Problem Solving

Problem Solving (Homework and Tests)

* The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece - divide and conquer!
* Problem types:
1. Problems testing memorization ("drill"),
2. Problems testing skills ("drill"),
3. Problems requiring application of skills to familiar situations ("template" problems),
4. Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type),
5. Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation.
In early courses, you solved problems of types 1, 2 and 3. By College Algebra you expect to do mostly problems of types 2 and 3 and sometimes of type 4. Later courses expect you to tackle more and more problems of types 3 and 4, and (eventually) of type 5. Each problem of types 4 or 5 usually requires you to use a multi-step approach, and may involve several different math skills and techniques.
* When you work problems on homework, write out complete solutions, as if you were taking a test. Don't just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don't just do some mental gymnastics to convince yourself that you could get the correct answer. If you can't get the answer, get help.
* The practice you get doing homework and reviewing will make test problems easier to tackle.

Tips on Problem Solving

* Apply Pólya's four-step process:
1. The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
2. Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
3. Carry out the plan.
4. Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.
* Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram, make a list, solve a simpler related problem, use reasoning, work backward, solve an equation, look for a formula, use coordinates.

"Word" Problems are Really "Applied" Problems
The term "word problem" has only negative connotations. It's better to think of them as "applied problems&quot. These problems should be the most interesting ones to solve. Sometimes the "applied" problems don't appear very realistic, but that's usually because the corresponding real applied problems are too hard or complicated to solve at your current level. But at least you get an idea of how the math you are learning can help solve actual real-world problems.

Solving an Applied Problem

* First convert the problem into mathematics. This step is (usually) the most challenging part of an applied problem. If possible, start by drawing a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it by a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equations which describe relationships among the variables, and describe the goal of the problem mathematically.
* Solve the math problem you have generated, using whatever skills and techniques you need (refer to the four-step process above).
* As a final step, you should convert the answer of your math problem back into words, so that you have now solved the original applied problem.

Be success for you

Mathematics Study Skills

Active Study mathematics

Be actively involved in managing the learning process, the mathematics and your study time:

• Take responsibility for studying, recognizing what you do and don't know, and knowing how to get your Instructor to help you with what you don't know.
• Attend class every day and take complete notes. Instructors formulate test questions based on material and examples covered in class as well as on those in the text.
• Be an active participant in the classroom. Get ahead in the book; try to work some of the problems before they are covered in class. Anticipate what the Instructor's next step will be.
• Ask questions in class! There are usually other students wanting to know the answers to the same questions you have.
• Go to office hours and ask questions. The Instructor will be pleased to see that you are interested, and you will be actively helping yourself.
• Good study habits throughout the semester make it easier to study for tests.

Studying Math is Different from Studying Other Subjects

• Math is learned by doing problems. Do the homework. The problems help you learn the formulas and techniques you do need to know, as well as improve your problem-solving prowess.
• A word of warning: Each class builds on the previous ones, all semester long. You must keep up with the Instructor: attend class, read the text and do homework every day. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep trouble.
• A word of encouragement: Each class builds on the previous ones, all semester long. You're always reviewing previous material as you do new material. Many of the ideas hang together. Identifying and learning the key concepts means you don't have to memorize as much.

College Math is Different from High School Math

A College math class meets less often and covers material at about twice the pace that a High School course does. You are expected to absorb new material much more quickly. Tests are probably spaced farther apart and so cover more material than before. The Instructor may not even check your homework.

• Take responsibility for keeping up with the homework. Make sure you find out how to do it.
• You probably need to spend more time studying per week - you do more of the learning outside of class than in High School.
• Tests may seem harder just because they cover more material.

Study Time

You may know a rule of thumb about math (and other) classes: at least 2 hours of study time per class hour. But this may not be enough!

Take as much time as you need to do all the homework and to get complete understanding of the material.

Form a study group. Meet once or twice a week (also use the phone). Go over problems you've had trouble with. Either someone else in the group will help you, or you will discover you're all stuck on the same problems. Then it's time to get help from your Instructor.

The more challenging the material, the more time you shoul

Be succes for you

the math

mysterious and cool