Search

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

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

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

The main challenge to the teachers in the field of mathematics in higher education is the fact that they are often confronted with the generally negative attitude of the students towards mathematics. This is partially due to their inadequate experience in the previous periods of learning mathematics that results in a certain mixture of essential mathematical illiteracy and personal animosity towards the subject. It is the main reason why mostly of the mathematics teachers in higher education are not able to achieve the needed efficacy in teaching mathematics. In this paper part we will envisage part of the problems we had to deal with in our efforts in making mathematics in higher education more approachable and more acceptable to our students. The main goal is to present suggestions for overcoming the existing problems and drawbacks that we are facing as mathematics teachers, mainly in faculties in technical sciences. [ABSTRACT FROM AUTHOR]

This paper presents data from a study comparing student experience and attainment when teaching statistics using Traditional Teaching (TT) and Flipped Learning (FL) approaches on a Foundation level module at a UK university. A survey of students' experience and perception of FL was conducted at the end of the year. The results showed that the students liked the flexibility of FL and believed that studying asynchronously encouraged them to improve their independent learning skill and motivated them to search for more information for the subject, a finding broadly supported by other studies (Price and Walker, 2021). However, what was surprising, is that students believed they learned 'better' with TT than with FL, a perception supported by student overall attainment data. The study concludes that careful considerations must be made to make FL effective. These include the student demographic and their mathematics competency, the module contents and difficulty level. Otherwise, the use of FL may reduce students' engagement and academic performance in mathematics at Foundation level. [ABSTRACT FROM AUTHOR]

This paper shows that students are less likely to specialize in mathematics when exposed to a high share of male peers. I exploit a curricular reform that incentivized students to obtain a mathematics qualification post-16. I show that, for those students affected by the reform, the higher the share of same-gender classmates, the higher the likelihood of obtaining a mathematics qualification for boys, and the lower the likelihood for girls. I interpret this as suggestive evidence that one's perceived ability in mathematics, a boy-dominated subject, decreases when the share of male classmates increases. This further affects STEM participation in higher education. [ABSTRACT FROM AUTHOR]

Offering explanations is a central part of teaching mathematics, and understanding those explanations is a vital activity for learners. Given this, it is natural to ask what makes a good mathematical explanation. This question has received surprisingly little attention in the mathematics education literature, perhaps because the field has no agreed method by which explanation quality can be reliably assessed. In this paper, we explore this issue by asking whether mathematicians and undergraduates agree with each other about explanation quality. A corpus of 10 explanations produced by 10 mathematicians was used. Using a comparative judgement method, we analysed 320 paired comparisons from 16 mathematicians and 320 from 32 undergraduate students. We found that both mathematicians and undergraduates were able to reliably assess the quality of a set of mathematical explanations. Furthermore, the assessments were largely consistent across the two groups. Implications for theories of mathematical explanation are discussed. We conclude by arguing that comparative judgement is a promising technique for exploring explanation quality. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has affected the way we learn, teach and support students in many different ways. In particular, the impact of the pandemic on the mathematical capabilities of students arriving at university is now starting to be seen and reported. Students arriving at UK universities in 2021, and having completed their A levels in 2021, had received disruption to almost all of their A level learning and it seemed likely that this might cause them to find the transition into higher education more difficult. Despite the disruption, the number of students achieving the top A level grade has more than doubled since 2019. In this paper, the data from a diagnostic test that has remained the same for the past 30 years are considered to measure the mathematical preparedness of students starting their courses at one UK university in September 2021, updating the work of Hodds (2021). Furthermore, an ordinal logistic regression model predicting A level grade based on test performance and other factors is developed to help determine if grades were perhaps inflated as suggested. The results show that students entering in 2021 are significantly less prepared for the mathematics on their courses than their colleagues who entered in 2020 and pre-pandemic. The regression model predicts a higher probability of being awarded an A*/A for students with A levels awarded in the pandemic, despite far lower scores on the diagnostic test, and in particular in 2021 when A levels were awarded through teacher assessment of the topics covered and not necessarily the whole A level syllabus. [ABSTRACT FROM AUTHOR]

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

In this paper we report on the outcomes of two surveys carried out in higher education institutions of Ireland; one of students attending first-year undergraduate non-specialist mathematics modules and another of their lecturers. The surveys aimed to identify the topics that these students found difficult, whether they had most difficulty with the concepts or procedures involved in the topics, and the resources they used to overcome these difficulties. In this paper we focus on the mathematical concepts and procedures that students found most difficult. While there was agreement between students and lecturers on certain problematic topics, this was not uniform across all topics, and students rated their conceptual understanding higher than their ability to do questions, in contrast to lecturers’ opinions. [ABSTRACT FROM AUTHOR]

An introduction is presented in which discuss various articles in the issue on topics including relation between inquiry-based learning, equity and student experiences; enrichment in first-year courses for academically strong mathematics students; and issues surround mathematics education.

Women's representation in Science, Technology, Engineering and Mathematics (STEM) is a powerful resource to motivate girls to study STEM degrees and fulfill the growing demands for professionals in these fields. From their youth, positive attitudes toward mathematics are characteristic of girls and boys who study STEM degrees. This research aims to identify the association between gender stereotypes and attitudes toward mathematics. The 6° grade generation from a middle school in Monterrey, Mexico, first answered tests on attitudes toward mathematics and gender stereotypes in mathematics. Afterwards, a sample group underwent a 4-week intervention during which students saw videos of STEM professionals and answered a questionnaire on student's self-perception in STEM careers. Finally, the tests were reapplied with a questionnaire on the use and ease of mathematics. Quasi-statistical and discourse analysis were used to obtain the results. These are presented through a model that highlights the mediating role that the mathematical self-concept and the interest/enjoyment for mathematics have in the association between gender stereotypes and attitudes toward mathematics. The role of gender on female's lower mathematical self-concept is also exposed, suggesting subsequent lines of research on improving self-concept as an approach to equitably increase students' interests in STEM degrees from their youth. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the trends of GeoGebra related studies. We focused on the articles published between 2009 and 2021 and existed in Web of Science database. The bibliometric analysis of the GeoGebra related articles exposed four-clustered structure according to the degree of relationships among terms that reflect the articles. The clusters were identified as learner anatomy (the use of GeoGebra to improve students' mathematics learning), teaching analytics (the role of GeoGebra in mathematics teaching), technological focus (the technological and procedural issues), and conceptual extension (the attempts considering the features of GeoGebra, mathematics topics and skills). This study offers evidence to show trends and practices in GeoGebra related studies, as well as to clarify their relationships with other concepts. The investigation into GeoGebra's dynamics would help researchers, teachers, students, and policymakers gain insight into areas that need further research, as well as plan for future studies. [ABSTRACT FROM AUTHOR]

This paper documents the author’s adaptation of team-based learning (TBL), an active learning pedagogy developed by Larry Michaelsen and others, in the linear algebra classroom. The paper discusses the standard components of TBL and the necessary changes to those components for the needs of the course in question. There is also an empirically controlled analysis of the effects of TBL on the student learning experience in the first year of TBL use. [ABSTRACT FROM PUBLISHER]

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/xand tan(x)/xasxapproaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the basic concepts of limits, but had room for further improvement in those that required them to explain their answers. An analysis of the students’ performances in the tests by using the APOS (i.e. action-process-object-schema) theory framework is reported. Reflections and suggestions on how to teach the topic more effectively are provided. [ABSTRACT FROM PUBLISHER]

Copyright of Review of Science Mathematics & ICT Education is the property of Library & Information Center and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Using three mathematical models, this study aims to optimize students' motivation for success in courses of mathematics at universities. The uniqueness of this study is crystalized in the novel graphical visualization of three models, which are integrated to analyze certain factors that help in optimizing students' motivation for mathematical success. The proposed models will benefit students, educators, administrators of higher education, and societies around the world. A quantitative approach is used to design the research, which involved 366 female and 319 male students in different mathematics courses. The results show that the third, second, and first models are the top three in order. The third model accounts for 71.3% of the shift in the motivation for mathematical success. The difference in the motivation for mathematical success is explained by 66.3% in the second model and 65.0% in the first model. [ABSTRACT FROM AUTHOR]

Universities invest significant resources in the provision of mathematics tuition to first year students, through both traditional and non-traditional means. Research has shown that a significant minority of students do not engage with these resources appropriately. This paper presents findings from a study of two groups of students at Maynooth University. Both groups had similar mathematical backgrounds on entry to university. The first group consisted of seven students who had failed first year mathematics and had very low levels of engagement with available supports. The second group consisted of nine students who had passed first year mathematics and had engaged with the supports to a significant extent. It emerged that while both groups initially displayed similar tactics and encountered similar difficulties, their levels of reaction to a number of critical events in their mathematical education were key to their engagement levels and their subsequent progression. Further analysis revealed aspects of the students' behaviour which caused them to approach or avoid difficulties. The reasons behind the different student behaviours were investigated, and the main categories of influence on student behaviour which emerged from the interview data were fear, social factors, and motivation. [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]

This article describes part of a study which investigated the role of questions in students’ approaches to learning mathematics at the secondary–tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics questions in England and Wales to focus on requiring students to demonstrate a routine use of procedures, whereas those in first-year undergraduate mathematics primarily required students to be able to draw implications, conclusions and to justify their answers and make conjectures. While these findings confirm the need for reforms of examinations at this level, questions must also be raised over the nature of undergraduate mathematics assessment, since it is sometimes possible for students to be awarded a first-class examination mark solely through stating known facts or reproducing something verbatim from lecture notes. [ABSTRACT FROM PUBLISHER]

Disrupting forms of exclusion in higher education requires culturally sustaining practices. However, in some areas of higher education, the notion of culturally sustaining practice remains unexplored. The present study addresses this disparity by exploring the concept of culturally sustaining supervision in the specific case of Pasifika research students in mathematics education. In particular, this case study examines what a group of 22 Pasifika research students in mathematics education valued most about their respective supervisors. Using talanoa (respectful and free-flowing conversation and discussion) to gather data, three characteristics of supervisors that the participants valued most were identified via thematic analysis: (a) being available and accessible; (b) developing the student's confidence; and (c) providing support beyond the thesis. The characteristics are discussed with respect to the Pacific concept of vā (relationships), which refers to the intricate relational and spatial realm in which connections among people exist and evolve. [ABSTRACT FROM AUTHOR]

To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major. [ABSTRACT FROM AUTHOR]

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare. [ABSTRACT FROM PUBLISHER]

Approaches to learning have been identified as crucial factors that influence students' mathematics performance. However, there have been mixed findings on which of the different approaches improve performance in undergraduate mathematics. Thus, this study aimed to unravel the specific effects of prior mathematics knowledge and approaches to learning on performance in mathematics among first-year engineering students. The design is cross-sectional, and the data are analysed with some structural equation modelling techniques. The findings show a positive effect of prior mathematics knowledge on performance. The effect of surface approaches to learning on performance is significant, negative, and surface approaches to learning mediate the effect of prior mathematics knowledge on performance. There are no substantial relations between prior mathematics knowledge, deep approaches to learning, and performance. Students who adopt surface approaches performed poorly but we found no evidence to claim that students who adopt deep approaches perform better in the course. By implication, our findings underscore the importance of discouraging engineering students from capitalizing on surface approaches to learning mathematics. [ABSTRACT FROM AUTHOR]

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks. [ABSTRACT FROM AUTHOR]

Graduate student instructors (henceforth, instructors) play a crucial role in teaching early STEM courses. Thus, professional development for these instructors addresses an urgent need to improve STEM student success. This paper focuses on a semester-long professional learning community in which six mathematics graduate student instructors engaged in regular cycles of peer observation, feedback, and reflection. In contrast to other professional development work, this approach emphasized that instructors give, not just receive, peer feedback. Analyses of post-semester interviews indicated that all instructors enhanced their noticing of students. The interviews also highlighted the challenges of providing critical, supportive feedback. [ABSTRACT FROM AUTHOR]

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

Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus students’ approaches to understanding, calculating, and interpreting answers to these types of limits are examined. The dynamic reasoning used by these students led to good justifications and meaningful interpretations of their answers. On the other hand, when students engaged less with dynamic reasoning, they struggled more and made less reasonable interpretations of their answers. Furthermore, dynamic reasoning helped the students in this study overcome previously documented pitfalls and encouraged covariational reasoning. The applied-science contexts at times helped the students engage in dynamic reasoning. [ABSTRACT FROM PUBLISHER]

Two previous studies mapping university mathematics students' summative assessment diet in the UK revealed a clear picture. In general, there was a dominance of closed book examinations with a strong relationship to departmental league table position. The decade since then has seen many changes in higher education in the UK, particularly in the strength of the student voice. The study we report here replicated the earlier work to see if there has been an impact on the assessment diet. While the analysis shows a very small decrease in the use of closed book examinations, this may be accounted for by the addition of adjunct modules, rather than a broadening of the assessment diet across mainstream mathematics topics. [ABSTRACT FROM AUTHOR]

The differential transform method (DTM) and the multi-step differential transform method (MsDTM) are numerical methods that most undergraduate students are not familiar with. The methods provide solutions in terms of convergent series with easily computable components. The aim of this article is to introduce the DTM and MsDTM as efficient tools to solve linear and nonlinear differential equations, at undergraduate level. We choose a population growth problem and a mixing problem to illustrate the simplicity and accuracy of its variants by comparing the results with the Runge–Kutta method. [ABSTRACT FROM AUTHOR]

We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students’ responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating mathematical arguments to hypothesize that mathematics majors hold four specific unproductive beliefs about proof reading. We then conducted a survey about these beliefs with 175 mathematics majors and 83 mathematicians. We found that mathematics majors were more likely to believe that when reading a good proof, they are not expected to construct justifications and diagrams, they can understand most proofs they read within 15 minutes, and understanding a proof is tantamount to being able to justify each step in the proof. [ABSTRACT FROM PUBLISHER]

Universities with a strong global presence host a large number of international doctoral students. Many of these students teach undergraduate courses as part of a teaching assistantship. There are many benefits associated with international teaching assistants. These include cultural exchanges within the universities and enhanced preparation for students entering into careers that are increasingly international in scope. These international teaching assistants, however, often encounter unique challenges. An understanding of these challenges is imperative in order to better meet their needs, as well as those of the undergraduate students in their classes. This qualitative study examined the experiences of international teaching assistants from science and math education departments in a Midwestern US university and their students' views about learning from them. Data sources included video and audio-taped semi-structured interviews conducted with seven international teaching assistants and their students. The findings revealed the teaching assistants experienced different kinds of language and cultural and contextual challenges. Accent and fluency in speaking, correct pronunciation of the words, and the differences in science and mathematics jargon across different countries are examples of linguistic challenges. The difficulty in understanding US humor, customs, values, and beliefs are examples of cultural challenges. In response to these challenges, the teaching assistants developed coping strategies such as honesty and being open to students. The findings revealed students experienced some difficulties such as language issues, but they also had positive experiences such as learning about different cultures. [ABSTRACT FROM AUTHOR]

An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as 'resource-based,' as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical strategic knowledge, and problem-solving skills, little evidence exists on how to support mathematical argumentation and proof skills based on its resources. To address this gap, a quasi-experimental intervention study with undergraduate mathematics students examined the effectiveness of different approaches to support both mathematical argumentation and proof skills and four of its resources. Based on the part-/whole-task debate from instructional design, two approaches were implemented during students' work on proof construction tasks: (i) a sequential approach focusing and supporting each resource of mathematical argumentation and proof skills sequentially after each other and (ii) a concurrent approach focusing and supporting multiple resources concurrently. Empirical analyses show pronounced effects of both approaches regarding the resources underlying mathematical argumentation and proof skills. However, the effects of both approaches are mostly comparable, and only mathematical strategic knowledge benefits significantly more from the concurrent approach. Regarding mathematical argumentation and proof skills, short-term effects of both approaches are at best mixed and show differing effects based on prior attainment, possibly indicating an expertise reversal effect of the relatively short intervention. Data suggests that students with low prior attainment benefited most from the intervention, specifically from the concurrent approach. A supplementary qualitative analysis showcases how supporting multiple resources concurrently alongside mathematical argumentation and proof skills can lead to a synergistic integration of these during proof construction and can be beneficial yet demanding for students. Although results require further empirical underpinning, both approaches appear promising to support the resources underlying mathematical argumentation and proof skills and likely also show positive long-term effects on mathematical argumentation and proof skills, especially for initially weaker students. [ABSTRACT FROM AUTHOR]

• First study investigating causal inference of a math remedial program in Germany. • Microanalysis of a math remedial program with detailed information of the sample. • Semester-long remedial courses can be helpful compensating missing math skills. Almost all German universities complain that the math skills of students entering the higher education system do not meet the level demanded by universities. This is a major problem, particularly in math-related study programs such as economics, engineering or science. To bridge the gap, almost all universities offer some remedial math courses. However, there is only weak empirical evidence for the effectiveness of these courses in Germany. This paper aims to fill this gap by evaluating a remedial math course given within the Economics Department of a German university. A key finding: taking a math remedial course on a regular basis will enhance students' math skills and increase the probability of passing the final math exam by 35 percent. [ABSTRACT FROM AUTHOR]

This study explores contradictions that emerge when utilizing a flipped classroom approach to university mathematics education. The work uses Activity Theory and its principle of dialectical contradiction as a theoretical framework to identify and analyse contradictions that arise in flipped mathematics classrooms for engineering students. Data were collected mainly by means of video recording of classroom activities and interviews with two cohorts of first-year engineering students in a Norwegian university over two years. An inductive approach to data analysis based on the interaction between the theoretical framework and the empirical data is used to provide evidence about the contradictions. The results show that contradictions manifest themselves as tensions in flipped mathematics classrooms. They emerge at different activity levels and affect student learning of mathematics. The aim of the study is to add to the lack of theoretical underpinning and limited research on tensions and contradictions in flipped mathematics classrooms at the university level. [ABSTRACT FROM AUTHOR]

Developmental mathematics, which is designed to prepare students for college-level mathematics courses, can be a barrier to students' success. In the United States, the majority of students placed into developmental mathematics courses fail to complete the developmental sequence. Alternative mathematics pathways offer some benefits when integrated with "just-intime support" or expedited instruction on specific prerequisite concepts needed solely for the current lesson. This study compares two statistics courses taught at a public community college: a complete course taught in one semester and a two-semester version with just-in-time develop - mental content integrated into the course. The study found that students placed into the onesemester statistics course accumulated significantly more credits after one and two years of college. These students also completed an associate's degree within two years at a significantly higher rate than students placed into the two-semester statistics course. The study also found students deemed non-proficient by the college's placement exam, who also had a strong high school average were significantly more likely to earn a grade of A- or higher or a grade of B- or higher compared to students originally deemed proficient. [ABSTRACT FROM AUTHOR]

The flipped classroom is gaining acceptance in higher education as an alternative to more traditional methods of teaching. In the current study, twelve students in a Norwegian higher education institution were in-depth interviewed about their learning experiences in a two-semester long mathematics course. The first semester was taught using flipped classroom and the second semester using lectures, where both teaching modes contained a substantial amount of active learning. Overall, students report a more positive learning experience and higher engagement in the flipped classroom. The analysis revealed seven categories that the students highlight as especially conducive to their learning; commitment to peers, being recognized, feeling safe, instructor relationship, physical learning environment, learning with peers and using videos to learn new content. The results indicate that the affective dimension of student engagement is particularly prominent when students reflect upon learning in the flipped classroom. [ABSTRACT FROM PUBLISHER]

There is a general agreement thatmany students strugglewith the transition fromsecondary to higher education, particularly in the context of mathematics modules. Lecturers often suggest or supply supplemental resources to give students the opportunity to overcome their difficulties. In addition, students often seek out resources independently, many of which are provided through digital-age technology. Current research in this area focuses on the effectiveness of resources that mathematics educators have developed. However, it is unclear which resource types students select themselves and what specific content they seek. In addition, the type of resources that lecturers recommend to students is not well documented. In this article, we present findings from two surveys carried out in higher education institutes in Ireland: one involving students and the other involving lecturers. In particular, we focus on the resource types favoured by students and lecturers, the specific content that they relate to and the issues they seek to address. [ABSTRACT FROM AUTHOR]

We report on a mixed-method study that compared students’ perceptions of summative assessment across two distinct disciplines – education and mathematics, at two research-intensive institutions in the UK. The disciplines chosen represent opposing positions in Biglan’s classification of academic disciplines, as well as having very different assessment practices. Results suggest that these education students prefer to be assessed by methods they perceive to discriminate on the basis of academic abilities. Moreover, they perceive the traditional closed-book examination as inadequate to assess the capabilities which are key to being successful in their subject, which fits some but not all of the general findings in the literature. However, comparing these results with those of an identical study with mathematics students, we find that the perceptions of summative assessment are very different. We account for that difference by suggesting that students’ epistemic beliefs play a role in shaping these perceptions and conclude that, in designing summative assessment in higher education, generalised and centralised forces for change need to be tempered by contextual and disciplinary factors. [ABSTRACT FROM PUBLISHER]

This study evaluated how calculus students' attitudes towards usage of technology changes according to their learning environment and thinking types at the undergraduate level. Thus, the study attempted to determine the place and importance of technological support in the process of attaining the aimed and obtained acquisitions by students. Participants of the study consist of forty-three calculus students who are studying in traditional or CAS-supported teaching environments, and have different thinking types. Pre-and post-assessment tools were used in the data gathering process, and the data were evaluated with descriptive statistics. The results of the study showed that students in the traditional group place more importance on procedural skills, while students in the CAS group attach more importance to conceptual skills in terms of instructional objects. It also determined that acquisitions, which students think developed differ according to learning environment and thinking types. The main implications of the study were discussed in terms of the related literature and teaching practice. [ABSTRACT FROM AUTHOR]

This article builds on previous results of the Transmaths studies concerning transmissionist teaching practices--and especially adds the significance of students' perceptions of these practices--in their association with students' declining dispositions for studying mathematics. It addresses a gap in this work, and the literature in general, regarding the relationship between teachers' and students' perceptions of pedagogy. Drawing on data analyses from a recent, large survey of teaching and learning mathematics in secondary schools, the article: (a) demonstrates and validates two new measures of perceptions of transmissionist practices, as experienced from students' and teachers' perspectives, (b) investigates the comparability of these two measures, and (c) identifies their associations with students' dispositions to study mathematics. Analysis draws on measures of students in Years 7 to 11 (involving 13,000+ students) and from 132 of their mathematics teachers, and shows low correlation at class level and negligible correlation at student level. Results of regression analysis confirm previous work with older students, i.e. that teachers' self- reported transmissionism is negatively associated with learners' dispositions, but adds that students' perceptions of transmissionism are much more strongly negatively associated with these dispositions, and largely mediate the effect of teachers' (self-reported) transmissionism. Further, the differences between year groups and gender show how girls and older learners suffer significantly larger negative effects. The article concludes with a brief discussion of these complexities and some implications for students' trajectories and transitions into (and out of) mathematics. [ABSTRACT FROM AUTHOR]

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students' overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education. [ABSTRACT FROM AUTHOR]

Flipped learning is gaining traction in K-12 for enhancing students’ problem-solving skills at an early age; however, there is relatively little large-scale research showing its effectiveness in promoting better learning outcomes in higher education, especially in mathematics classes. In this study, we examined the data compiled from both quantitative and qualitative measures such as item scores on a common final and attitude survey results between a flipped and a traditional Introductory Linear Algebra class taught by two individual instructors at a state university in California in Fall 2013. Students in the flipped class were asked to watch short video lectures made by the instructor and complete a short online quiz prior to each class attendance. The class time was completely devoted to problem solving in group settings where students were prompted to communicate their reasoning with proper mathematical terms and structured sentences verbally and in writing. Examination of the quality and depth of student responses from the common final exam showed that students in the flipped class produced more comprehensive and well-explained responses to the questions that required reasoning, creating examples, and more complex use of mathematical objects. Furthermore, students in the flipped class performed superiorly in the overall comprehension of the content with a 21% increase in the median final exam score. Overall, students felt more confident about their ability to learn mathematics independently, showed better retention of materials over time, and enjoyed the flipped experience. [ABSTRACT FROM PUBLISHER]

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even graphics calculator technology in assessment is a serious sticking point. We review some of the issues in the literature and established local practice and prospects for change within tertiary mathematics with reference to international concerns and the experience in the secondary sector. Problems identified could argue for increased technology use in service courses. [ABSTRACT FROM AUTHOR]

Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group interviews were carried out with 27 students. Data analysis is based on the theory of cognitive structure of emotions, which specifies eliciting conditions for each emotion and the variables that affect intensity of emotions. Results show that the participants' emotional experiences in Linear Algebra courses are: satisfaction and disappointment emotions, fear emotions, distress emotions and self-reproach emotions. These emotions are triggered by the appraisal of different situations like the difficulty attributed to Linear Algebra courses, solving problems, asking questions in class, going to the blackboard to solve problems and failure in a course. The students' emotional experiences are based on their appraisal of the situations in terms of specific goals and standards. Some implications for future research on affect in Mathematics Education are discussed. [ABSTRACT FROM AUTHOR]

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students’ ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes. [ABSTRACT FROM PUBLISHER]

Existing research into students' preferences for assessment methods has been developed from a restricted sample: in particular, the voice of students in the 'hard-pure sciences' has rarely been heard. We conducted a mixed method study to explore mathematics students' preferences of assessment methods. In contrast to the message from the general assessment literature, we found that mathematics students differentially prefer traditional assessment methods such as closed book examination; they perceive them to be fairer than innovative methods and they perceive traditional methods to be the best discriminators of mathematical ability. We also found that although students prefer to be assessed by traditional methods they are also concerned by the mix of methods they encounter during their degree, suggesting that more account needs to be taken about the students' views of this mix. We discuss the impact of the results on the way general findings about assessment preference should be interpreted. [ABSTRACT FROM AUTHOR]

This study aims to broadly examine how commonly various conceptualizations of the definite integral are drawn on by students as they attempt to explain the meaning of integral expressions. Previous studies have shown that certain conceptualizations, such as the area under a curve or the values of an anti-derivative, may be less productive in making sense of contextualized integrals. On the other hand, interpreting the integral using Riemann sum-based conceptions proves much more productive for understanding contextualized integrals. This study investigates how frequently students from a US calculus population drew on these three conceptualizations (as well as others) to interpret the meaning of definite integrals. The results were achieved by asking a large sample of students from two US colleges (n = 150) four open-ended questions regarding the underlying meaning of definite integrals. Data from the student responses show a high prevalence of area and anti-derivative ideas and a relatively low occurrence of multiplicatively based summation ideas for interpreting these integrals. Possible reasons for and implications of the results are discussed. [ABSTRACT FROM AUTHOR]

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students’ attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students’ attitudes toward mathematics during a ‘mainstream’ calculus course while controlling for student backgrounds. The attitude measure combines students’ self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted ‘good teaching’ practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational ‘technology’ (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students’ attitudes towards mathematics. (3) ‘Ambitious teaching’ (e.g. group work, word problems, ‘flipped’ reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional ‘good teaching’ practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics. [ABSTRACT FROM PUBLISHER]