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S. Linow
Table 1 Aspects of exercises versus problems
Aspect
Exercise
Problem
Synonym
Well-structured problem, Story
problem, Word problem
Ill-structured problem
Specification of the task Complete
Incomplete, often contradictory
Defining it is part of the solution
Degree of complexity
Low, constrained
High/usually unconstrained/often
infinite
System boundary
Complete, well defined, closed
Incomplete, contradictory, open
Defining it is part of the solution
Context
None or irrelevant for the
exercise
Real world, incomplete,
contradictory
Conflicting aims
Defining it is part of the solution
Number of solutions
Exactly one
Zero or any number
Solution method
One, obvious for the expert
If there are more than one, they
are mathematically equivalent
Non-obvious or non-existent
Choosing one is part of the
solution
Criteria for the solution Obvious, part of the assignment Non obvious, not known,
incomplete, contradictory
Defining them is part of the
solution
Quality of the solution
Deviation from exact solution is
measurable or can be calculated
Unknown
Defining criteria is part of the
solution
Disciplines involved
Exactly one
Many (all, depending on
perspective)
Interactions
None
Feedbacks into other systems
Feedbacks from evolving other
systems will change and influence
Explanation
Obvious
It is part of the assignment
Many and sometimes
contradictory explanations are
possible
Providing one is part of the
solution
competence-oriented teaching, exercises are part of acquiring the two lower levels
of Bloom’s taxonomy, namely (context) knowledge and comprehension (Biggs and
Tang 2011), thus problems are a necessary part in learning the levels of application
and beyond.
There exists a relevant hurdle both for student and teacher in going from exercises
to problems, caused by the large systemic gap between these concepts as Jonassen
et al. (2006) argues:
• From the student’s perspective, exercises come first in a specific course or during
learning. Students get used to this structure and may start to believe that doing
S. Linow
Table 1 Aspects of exercises versus problems
Aspect
Exercise
Problem
Synonym
Well-structured problem, Story
problem, Word problem
Ill-structured problem
Specification of the task Complete
Incomplete, often contradictory
Defining it is part of the solution
Degree of complexity
Low, constrained
High/usually unconstrained/often
infinite
System boundary
Complete, well defined, closed
Incomplete, contradictory, open
Defining it is part of the solution
Context
None or irrelevant for the
exercise
Real world, incomplete,
contradictory
Conflicting aims
Defining it is part of the solution
Number of solutions
Exactly one
Zero or any number
Solution method
One, obvious for the expert
If there are more than one, they
are mathematically equivalent
Non-obvious or non-existent
Choosing one is part of the
solution
Criteria for the solution Obvious, part of the assignment Non obvious, not known,
incomplete, contradictory
Defining them is part of the
solution
Quality of the solution
Deviation from exact solution is
measurable or can be calculated
Unknown
Defining criteria is part of the
solution
Disciplines involved
Exactly one
Many (all, depending on
perspective)
Interactions
None
Feedbacks into other systems
Feedbacks from evolving other
systems will change and influence
Explanation
Obvious
It is part of the assignment
Many and sometimes
contradictory explanations are
possible
Providing one is part of the
solution
competence-oriented teaching, exercises are part of acquiring the two lower levels
of Bloom’s taxonomy, namely (context) knowledge and comprehension (Biggs and
Tang 2011), thus problems are a necessary part in learning the levels of application
and beyond.
There exists a relevant hurdle both for student and teacher in going from exercises
to problems, caused by the large systemic gap between these concepts as Jonassen
et al. (2006) argues:
• From the student’s perspective, exercises come first in a specific course or during
learning. Students get used to this structure and may start to believe that doing