College Algebra

Abstract

This textbook is designed to provide you with a basic reference for the topics within. That said, it cannot learn for you, nor can your instructor; ultimately, the responsibility for learning the material lies with you. Before beginning the mathematics, I would like to tell you a little about what research tells us are the best strategies for learning. Here are some of the principles you should adhere to for the greatest success: • It’s better to recall than to review. It has been found that re-reading information and examples does little to promote learning. Probably the single most effective activity for learning is attempting to recall information and procedures yourself, rather than reading them or watching someone else do them. The process of trying to recall things you have seen is called retrieval. • Spaced practice is better than massed practice. Practicing the same thing over and over (called massed practice) is effective for learning very quickly, but it also leads to rapid forgetting as well. It is best to space out, over a period of days and even weeks, your practice of one kind of problem. Doing so will lead to a bit of forgetting that promotes retrieval practice, resulting in more lasting learning. And it has been determined that your brain makes many of its new connections while you sleep! • Interleave while spacing. Interleaving refers to mixing up your practice so that you’re attempting to recall a variety of information or procedures. Interleaving naturally supports spaced practice. • Attempt problems that you have not been shown how to solve. It is beneficial to attempt things you don’t know how to do if you attempt long enough to struggle a bit. You will then be more receptive to the correct method of solution when it is presented, or you may discover it yourself! • Difficult is better. You will not strengthen the connections in your brain by going over things that are easy for you. Although your brain is not a muscle, it benefits from being “worked” in a challenging way, just like your body. • Connect with what you already know, and try to see the “big picture.” It is rare that you will encounter an idea or a method that is completely unrelated to anything you have already learned. New things are learned better when you see similarities and differences between them and what you already know. Attempting to “see how the pieces fit together” can help strengthen what you learn. • Quiz yourself to find out what you really do (and don’t) know. Understanding examples done in the book, in class, or on videos can lead to the illusion of knowing a concept or procedure when you really don’t. Testing yourself frequently by attempting a variety of exercises without referring to examples is a more accurate indication of the state of your knowledge and understanding. This also provides the added benefit of interleaved retrieval practice.