Problem solving strategies
Kalle Ruttik
Department of Communications and Networking
School of Electrical Engineering
Aalto University
Content
• Scientific method
• Problem solving strategy
Scientific method
Scientific method
• Observation and description of phenomena
• Hypothesis: formulation of an explanation of the
phenomena
• Make predictions about phenomena by using
hypothesis
• Test predictions by experiments
Validation of an hypothesis
• Hypothesis are confirmed or rejected by tests
– If predictions are not confirmed by measurements the
hypothesis has to be rejected (usually modified).
• Experiments
– Can test hypothesis directly
– Can test predictions of the hypothesis
• Even if rejected, the theory can be used in some
limited "special" cases where it agrees with
measurements.
Measurement errors
• Measurements are described by their
– Accuracy - how close the measured value is to the true value
– Precision - how close two measured value are to each other
• Always when you give quantitative results provide
also their precision - range of the measurement
errors
• Measurement errors are classified
– Random errors
• Unpredictable variation in the measurement process
– Systematic errors
• Systematic discrepancy compared to exact value
Common mistakes while using scientific
method
• Scientific method attempts to minimize human impact
on the outcome of the experiment
• Without experimental validation the hypothesis is not
considered to explain the phenomena
• Common missteps
– Some experimental data points are ignored
– Wrong estimation of systematic error
– Some phenomena are ignored as systematic error
• In open research environment with multiple
independent measurements the biases of individual
research groups tend to average out
Stage of acceptance of the knowledge
about phenomenon
• Hypothesis
– Hypothesis is a proposed explanation of a phenomenon. It can
exists before measurements are performed.
• Model
– Model describes the phenomena only with limited precision and
in limited domain.
• Scientific theory or law
– Law is hypothesis or group of hypotheses which are confirmed
through the experiments.
Problem solving and scientific method
• Everyday problem solving process has similarities
with scientific method
• Scientific method can be applied when the
phenomena can be isolated
– External factors can be eliminated
– Repeated tests with controlled changes can be conducted
• The method is not suitable when the phenomena
can not be isolated
– The result depends on the system initial state (history)
Problem solving strategies
Problem solving methods
• University courses mostly teach routines
– Most routines require only the problem diagnosis skills
– Diagnosis – identification of the nature and cause of certain
phenomenon
• Problem solving methods contain also
– Strategy - high level plan to achieve goals under conditions or
uncertainty
– Interpretation - explaining the meaning
– Generalization - extension of concept to less-specific criteria
Amateurs vs Professionals
• Knowledge is presented as patterns not as single
facts
• Patterns can be learned by
– Practicing in defining problems and drawing sketches
– Paraphrasing the problem statement
– Giving new interpretation of the problem
Problem solving strategies
Strategy is the set of steps followed during problem
solving process
– Amount of steps can vary (usually 4 - 15 steps)
Example of steps
1. I can
2. Define
3. Explore
4.
5.
6.
7.
Plan
Do
Check
Generalize
Motivation
• Confidence
• Why you think that you can solve the problem
– Similar problem has been solved before
– Vision that known results can be applied
• Modification of know results
– Use of new theoretical method that can help to solve the
problem
Define
• What
– List the knowns and unknowns
– Describe the relationship between the variables
• Identification of the constraints and criteria for
solutions
Define: Problem analysis
• Requirements
• Constraints
• Scope
Define: Requirements
•
•
•
•
What information the solution has to provide?
What functionality the solution provides?
What data is needed for the solution?
Used tools:
–
–
–
–
Context diagrams,
data flow diagrams
use cases
…
Define: Constraints
• What conditions need to be considered
– Cost, speed of processing, compatibility, legal aspects etc.
Define: Scope
•
•
•
•
What can or can’t the solution do?
What are the benefits of the solution to the user?
Boundaries and parameters of the solution,
efficiency and effectiveness
Explore
• Ponder about the problem
– Get familiar with it
• Expert solvers ask questions and explore
dimensions
–
–
–
–
–
Is it routine problem?
What parts are present what not?
How to apply the known methods in this field?
What are alternative approaches?
Is this problem worth to be solved?
Plan
• Design the solution
• Define evaluation criteria
Plan: Design the solution
• Formalizing the problem
– Solve the problem analytically (in symbolic form)
• Define how the solution will function. What will
appear in result of applying the solution?
• Tools
– Data dictionaries, data structures, Diagrams, Flowcharts,
Pseudocode, Object description
• Define how different components of solutions are
related to each other
– Storyboards , Sitemaps, Relation diagrams, Hierarchy charts
Plan: Define evaluation criteria
• How to know that the problem is solved?
– How to measure how good the solution is?
• Criteria relate the designed solution (functionality)
output and the solution requirements
Do
•
•
•
•
•
Evaluate the equations with numerical values
Implements the code
Implement the test
Documentation
etc.
Check
• Check that the solution is correct
– Validation of numerical correctness
• Evaluation that the solution makes sense
– External criteria
– Validate the solution in extremes
• Check: strategy
– How to identify that the solution meets the required needs. What
data will be collected, what methods techniques will be used in
analysis etc.
• Check: report
– How good is the solution, how well it meets the requirements.
Generalize
• What has been learned about the problem field
• How can the problem be solved more efficiently
– For instance what inputs can be ignored