Undergraduate mathematics achievement in the emerging ethnic engineers programme

This paper addresses the issue of collegiate mathematics achievement of underrepresented minority students as it investigates the impact of a cooperative learning calculus programme on the first-year calculus experience of non-Asian ethnic minority engineering students. The Emerging Ethnic Engineers Programme in the College of Engineering at the University of Cincinnati is a successful, comprehensive programme that focuses on the recruitment, retention, academic success, professional development, and timely graduation of underrepresented coloured students. The objectives of the programme are accomplished through three interrelated phases: pre-college science and mathematics programmes, first-year collegiate programmes, and upper-division programmes. The underlying principles of the first-year programme include academic achievement and establishing a strong sense of community among the cohort. This report will focus on the cooperative learning calculus programme that has been successful in improving retention and academic success rates for coloured freshmen engineering students.     

A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.     

Impact of first-year mathematics study groups on the retention and graduation of engineering students

Many interventions have been proposed to improve the retention and graduation rates of engineering students. One such intervention is to use study groups for first-year college students; such groups provide a structured environment in which the students can learn course material from each other outside of class and can provide the students with a sense of community. In this paper, we report on the impacts fostered by study groups in first-year mathematics courses on the odds of retaining and graduating engineering students. Students who participated in the study groups are compared to students of similar academic preparation who did not participate in such groups. It is found that student participation in study groups is significantly associated with the higher odds of being retained in engineering studies through the first 3 years of college. The results reported here are not as certain for the effect of study group participation on 5-year graduation odds for engineering students and some possible reasons for this are discussed.     

Factors affecting student success in a first-year mathematics course: a South African experience

In spite of sustained efforts tertiary institutions implement to try and improve student academic performance, the number of students succeeding in first-year mathematics courses remains disturbingly low. For most students, the gap between their mathematical capability and the competencies they are expected and need to develop to function effectively in these courses persists even after course instruction. In this study, an instrument for identifying and examining factors affecting student performance and success in a first-year Mathematics university course was developed and administered to 86 students. The overall Cronbach's Alpha coefficient for the questionnaire was found to be 0.916. Having identified variables from prior research known to affect student performance, factor analysis was used to identify variables exhibiting the greatest impact on student performance. The variables included prior academic knowledge, workload, student approaches to learning, assessment, student support teaching quality, methods and resources. From the analysis, students' perceptions of their workload emerged as the factor having the greatest impact on student's performance, followed by the matriculation examination score. The findings are discussed and strategies that can be used to improve teaching and contribute to student success in a first-year mathematics course in a South African context are presented.     

A mathematics support programme for first-year engineering students

This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The success of the programme was evaluated using student feedback as well as a comparison of the performance of students who participated in the support programme with those of a similar background who briefly attended or did not attend the programme. The pass rate in the supported group of regular attendees was 79% compared with 43% and 46% in the briefly supported and unsupported groups, respectively. Both student feedback and statistical data indicate that the programme was highly successful in improving the performance of those who regularly engaged with it.     

Academic maturity of students in an extended programme in mathematics

ABSTRACT

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

A support learning programme for first-year mathematics*

ABSTRACT

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

Simulating student flow through a college of business for policy and structural change analysis

Under the pressure of sharp budget cuts and external demands for better performance, public institutions of higher education must examine how they can facilitate student graduation even as institutional resources diminish. This paper describes a computer model simulating the movement of undergraduates through a large, public college of business. The model allows changes in curriculum policy, prerequisite structure, and staffing capacity to be tested prior to implementation. Outcome measures focus primarily on the expected time to degree of two types of students who enter the university, first-time freshmen and upper division transfers, along with their respective 6-year and 4-year graduation rates. The validated model is used to experiment with both actual and potential scenarios facing the college and gauge their possible impact.     

How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to ‘make maths relevant’ for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources.     

Factors influencing first-year students' success in mathematics

Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in first-year mathematics courses. The study was conducted in three phases involving exploratory open-ended questionnaires, Likert-type questionnaires, and interviews. The results highlight both areas of similarities and areas of differences in lecturers' and students' perceptions about influences on student success and failure. While both students and lecturers acknowledged the importance of motivation, differences in perceptions suggest further research is needed in the areas of active learning, help-seeking, and student effort and workload.     

Student and Teacher Perspectives Across Mathematics and Science Classrooms: The Importance of Engaging Contexts

Substantial recent focus has been placed upon the competitiveness of American students in increasingly global economies and entrepreneurial enterprises. As concerns center on students’ educational preparedness and their efforts at continued learning, researchers acknowledge the importance of student engagement with school. In order to foster engaged learners, teachers must be able to determine and monitor their students’ levels of engagement. The current study examined the alignment of perceptions of engagement by students, teachers, and outside observers across middle and high school mathematics and science classrooms. Results indicated significant teacher‐student differences in perceptions of student cognitive engagement across mathematics and science classrooms with teachers consistently perceiving higher levels than students. Moreover, most effect sizes were moderate to large. A subsequent multi‐level analysis indicated that while teacher perceptions of student cognitive engagement were somewhat predictive of student reported cognitive engagement, academic engagement ratings by outside observers were not.     

On flipping first-semester calculus: a case study

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are ‘flipping’ (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.     

Students’ ratings of teacher practices

In this paper, we explore a novel approach for assessing the impact of a professional development programme on classroom practice of in-service middle school mathematics teachers. The particular focus of this study is the assessment of the impact on teachers’ employment of strategies used in the classroom to foster the mathematical habits of mind and mathematical self-efficacy of their students. We describe the creation and testing of a student survey designed to assess teacher classroom practice based primarily on students’ ratings of teacher practices.     

An analysis of the amount and characteristics of writing prompts in Grade 3 mathematics student books

Curriculum guidelines and professional organizations’ recommendations lack details about how often and how much students should write in mathematics and what characteristics should define their writing. This study presents an analytic framework that addresses how often students are prompted in student mathematics books to write, how much they may be encouraged to write, and the characteristics of the writing prompts. Consequently, 2,095 writing prompts in student books across 10 comprehensive Grade 3 resources were analyzed. Findings indicate a marked variation in how often and how much students are positioned to write. Most prompts have students explain what they did to solve a problem and why about number concepts, with most pressing for procedures. The greatest percentage of prompts had students write about their own solutions and do not urge them to include specific writing features.     

Mathematical tasks,study approaches,and course grades in undergraduate mathematics: a year-by-year analysis

Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students’ academic outcomes. This study takes a cross-sectional look at the approaches to learning used by students from courses across all four years of undergraduate mathematics and analyses how these relate to the students’ grades. We find that deep learning correlates with grade in the first year and not in the upper years. Surficial learning has no correlation with grades in the first year and a strong negative correlation with grades in the upper years. Using Bloom's taxonomy, we argue that the nature of the tasks given to students is fundamentally different in lower and upper year courses. We find that first-year courses emphasize tasks that require only low-level cognitive processes. Upper year courses require higher level processes but, surprisingly, have a simultaneous greater emphasis on recall and understanding. These observations explain the differences in correlations between approaches to learning and course grades. We conclude with some concerns about the disconnect between first year and upper year mathematics courses and the effect this may have on students.     

Optimal staffing of specialized programme trainees under uncertainty

We propose a stochastic model and provide an easy-to-implement optimization tool for admission decisions to specialized training programmes designed for service industries. The model can be applied for staffing of trainees in medical residency programmes, vocational schools, management trainee programmes, and similar. Especially towards graduation, trainees in these programmes substantially contribute to workforce of their affiliated institutions, thus having a targeted number of advanced level students become a potential performance metric for administration. For uncertain attrition rates and study duration, we model and provide an iterative solution algorithm to find the optimal annual admission number for these programmes. Our numeric analysis results show that the solution is robust to changes in attrition and study duration probabilities; hence, our model is robust against specification errors for these parameters, which could be hard to estimate due to data unavailability and fluctuations in educational and economic conditions.     

Improving student learning in calculus through applications

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.     

The Impact of Automated Timetabling on Universities — A Case Study

Since September 1978, Memorial University of Newfoundland has registered its first-year students by a fully computerized timetabling and registration process. This system includes the provision of an individual class schedule for each student in a manner which optimizes the use of the University's classroom and timetable resources. This paper describes the reasons for the design of the computerized system, the characteristics of the system which was created, how the system currently works and its impact on the University. In particular, it illustrates how, given the appropriate administrative structure, the system can be used to help control (or even decrease) expenditures, at a time when increases in enrolment have outpaced those in budgets.