Was it good for them? Reflections on the use of MENTOR and changes in course design using general performance measures

This paper considers the use of general performance measures in evaluating specific planning and design decisions in higher education and reflects on the students' learning process. Specifically, it concerns the use of the MENTOR multimedia computer aided learning package for helping students learn about OR as part of a general business degree. It includes the transfer of responsibility for a learning module to a new staff member and a change from a single tutor to a system involving multiple tutors. Student satisfaction measures, learning outcome measures and MENTOR usage patterns are examined in monitoring the effects of the changes in course delivery. The results raise some questions about the effectiveness of general performance measures in supporting specific decisions relating to course design and planning.     

Diagnostic assessment of preparedness of level one sports science students for biomechanics modules

The primary objective of this study was to investigate the use of a diagnostic test to assess the prepardness of level one students for a sports biomechanics module. During their first week at university, a cohort of 108 students completed a diagnostic test at the end of their first lecture in sports biomechanics, with no prior notice. Upon completion of the 12-week module, the students sat the same diagnostic test, again with no prior notice. The results from the initial test were used to identify areas that required emphasis and additional resources during delivery of the module. The comparison of test results from the two sittings was used as a measure of the level of success of the module in increasing the level of student understanding. It is concluded that the design of a diagnostic test specific to a module can be used both to inform subsequent teaching and to assess success of teaching methods.     

Mathematics performance on integers of students with mathematics difficulties

The purpose of this study was to report on findings regarding an integer module intervention. We provided the effects of the integers module lessons intervention on the mathematics performance of 7th grade students with mathematics difficulties. We provided an analysis of the mathematics interventionists’ and their students’ perspectives about the integer module to help explain the findings. A total of 908 students participated in the study and were randomized to one of two conditions. The research design was class-randomized with classes allocated to the treatment or control condition. The analyses showed that the condition predicted students’ slope estimate, on average (β = 0.61, p = .004) where students receiving treatment made greater gains than students in the control condition. Regarding the interventionists’ and students’ perspectives about the integer module lessons, both interventionists and students had overall positive ratings of the intervention components. Implications of these findings are discussed.     

Teaching objectives: the value of using cases in teaching operational research

This paper describes our experience with a case study that was intended to provide business students with a straightforward exercise in operational research/management science (OR/MS) but which consistently produces a learning experience for students that is quite different from that envisaged when the case was originally written. An effort is made to explain the surprising results in the classroom. This example demonstrates the fact that building OR/MS models often reveals important dimensions of a problem that otherwise might remain unexplored. The richness of this case also demonstrates the value of exposing OR/MS students to real problems through the use of cases.     

在数学专业运筹学教学中引入计算机实践环节的探索

运筹学是应用数学的一个重要分支,在许多学科领域及工程问题中均有应用.自从运筹学在上世纪建立以来,其算法及理论的发展都受到了电子计算机的发展的极大影响.因此在本科运筹学教学中引入适当的计算机实践是非常必要的.这将有助于学生更加深入清晰地理解算法的工作步骤、算法建立的思想以及每个算法的优缺点.在本文中我们试着探讨了为何应在数学专业的运筹学教学中引入计算机实践环节,以及应当如何引入这些实践活动.     

Communication Skills: Information-Seeking Interviews

Communication with managers is important throughout every O.R. project, and information-seeking interviews are especially important. Yet the subject of communication has not been studied scientifically in O.R. This paper describes efforts to develop interview skills within a module on communication in an M.Sc. course. The interview skills component of the module consists of three phases in the university, followed by a fourth phase when the students carry out interviews in a real organization as part of the M.Sc. project. Some analysis has been made of processing skills in interviewing where language assistance given to overseas students was turned to account with British students.     

Outcomes of a service teaching module on ODEs for physics students

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore, necessary that students develop conceptual understanding of differential equations in addition to procedural skills. We have investigated the difficulties encountered by third-year students at Dublin City University in an introductory differential equations module. We developed a survey to identify these difficulties and administered it to students who had recently completed the module. We found that students’ mathematical ability in relation to procedural competence is an issue in their study of differential equations, but not as severe an issue as their conceptual understanding. Mathematical competence alone is insufficient if we expect our students to be able to recognize the need for differential equations in a physical context and to be able to set up, solve and interpret the solutions of such equations. We discuss the implications of these results for the next stages of the research project.     

Teaching communication in an MBA operations research/management science course

This paper discusses the inclusion of a writing requirement within a first-year Operations Research/Management Science (OR) course of a Masters of Business Administration (MBA) curriculum. The inclusion of a writing requirement addresses the importance of communication in OR. It is the authors’ supposition that many of the recent criticisms of OR teaching have their roots in poor OR communication. Although OR faculty members can well argue relative values, we have failed to adequately prepare our students to communicate relevant insights from OR studies. The integration of a writing requirement, consisting of short executive summary-style reports and a major term project, within an MBA OR course can do much in promoting further OR study and OR work. This paper describes our experience in instituting a writing requirement within a first-year MBA course in OR.     

Live lectures or online videos: students’ resource choices in a first-year university mathematics module

In Maths for Business, a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students’ specific usage patterns with both of these resources and discuss their reasons for the preferences they exhibit. In 2015–2016, we collected quantitative data on each student's resource usage (attendance at live lectures and access of online videos) for the entire class of 522 students and employed model-based clustering which identified four distinct resource usage patterns with lectures and/or videos. We also collected qualitative data on students’ perceptions of resource usage through a survey administered at the end of the semester, to which 161 students responded. The 161 survey responses were linked to each cluster and analysed using thematic analysis. Perceived benefits of videos include flexibility of scheduling and pace, and avoidance of large, long lectures. In contrast, the main perceived advantages of lectures are the ability to engage in group tasks, to ask questions, and to learn ‘gradually’. Students in the two clusters with high lecture attendance achieved, on average, higher marks in the module.     

The potential of recreational mathematics to support the development of mathematical learning

ABSTRACT

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts. Recreational mathematics can be used in education for engagement and to develop mathematical skills, to maintain interest during procedural practice and to challenge and stretch students. It can also make cross-curricular links, including to history of mathematics. In undergraduate study, it can be used for engagement within standard curricula and for extra-curricular interest. Beyond this, there are opportunities to develop important graduate-level skills in problem-solving and communication. The development of a module ‘Game Theory and Recreational Mathematics’ is discussed. This provides an opportunity for fun and play, while developing graduate skills. It teaches some combinatorics, graph theory, game theory and algorithms/complexity, as well as scaffolding a Pólya-style problem-solving process. Assessment of problem-solving as a process via examination is outlined. Student feedback gives some indication that students appreciate the aims of the module, benefit from the explicit focus on problem-solving and understand the active nature of the learning.     

Software to support numerical analysis teaching

This paper describes a Fortran90 library designed to support the teaching of numerical analysis and its applications. As well as covering traditional material it introduces recent and important ideas in numerical computation such as interval arithmetic and automatic differentiation. The library rests on a module realpac which provides real arithmetic in a range of precisions with a choice of rounding strategies. This, in turn, supports the implementation of an interval arithmetic module intpac. Derived data types and overloaded operations help inexperienced users to interface with unfamiliar data types such as intervals. The library also includes more conventional modules such as lepac for solving linear systems and minpac for nonlinear optimization. These, however, can be enhanced by being linked to more sophisticated tools for sparse matrix handling and automatic differentiation. As well as showing the main structure and scope of the software, the paper mentions some exercises that have successfully been performed by students.     

Areas and the Fundamental Theorem of Calculus

We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component.     

独立学院数学课程体系的探索

为解决独立学院数学教学中能力强的学生"吃不饱",能力欠佳的学生"吃不消"的问题,提出了"基础+提高"统筹优化的数学课程体系."基础"模块的教学坚持为后续专业课服务,并穿插教书中"育人"理念;"提高"模块作为公共选修范畴,具有自主性、多元化特点,并突出人才培养的阶梯式发展.通过近5年的教学改革与实践,新课程体系有效地提高了学生学习数学的兴趣,降低了期末考试的不通过率,并造就一批有创新意识的人才.     

逐位模2加运算与模2n加运算的相容程度分析

深入分析了逐位模2加运算和模2^n加运算的相客程度问题，给出了它们的相客概率的计算公式；同时给出了它们的一些性质．井对用这两种群运算的组合作为编码环节的特性做了一定的分析。     

A teaching module on the history of public-key cryptography and RSA

This article describes some empirical research into using history in mathematics education. More precisely, it discusses a teaching module on the history of public-key cryptography and RSA, implemented in a Danish upper secondary mathematics class in the autumn of 2007. As part of the module the students were expected to write several essays illuminating different aspects of this history. The article discusses whether the students were able to reflect on meta-perspective issues of the evolution and development of mathematics and if so, then whether these reflections were anchored in the taught (and acquired) mathematics of public-key cryptography and RSA. The question of how teaching modules may be designed to take such matters into account is also discussed.     

Sampling the OR World: The Strathclyde ‘Apprenticeship’ Scheme

A few years ago, Strathclyde University's postgraduate course in OR was redesigned. A significant innovation was to introduce a short working placement part-way through the course-the ‘apprenticeship’ period - which students spend as temporary members of real-life OR (or directly-related) groups. This paper reports on two aspects of this apprenticeship scheme; how it has worked as an educational exercise, and what the students' experiences have told us about the general state of OR in the UK     

A historical teaching module on ‘the unreasonable effectiveness of mathematics’: Boolean algebra and Shannon circuits

This article describes the design and implementation of a historical teaching module, where Danish upper secondary students studied primary source material from the mathematicians R W Hamming, G Boole and C E Shannon. The module is an example of a so-called HAPh-module, which focuses on elements of the history, application and philosophy of mathematics. A previous version was presented at the History and Pedagogy of Mathematics (HPM) meeting in Deajeon, Korea in 2012.     

Operations research practice on logistics management in Taiwan: An academic view

The opinions of logistics educators in Taiwan on OR practices in the domestic logistics industry are explored in this research. In this study, questionnaires were given to 42 pre-screened educators at 10 logistics departments and graduate institutes. According to the 37 valid returned questionnaires, 70% of the responding educators believe the major source of OR techniques in Taiwan’s logistics industry originates from individual employee training, while 92% believe OR is not widely used primarily because companies are unfamiliar with OR techniques. OR techniques were considered helpful in solving problems by 73%. Generally speaking, familiarity with OR techniques is not associated with implementation of OR techniques by educators. Additionally, logistics educators express concern about insufficient training for logistics students in Taiwan. However, they are optimistic about the logistics industry’s willingness to more actively adopt OR techniques in Taiwan in the next two years.     

Teaching OR: automatic evaluation for linear programming modelling

4OR - Learning how to model a problem described in natural language as a linear program requires students to practice using various and numerous exercises. Moreover, immediate feedback on the...