Activity 2.2

Consider Woods Problem Solving Model endorsed by the Centre for Teaching Excellence, University of Waterloo.

2. In a topic you teach, consider what you would provide to students with direct instruction and drilling before undertaking a problem solving exercise and what knowledge, understanding and skills you would have them acquire while problem solving.

Woods’ Problem-solving Model

1. Define the problem

   • The system. Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.

   • Known(s) and concepts. List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.

   • Unknown(s). Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.

   • Units and symbols. One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.

   • Constraints. All problems have some stated or implied constraints. Teach students to look for the words only, must, neglect, or assume to help identify the constraints.

   • Criteria for success. Help students to consider from the beginning what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

2. Think about it

   • “Let it simmer”. Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.

   • Identify specific pieces of knowledge. Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.

   • Collect information. Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

3. Plan a solution

   • Consider possible strategies. Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.

   • Choose the best strategy. Help students to choose the best strategy by reminding them again what they are required to find or calculate.

4. Carry out the plan

   • Be patient. Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.

   • Be persistent. If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

5. Look back
   Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

   • Does the answer make sense?

   • Does it fit with the criteria established in step 1?

   • Did I answer the question(s)?

   • What did I learn by doing this?

   • Could I have done the problem another way?

( Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.) cited in "Teaching Problem Solving Skills", University of Waterloo Centre for Teaching Excellence, Teaching problem-solving skills | Centre for Teaching Excellence | University of Waterloo (uwaterloo.ca)