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Precalculus: An Investigation of Functions, by David Lippman and Melonie Rasmussen, licensed under CC BY-SA 4.0. Read the original free This shelf’s study material is shared under the same license (CC BY-SA 4.0).
Chapter 4 · pp. 8–8
College-level math asks more of you than most high school math does. You must learn faster, work more outside class, and use ideas in unfamiliar ways. This section explains what the course expects and gives a study routine that fits those demands.
Apply, don't just imitate. In earlier courses you may have seen one method and then repeated it on many look-alike problems. Copying a pattern only proves you can imitate. Here you must be able to change a method when a problem looks different. For example, suppose you learn to solve one type of equation. Later you may meet a word problem you have never seen, and you must spot that the same idea applies and adapt it to the new setting. (p. 8)
Each topic builds on the last. Math courses are cumulative. Ideas from early lessons become tools for later ones. If one early topic is shaky, later topics get much harder, because they rest on it. So do not treat each lesson as a separate island. Ask yourself how today's topic connects to what you already know and how it might lead to the next one. (p. 8)
A common rule of thumb is about 2 hours of focused study outside class for every 1 hour in class. A course that meets 3 hours a week would then need about 6 more hours of study each week. This is an average:
Add class time and study time together and the course can be like a part-time job. A full course load can add up to more than a full-time job. Students who also work or care for a family should get organized early and start ahead of schedule. (p. 8)
Many students think that learning a lot the night before an exam is a good plan. It rarely works in math. Math skills grow slowly, and each depends on earlier ones, so you cannot absorb them in one rush. Short daily study sessions work much better. For example, 1 hour a day for a week usually beats 7 hours the night before a test. The daily habit gives your brain time to connect ideas and gives you time to find and fix gaps. (p. 8)
The routine has five steps. Each step gives you another exposure to the ideas.
(p. 8)
Read the lesson before the instructor covers it, so the lecture is not your first look. While reading:
The marks tell you what to listen for in class. For example, if you highlight a definition you do not understand, you can pay close attention when the instructor explains it, or ask about it. If you cannot solve a practice problem, try it again after class. If you are still stuck, ask for help. (p. 8)
As soon as you can after class, turn the day's lecture or activities into a form that makes sense to you. This is your third exposure to the material (reading, lecture, recap). Two good ways to do it:
The second method shows what you really know. Cover the solution to a class example and solve it again. Any step you cannot remember is a spot to review. (p. 8)
After the recap, begin the assigned homework. It tests whether you understood the lesson well enough to use it on your own. (p. 8)
Some students think that asking questions shows weakness, or that it is fine to wait if a topic is unclear. Both ideas are mistaken. Waiting lets confusion pile up, and in a cumulative subject that makes later topics harder. If your instructor offers time for questions the next day, use it. If not, go to a tutoring center or form a peer study group. You can also ask a teacher or tutor. Keep a list of specific questions so your requests for help are focused. (p. 8)
The lesson gives a memory aid. When you do not understand a topic, act right away instead of waiting.
The common thread is to be specific. Naming exactly what you are stuck on makes it easier for others to help you. (p. 8)
