Math Has a Sequential Learning Pattern
With math, material learned in one lecture and course builds on the material from previous lectures and previous math knowledge. This is called a sequential learning pattern, or in common language, math is cumulative. In this way, success in one course relies on solid foundational understanding from previous math.
“Each problem that I solved became a rule, which served afterwards to solve other problems.”
–Rene Descartes, French philosopher and mathematician (1596-1650)
Math as a Skill Subject
Math is a skill subject, in that active and intentional practice is required to master it. Listening to lectures and reading the textbook is not sufficient for learning. This is analogous to playing a sport or playing an instrument, or another skill. You cannot learn to play a sport or instrument solely by reading about it or by watching others play. This is called active learning, and it involves experimentally taking part in the learning process.
“The only way to learn mathematics is to do mathematics.”
–Paul Halmos, American mathematician (1916-2006)
Math is unlike some other courses in this aspect. For example, social studies can be learned by paying attention in class, taking good notes, and participating in class discussions, and by rereading notes, etc.
The Importance of the First Math Test
Treat the first math test with very high importance. In math courses, the first test is typically the easiest, so it is a good opportunity to score a high grade. A high grade on the first test can compensate for a lower grade on a future, more difficult test. Also, strong mastery of the first test material builds a solid foundation that leads to improved understanding of material on future tests (because math is sequential). Finally, doing well on the first test can be motivating and boost confidence.
If you still end up with a low grade, this may mean you need to reevaluate for the next test, or reconsider whether this math course is right for you. Failing the first math test probably means you should drop the course for a lower math class.
Math as a Foreign Language
One idea that can be helpful is to think of math as a foreign language. Like a foreign language, math requires consistent practice in order to not forget what was learned.
Gaps Between Math Classes
If you are taking math courses, it is best to take them as close together as possible. In other words, schedule them in back-to-back terms. More time between classes (months or years) means you are more likely to forget important concepts in that time, weakening the building blocks of your understanding.
College Math vs. High School Math
College math classes often cover more material than high school math classes, and do so in less lecture time. This means that more learning must occur outside of lecture, and self-study and practice is even more essential.
This factor is more relevant in summer math classes, where the speed of learning can be 2 to 3 times faster than a regular class. Falling behind in a summer class may mean you never catch up.
Math Attitude
Many students who have had bad experience with math do not like math, or even hate math, even though they have positive experiences with other courses.
Popular society reinforces negative attitudes towards math. It is socially acceptable to do poorly in math, to fail math, and to hate math.