Study mathematics part 3
Last week, a first-year student came to see me and lamented: “I came here to study Computer Science but failed “Introduction to Computer Systems, Java Programming, and Math and Statistics classes. Now, I do not know what to do? I am frustrated and worried about being dismissed from school as my grade is very low. I do not know what to tell my parents as they expect me to do well, and get a good job. Please help.”
He is not a particular case. In the past few years, I have seen more and more students struggled and failed in the first year. The main problem they have difficulty because most do not have a good foundation in math. They only learn enough to pass tests and move on to the next level throughout their school years. Mathematics is a cumulative knowledge, which means every concept is building on top of others. Students must have a strong foundation before they can move on to the next level. They must know one level well before efficiently move on to the next. Just like building a house, you must start with the foundation, then the frame and walls, before you can build the roof and other details. The basic foundation is established early in elementary school when students learn arithmetic rules for addition, subtraction, multiplication, and division. In high school, students continue to learn the concepts of algebra such as symbols, formulas, and operations, etc. This is the framework where many advanced concepts can be built upon, just like the frame of a house. Only understand these basics well, students can advance to the next level to enlarge their knowledge.
The problem that I have observed among college students is sometime in high school; they move on to next levels before they really comprehend what they should know. Many students memorize formulas to pass tests or learn “Tricks” to complete homework to get good grades, and they think that they already know mathematics well enough. Many continue to move on without a good foundation or framework to build upon. Their teachers and family may not realize that continue to the next level without a full understanding of the previous concept can be a problem for them in college. Sometimes parents are angry if teachers do not pass their children to the next class, and most teachers do not have time to ensure that every student understands every concept.
When a house is built on a weak foundation, it cannot stand for long. Sooner or later it will collapse. The same thing happens to many students who continue to move on to the next level with a weak foundation. The issue is when they go to college, they will face a dilemma when they study science, technology, engineering, and math (STEM). The matter is worst when they study overseas as I have seen many foreign students failed in U.S. Universities in the past few years. Many students who study engineering or computer failed in the first year due to their lack of foundation in math. Last year, a student asked me: “Is it possible to learn computer without math? I answered: “Is it possible to write a novel without knowing the alphabet? The fact is you do not have to be perfect in math, but you must have a good foundation and understand how to manipulate data and numbers using symbols and formulas.
Today, many students come to U.S. to study Computer Science and Software Engineering because these fields are in high demand with many job opportunities. But many could not even pass the first year because they lack the proper foundation that allows them to continue. To some students, I advise them to take remedial courses or retake classes such as Algebra, Calculus before taking Computer Science courses. I explain: “Math is not difficult. It only seems difficult because it takes times to learn and you must understand that due to the cumulative nature, you must carefully put in the effort to understand each concept well before move on to the next. You cannot memorize formulas or learn “Tricks” to do the math. It will not help you in the next level when you must solve complex problems. The reason students do not like math because it requires a lot of practice. For them, math is not something that comes naturally or automatically. But as long as you are willing to put in the efforts and learn well, you will succeed. You cannot rush to learning math. You cannot memorize equations or formulas in math. Math is all about practice, NOT memorization. No matter where you are in high school or college, you can still do well in math, if you reinforce your foundation.
My advice to students who want to study science, technology, engineering and math (STEM) in college. Make sure that you have a solid foundation to prepare for your education. Any student who barely passes the math test should review carefully to make sure that you have a good understanding of the concepts because you will need it to move to the next level. If you are still in high school, do not attempt to move on until you understand the basic concepts fully. I rather see that you spend time in high school studying math than struggle in college, especially when you are having difficulty in a foreign country.
- Blogs of Prof. John Vu, Carnegie Mellon University