Understanding Scale in Wicked Problems …
57
3 A Classification of Work Assignments
Teaching new or complex subjects in higher education involves using many different
approaches. Lectures are only a part of the learning experience; all kinds of additional formats add to learning (seminars, laboratories or tutorials). A relevant part of
teaching is assignments, where the students do some kind of reflection or application of learned content with the intent to advance their understanding, enable their
development of questions, hone their art and craft, acquire skills and become fluent
in using them.
The solution of exercises happens early in courses, often as a first level of assignments which grow more complex over time. Here, exercise is understood as an
“objective which can be achieved using known means” (DE “Aufgabe”, VDI 22211). In an exercise, there is exactly one solution, there is one or a small number of
possible paths to reach the solution. All necessary information to reach the solution
is given with the description of the exercise; it is fully defined. The possible paths
for the solution are usually identical from a purely mathematical perspective. Exercises need to be very abstract, as this is necessary to enable their simple structure.
Thus, context including scale of real-world problems is seldom a part of an exercise.
Numbers, while often relevant for the discipline, are often chosen to help students
understand some typical numbers in this discipline, but can also be totally arbitrary.
Example Calculate the mass of 5 m
3 dry air at 2 bar using the ideal gas assumption.
The didactic value of exercises stems from the experience that learners will need
to start from simple well-defined tasks, to acquire the basic competences, skills and
tools of their discipline. Thus exercises are of high value in teaching.
On the other hand, no one expects that graduates will solve exercises in their
jobs. Quite the contrary, they will work on real world problems where a problem is
understood as an “issue whose solution is not obvious and cannot be directly specified
using familiar methods” (DE “Problem” VDI 2221-1).
Example Define a stationary gas turbine for pumping natural gas through a pipeline.
The rated flow of the pipeline is …
This second example includes many tasks that could have been framed as an
exercise as well, but completing them would require a clear understanding of the
problem, its context and a definition of boundary conditions (not fully given in the
problem description).
There is a very clear distinction between an exercise and a problem, as Table 1
illustrates. This is not a gradual difference of scale (more or less of the same). On
the contrary, these are fundamentally different concepts, which need separate terms.
Using additive adjectives, as is often seen in the literature (e.g. well-structured vs.
ill-structured), is descriptive but does not illuminate the difference sufficiently.
Learning and teaching switches to problems at a later stage: when the basic
concepts are understood and have been trained through exercises, and when the
students have established sufficient contextual knowledge. In the framework of
57
3 A Classification of Work Assignments
Teaching new or complex subjects in higher education involves using many different
approaches. Lectures are only a part of the learning experience; all kinds of additional formats add to learning (seminars, laboratories or tutorials). A relevant part of
teaching is assignments, where the students do some kind of reflection or application of learned content with the intent to advance their understanding, enable their
development of questions, hone their art and craft, acquire skills and become fluent
in using them.
The solution of exercises happens early in courses, often as a first level of assignments which grow more complex over time. Here, exercise is understood as an
“objective which can be achieved using known means” (DE “Aufgabe”, VDI 22211). In an exercise, there is exactly one solution, there is one or a small number of
possible paths to reach the solution. All necessary information to reach the solution
is given with the description of the exercise; it is fully defined. The possible paths
for the solution are usually identical from a purely mathematical perspective. Exercises need to be very abstract, as this is necessary to enable their simple structure.
Thus, context including scale of real-world problems is seldom a part of an exercise.
Numbers, while often relevant for the discipline, are often chosen to help students
understand some typical numbers in this discipline, but can also be totally arbitrary.
Example Calculate the mass of 5 m
3 dry air at 2 bar using the ideal gas assumption.
The didactic value of exercises stems from the experience that learners will need
to start from simple well-defined tasks, to acquire the basic competences, skills and
tools of their discipline. Thus exercises are of high value in teaching.
On the other hand, no one expects that graduates will solve exercises in their
jobs. Quite the contrary, they will work on real world problems where a problem is
understood as an “issue whose solution is not obvious and cannot be directly specified
using familiar methods” (DE “Problem” VDI 2221-1).
Example Define a stationary gas turbine for pumping natural gas through a pipeline.
The rated flow of the pipeline is …
This second example includes many tasks that could have been framed as an
exercise as well, but completing them would require a clear understanding of the
problem, its context and a definition of boundary conditions (not fully given in the
problem description).
There is a very clear distinction between an exercise and a problem, as Table 1
illustrates. This is not a gradual difference of scale (more or less of the same). On
the contrary, these are fundamentally different concepts, which need separate terms.
Using additive adjectives, as is often seen in the literature (e.g. well-structured vs.
ill-structured), is descriptive but does not illuminate the difference sufficiently.
Learning and teaching switches to problems at a later stage: when the basic
concepts are understood and have been trained through exercises, and when the
students have established sufficient contextual knowledge. In the framework of