1. “But I’ve always been good at math!” How High School and University Math are different and what you need to do to succeed in University Math

2. High School Math: Imitation and Memorization. What you may have been good at in high school is imitation and memorization. The teacher shows you a problem, and then you are given the same problem on the test with different numbers. You are expected to remember the pattern and change the numbers. Very little thinking is required. High School Math : University Math = Microwaving a frozen meal : Cooking.

3. University Math: Conceptual Understanding and Creative Application. At the university level, you are expected to understand the underlying concepts and be able to apply them independently to fresh problems that you may not yet have not yet encountered in that exact form. The only review you may get is a list of concepts. If you get a review test, the review test will cover the same concepts, but it will not be the actual test with just a few numbers changed. University math emphasizes critical thinking over memorization and imitation.

4. Examples of High School Math vs. University Math

5. Common Reactions to Misunderstood University Math “The tests were unfair!” Some students think it is unfair to be expected to master the concepts and to have to demonstrate independent, critical thinking. Like it or not, that is the nature of higher education. If universities are the wrong place for cultivating understanding and critical thinking, then where is the right place? “The test asked trick questions!” A trick question is a question that is intended to make you fail. Most alleged trick questions in university math are actually just concept questions – they ask you to demonstrate that you understand the underlying theory, and are perfectly answerable if you acquired the necessary understanding through persistent and proper study. “We never covered this in class!” In a way, that’s the point. The exact question was not supposed to have been covered in class. What was covered in class, though, were the principles that enable you to solve the problem. If the exact question, or a nearly identical question with just a few numbers changed, had been rehearsed in class, the question would no longer test your understanding, just your ability to memorize and imitate.

6. You are responsible, not the teacher In high school, the teacher is responsible for your learning, and most of that learning happens in the classroom. At the university, you are responsible for your own learning, and much of that learning happens outside of the classroom. There are many resources to help you learn, but you need to take the initiative and take advantage of them. High school math proceeds slowly and offers redundant review and repetition. University math is fast paced and offers minimum repetition. If you don’t understand material even after it has been covered in class, and fail to make up for it, the class will move on without you. Each lecture proceeds from the assumption that you have understood the contents of all previous lectures.

7. Math is a “Cumulative” Subject. Concepts build on one another. If you fail to understand one concept, everything on top of that will be incomprehensible. It is therefore necessary that you review and thoroughly understand the concepts that were taught in each lecture before you come to the next lecture. It’s like climbing a mountain – each step is a prerequisite for the next step. To get to the top, you need to get up early and then do the hard work of climbing, step by step. If you sleep in and relax for most of the day, thinking that a quick sprint in the late afternoon will get you there, you will suffer a rude awakening when you realize that this mountain is much taller and steeper than it looks, and has much more difficult terrain than the similarly named hill you climbed in high school.

8. Proper Study Habits In University math, doing homework alone will usually not prepare you for the exams. You must study the textbook and your notes with the goal of understanding the theory. In particular, you must commit definitions and theorems to memory; but not in the mindless fashion of just memorizing empty words that mean nothing. The definitions and theorems and their interplay must come alive in your mind. To create these kinds of mental associations, you must actively engage with the theory. Each time you study, you should make or expand a list of important concepts (definitions, theorems and algorithms), and learn them like you would learn vocabulary in a foreign language. This type of mastery is not achieved overnight. It can only be achieved through persistent, regular study, starting on the first day of class. Last- minute cramming will get you nowhere and practically guarantees failure. Do not fall into the trap of thinking that because the material seems superficially similar to material you may have learned in high school, the university course is just a review.