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This paper captures and reports on mathematics pre-service teacher (PST) voices. Mathematics PSTs, in a tertiary mathematics secondary curriculum teaching subject assessment, were asked to perform a small-scale literature review on an issue they identified as important in mathematics teaching. The assessment, written as an article, required literature-based recommendations, a reflection on how this would impact the PST's future teaching and guidance for all mathematics teachers. The article was aimed for publication by the Mathematics Association of Victoria—a state-based mathematics professional association in Australia. PSTs were advised that articles would potentially be published, and their voice would reach practicing mathematics teachers. The published articles, which capture pre-career mathematics teacher voices were analysed for insight into what four PSTs said of their future teaching to a mathematics teacher audience. The professional teacher standards were recognised to influence comments given the strong emphasis of standards within initial teacher education courses. Findings speak to what mathematics PSTs expect of their future teaching role prior to being in-service. The paper contributes a snapshot of early established professional voices in a discipline where there is currently a shortage and highlights the messages that emerged. [ABSTRACT FROM AUTHOR]

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]

Due to the fixed school start in Norway in August of the calendar year of students' sixth birthday, the age span in one class is up to twelve months. This can impact academic performance both in the early years and later. In this paper, we investigate the relationship between birth month and mathematics performance by paying attention to the content and cognitive domains addressed in the Trends in International Mathematics and Science Study (TIMSS) 2015. In Norway, the TIMSS 2015 included four cohorts, enabling a comparison between grades. We find significant correlations between birth month and mathematics performance overall as well as in all content and cognitive domains for grades 4, 5 and 8. Furthermore, the gap in mathematics results between the youngest and the oldest in a cohort is less in grade 9 than in grade 4. We suggest that these findings have implications for mathematics teachers' practice. [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]

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]

The voice of disabled students in higher education (HE) has been widely explored in the global North but relatively little is known about the experiences of their counterparts in the global South. The paper attempts to address this lacuna by focusing on disabled students in HE in India. A part of the author's doctoral study in 2013–14 explored the lived experiences and aspirations of 29 students with a visual impairment using phenomenological methodology. Their access to courses and subsequently, career opportunities were found to be restricted by an interplay of systemic exclusion, lack of information, internalised oppression, pedagogy, and employment opportunities. While disability legislation in India focuses on widening participation in HE, the issue of access to courses for students with a visual impairment has received little attention. This paper emphasises the importance of facilitating their access to their desired courses in HE and to this end, provision of support in school. This article highlights the experiences of students with a visual impairment regarding enrolling in different courses in higher education (HE) in India. The research found that four main factors prevented many students with a visual impairment from pursuing science-and mathematics-based courses in HE. These were i) exclusion from science and mathematics in early education, ii) inadequate support systems, iii) inaccessible teaching practices, and iv) limited work opportunities. Little or no support and motivation was available for them to study these subjects. The research recommended that HE authorities must recognise the ability of students with a visual impairment to learn visual-based subjects. It also highlighted the need to provide support for learning mathematics and science to these students in school so that they can study mathematics- and science-based courses in HE. [ABSTRACT FROM AUTHOR]

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K–12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem and share preliminary evidence of success in a multi-year application of this model. The paper highlights the benefits of implementing the model, particularly to support collaboration between faculty in mathematics and teacher education. [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]

Professional bodies expect engineers to show competence in both mathematics and engineering topics such as mechanics, using their abilities in both of these to solve problems. Yet within engineering programmes there is a phenomenon known as ‘The Mathematics Problem’, with students not demonstrating understanding of the subject. This paper will suggest that students are constructing different concept images in engineering and mathematics, based on their perception of either the use or exchange-value for the topics. Using a mixed methods approach, the paper compares 10 different types of concept image constructed by students, which suggests that familiar procedural images are preferred in mathematics. In contrast strategic and conceptual images develop for mechanics throughout the years of the programme, implying that different forms of competence are being constructed by students between the two subjects. The paper argues that this difference is attributed to the perceived use-value of mechanics in the career of the engineer, compared to the exchange-value associated with mathematics. Questions are raised about the relevance of current definitions of competence given that some routine mathematical operations previously performed by engineers are now being replaced by technology, in the new world of work. [ABSTRACT FROM PUBLISHER]

This paper considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support. [ABSTRACT FROM AUTHOR]

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories –explanation,motivationandquestion posingroutines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines includeknown mathematical facts,summary and repetition, different representations,everyday language, andconcretization and metaphor; the motivation routines include reference toutility,the nature of mathematics,humourandresult focus; and the question posing routines includecontrol questions, asking forfacts,enquiriesandrhetorical questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics. [ABSTRACT FROM PUBLISHER]

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[1] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering. [ABSTRACT FROM PUBLISHER]

BackgroundThis paper is a qualitative evaluation of a small-scale pilot study that attempted to generate parental involvement in children’s learning. It used problem-solving mathematics homework in order to raise the children’s self-efficacy, or, put another way, the child’s belief that success lies in their own hands. PurposeHomework is often seen as a common sense practice which is conducive to the development of the attributes of an effective learner. The pilot investigated whether situating homework tasks in everyday mathematical contexts enhanced parent–child interaction. If so, the child was then more likely to commit to learning, recognise the usefulness of mathematics as a life skill, and the value of sharing ideas and accepting feedback. Design and methodsThe pilot took place between April and July 2015 in a primary school in the Northwest of England. Participants were a class of nine- and ten-year-old children (n = 27), their two class teachers and a self-selecting sample of parents. Children were asked to work on open-ended problem-solving activities designed to connect with everyday use of mathematics. The parental role was to model, encourage and reinforce rather than instruct. Data was collected from focus groups, from parent feedback sheets and from a self-efficacy questionnaire. The data was analysed thematically. Findings and conclusionsDespite limitations of time and scale, evaluation of the pilot suggests that the homework strategy does justify further research. The qualitative analysis of the data indicates that greater involvement of parents in learning was generated, the homework was well received by children and self-efficacy levels remained stable. The next step should be to run an extended version of the pilot. [ABSTRACT FROM PUBLISHER]

Increased efforts to diversify science, technology, engineering, and mathematics (STEM) education in the United States have drastically increased the number of studies offering insight into the experiences of women in STEM programs in higher education. This paper presents a thematic review of the literature regarding their status from 2007 to 2017 including journals, trade magazines, theses, and dissertations. It focuses on areas of recruitment, retention, barriers, and faculty issues. Stereotypes, biases, campus culture, classroom experiences, identity, and sense of belonging are also explored. The author additionally identifies gaps and suggests related areas for new research as well as implications for librarians. [ABSTRACT FROM PUBLISHER]

Innovation in learning and teaching is an everyday requirement in contemporary higher education (HE), especially in challenging subjects such as mathematics. Teaching mathematics to students with limited experience of formal mathematical instruction is a good example of a demanding pedagogical undertaking where innovatory practice can help HE teachers rise to the challenge. This paper presents an innovative game-based learning approach to the teaching of basic mathematics in HE through the example of a first-year mathematics module of the BSc Computer Science course offered by the Aberystwyth University (UK). Excellent examination results and positive student feedback concerning the learning experience point to the value-addedness of this approach in HE and it is, therefore, offered here as an example of good teaching practice to be disseminated more widely in the sector. [ABSTRACT FROM AUTHOR]

Undergraduate research has become the centerpiece of many institutions of higher education’s efforts to attract and recruit high school graduates. Since 1987, throughout my tenure at Bloomsburg University, I have involved over 20 students in my research. In my experience, there is clear evidence that students of mathematics substantially benefit if they engage in research during their undergraduate studies. Whether the student plans to apply for employment after graduation or continue with graduate studies, the undergraduate research experience has a tremendous effect on the student’s success. In this paper, I will provide some personal insight on my experience in working with undergraduate students. In most cases, my experience has been in working with one student on a long term (one semester or mostly year-long) research problems. I will discuss my approach to identifying students, the type of projects, providing guidance, and finally the challenges that we face in supervising undergraduate research. To exemplify, emphasis will be placed on the status of a recent 1-year research project, which was funded by the Pennsylvania State System of Higher Education, and a senior undergraduate student worked on it for one year. [ABSTRACT FROM AUTHOR]

The relationship between research and policymaking has been discussed repeatedly. However, the debate tends to be in general, abstract terms or from a macroeconomic perspective with any examples described in a fairly cursory way. Despite the inherent complexity of the research-policy interface, analyses tend to homogenise ‘research’ and ‘policy’ as coherent entities with discussions often focusing on products (research and policies) rather than on the relationships between producers (researchers and policymakers). Here, we take one piece of research on qualifications that has influenced policy rhetoric over the last 5 years. We trace the career of the research from its production in the late 1990s in order to understand the conditions of its dormancy, re-emergence and use over the ensuing years. The paper serves to document the case, which is important in its own right, but also proposes a typology of ways in which research gets adopted and adapted into policy. [ABSTRACT FROM PUBLISHER]

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n= 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n= 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group. [ABSTRACT FROM PUBLISHER]

This paper explores the views of a group of students who took an oral performance assessment in a first-year mathematics module. Such assessments are unusual for most subjects in the UK, but particularly within the generally homogenous assessment diet of undergraduate mathematics. The evidence presented here resonates with some, but not all, of the existing literature on oral assessment and suggests that, despite concerns about anxiety and fairness, students see oral assessments as encouraging a focus on understanding, being relatively authentic and reactive to their needs. We argue that, suitably implemented, oral assessment may be a viable assessment method for straddling the ‘assessment for’ and ‘assessment of’ learning divide in higher education. [ABSTRACT FROM PUBLISHER]

Rarely do university departments of mathematics redesign their basic mathematics courses. Through developing an online version of our associate degree in engineering in collaboration with Open Universities Australia, we redesigned the first in a sequence of five engineering mathematics courses. The online cohort proved different to our face-to-face experience. We embarked on a process of refining the unit using experiential learning and action research. The 13 week unit is delivered up to four times a year and this paper reviews the first 10 cycles of enhancements over 3 years and unpacks the layers of hypotheses underlying development decisions. Several category themes were identified with a focus on students, teachers and learning activities. Investment in online developments for mathematics can have multiple flow-on impacts for other teaching modes. Good curriculum design, regardless of environment, will always be a cornerstone of effective course development processes. [ABSTRACT FROM PUBLISHER]

Open book assessment is not a new idea, but it does not seem to have gained ground in higher education. In particular, not much literature is available on open book examinations in mathematics and statistics in higher education. The objective of this paper is to investigate the appropriateness of open book assessments in a first-year business statistics course. Data over two semesters of open book assessments provided some interesting results when compared with the closed book assessment regime in the following semester. The relevance of the results is discussed and compared with findings from the literature. The implications of insights gained for further practice in the assessment of mathematics and statistics is also discussed. [ABSTRACT FROM PUBLISHER]

This study looks at the impact of college students’ writing on a regular basis about mathematical concepts. Specifically we examine the effect of this practice on performance and attitude while controlling for confounding factors. Two professors and a total of 97 students in four different classes participated in the study. Students in the writing groups were required to write a total of eight papers, each concentrating on an important concept in the course. All students were given a visual skills assessment at the beginning and end of the course. Students in the writing group were assessed to determine their attitude toward the writing assignments. Positive trends were associated with the writing group over the non-writing group in overall score and in all but one of six individual components. However, within the writing group, students’ attitude toward writing in mathematics class was negative. [ABSTRACT FROM PUBLISHER]