How to Solve Problems in Science and Engineering

This article gives you an approach for solving problems that involve the application of math and science.

This approach works for problems in engineering and science courses. For example, problems in circuits course, problems in a statics course, and problems in a chemistry approach. Thus, this approach is well suited for application to exams and textbook problems.

This approach also works for real-world problems such as sizing a motor to spin a large roll of paper or determining the maximum stress in the handlebars of a mountain bike.

Why Learn this Approach

  • Transfer. Use the same approach for problems on the job and problems in all your courses. This makes things much easier.
  • Speed. Much faster way to solve problems (after you get good at it).
  • Effective. You will be able to solve more problems and harder problems. That is, you will be a much better problem solver.

Background on this process

  • Based on the research literature that describe what experts do when they solve problems
  • Basic structure was developed by Professor Charles Wales in 1980s
  • Adapted to engineering classrooms by Professor Elger over the past 15 years
  • Learning the process is like learning the golf swing
    • you can acquire knowledge of the process in about 30 minutes.
    • refining the process is a life-long endeavor (but worth it)
    • people always have bad habits that they need to stop doing (hard)
    • the process = fundamentals = foundation of great problem solving.
    • the process is done differently by people, but the fundamentals are the same
    • the process is adapted to the context

The PDM Process

The process is identified by the name used by Wales, Professional Decision Making process or PDM process.

Problem Definition—Change the problem so that it is clear & specific & meaningful.

  • situation analysis. get needed facts about present situation.
  • goal. describe what a great solution looks like.

Idea Generation/Planning—Figure out best way to reach the goal.

  • brainstorm. identify what equations and ideas will help you reach your goal.
  • logical reasoning. Find an equation with your goal in it. Determine what is known and what is unknown. If you have too many unknowns, then identify another eqn. Continue until (# eqns) = (# unknowns).
  • plan. figure out the steps (usually order of calculation) needed to reach your goal.

Action—implement your plan & reach your great goal.

Review-Check your solution and then get value for yourself from your solution.

  • validation. check your solution in multiple ways; prove to yourself that you can trust it
  • implications. Identify conclusions/consequences of your solution as related to the bigger picture.
  • reflections. Identify and solidify gains in your knowledge.
  • QI (quality improvement)
    • Strengths. Identity actions that worked and that you can repeat in the future.
    • Improvements. Identify issues and figure our specific and simple actions you can take in the future to make these issues go away.

Troubleshooting

The PDM process is a way to organize your actions so that you increase the probability that you will solve the problem you are facing. Since everyone gets stuck, it is useful to have strategies for when you are stuck. Below is a list of useful strategies (posed as questions)

  1. Can you simplify the problem and solve this simpler problem?
  2. Who can you ask for help?
  3. Did you miss any key information in your situation analysis?
  4. Are there other equations that you can bring to bear?
  5. Do you know the knowledge needed to solve this problem?
  6. What does this look like in the real world?
  7. Can you draw a picture or make a sketch?
  8. Can you make a simplifying assumption?
  9. Have you checked your units?
  10. Is this problem worth solving? (sometimes the dragon wins! its ok to let go!)

Resources

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