Problem Solving

This project is devoted to teaching problem solving skills to students through the use of examples. In particular, the introductory topics of chemical engineering will be used to build up a student's hierarchical approach to solving new problems they have not encountered before. I used the term 'hierarchical approach' because I want to stress that no good problem solver became that way through chance or by accident. It takes hard work and repetition to build up a problem solving method that works for each person. The hard work comes in through trying to understand how problems are similar and how you can use the same techniques to solve new problems you haven't seen before. Once again, it does take work.

I want to stress that last point again:

It takes a lot of hard work and persistence to be able to look at a problem and confidently know where to start. It doesn't happen overnight. It doesn't happen in a week. Small improvements are made overnight or over a week's worth of effort. However, all those small improvements add up until your ability to solve problems becomes second nature.

This project has come out of my own experiences as an undergraduate student at Michigan State University, and out of my contact with students at the University of Illinois where I was a teaching assistant for 7 semesters. Some of the problem solving techniques I use are born of several years of struggle to be able to explain to students how I know what the next step of a problem solving effort should be. Other methods I encourage students to use involve asking questions of yourself as the problem is being worked. These questions include:

What am I looking for?

What do I know?

Have they told me how to work the problem?

What can I do right away?

And, how do I know if my answer is a good one?

Click here if you'd like to see how you could use these questions to solve a problem.

All of these topics will be covered in these webpages. Remember that the point of this project is to teach students how to solve problems on their own, and not to lead them by the hand through only specific problems. So, the information here is arranged in layers so that students can identify particular places where they have difficulty and concentrate on those. The areas where they encounter less difficulty can be covered more quickly. These informational layers are arranged into several overtopics, such as getting started, where learning how to start a problem is covered.

Organization of Information

Getting Started on a Problem

Techniques for Solving Problems

  1. Terminology
  2. Definitions
  3. Sign Conventions
  4. Keeping Track
  5. Writing Equations
  6. Given Formulas
  7. Units
  8. Interrelations

Examples of Some Problems (hit the back button to return to this page)

A problem concerning units and how to read a problem correctly.

Another problem concerning units and how to read a problem correctly.

Solving homework problems is one of the best ways to learn any material. However, students sometimes get frustrated or don't know how to use their homework assignments to their best advantage. If you'd like to see some comments from one student, click here.

It doesn't do any good to know how to solve the homework problems if you can't apply the techniques that you've learned to the exams.  Sometimes, problems look completely different when you are trying to solve them during an exam.  Or sometimes you just don't think that you test very well.  If you'd like to see some of the comments that one student made after thinking about their exam performance after each exam, look here.

2007 Arizona Board of Regents for The University of Arizona