Many students find problem-solving in their math and science-based courses very difficult and can end up feeling deflated or frustrated with the challenge. I often hear students say, “The test was NOTHING like the homework!” or “The problems on the test were not the same as the problems we worked on in class!” If this sounds like you, here are some questions to ponder…
What is your approach to solving problems? Do you jump right into the first problem assigned? Do you have a consistent process, system or strategy for solving problems, or are you approaching problems with random, unfocused methods? Do you attempt to see the BIG PICTURE before starting to solve? Seeing the BIG PICTURE can be the difference between a good grade and a poor grade. In order to do well, it is important to review and be aware of your approach to solving problems. The following BIG PICTURE APPROACH to problem solving is a valuable tool that can improve your problem-solving skills and results:
Part 1: Seeing the BIG PICTURE
CONCEPT – the first question to ask is, “what is the concept?”
A concept is a main idea. When you have a problem, it is important to be familiar with the concept that is associated with the problem. If you don’t know the concept for your problem, then review your lecture notes or textbook to better understand the concept.
S.A.M. – the next question is, “what is the S.A.M?”
Every concept has a specific S.A.M. or steps to follow for solving problems. If you don’t know the S.A.M. for your problem, return to examples in your textbook or lecture notes to gain an understanding of the process for doing the calculations and problem solving operations.
VARIATION – now that you have identified the Concept and S.A.M., ask yourself, “what is the variation?” and how does it AFFECT the S.A.M.?”
When you have a group of problems – review all of the problems in the group. They may share the same concept, but are the problems different or the same? The “difference” is the variation.
Does the variation affect the S.A.M.? How do you need to modify the S.A.M. for different problems?
Be resourceful and find other examples of different problems. If you still need help, see your instructor or chat with peers to gain an understanding of the variation.
Now that you understand the Concept, S.A.M. and Variation, you can see the BIG PICTURE and are ready to begin solving problems.
Part 2: Solving the Problem
COME UP WITH A PLAN – Using the S.A.M. from Part 1 of the Big Picture
Approach to Problem Solving, make a plan for solving your specific problem.
Before making a plan, check that you have a clear understanding of the problem. What is the problem asking? Do you understand all the words in the statement of the problem? Can you restate the problem in your own words? Is there missing information that, if known, would allow you to solve the problem? Still don’t understand the problem? Then return to the steps in Part 1 of the Big Picture Approach to Problem Solving.
What are your techniques to solve problems? Successful problem solvers use a variety of techniques when they attempt to solve a problem. Here are some recommended strategies:
Make a list of the known and unknown information. Can you express the unknowns in terms of the knowns?
Make a list of information that is needed
Draw a diagram
Make a table
Try to solve a similar but simpler problem
Research the problem to determine whether there are known techniques for solving problems of its kind
Try to determine whether some pattern exists
Write an equation
Guess at a solution and then check it
Need help coming up with a plan? Then STOP here BEFORE continuing. Explain the problem to someone who may help (other classmates, tutors or professors). Ask them how they would solve it.
USE YOUR PLAN TO SOLVE THE PROBLEM
If you can see the Big Picture and have come up with a good plan, then this should be the easiest step in the Big Picture Approach to Problem Solving.
Don’t skip steps
If you have trouble solving the problem, then go back and make sure you didn’t make any mistakes. No mistakes? Then maybe you need to come up with a new plan. Don’t worry, this is part of the learning process. It may help to take a break and come back later with a clear mind. Remember “20-minute rule”– do not stay “stuck” on a problem more than 20 minutes. Skip it and get help later!
THINK ABOUT YOUR ANSWER – Does your answer make sense? Does it fit with the Big Picture? This is the most rewarding and important step. Getting the right answer proves that you have mastered the learning, and it is the learning that matters most.
Check that your answer is correct. Does it fit with your expectations? If your answer is not correct, then step back through each step. Where is the error?
How would the answer change if the problem changed? (See VARIATION in Part 1)
Marvel at your accomplishment. Enjoy the rewards of your hard work.
CONGRATULATIONS! You are now trained in the Big Picture Approach to Problem Solving.
Engaging in learning processes and strategies can lead to student success! If you need help with this or any other learning strategies please visit me!!
To book an appointment call 403-529-3819.