This class meets four days a week. Typically the first three meetings will be lecture-based. During these three days you should focus on (1) doing exercises to develop mechanical skills and (2) reading to understand core concepts. At the fourth meeting each week you will solve problems in groups based on the week’s lessons. It’s crucial that you exercise and read during these first three days so that by the fourth class meeting you are prepared to focus on solving problems and won’t be bogged down focusing on the mechanics.
Schedule time each week dedicated to focusing on this class, and be intentional about where you spend that time: ideally a spot free of distractions and surrounded by other people quietly studying. The library is usually a good choice, or the small space outside the instructor’s office. The classroom is available at the usual meeting time on non-meeting days for this as well. Practice on your own at first to keep from getting distracted; only study with your peers later when preparing for an exam.
To avoid exhausting yourself (burning out), try to relegate the time you spend thinking about this class to the workweek and reserve a sincere break for yourself from mathematics during the weekend.
Before each Week’s Class Meetings …
Briskly read about the topics for the week: you’ll get more out of the lecture if you’re already familiar with the topics and if you’ve already encountered the ideas and begun to form questions.
After Lecture, Before the Next Class …
Reflect on what the skills and concepts core to the day’s lesson were, and get started doing exercises, either in the online homework or directly from the textbook, to practice those skills. If any homework exercise has you stumped, ask a peer from class to demonstrate the exercise for you, or visit the campus tutoring center or the instructor’s office hours to ask for a demonstration of the exercise. Most tutors and the instructor are also available to supervise you doing exercises on your own to “check your form”. If you finish all the exercises for a certain skill from the online homework but would like more practice, ask a tutor or the instructor to design more exercises for you. Make a note of any exercises you found particularly difficult and remember to revisit them before the next exam.
After each Problem-Solving Session …
Read over all the problems handed out in class and ensure that you understand each problem; ask a peer or tutor or the instructor to explain any problem you don’t understand. Then work through each problem only to the degree that you’re confident you could write a full solution for it if it were to appear on a exam. If you have any doubts, just write up a full solution. Certainly discuss the problems with your peers or the campus tutors or your instructor. The instructor is also available to read and provide feedback to your written solutions in preparation for writing an exam; just visit their office hours or drop off your writing with them at the beginning of class.
Before Each Midterm Exam …
Glance over the Course Trivium and the Student Learning Outcomes (in the syllabus) to calibrate your focus. Print out past midterm exams from this course for practice. Consider simulating the experience of taking the midterm exam by setting a timer and “taking” each past exam rather than just working through the problems. Consult the campus tutoring center or the instructor about any exam problems you’re unsure about. Remember the instructor is available to read your solutions and provide feedback.
In General, While Studying …
Avoid the “spectator trap” It’s easy to convince yourself you understand something when you are watching someone talk about it, whether you’re listening to a lecture or watching someone demonstrate an exercise. But unfortunately this understanding may be an illusion; even though you can follow the information as it’s being presented, this doesn’t mean you could reproduce it yourself. You must deliberately practice by yourself, without references, to avoid this trap. You have to learn in such a way that you can recall facts and procedures from your mind, not just recognize correct information when it’s presented.
Look for the narrative thread Studying involves doing exercises and solving problems and memorizing facts. There’s a cognitive pitfall though to reducing a subject simply to a collection of isolated exercises and problems and facts. Look for the big picture, the overarching themes of a subject. Organizing your thoughts within this big picture is the key to sincerely understanding a subject rather than just practicing a superficial performance.
Remain cognizant of technology’s role in the purpose of your work Mentally categorize all the work you do as either job-work or gym-work. Job-work consists of all the banal tasks that just need to get done, while gym-work is the work you do for yourself, to improve yourself. The purpose of gym-work is the change you experience in the time you spend working. While job-work should be offloaded to technology if it’ll save time, letting technology encroach on your gym-work subverts its purpose.
Use technology as a tool, not a crutch Technology wears a veneer of authority it doesn’t deserve. While its capabilities are impressive, technology is still only a tool to wield. Only you can ascribe meaning to what it produces. To defer critical thought to technology is to relinquish your power to that technology. Maintain your primacy; don’t surrender your cognition to technology.