Mathematics is a language, but it can not be learned the same way most languages are learned. Mathematical principles and concepts must be learned in a specific order. Much like the way we learned to walk. When we were learning to walk we found that we had to crawl first, if we went too fast and tried to stand or walk before we were ready we fell and got a boo boo. The same is true for math, except if we jump ahead of our selves or miss something along the way, we don’t fall and get a boo boo, we begin to believe that we are just no good at it.
To prove my point about the need to learn mathematical concepts and principles in a particular order, most City Colleges around America have elementary to high school level math classes that are offered to students that don’t have the required college level skills in mathematics needed to enter the college system. So the problem is real and recognized by Authoritative Institutions go math grade 3. Mathematical concepts need to be learned in a particular order no matter how intelligent you are. Trying to become proficient in mathematics by learning random bits and pieces will be very difficult if not impossible. Each level in mathematics requires a working knowledge of all the prier levels.
Because Mathematics is a language, you also need to immerse yourself in solving math problems to become proficient. Doing this is a lot easier these days with the aid of the Internet and calculators that do symbolic manipulation. Spending at least one to four hours a day working math problems, everyday, will develop and reinforce the skills needed to become proficient in math. Why so much time? To build, what I like to call, brain circuits.
Solving a problem requires a number of steps to be taken by the brain. Simply put, to solve “1+1=2” the brain needs to look at each character and then calculate what actions to take. If this is the first time attempting to solve this type of equation the brain has not connected up the wires or developed the circuits yet, it resorts back to circuits it has used in the past when attempting to do new things. Try writing with your other hand. Most will find it very difficult. That’s because the brain has not developed the circuits yet to perform the task. As the brain creates and hard-wires the correct circuits used to solve the mathematical problems your working on your mathematical abilities will grow, and as a side benefit, those same circuits will aid in other brain functions. But like everything in nature, the brain is very conservative.
The brain is not going to create and hook up circuits unless there is a real need for them. You need to let the brain know you mean business. The way you do this is by forcing the brain to work on math problems. The brain does not like change, so it will produce chemicals that will make this uncomfortable for you. You must fight back and continue. Soon the brain’s own need to be conservative will require it to build the circuits needed to more efficiently solve these problems. Result, you get better. And if you do things right and stick with it, the brain will become proud of these new circuits it has built and begin to produce chemical that will make you feel real good. In the beginning it will be hard, but after a bit you’ll enjoy the brains reward. Video game developers have learned how to trigger these chemical in the brain via their software. That’s why kids will spend hours, even days, in front of a monitor pushing buttons on a game pad.
Building circuits in the brain takes a lot of hard work and time. It took all of us years to learn to walk, talk, write, and perform many other abilities we take for granted. We learned most of these abilities when we were very young. It was called play time. It was fun, exiting and we couldn’t wait to get started. We also had many examples to draw from, people were walking, talking and doing things that helped us see how others performed these tasks we were trying to do. Not true with math. There’s the math book from school, well people with the IQ of a thousand don’t seem to have a problem with it so who am I to complain?
We learn best by example. Here’s the dilemma, there are not too many TV shows dedicated to mathematical problem solving. There are not even too many math courses dedicated to mathematical problem solving. There’s a teacher going at the speed of light spewing out concepts and principles while you try to listen and write at the same time. That’s not the best learning environment for mathematics. Thank God math is so easy or we’d be in trouble. Maybe it’s not you, you may have the makings of a brilliant mathematician, but have never been in a suitable situation to learn.
Solution, look at the answers to as many problem as possible and see how those answers were found. Use the Internet to study ahead of your class, so you’ll know whats being talked about when your instructor buzzes by at the speed of light with new concepts and principles. Remember, one missed item, principle or concept and you won’t be prepared for the next level. It’s very possible that your very good at math, it may be that the tools and road map to learn are missing.
Most problems encountered in learning upper level math come from not fully understanding elementary math. Algebra requires proficiency in elementary math, calculus requires proficiency in both elementary math and algebra. Most kids in elementary school can’t see the importance of math, so they lack the effort. Kid in high school don’t have time for math, so they do the minimum to get by. Then these young men and women, now ready to enter college, feel they are just no good at math, so they opt for other majors. Has a future Einstein been lost to this chain of events.