The role of mathematics learning centres in engineering education

Mathematics departments in many universities, in many countries, are under pressure. The demand for mathematics undergraduate programmes is diminish- ing and service mathematics is under threat. In particular, engineering schools are either reducing the number of mathematics courses in degree programmes or engineering staff are teaching mathematics as part of engineering analysis courses. There is also a strong trend in engineering education to make greater use of computer courseware like Mathcad, Matlab and other software systems for the mathematical and statistical components of engineering programmes. Engineer- ing education is undergoing substantial change. The mathematics of engineering programmes will need to change accordingly. Mathematics learning centres have been established in many universities world-wide. Initially their main role was to provide assistance for those who had insufficient levels of competency in pre- requisite mathematics. However, these centres can also make a very useful contribution to the latest trends in the mathematics education of engineering undergraduates. This paper will describe that contribution.     

Analysing the correlation between secondary mathematics curriculum change and trends in beginning undergraduates’ performance of basic mathematical skills in Ireland

The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the ‘Maths Problem’, has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates’ performance of basic mathematical skills showing signs of significant decline in recent years. New mathematics curricula, commonly referred to as ‘Project Maths’, were gradually introduced into the Irish secondary school education system from 2010 onwards. These new curricula aim to place greater emphasis on student understanding of mathematical concepts, use of contexts, and applications of mathematics. This study analyses, through mathematics diagnostic test data gathered between 2008 and 2014, the change in the basic mathematical skills of beginning undergraduates over the time period in which the new mathematics curricula were introduced to secondary education in Ireland. It was found that students’ basic mathematical skills have declined over the time period during which the new mathematics curricula were introduced. Significant declines in beginning undergraduates’ performance of basic mathematical skills were observed during the period 2008–2014, particularly among students who have achieved Higher Level C grades and Higher Level D grades.     

Core skills assessment to improve mathematical competency

Many engineering undergraduates begin third-level education with significant deficiencies in their core mathematical skills. Every year, in the Dublin Institute of Technology, a diagnostic test is given to incoming first-year students, consistently revealing problems in basic mathematics. It is difficult to motivate students to address these problems; instead, they struggle through their degree, carrying a serious handicap of poor core mathematical skills, as confirmed by exploratory testing of final year students. In order to improve these skills, a pilot project was set up in which a ‘module’ in core mathematics was developed. The course material was basic, but 90% or higher was required to pass. Students were allowed to repeat this module throughout the year by completing an automated examination on WebCT populated by a question bank. Subsequent to the success of this pilot with third-year mechanical engineering students, the project was extended to five different engineering programmes, across three different year-groups. Full results and analysis of this project are presented, including responses to interviews carried out with a selection of the students involved.     

Integrating Case Studies in Engineering Mathematics: A response to SARTOR 3

Case studies have long been used to support the mathematics education of undergraduate engineers. Changes in the mathematical ability of entrants to engineering programmes and, indeed, the changing nature of many of the programmes themselves indicate the need to make the students' mathematical experiences more 'user friendly'. We describe here an approach which uses case studies, not as illustrations of applications of mathematics after a mathematical topic has been discussed, but in a fully integrated central role as vehicles for whole group discussion from which the students 'discover' the necessary mathematics which is taught subsequently. Not only is the 'carrot' of the application then central to their learning, but the need for the mathematics being taught is also clearly demonstrated. This approach has been tried with a group of 50 first year engineers. The effects on student motivation, ability and knowledge retention are discussed together with an indication of the Integrated Case Studies which were used.     

Empathy among students in engineering programmes

Engineers face challenges when they are to manage project groups and be leaders for organisations because such positions demand skills in social competence and empathy. Previous studies have shown that engineers have low degrees of social competence skills. In this study, the level of empathy as measured by the four subscales of the Interpersonal Reactivity Index, perspective taking, fantasy, empathic distress and empathic concern, among engineering students was compared to students in health care profession programmes. Participants were undergraduate students at Linköping University, 365 students from four different health care profession programmes and 115 students from two different engineering programmes. When the empathy measures were corrected for effects of sex, engineering students from one of the programmes had lower empathy than psychology and social worker students on the fantasy and perspective-taking subscales. These results raise questions regarding opportunities for engineering students to develop their empathic abilities. It is important that engineering students acquire both theoretical and practical knowledge and skills regarding empathy.     

A modern and interactive approach to learning engineering mathematics

The challenges facing those charged with teaching mathematics to engineers are enormous. Faced with large groups of students possessing a considerable range of abilities, prior experiences, and motivations, it is incumbent upon the developers and deliverers of mathematics programmes to engineers to ensure that such programmes are as inclusive as possible and take into account the particular and often individual needs of the student. Often a mathematics lecturer is caught between the demands of an engineering department expecting students to know and apply advanced techniques, and the needs of groups of students who lack confidence, have serious gaps in their knowledge and sometimes lack ability in mathematics. This paper describes an innovative approach to these challenges which involves a mix of traditional and modern technologies and which has been used with some effect at Loughborough University, for the teaching of mathematics to first year undergraduate engineering students.     

The impact of the pre-instructional cognitive profile on learning gain and final exam of physics courses: a case study

The case study described in this paper investigates the relationship among some pre-instructional knowledge, the learning gain and the final physics performance of computing engineering students in the introductory physics course. The results of the entrance engineering test (EET) have been used as a measurement of reading comprehension, logic and mathematics skills and basic physics knowledge of a sample of 47 Computing Engineering freshmen at the University of Palermo (Italy). These data give a significant picture of the initial knowledge status of a student choosing engineering studies. The students' physics learning gain has been calculated using a standardized tool in mechanics: the force concept inventory (FCI). The analysis shows that mathematical and physical background contribute to achieve a good final preparation in physics courses of engineering faculties; however the students' learning gain in physics is independent of students' initial level of mathematics skills and physics knowledge. Initial logic skills and reading comprehension abilities are not significant factors for the learning physics gain and the performance on physics courses.     

Breaking the habit: engineering students’ understanding of mathematical creativity

ABSTRACT

In higher education, engineering students have to be prepared for their future jobs, with knowledge but also with several soft skills, among them creativity. In this paper, we present a study carried on with 128 engineering undergraduate students on their understanding of mathematical creativity. The students were in the first year of different engineering first degrees in a north-eastern Portuguese university and we analysed the content of their texts for the question ‘What do you understand by mathematical creativity?’. Data collection was done in the first semester of the academic years 2014/2015 and 2016/2017 in a Linear Algebra course. The results showed that ‘problem solving’ category had the majority of the references in 2014/2015, but not in the academic year 2016/2017 were ‘involving mathematics’ category had the majority. This exploratory study pointed out for ‘problem solving’ and ‘involving mathematics’ categories and gave us hints for teaching mathematics courses in engineering degrees.     

Authentic Research Experience and “Big Data” Analysis in the Classroom: Maize Response to Abiotic Stress

Integration of inquiry-based approaches into curriculum is transforming the way science is taught and studied in undergraduate classrooms. Incorporating quantitative reasoning and mathematical skills into authentic biology undergraduate research projects has been shown to benefit students in developing various skills necessary for future scientists and to attract students to science, technology, engineering, and mathematics disciplines. While large-scale data analysis became an essential part of modern biological research, students have few opportunities to engage in analysis of large biological data sets. RNA-seq analysis, a tool that allows precise measurement of the level of gene expression for all genes in a genome, revolutionized molecular biology and provides ample opportunities for engaging students in authentic research. We developed, implemented, and assessed a series of authentic research laboratory exercises incorporating a large data RNA-seq analysis into an introductory undergraduate classroom. Our laboratory series is focused on analyzing gene expression changes in response to abiotic stress in maize seedlings; however, it could be easily adapted to the analysis of any other biological system with available RNA-seq data. Objective and subjective assessment of student learning demonstrated gains in understanding important biological concepts and in skills related to the process of science.     

Courses for teaching leadership capacity in professional engineering degrees in Australia and Europe

Recently, many educational institutions across the globe have implemented engineering leadership programmes either as a part of a formal engineering curriculum or where leadership development is embedded into separate in-house programmes. This shows the clear intent of these educational institutions to prepare their engineering students for solving real-world problems, recognising that both technical and leadership skills are valuable for tomorrow's engineers. Leadership programmes in engineering education have been implemented in various formats with varying degrees of success. It has already been identified in research studies that 80–90% of engineering leadership programmes offered explicitly across the globe were based in the United States of America. However, in Europe and Australia, there is a noticeable lack of engineering leadership programmes, particularly in undergraduate curricula. The programmes that are offered across Australia and Europe have distinct design and delivery styles but there are certain key features that are common to most of the programmes, including professional partnerships, mentoring, engineering design and project-based approaches.     

When Basic Mathematics Skills Predict Nothing: implications for education and training

A study was conducted into the mathematical needs of engineering apprentices, triggered by a decline in the basic number skills of applicants. The mathematical challenges of engineering differ from the mathematics taught in school. In particular, great precision is required and different techniques; a good deal of practical problem solving is necessary, too. Conventional measures of educational attainment had high predictive validity; a test created to sample the mathematical skills directly involved in engineering had low predictive validity. We conclude that perfect mathematical technique is essential in engineering; the competencies learned from a broad‐based education generalise to practical work; acquisition of mathematical technique does not; technical perfection is not a ‘foundation’, but rather is a component of mathematical education; mathematics education should encourage the development of a broad range of skills and some successful application of technique; and the deployment of skills in a range of contexts should be encouraged.     

Games Teachers Play

An important social concern in mathematics education is that the educational attainment of pupils may be influenced by teachers' competence in the curricular area they are teaching. This paper provides some insight into the relationship between student primary teachers' mathematics subject knowledge and their reported confidence to teach that subject. Eighty Bachelor of Education first year students completed an attitudes survey as well as an online mathematics competence test which consisted of 28 randomly generated questions from a bank of approximately 300 questions based on the attainment targets of the Scottish curriculum 5–14 document at level F with some E. Students were asked to rank teacher attributes. Though 98% of the students ranked basic numeracy skills as the most important, 65% of the cohort did not possess these skills. Moreover 95% suggested confidence was important, but confidence levels were found to be low even among students with higher than minimum entry requirements to the undergraduate primary teaching programme. It is perhaps not the level of mathematics that needs to be changed but the nature of mathematics taught and learned at that level that needs to be addressed. This in turn has implications for the approaches and the programmes deployed by Initial Teacher Education courses.     

职教大改革背景下的高职数学文化教育

在职教大改革背景下,特别是随着"双高计划"的启动和高职本科层次办学持续深入,传统数学教育教学方式已很难满足高职教育质量发展的需求。为顺应改革和发展需要,切实提升数学基础课助推学生技能素质提升的内在育人作用,高职院校的数学教学,既要在第一课堂中进行教学渗透,更加注重数学文化理念、丰富数学教学内容、扩展数学文化教育方式,切实培养学生的数学应用意识和创新思维;也要重视二、三课堂的实践激发和价值引领,使学生既能在学习生活中提升数学文化素养,也可以在今后实际工作中潜移默化地运用数学知识解决问题。     

Deficit or Difference? the Role of Students' Epistemologies of Mathematics in their Interactions with Proof

The ability to handle proof is the focus of a number of well-documented complaints regarding students' difficulties in encountering degree-level mathematics. However, in addition to observing that proof is currently marginalised in the UK pre-university mathematics curriculum with a consequent skills deficit for the new undergraduate mathematics student, we need to look more closely at the nature of the gap between expert practice and the student experience in order to gain a full explanation. The paper presents a discussion of first-year undergraduate students' personal epistemologies of mathematics and mathematics learning with illustrative examples from 12 student interviews. Their perceptions of the mathematics community of practice and their own position in it with respect to its values, assumptions and norms support the view that undergraduate interactions with proof are more completely understood as a function of institutional practices which foreground particular epistemological frameworks while obscuring others. It is argued that enabling students to access the academic proof procedure in the transition from pre-university to undergraduate mathematics is a question of fostering an epistemic fluency which allows them to recognise and engage in the process of creating and validating mathematical knowledge.     

Design,implementation, and evaluation of a multi-disciplinary professional development program for research mentors

ABSTRACT

Undergraduate research experience has been shown to enhance student learning and improve persistence in science, technology, engineering, and mathematics (STEM). Researchers studying undergraduate research experiences have largely focused on student outcomes and have seldom investigated the outcomes of graduate and postdoctoral mentors. Here, we report a non-credit, year-long mentor professional development program designed for graduate students, postdoctoral scholars, and research staff in STEM. Mentors attended a series of six interactive and discussion-based workshops and mentored first-year undergraduate students in independent summer research projects. We report evaluation findings for three mentor cohorts using a combination of qualitative analysis of mentoring philosophies and quantitative assessment of pre- and post-surveys about mentoring objectives and skills. Results indicate that mentors gained self-efficacy in some objectives and skills. However, many other objectives and skills remained unchanged. We explore possible explanations for the lack of more broad-scale gains across survey items and present ideas for program improvement.     

关于奥数与小学生数学思维能力发展冲突的思考

近年来,小学“奥数”越来越热。小学生做奥数题是否真的有利于小学生的数学思维能力发展,这一问题成为一些教育界人士与家长关心的重要议题。文章认为,大面积的小学生“奥数”培训热,降低了小学生数学学习的兴趣,不利于提高小学生的数学能力。小学数学教学应该把提升小学生的数学素质作为基本出发点,促进小学生的数学思维能力发展。     

Common elements of capstone projects in the world's top-ranked engineering universities

‘Capstone’ is a metaphor used to describe a final achievement that builds upon previous works and encapsulates them. Capstone projects are included in engineering curricula to integrate multi-disciplinary subjects and teach professional skills that are difficult to impart in a traditional lectured course. Since these projects serve to transition students into professional engineers, they have a direct impact on a university's industry reputation and ranking. Therefore, it is worthwhile to study the capstone programmes implemented at the world's top-ranked engineering universities to discover common elements which characterise them. In this paper, common elements of the capstone programmes implemented in mechanical and aerospace engineering undergraduate programmes in the world's top-ranked engineering universities are identified and analysed to determine established best practices. These practices can be modelled and applied to the pedagogy of engineering programmes at universities around the world to improve the development of professional skills of future graduates.     

Management Training of Engineering Students at the Indian Institute of Technology,Delhi

For an engineer to become an effective manager, he must have a basic concept about management principles and techniques. Some amount of management capacity can be developed in engineers by creating an awareness of the scope of management, imparting basic knowledge about management principles and identifying more closely with the management team. This paper describes the way in which the Indian Institute of Technology, Delhi promotes engineering management training to its students. The training consists of introducing some management courses to undergraduate engineering students, conducting lectures and seminars related to management disciplines, encouraging students to do management related industrial projects and arranging vacation training programmes in industry. Moreover, a full M. Tech, programme in Systems and Management exclusively for engineering graduates is conducted. In addition, the paper discusses the other postgraduate and research programmes in management that the Institute conducts through its Management Centre.     

The role of a children's mathematical thinking experience in the preparation of prospective elementary school teachers

Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics.     

A study of competence in mathematics and mechanics in an engineering curriculum

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.