in these students' beliefs about the subject, their dispositions towards mathematics were less positive across the transition from primary to secondary school, and with respect to motivation this decline was stronger for girls than for boys. Furthermore, medium to strong correlations between belief- and motivation subdomains were found, for instance, students who view mathematics as a creative subject and/or have a growth mindset of mathematics also tend to find this subject enjoyable and perceive it as useful. Finally, our results indicate that inquiry-based teaching has a potential for fostering positive dispositions towards mathematics, as students who often experience inquiry-related activities in class also tend to see mathematics as a creative and interesting subject that will be useful for them in the future. [ABSTRACT FROM AUTHOR]

This paper targets patterns of expressed emotional directions towards mathematics. By using TIMSS data and recoding two of the instruments, we compared responses from the same student cohort in Grade 4 (11 years old) and Grade 8 (15 years old) in Sweden. Two hypotheses were tested: negative emotions including negative motivations increase with age, and there will be gender differences. By using statistical analyses, including Cramer's V, the two hypotheses were confirmed. The results also illuminated patterns within the responses, such that boys and girls in Grade 4 differ in expressed intrinsic motivation but not extrinsic motivation. There are also indications that girls might be more likely to form negative emotional directions between grades 4 and 8 than boys, and some implications of this is discussed. [ABSTRACT FROM AUTHOR]

Although research in mathematics education has yielded a great number of results on mathematics teachers' beliefs in recent decades, it is still an open question as to whether these teachers' beliefs are stable or not. However, since mathematics teachers' beliefs are perceived to be the default of their classroom practices, it is important to gain insight into these beliefs and into their development. In this paper, we contribute to this field of research by providing an approach designed to analyse a change in teachers' belief systems. We study a sample of 20 prospective teachers during their first practical experience. We analyse the structure of teachers' belief systems with interviews and a questionnaire set twice within one year. To analyse development of these teachers' belief systems, we assigned the young teachers of the first and second survey to clusters that were developed in a former study and re-analysed for our purposes here. Our results show considerable changes in mathematics teachers' central beliefs during their first practical experience. However, a general pattern of belief changes is not found. [ABSTRACT FROM AUTHOR]

This paper aims to examine the extent to which pre-service teachers' mathematical connection skills were promoted through the course designed within the scope of pedagogies of practice (Grossman et al. [2009]. Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100. https://doi.org/10.1177/016146810911100905) in the teacher education programme. Data were collected in a course that was designed to develop pre-service mathematics teachers' (PSTs) mathematical connections skills through a classroom teaching experiment with individual contributions to the whole class learning process. Thirty-six PSTs who were enrolled in the course participated in the present study. Initial and revised lesson plans were used as primary data collection instruments. In the most general sense, the findings demonstrated that most of the PSTs improved their mathematical connection skills during the course. The results of the current study provide insight into how the courses in undergraduate education should be implemented to give PSTs opportunities to develop their mathematical connection skills. [ABSTRACT FROM AUTHOR]

Improving the mathematical skills of undergraduate Engineering and Information Technology (EIT) students has been an enduring challenge for educators. Lecturers continually implement new strategies that try to overcome the challenges encountered in teaching university students with varying levels of success being encountered. This paper provides insight into how educators have handled the challenges students face in their mathematics learning journey. In addition, the paper highlights some of the methods used to improve the performance of these students as problem solvers, as well as the development and implementation of creative techniques that may have made the situation more successful and less challenging. The literature was searched through using a structured literature review approach based on the primary databases: Scopus; the Education Research Complete (ERC); and the Education Resources Information Centre (ERIC). This study followed the three main steps of a systematic literature review: retrieval, selection, and analysis of the literature. Analysis of the literature showed that there is still a need to further develop and deliver innovative pedagogical strategies for teaching mathematics to EIT students. It is recommended that an interdisciplinary approach, inclusive of technology, will lead to increased understanding, improve performance and, ultimately, enhance student satisfaction. [ABSTRACT FROM AUTHOR]

An editorial is presented on INDRUM being the acronym for the International Network for Didactic Research in University Mathematics. Topics include contributing to the development of research in didactics of mathematics at all levels of tertiary education; and focusing on building research capacity in the field showing concern for the development of early-carreer researchers and dialogue with the mathematics community.

Mathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an empirical base, elucidating its educational potential. To pursue this goal, a two-year ethnographic research study has been conducted in a selection of social media communities that exchange mathematical memes. In the paper, a twofold theoretical lens is used to investigate the phenomenon from a memetic perspective focused on the general characteristics of Internet memes, and from a cultural perspective considering the Web 2.0 environment. Analysis tools derived from the memetic and cultural theoretical background are applied to an instrumental case study, to reconstruct how mathematical memes activate the interaction among members of an online community. The investigation elicits key characteristics of the phenomenon, provides grounds to conceptualize mathematical memes as hybrid representations of mathematical statements, and sheds light on the traits of the epistemic culture they establish in the community. [ABSTRACT FROM AUTHOR]

The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The aim of the research was to describe the development of students' conceptions of infinity. These conceptions are built on the intuitive phenomenon of the horizon. We monitor the proportional representation of these conceptions in four combinations of views (into the distance and in depth) and contexts (arithmetical and geometrical). It can safely be maintained that the development of the proportional representation of the earliest conception comprehension of the concept of infinity, the so-called natural infinity, is not concurrent with the students' age. The development of the proportional representation of the conception of actual infinity is non-decreasing, at least in the view into the distance, in both contexts with respect to age. In general, it can be stated that the proportional representation of individual conceptions of infinity is strongly dependent on both context and view. [ABSTRACT FROM AUTHOR]

In this paper, we will show a characterization for pairs of commensurable diagonals of regular n-gons. This result gives a positive answer to a recent question. [ABSTRACT FROM AUTHOR]

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are introduced to the key concept of distributivity of multiplication over addition. The results show that modelling activities designed through the heuristics of didactical phenomenology, guided reinvention and emergent modelling may support the accessibility of distributivity, as these students were able to reinvent this concept solving an experientially significant problem. This result can be attributed to a combination of several factors: the choice of a realistic and rich problem, that stimulated students to elaborate formal mathematical concepts mathematizing their informal solving strategies, rooting new understandings in experientially real phenomena; the use of a suitable artifact, that presented mathematics as a means of interpreting and understanding reality and increasing the opportunities for observing mathematics outside of the school context; the role of the teacher, who guided students in reinventing mathematics in an active way. [ABSTRACT FROM AUTHOR]

Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of cognitive load theory, we propose to strengthen students' prior knowledge of simpler linear equations before they learn complex linear equations with the aid of worked examples. Because a subset of the complex linear equation shares the same schema as the simpler linear equation, students can draw on their schema for the simpler linear equation to understand the complex linear equation, thus alleviating the limitation on working memory load. Based on the principles of learning by analogy, we place a simpler linear equation and a complex linear equation side-by-side and label the solution procedure of both linear equations to encourage active analogical comparison between these two equations. Making both the simpler linear equation and the complex linear equation visible to learners may help to reduce cognitive load demands in retrieving the simpler linear equation in order to facilitate the learning of the complex linear equation. [ABSTRACT FROM AUTHOR]

In this paper a class of regular surfaces, generated by rotation and twist of a rigid line segment, is considered. Firstly a complete description of those surfaces by means of local charts is obtained and then its orientability is characterized in terms of the number of half-twists, taking into account their direction (clockwise or counterclockwise) since changes in the sense of twist are allowed. Indeed a procedure to construct nonorientable surfaces is provided. Illustrative examples and computer-generated plots using the free software Maxima are included. [ABSTRACT FROM AUTHOR]

LEGO® stop-motion animations were developed to engage first-year university students in the topics of matrices, vectors, linear geometry and linear transformations. LEGO® provided a versatile medium through which a wide range of concrete and abstract concepts could be physically demonstrated in both two and three dimensions. It was also familiar to most students, making the mathematics videos accessible and fun. When designed according to key principles around reducing cognitive load in multimedia learning, animations in education have been shown to increase learning compared to static images for concepts involving dynamic systems and processes. Multimodal approaches including video and narration have also been shown to be beneficial to students in terms of demonstrating mathematical problem solving. The videos created in this project were a mix of conceptual explanations and problem-solving examples, where the word problems were physically modelled before being converted to formal mathematical notation and then solved. Some animations were short clips that were integrated into online lecture recordings, others were stand-alone videos designed either as short introductions to topics or examples of common questions. This paper describes the theory underpinning the design of the animations. [ABSTRACT FROM AUTHOR]

In Australian universities, mathematics is often an essential core subject for disciplines such as engineering, information technology and science. These first-year mathematics subjects may have large enrolments of which a significant number fail the subject and repeat. While interventions to retain students are common, those who have failed before and are repeating the subject are often overlooked. In this paper, we undertook a statistical analysis based on demographic and performance data of six cohorts of students undertaking a first-year university-level mathematics subject. We found that pass rates for students on their second attempt were significantly lower than pass rates for students enrolled on their first attempt, and that age, degree enrolled in and pathway into university were predictors for who was more likely to repeat. Students in their second attempt were less likely to complete all assessment items and were more than twice as likely not to attend the final exam. We argue for an increased focus on and efforts targeting repeating students; that demographic data are used to predict students likely to repeat before they have failed a subject, and that this group of students, as well as those repeating, are supported to increase their chances to pass. [ABSTRACT FROM AUTHOR]

This paper reports on themes that arose in an investigation of university lecturers' views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course? Are there tools that should/should not be used; and do the answers to these questions vary according to the degree (Engineering or Mathematics) the students follow? Questionnaire data was coded using thematic analysis which generated 11 themes related to the four questions above. The Results section presents the themes. The Discussion section considers the themes as a whole; splits – dualities – in teaching linear algebra; students' challenges with abstraction; aspects of doing mathematics; and pedagogical issues. [ABSTRACT FROM AUTHOR]

This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response protocol when solving a task on the derivative. First the mathematical connections were identified from the perspective of the ETC and, second, an onto-semiotic analysis was carried out where the mathematical practices, the primary mathematical objects activated in them and the semiotic functions established between these objects were analysed. The main conclusion is that both theories complement each other to make a more detailed analysis of the mathematical connections. In particular, the more detailed analysis carried out with the OSA tools, visualizes a mathematical connection like the tip of an iceberg of a conglomerate of practices, processes, primary objects activated in these practices and semiotic functions that relate them, which enables a thorough analysis that details the structure and function of the connection. [ABSTRACT FROM AUTHOR]

This study used a modified mathematical knowledge for teaching (MKT) framework to compare the common content knowledge (CCK) of two groups of purposively selected pre-service primary mathematics teachers (n = 86) in relation to spatial visualization. Specifically, thirty-five pre-service teachers (n1 = 35) with a pure school mathematics background and fifty-one pre-service teachers (n2 = 51) with a high school mathematical literacy background worked on problems that involved spatial objects, their properties and relationships. The responses of pre-service teachers with a mathematical literacy content background to the Surface Development Test (SDT) were significantly different from their counterparts' which suggested that their CCK in relation to spatial visualization was thin. Analysis of the Probes questionnaire which inquired about the pre-service teachers' views on the concept of spatial visualization showed that misconceptions hindered their performance. Future research directions are discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra and geometry, like other branches of mathematics, are interrelated. [ABSTRACT FROM AUTHOR]

This article is a follow-up to an earlier paper on the mathematics support learning tutorial programme (SLT), an intervention programme at The University of Queensland that targets students considered to be at risk of failing Calculus and Linear Algebra I, the first tertiary level mathematics subject at The University of Queensland. The first paper (Hillock, P., Jennings, M., Roberts, A., & Scharaschkin, V. (2013). Amathematics support programme for first-year engineering students. International Journal of Mathematical Education in Science and Technology, 44(7), 1030–1044) reported on the inaugural programme implemented in 2012. This article provides an update of the progress of the SLT since 2012. We provide statistics for the subsequent 12 semesters to Semester 2, 2018 and describe the evolution of the SLT since its implementation. Statistical analysis of the additional data and student feedback indicate that the SLT continues to have a positive impact on student learning, with weak students making significant gains from attending the programme. [ABSTRACT FROM AUTHOR]

In order to learn the concept of statistical techniques one needs to run real experiments that generate reliable data. In practice, the data from some well-defined process or system is very costly and time consuming. It is difficult to run real experiments during the teaching period in the university. To overcome these difficulties, statisticians developed simple and very economical experiments, which can be performed in the class by the students. Stone studied the variation, bias, stability and statistical quality control through the Blind Paper Cutting (BPC) experiment. In this article, the Blind Paper Cutting experiment is demonstrated on the basis of basic principles of experiment design. A BPC experiment is performed considering different factors, and important factors to optimise the response are identified through complete factorial design. The appropriate response model using important factors has been constructed. [ABSTRACT FROM AUTHOR]

Mathematics is traditionally considered necessary for engineering courses. Over the last three decades, the mathematics requirements for entry into engineering programmes has steadily weakened in Australia. Further, the mathematics component of engineering programmes has progressively decreased. This research aims to investigate the following two questions. First, is mathematics a barrier for students to complete an engineering programme? And second, is performance in mathematics associated with performance in engineering? We identified the significant factors associated with weighted average mark and the completion status of engineering studies at both an undergraduate level and a Masters level. Of particular interest was the students' mathematical background. Furthermore, a survey of students enrolled in engineering at the University of Western Australia was conducted to obtain more in depth views of student attitudes and perceptions towards how mathematics has affected their engineering studies. Binary logistic models were fitted to the survey data. Additionally, focus group interviews were conducted to gain insight on student perspectives regarding the effectiveness of mathematics teaching in engineering. The results are discussed in relation to the importance of mathematics and statistics for the engineering curriculum. [ABSTRACT FROM AUTHOR]

This replicated research project [see Hine, G. S. C. (2019). Reasons why I didn't enrol in a higher-level mathematics course: Listening to the voice of Australian senior secondary students. Research in Mathematics Education, 21(3), 295–313. https://doi.org/10.1080/14794802.2019.15999982019] explored the reasons why senior secondary (i.e. Year 11 and Year 12) students elected not to enrol in a higher-level mathematics course. For this project, all senior secondary Australian Tertiary Admissions Ranking (ATAR) students within Western Australian schools (aged 17–18 years) were invited to participate in an anonymous, online survey comprised predominantly of qualitative items. The researcher analysed 1633 ATAR students' perspectives of enrolments in mathematics courses, according to a symbolic interactionist paradigm. Reasons included the extent to which students feel higher-level courses are too challenging, time-consuming, not required for university nor future life, and requiring more effort and stress to complete than lower-level mathematics courses. Especially outlined is the extent to which participants feel a 10% bonus is a sufficient incentive to increase higher-level course enrolments, an extension of the original project. Participants indicated a range of responses either supporting or opposing this incentive. While approximately 47% of participants agree that the incentive is sufficient, a small proportion of these supporters offer their agreement conditionally. Within the proportion asserting the incentive is insufficient, a majority of participants suggested that a higher percentage bonus should be offered to students enrolled in Mathematics Specialist. [ABSTRACT FROM AUTHOR]

This study investigates teachers' beliefs about the inquiry-based learning approach in mathematics. In particular, as the first research problem, it addresses teachers' beliefs about the appropriateness of inquiry activities for all students, after three years of attendance in a professional development programme, focused on inquiry. As a second research problem, it studies the evolution of teachers' beliefs and practices, during their fourth year of attendance of the programme. The results show that, at the beginning of the fourth year, the teachers, despite thinking that inquiry activities in mathematics have several valuable aspects, held the belief that they are not appropriate for all the students, but only for the high-achieving ones. The two case studies, analysed to address the second problem, refer to two teachers with different outcomes of their developmental paths. During the fourth year, in which the teachers have been invited to experiment with inquiry activities in their whole classes, one of them accepted the challenge and, as a consequence, had the opportunity to change both her practices and her beliefs. The second teacher, instead, continued to propose inquiry activities only to her high-achieving students and, consequently, showed no signs of change, either in her practices, nor in her beliefs. [ABSTRACT FROM AUTHOR]

In undergraduate mathematics education, students' collaborations have gained a reputation as a 'good' learning practice. A more complex image emerges once collaborations are construed as an arena where cognitive, social, and affective matters intertwine in ways that can fuel and impede learning. In this study, I take a close look at a twenty-minute-long interaction between two first-year students who engaged in a sequence of routine problems about dot products presented in a computer-based learning-support system. The commognitive analysis of the interaction revealed an asymmetrical structure: one student led the mathematizing, while his partner followed and invested considerable efforts to avoid making a mathematical contribution. The leader's attempts to switch positions and inquiry into the follower's recurrent refusals to mathematize entailed loaded exchanges that took a toll on both students in terms of identity and affect. I compare these findings to previous studies with school students to discuss possible sources of ineffective communication in situations where students are expected to learn through collaborations. [ABSTRACT FROM AUTHOR]

The study focused on the similarities and differences students and mathematics teachers have regarding values in mathematics classrooms in the same school culture. The study aimed to determine students' and mathematics teachers' values at Imam-Hatip high schools, a type of vocational school in Turkey. The study was carried out with students (n = 2,912) and mathematics teachers (n = 861) from Imam-Hatip high schools in seven regions of Turkey who voluntarily responded to the online data collection tools. The collected data were analysed using a latent profile analysis. As a result, students and mathematics teachers were divided into three latent profiles; however, these profiles differed according to value components. Some of the study's key results revealed practice as the essential value component. Information and Communication Technology (ICT) was the least for all teachers' and students' profiles, with relevance being the second least important value. [ABSTRACT FROM AUTHOR]

Teachers' beliefs about mathematics play an important role in the teaching of mathematics. Future teachers' views of mathematics are the basis of the quality of instruction they will deliver, as well as the teaching materials that they will present to their students and the means necessary to learn and participate in mathematical tasks. This article studies Colombian future teachers' beliefs about mathematical knowledge, taking into account two different training programmes for pre-service mathematics teachers from the same country, both of them qualify students to teach mathematics at elementary levels. Specifically, 213 mathematics graduate students and 405 normal school students from the Colombian Caribbean coast in their last term of their studies participated. Data were collected regarding four dimensions of beliefs: (i) on the nature of mathematics, (ii) about learning mathematics, (iii) about factors affecting students' achievement in mathematics, and (iv) about the quality of their training programme. Results show remarkable differences in the future teachers' beliefs depending on their training programme. [ABSTRACT FROM AUTHOR]

This study explored school principals' and teacher educators' perceptions of STEM education based on how they described STEM as a discipline, their understanding of the nature of teaching and learning of STEM, and the capabilities of a STEM-educated person. Data were generated through the Draw a STEM Learning Environment (D-STEM) instrument comprising drawn and written descriptions where participants drew a picture of a STEM learning environment and completed five prompt statements about what STEM is and how an individual develops personal STEM capability. The Legitimation Code Theory (LCT) specialization codes were used for data analysis (198 individual response items in total) to understand how the participants perceive STEM education. Almost half the participant responses indicated knowledge-code perceptions with a smaller but significant number (approximately a third of responses) indicating knower-code perceptions. The remaining responses showed élite-code perceptions, indicating a small proportion of participants valued the development of both disciplinary knowledge/practices and generic skills/attributes in STEM education. We posit that curriculum structure and reporting requirements influence these perceptions. Further research in relation to the influence of such understandings on enacted curriculum is warranted. [ABSTRACT FROM AUTHOR]

The transition from school to university is a challenging process for many students which is reflected in high dropout and low examination success rates during the first year at university. Qualitative studies have found hints that students' beliefs play an important role during the transition. Due to their dialectic nature with cognitive as well as affective valences, it is sensible to assume that beliefs influence rather cognitive and objective criteria of a successful transition such as exam achievement as well as subjective criteria like satisfaction that draw on affective sources. However, quantitative studies have been mostly focusing on the role of students' beliefs for study achievement, neglecting possible effects on students' satisfaction and actual dropout. In this contribution, I draw a more holistic picture of the effects of beliefs during the transition by analysing effects on students' achievement, students' satisfaction and students' actual dropout behaviour. Data from over 600 first-year students in a longitudinal quantitative study show that dynamic beliefs (that emphasize the process character of mathematics and the usability of mathematics in everyday life and other disciplines) have a positive impact during the transition, while static beliefs (focusing on schematic aspects of mathematics) are problematic. [ABSTRACT FROM AUTHOR]

There is evidence that student attitudes towards mathematics become more negative as students move through their schooling. However, less is known about the different factors that shape student attitudes at various stages. This qualitative study sought to shed light on this issue and consider how stage of schooling influenced self-perceived supports for what helped underperforming students to learn mathematics. One hundred and seventy-nine students in Grades 2/3 and 5/6 completed a questionnaire before they participated in a mathematics intervention program, targeting students who had fallen behind in mathematics. Participating students were asked to complete the sentence stem. The best thing about learning mathematics in my classroom is ... and answered the question: What helps you learn mathematics in the classroom? Thematic analysis revealed that the majority of younger students emphasized specific tasks (e.g. games) and mathematical content areas (e.g. counting) when describing the best thing about learning mathematics at school and were twice as likely to highlight such aspects compared with older students. By contrast, older students were far more likely to indicate the importance of being supported directly by their teacher or peers when learning mathematics, compared with younger students. [ABSTRACT FROM AUTHOR]

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with alternating series of real or complex numbers. The main goal of this note is to provide a supplementary material for courses dealing with infinite series of real or complex numbers. [ABSTRACT FROM AUTHOR]

In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across the entirety of Latin America and South America. Whereas lack of financial resources often predicts low measures, the history of educational practice teaches us that students' poverty need not predict their educational outcomes – creative instructional approaches may turn the tables. Here we report on an innovative, body-based arithmetic technique, the Botetano Method, that has been enabling poverty rural children from remote mountainous regions of Peru to match and even greatly surpass their urban peers on comparable test items. The article explains the method's guiding humanistic and cognitive principles and then reports on findings from explorative action research that implemented and evaluated the method. Using observational methodologies, we argue that the students developed in their conceptual understanding of the content as well as in their attraction to the discipline, their professional identity, their personal pride in their achievement, and their general epistemic capacity for concentration and self-regulation. Throughout, we emphasize the methodological limitations of this grassroots proof-of-concept action research, which threaten the validity of the assertions. We speculate on early extensions of the method to literacy studies. [ABSTRACT FROM AUTHOR]

This paper focuses on the students who are registered in the University of Pretoria's academic development programme, named the Four-year Programme (FYP). The programme was introduced as a gateway for students who are underprepared but have the potential to succeed and then continue their studies into the mainstream science programmes. Our research focuses on measuring the change in the academic maturity of these students. In the theoretical framework that we developed, academic maturity is subdivided into two components namely non-subject based maturity and subject based maturity (mathematical maturity). This paper focuses on measuring non-subject based academic maturity. The survey used for this purpose is called the Student Academic Readiness Survey (STARS), taken at the beginning of the year and after the first semester respectively. The results of the surveys are compared to measure the change in students' views. Results show that in all constructs there is a surprising decline in students' perceptions regarding their own abilities over the first semester at university. We use the Dunning–Kruger effect to explain this unexpected decline, in that students seem to develop a more realistic view of their own maturity, which in itself can be seen as a growth in academic maturity. [ABSTRACT FROM AUTHOR]

To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete examples of what lapses of integrity look like in this context. The intent is to lay groundwork for discussion and a response to this issue from within our discipline. [ABSTRACT FROM AUTHOR]

This paper uses a framework established by one of the author's in a previous study and refines it to develop a rubric for mathematics tutor training in third-level education. The paper further opens the discussion on the necessity of, and practical methods for, providing high quality, efficient tutor training at third-level. Models of mathematics teacher knowledge are unanimous in stating that solely possessing strong subject matter knowledge (SMK) is not sufficient for one to be deemed to be a good teacher. Despite the necessity of high quality tutoring at third-level, past research indicates that though tutors' SMK is usually of high quality, their ability to transform their knowledge so that students will understand the content, as well as their general teaching skills (e.g. board work, speech), often has room to improve. This paper discusses the development of the rubric and its use in a mathematics tutor training programme at third-level. The tutor training programme was found to lead to improvements in multiple elements of the tutors' teaching. [ABSTRACT FROM AUTHOR]

This paper examines the effect of the use of dynamic geometry environments on young children's (ages 5–6, kindergarten/grade 1) thinking about angle. It provides a detailed description of introductory sessions of a geometry unit about angle, during which children worked in a whole classroom setting in which they could interact directly with Sketchpad through an interactive whiteboard. Using Sfard's [2008, Thinking as communicating: Human development, the growth of discourses and mathematizing. Cambridge: Cambridge University Press] communicational approach, an attempt is made to show how children developed a reified discourse on angles and were able to develop an understanding of angle as 'turn', that is, of angle as describing an amount of turn. This discourse focused on the behaviour of a pre-constructed sketch which instantiated both dynamic and static representations of angle. Extending prior research on children's difficulties in unifying static and dynamic conceptions of angles, this study provides one way of establishing a relationship between angle-as-turn and angle-as-shape conceptions. Gestures and motion played an important role in children's developing conceptions of angles. It presents implications of considering young children's embodied forms for communications along with their verbal communication for understanding their mathematical thinking. [ABSTRACT FROM AUTHOR]

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional theories of learning that draw attention only to the individual learner or the mind. Focus is on the ways that learners, tools and mathematics are entangled in provisional reconfigurations of the world and on how the tool partakes in this movement. Starting from our theoretical commitment, we discuss some episodes from a research study in which grade 9 students were introduced to function through a graphical approach. The study took advantage of graphing motion technology, which allows working with couples of position over time graphs, capturing spatio-temporal relationships. The episodes provide insight into the complex nature of learning in this context, valuing the mobile way that mathematics emerges from activity with the tool. [ABSTRACT FROM AUTHOR]

Partial Latin squares constitute an interesting approach to improve the teaching of different subjects in the mathematics classroom. This paper delves into this topic by introducing the use of a Dynamic Geometry System to deal with these combinatorial structures as a source of loci of points in the Euclidean plane. It is assumed to this end that the distance matrix among all these points contains a zero-diagonal symmetric partial Latin square with at least one non-zero filled cell per row. [ABSTRACT FROM AUTHOR]

The initial training of mathematics teachers in Spain can start in the final year of the mathematics degree when the students, and future teachers, select courses related to teaching the discipline. At that time, since over the next two years they will probably be certified to enter the profession, it is worth asking oneself what mathematical knowledge they should have and what is needed to teach at the secondary education level. This paper describes one case study in which a group of final-year students solves a task containing aspects of mathematical understanding that are present in solving problems using GeoGebra. This was done using a solution protocol intended to emphasize the different possibilities offered by GeoGebra, presenting three approaches for the solution: dynamic, numeric and algebraic. We noticed that the use of technology is key to bringing out some of aspect and to demonstrating an understanding of mathematics for teaching. [ABSTRACT FROM AUTHOR]

Flipped classrooms serve as a new pedagogical approach for teaching and learning, which involves switching from the traditional teacher-centred academic agenda. Unlike the traditional classroom model, the flipped classroom enables students to understand the lesson better while learning at their own pace and enhancing their communication skills among peers. At the same time, lecturers are provided with an opportunity to extend the discussion time in class through a more interactive session between students. While research works regarding the success of implementing flipped classrooms have been widely undertaken in the literature, only a few of these works considered exposing such models to secondary students. Engaging secondary students in the flipped classroom and investigating its impact on students paves the way for preparing an academic environment for students' advanced courses in the future. In this work, a case study was conducted at Barstow High School (Barstow, California) to evaluate the implementation of flipped classrooms in Mathematics education from an interplay of factors such as gender, ethnicity, and students' attitude. The students showed positive usability of the model from the end-activity evaluation and further noted an improved communication channel inside the classroom, allowing them to pace their own learning. [ABSTRACT FROM AUTHOR]