Studying Mathematics at the University

Dr. Lynn E. Garner, Former Chair, Department of Mathematics, Brigham Young University

Brigham Young said, “Education is the power to think clearly, the power to act well in the world’s work, and the power to appreciate life.” Mathematics and quantitative reasoning are fundamental to these three powers, especially in our technological world in which reality is described in increasingly mathematical terms.

The goals of university mathematics courses are not only to develop manipulative skills in arithmetic, algebra, etc., but also to impart an understanding of mathematical ideas in new contexts and with much more flexibility. For example, most of you expect to use mathematics as a fundamental tool. The power to use mathematics effectively in your discipline requires you to have

• a conceptual understanding of both mathematical principles and the principles of your discipline,
• the ability to translate features of your discipline into a mathematical model,
• the knowledge and skill to apply mathematics to the model, and
• the ability to express the mathematical results as predictions in the discipline.

As you see, manipulative skills are necessary but inadequate without conceptual understanding, and this is true in any major. If you wish to study mathematics itself, the expectation is that you will not only master the knowledge and skills of the mathematics courses, but also learn to communicate in mathematical terms. The language and theory of proof will become critically important to you.

Attitudes toward learning in mathematics courses must be consistent with these goals. In high school, most learning took place in the classroom and students usually didn’t spend as much time on homework as in class. One who was attentive in class could usually succeed with modest effort. At the university, most of your learning will take place outside the classroom and you will be expected to spend at least twice as much time on homework and reading as you spend in class. In addition to being attentive in class, you will have to exert considerable effort outside of class in order to succeed. You will be expected to learn the basic ideas in a course from the textbook because there is typically not enough time to cover all of them in class. And, given this change in the location of learning activities, it is obvious that your instructor is no longer primarily responsible for what you learn; you are. Finally, go beyond solving problems like the examples in your text. The problems you will meet on the job have not yet been solved and are not in the textbooks. If all you can do is solve text problems, you will be replaced by a computer. Practice solving problems you have not seen before. Learn to think; that, a computer cannot do.

Taking responsibility for your own learning includes gathering pertinent information, enhancing the learning environment, being committed to academic integrity, and using responsibly the exceptions afforded by extenuating circumstances.

• You are responsible to know all the requirements in your major, your minor, the university generally, and every course you take. Verify advice from anyone else with authoritative sources: your instructor, the syllabus, the textbook, or your advisement center. Ignorance is never an excuse. Exert every effort to master the material of each course. Strive for excellence. You can study harder than you now know.
• Your actions should enhance the learning environment. Avoid distracting activities in the classroom, the library, and the dormitory. Always prepare for class by completing homework and reading assignments.
• Academic integrity means that you will not allow yourself or others to profit from information to which you or they have no right. Not only do you avoid plagiarism, but you do not receive or give inappropriate information about tests, quizzes, or homework. Grades are given only on the basis of academic performance; to ask for grades on any other basis is a form of academic dishonesty.
• Extenuating circumstances include serious illness, family emergency, and official university business. Instructors usually allow you to make up work missed because of extenuating circumstances, but do not expect heroic efforts in your behalf; some activities can’t be made up. Arrange ahead of time or as soon as possible afterward. The timing of an extenuating circumstance may be critical, so act quickly.

Strategies for learning in mathematics courses include

• managing your time, now your most precious resource, by observing and adjusting your use of it;
• making sure you are in the appropriate class and have the proper prerequisites;
• studying with classmates, teaching each other the principles involved and discussing difficult concepts;

• getting help after reasonable effort, without wasting too much time "spinning your wheels;"
• being willing to review on your own time topics you have seen but have forgotten;
• using instructor office hours and the Math Lab effectively;
• reading the textbook for basic ideas, additional information, and more examples; and
• Making efficient and responsible use of the library and technology.