University rankings - Badat, 2010

 I have recently read Elaine Unterhalter and Vincent Carpentier’s 2010 edited book University into the 21st century: Global Inequalities and Higher Education: Whose interests are we serving? Here I shall summarise the chapters which were of greatest relevance to my interests.

 

Badat, S. (2010). Global rankings of universities: a perverse and present burden, in E. Unterhalter, V. Carpentier (eds.) Universities into the 21st Century: Global Inequalities and Higher Education. Whose Interests Are We Serving? Basingstoke, Hampshire UK: Palgrave Macmillan.

 

Several different ranking of “world class” universities exist. Badat mentions the Times Higher Education-Quaxquarelli Symonds (THE-QS) and Shanghai Jiao Tong Institute of Higher Education (SJTIHE) as being the best known rankings. The purposes of a university are many, chief amongst which are the broad goals of production of knowledge, the dissemination of knowledge and cognitive development of students, and community engagement. Neither of the rankings mentioned above is a good measure of all of these purposes and no linear ranking really could be. The purposes of a university are too many and too varied for any one institution to pursue them all and to continually improve across all area. Universities need to choose and build on areas of strength which are aligned with their missions and their goals. Badat is witheringly eloquent about the acceptance of the worth of these ranking systems in the face of overwhelming evidence of their uselessness. Universities of the global South are encouraged to “catch up” to their Western and Northern counterparts. Rankings play a role in this way of looking at university worth and they should not. Badat calls for universities of the global South to join with one another and with other social actors to develop alternative instruments which measure qualities more in line with university purposes and gaols and with the educational endeavour.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Pedagogy for being - Walker, 2010

 I have recently read Elaine Unterhalter and Vincent Carpentier’s 2010 edited book University into the 21st century: Global Inequalities and Higher Education: Whose interests are we serving? Here I shall summarise the chapters which were of greatest relevance to my interests.

 

Walker, M. (2010). Pedagogy for rich human being-ness in global times, in E. Unterhalter, V. Carpentier (eds.) Universities into the 21st Century: Global Inequalities and Higher Education. Whose Interests Are We Serving? Basingstoke, Hampshire UK: Palgrave Macmillan.

 

Higher education has become driven by the economy, with aims related to making the graduates better producers and better able to contribute to the national economy. As economies collapse and as graduates struggle to find jobs demanding their level of education, Walker suggests that “we need rather to rebalance higher education goals in the direction of a much more expansive public good, and the formation of graduates as rich human beings” (p. 220-1). She discusses a project in which she was involved, looking at the “research/teaching nexus”. The students involved in the project, across the three departments of history, politics and animal and plant sciences, engaged in research and learned how to interrogate knowledge, develop critical and reflective thinking and recognise a “plurality of views”. Walker argues that university pedagogies, often oriented towards marketization, need to rebalance by cultivating “human being-ness” addressing issues of global citizenship, critical thinking and social justice.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Engineering maths curriculum - Mustoe, 1995

 Mustoe, L. (1995). Industry expects – but who should determine the curriculum? European Journal of Engineering Education, 20(3), 313-323.

 

Mustoe asks “How far should an undergraduate education in engineering aim to meet the needs of industry as perceived by industry?” (p. 313). He proceeds to come at this question from multiple directions: the requirements of industry, of engineering academics, of mathematicians, of professional bodies. He finds that the views of what maths is necessary and desirable varies widely across these groups and that it is impossible to meet everyone’s demands. For example, does the engineering mathematics lecturer teach mathematical concepts in context or not? In-context problems at the first-year level are hard to find as real-world problems are messy and ill formed. In addition, the students might not yet be familiar with the engineering context and confusion rather than a sense of relevance will result. Mustoe cites a view that concepts are easier to study in the abstract without confusing contexts, however, many clamour for relevance in the maths curriculum and show how students lose interest due to no clear links between maths class and other courses.

 

Throughout Mustoe’s literature review of a wide variety of viewpoints, there is an emphasis on basic manipulative skills as well as modelling. “Five general areas of competence worth aiming for are: a ‘feel’ for the magnitudes of quantities, an ability to handle fractions without fear, an appreciation of the use of approximations, the ability to manipulate formulae confidently and the skill to cope with calculus.” (p. 320) Mustoe has little patience for long integration problems: “Other than training in patience, persistence and concentration, there is little to be gained from an exercise in integration, for example, which requires three successive substitutions and the use of a trigonometric identity for good measure.” (p. 321). There is not much mention of the role of proof in engineering mathematics courses within this paper, except for a citation of Craggs (1978): “Craggs was concerned about the level of rigour in the mathematics taught to engineers. His conclusion was that the aims for teaching were to encourage accuracy in manipulation, to state theorems with proof where it was easy and with heuristic justification where it was not, to illustrate the possible gains and losses if work was undertaken outside the domain of these theorems and to respect the additional expertise of the trained mathematician.” (p. 318).

 

Mustoe concludes that curricula should be dismantled and rebuilt from the ground up with a clear view of what the role of mathematics is in the degree programme. (Note that this is a 1995 paper, so hardly current.) I loved this paper for its variety of views and broad literature review.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Interdisciplinary engineering maths - Zenor, Fukai, Knight, Madsen & Rodgers, 1995

 Zenor, P., Fukai, J., Knight, R., Madsen, N., & Rogers Jr, J. (1995). An interdisciplinary approach to the pre-engineering curriculum. In Frontiers in Education Conference, 1995. Proceedings, (pp. 3c1.18-3c1.22). IEEE.

 

The first author has already been involved in the design and running of a course integrating calculus and physics. That course has proved to be effective. This paper is on designing a sequence of courses which proceed seamlessly and integrate calculus, other maths topics, physics and several engineering courses such as dynamics, statics, thermodynamics and signals. The maths content will be the heart of this two year programme of study with topics flowing one into the other and physics and engineering topics being included as appropriate for increasing the depth of the mathematics. The idea is that new maths topics will be encountered at a reasonable pace, rather than too fast, and understanding of each will be enriched by immediate application. I am rather daunted by their plan to include vector calculus right from the beginning, but, if I understand correctly, they will start with things like differentiating vector-valued functions and things like Stokes’ Theorem will occur much later in the syllabus. The courses will be team taught and the students will remain together as a cohort for two years. At the time of writing this paper, this project was in its design phase. That was 19 years ago. I wonder if I could find out how it all went. I’ll go scrounging for that at some later date.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Engineering maths support - Budny, LeBold & Bjedov, 1998

 Budny, D., LeBold, W. & Bjedov, G. (1998). Assessment of the impact of freshman engineering courses. Journal of Engineering Education, 87(4), 405-411.

 

The authors describe the first years of the engineering degree at Purdue University. Students enter a “Freshman College” at first, where they cover calculus, physics, chemistry, English and computers. Once they have achieved a C aggregate in these courses, they proceed to register with one of the engineering disciplines. Entering students write an algebra placement exam. If they fail this exam, they do a pre-calculus semester before beginning calculus. Students also have the opportunity to be fast tracked and proceed straight to second semester calculus. In a quantitative longitudinal study, the authors study the effectiveness of the various courses and the retention and graduation rates of different cohorts of students. At a point in the study, a counsellor-tutorial (CT) program was started, providing “additional services” to make the first-year experience “less lethal” (p. 409). This program was found to be successful, and became even more successful when the program was expanded to take on more students (from 80 to over 400). One concern was that providing support in first-year would merely delay drop out, however that pattern was not apparent in the data.

 

“There is a relationship between ultimately graduating in engineering and first obtaining a thorough understanding of basic mathematics and science principles. As the academic skills of the average student are honed, this relationship between these skills and the “world of engineering” becomes clearer to the engineering recruit. At Purdue University, we believe that the courses in calculus, chemistry, and physics supply the collegian with these necessary skills. We also believe that if you treat these courses as high-risk and supply additional assistance to those students with a higher probability of failure, then those students will acquire the critical background skills that will make it possible to persist in engineering.” (p. 410)

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Outcomes based vector calculus - Goulet, 2001

 Goulet, J. (2001). An outcomes oriented approach to calculus instruction. Journal of Engineering Education, 90(2), 203-206.

 

Goulet describes a multivariable calculus course which was outcomes-based in that 15 goals were determined through communication with lecturers of subsequent courses. The students’ assessments were not simply graded as usual, but each question was graded towards achievement of a goal. If goals were not achieved in any particular assessment, a retest had to be taken until all goals were achieved. This way poorly understood concepts would remain current for the students rather than becoming “history”. The students liked “having clear cut objectives stated and pursued, the chance to get better at something if not initially successful, and the means to improve their grade” (p. 205). The response was good, from students and lecturer, although Goulet observes that assessing in this way does add to the lecturer’s workload. I am interested in the role of theory in engineering maths so I find it interesting than none of the goals had anything to do with theorems, proofs or even derivations. Food for thought.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Real-world vector calculus problem - Ollerton, Iskov & Shannon, 2002

 Ollerton, R.L., Iskov, G.H. & Shannon, A.G. (2002). Three-dimensional profiles using a spherical cutting bit: problem solving in practice. International Journal of Mathematical Education in Science and Technology, 33(5), 763-769.

 

This paper is a very interesting application of vector calculus in a real-life context. Computer Numerical Controlled milling machines often use a spherical bit for the milling of high precision 3d surfaces, such as the gripping surfaces of surgical tissue clamps. If we start with a two dimensional curve approximating the undulating surface, we can find three methods of plotting the path of the centre of the spherical bit: basic calculus, Lagrange multipliers and vector calculus. Extending to the 3d surface, the vector calculus method transfers best. In the process of the calculation the concepts of radius of curvature and cycloids come up.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Recorded lectures - Rees, Atkin & Zimmerman, 2005

 Rees, J.M., Atkin, R.J. & Zimmerman, W.B. (2005). On the use of audio-tapes for teaching vector analysis to engineering undergraduates. International Journal of Mechanical Engineering Education, 33(4), 358-368.

 

Rees, Atkin and Zimmerman discuss their teaching innovation to replace four vector analysis lectures with audio-tapes and accompanying notes. They open the paper talking about how maths for engineers is best understood through covering fundamental concepts, mathematical techniques and, crucially, applications to engineering. They point out how their course (as with most maths courses) is so packed with content over a short time that there is scant time for applications. I therefore expected that they were using the tapes as replacements for lectures but that the actual lecture time slots would be taken up with examples and applications. This was not the case. The conventional lectures were simply cancelled with the students encouraged to attend the single “examples” class per week.

 

In the first wave of this initiative, the tapes were poorly used by the students and attendance at the examples classes was poor. In the second wave, the students were given increased ownership over the process, choosing when to receive the tapes and when the replaced lectures would be scheduled. Use of the tapes was better this time and attendance was improved. Also, approval of the initiative was increased, although in both waves many students claimed to prefer conventional lectures to the tape system. I was disappointed with the cancelling of lectures; surely this time could have been spent much more valuably? I was also disappointed that the vector analysis topic coverage was not described. It must be far less than my course since it is only 4 lectures long and mine is closer to 50. Mention is made of scalar and vector operators in the context of fluid flow, but that is all. The use of tapes is outdated now, but this initiative would be analogous to having lectures recorded, for instance on a tablet. I approve of this system, but only in the context of “the flipped classroom” which would mean keeping those lecture time slots active and filling them with worked examples, some sort of workshop, group activities, or whatever is appropriate for deeper learning.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understandings and opinions of Torquetum only and could contain errors, misunderstandings and subjective views.

Ill-structured problems - Jonassen, Stroble & Beng Lee, 2006

 Jonassen, D., Stroble, J. & Beng Lee, C. (2006). Everyday problem solving in engineering: lessons for engineering educators. Journal of Engineering Education, 95(2), 139-151.

 

This is quite a lengthy paper which I shall summarise very briefly. The authors disagree (as many do) with the notion that students can transfer problem solving techniques from typical classroom problems (word problems, usually) to workplace problems, which are ill-structured. They conducted interviews with approximately 90 professional engineers about problems they had encountered and how they had solved them. The authors develop 12 themes which emerged from the interviews, such as “most constraints are non-engineering” and “Engineers primarily reply on experiential knowledge”. The authors close with suggestions for education, such as using PBL (problem based learning). This requires huge commitment from staff and wide ranging reform, however, and can be hard to achieve. Other than that they give suggestions on how to make classroom activities more like workplace situations.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

Curl in fluid flow - Burch & Choi, 2006

 Burch, K.J. & Choi, Y. (2006). The curl of a vector field: beyond the formula. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 16(3), 275-287.

 

The authors contextualise curl and Stoke’s Theorem in fluid flow. They begin by considering an infinitesimal rectangle deformed by a vector field. They calculate the angular velocities of two adjacent edges and show how that relates to the concept of viscosity in fluid dynamics and to the familiar curl formula. They show how that means that curl relates to spin about an object's own axis (independent of translation through a fluid) and give some examples. For several given vector fields, they draw the direction field and intuitively predict spin, then they back that up with curl calculations. The authors close with a discussion of the meaning of the Stokes’ Theorem formula and how the curl side of the formula is measuring the viscosity flux of V across S. I found this paper really interesting.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.