(October 7, 2016 at 1:32 pm)Kernel Sohcahtoa Wrote:LastPoet Wrote:What do you like most about Math?
I like the fact that there are multiple ways to arrive at a correct answer. This mathematical fact has taught me not to dismiss the conclusions of others when they approach a problem differently than I would've; it's very possible that they have found an alternative and simpler approach that I hadn't considered.
Rozkek Wrote:Do you have any advice on how to significantly improve problem solving skills in mathematics?
I feel as if my problem solving skills in mathematics aren't good enough, is practice actually enough to improve, are there methods, or the most common question, is it mostly innate?
I will not deny the existence of people who can innately create brilliant mathematical theory that will shift the course of human thought (I'm definitely not one of these people). However, from my studies, I've learned that you do not have to possess innate talent to be a good and dedicated mathematician; you do not have to be a born math wiz to enjoy the beauty of mathematics. IMO, this misconception prevents a lot of bright people from engaging mathematics and developing talents and reasoning skills that they never knew they had. Having acknowledged this, getting good and skilled at mathematics requires the following reality check: you've got to make peace with the fact that you're going to have to work at it. When a mathematician creates a brilliant proof or discovers a new mathematical concept, it is important to realize that he did not do this from a blank, innate slate: he did lots of research on the matter at hand and made use of existing facts, knowledge, and mathematical concepts to produce his innovation. Math problems are no different. When you find yourself challenged, there's no shame in doing research or acquiring more information that can help you resolve your problem. From my experience, if you are going to effectively study mathematics, then you need to have plenty of resources that are available to you.
Also, don't be afraid to get your hands dirty. Do not try and create perfection right from the get go. The process of producing exceptional math work (especially when the problem is challenging) is similar to the process of producing exceptional writing: brainstorm your ideas freely and get them out on paper (don't worry about logical organization, as this can be perfected in later drafts), then slowly and systematically connect all of your ideas and make it into a coherent, well-written product.
Rozkek Wrote:When I stumble upon problem solving tasks in mathematics one too many times I can't figure out how to solve it, and need it explained to me in order to solve it in the future. I don't like that dependency. It can be quite frustrating when one is aiming for high goals.
Based on an earlier post of yours in the math proof thread, you were given a challenging book of math problems by one of your teachers. Hence, you are probably being challenged in a way that you are not accustomed to. I would like you to know that what you are experiencing is quite normal: sometimes, especially in the beginning, a particular math problem will knock you on your rear end and you will ultimately have to embrace the fact, that for the time being, you are out of your element; you need to acquire additional knowledge (whether it be asking a teacher for guidance or doing some form of information gathering), so that you can engage the problem, own it, and solve it.
Now, when solving math problems, there is one thing that you need to have if you are going to enhance your problem solving ability: you have to be interested, fascinated, and curious about the subject matter. Now, even if you have all of these things, it is still normal to get stuck and ask others for guidance. However, once you ultimately resolve that problem, a good approach is to find similar problems and see if you can resolve those (use the one that you have solved as a template but don't assume that new problems will be exactly like it); this will ultimately reinforce your understanding of the concepts and build your confidence. Hence, based on my experience, there is truth in the observation that you really do have to work more math problems in order to solidify your mathematical understanding and fluency.
P.S Thank you for your inquiries, Rozkek and LastPoet. Live long and prosper
Thank you for your answers and time taken, I truly appreciate it.
I have not been studying the challenge book yet, I've been 'stormed' with lots of other things to do, luckily this Monday, I'll be done with all of it, at that point I will work with the book. It is quite interesting, filled with stuff I've never stumbled upon before. It will be good practice before senior high school.
