Ever wonder why some students just whiz through upper math subjects like Algebra, Geometry, Trigonometry, or Calculus, and others just drag there way through it, stuck in the rut of "I don't understand any of this!" Well, I have my theory. I believe it has much to do with the way we think. You may have heard the terms 'Global Thinker', or the polar opposite to this way of thinking, the 'Linear Thinker'?
So what do these terms mean? A global thinker absorbs and processes information by visualization as a whole. They prefer not to take steps 1, 2, 3, to get to step 4. A global thinker wants all the steps laid out so they can relate the information to what they already know, how each step in a process is significant to the other, or relational values. In direct opposition, a linear thinker, MUST take step 1, then step 2 (and only step 2), then if they understand that, they will crawl to step 3, and on to 4 likewise. A linear thinker must follow a sequential set of instructions. Many linear thinkers are wonderful with math, because math is progressive, and "linear".
Myself, I am a global thinker. However, I am relatively good at math, and it took lots of patience, which I am in little supply. I did finally discover some simple tricks to help me pull out of the rut. So here are tips for those of you out there who are also global thinkers, stuck in the rut of "I don't understand any of this!"
Learn by Doing:
All textbooks give example problems for the new concepts before the given exercises. I found that I liked doing these over and over, you already had the 'answer' right there in front of you. So being the global thinker, I was simply trying to understand the answer to the sample problem related to the various steps for solving. So basically, I learn math backwards! Weird huh! But, it works for us global thinkers. Once we understand the relational values of the steps for a solution in a math problem, we then can more easily apply those steps to an unfamiliar math problem. Use Multiple References: Speaking for us global thinkers, we like our information provided to us in more than one medium.
I found that video lectures of the math topic I was studying was very helpful. Because every instructor presents material in their own way, so watching another instructor lecture the same topic, giving different examples, and having his own point of view, satisfied my need to 'relate' the information. I could compare notes from my class, with notes I had taken from the other instructor's video lecture, thereby finding comparisons and seeing a more 'global' perspective of a particular math topic.
Use math reference guides. For example, there are several math short-cut guides out there now, like Trigonometry for Dummies, etc.. However, my preferred series of books to use as additional guides are the Demystified series. It runs across disciplines and subjects, but you can begin with Pre-Algebra and go from there to Calculus and Physics and beyond. Compare how the short-cut guides present the information to the textbook. Many of the short-cut guides leave out a lot of the 'math jargon' and simply show you the steps to finding the solution. I like that, just give me the facts; I'll figure it out later!
I hope these tips have been helpful. When we can better understand ourselves, we can understand better how to help ourselves. Written by a Global Thinker. More helpful tips.