Effective Quantitative Problem Solving Methods

January 5, 2010

Solving applied quantitative problems is both an art and a skill. People often give up early even though they have the ability to solve them. Often, it is because they do not have a clear idea of a few key points of the problem solving method. The three topics below can help you to become more effective with solving these problems.

1. Understand the Problem Solving Process

Expect to be confused and frustrated “I have no idea what to do.”

Confusion and frustration are part of the process of learning. The important point is not to be defeated by them. Everyone in a college course has the ability to do the assigned problems. No exceptions, you have gotten into the college program. The problems may be difficult and require significant effort, but you should be confident that you can do them.

After you work through confusion a few times, confidence (and persistence) will begin to grow.

Experiencing confusion and frustration is similar to weathering a summer storm. The storm often comes on suddenly and strongly, but then it passes and the sunshine returns.

Watching is not doing

Problem solving is a participatory sport, not a spectator sport. Hearing an explanation, or seeing a worked out problem is different from being able to do it. Make the effort to do the problems, not just follow the explanations.

The explanation is the first step, but you must go beyond it. For exams, you will be asked to solve problems yourself and demonstrate that you can do that. You will not be asked if you can understand the explanation given in class.

2. Effective Thinking

Identify a Known Starting Point–The First Step to Ending Frustration

Suppose that you fall down a steep hill. First you grab on something to stop the    fall. Then, you pull yourself back up a step at a time using rocks, trees or whatever is within reach to grab on and use. Getting started on a problem is like that.

Read the problem with the intent to understand the words and content, not to solve it. If you are not clear how to begin, take a step back and find a fact that you do know. The important point is to find a foothold to begin.

Example Starting Points:

A worked out example.

A definition of a key word that is in the problem.

A diagram.

A short conversation with a classmate or a teacher.

It is important that you look and find a starting point to progress, rather than allowing time to go by.

Understand by DOING the worked out examples.

If you have worked examples available, COVER the solution and work it out yourself. If the examples are not understood, it is usually a waste of time to spend much effort on the new problem before understanding this. Go back to the earlier step and find a new starting point.

After doing the example yourself, read the new problem slowly, understand what it is stating and what it is asking. See how the information in the new problem relates to the earlier examples. The examples will show you which formulas or equations are needed. Formulas are the key that turns the words of a problem into symbols. It may help to draw a diagram.

3. Doing the Math

Stay organized so that it is easy to retrace your logic when you make a mistake.

Write slowly and neatly. Sloppy writing leads to errors. Leave plenty of blank space to make it easier to follow. There is the temptation to just write things down and hope for the best. This approach takes more time in the long run. Errors are part of the process and it is much faster to find them when the work can be easily traced back.

Make the units work for you.

Know the units of the final answer to the problem. Keep these in mind so that your solution is consistent.

Every time you write a number or symbol down, include the unit right after it in clear writing. Keep track of the units throughout. Inconsistent units can alert you to logical errors.

When a spicy meal is prepared, the spices are added during the cooking process. They are part of the food. If spices are added when the meal is served, the taste is not nearly as good. Units are like that. Make them an integral part of cooking the problem.

Do the calculations last–after the set up is right.

Get the logic right before you do the math. Then, substitute the numbers for the symbols of the equation. Set up all of the numbers and units before you do the calculation.

Doing the calculations at the end makes it easier to distinguish between errors in the logic applied to the problem and math errors.

Check for reasonableness and unit consistency.

Remember that all of these problems relate to the physical world. In some cases, you may have an idea or estimate of the range that the numerical answer should be. If it is far off, then, you can begin to check.

Keep these points in mind, when you find yourself “losing it” working on a problem. You can surprise yourself by the difference they can make.

Strategies for Difficult Exams may be useful when it comes time for the test.