There was a time when I struggled with an advanced mathematics class in High School when the teacher presented math theory from an abstract perspective. This bothered me, but I was determined to allow the subject to seep into my mind, as well as I possibly could, while listening to my teacher lecture. When he, the teacher, decided to give us one problem for homework, I secretly thought that I got off easy for a 1 problem math homework night. Little did I know that the question was posed in such an abstract, new language, manner that I really did not know how to approach solving the problem because I did not completely understand the question.
First of all, it is difficult for any of us to admit weakness. This is just not built into our DNA. We want to feel capable, and when we do not, we panic. This is a major issue for many students who want to more easily learn mathematics. When I stumbled upon the same issue with trying to understand the one question given to me, I was petrified. One question my teacher gave me and I did not get it. I remember thinking that the new language he used during his lecture went over my head. I did not record his sentences but I did take notes. I struggled desperately to understand what he said as he jotted notations on the board. But, no, I was at a stand-still. Mentally, I just could not wrap my mind around the new concepts presented.
What was I to do? I did not want to continuously struggle, for this was wearing me out. In my stupor, I decided to go to the school library, hoping that the studious atmosphere might rub off onto me and somehow the answer would pop into my head. So, I quietly entered the library and found a quiet remote table to sit at. I put the paper on the table directly in front of me and stared at it. "I can't believe this," I said to myself, "I just don't get it. It's like a foreign language to me." Sitting there frustrated, I again became much stressed, and then the tension simply wore me out. "I need to not think about it so much," I decidedly told myself. "Hmm, let me lay my head down on the table and take a little rest."
I simply followed this little voice inside of me. I put my head down and went into a semi-meditative resting state. All the stress left my body, and my mind was free to roam with new information that left my conscious mind and seeped into my subconscious. Suddenly, I visualized while resting with my eyes closed, the ideas clearly needed to answer the question. Suddenly, the teacher's presentation of newly formed ideas came together perfectly. When I opened my eyes, I hurriedly wrote down what I discovered. Then I reviewed it again with such clarity, that it was hard to understand why my conscious mind could not figure it out. I needed my subconscious to communicate to my waking mind and it did so; calmly and without hesitation once I allowed my resting mind to reach a peaceful state pulling all the new information together in a very clear, logical manner.
I was lucky to learn this technique prior to college. Many times, especially when studying difficult math theory, I used this technique to ease the completion of homework while either dreaming at night, or going into this meditative state during the day. I hope to help students overcome unproductive tensions while attempting to learn mathematics and teach them this stress-free technique. My students will be amazed of their minds' innate capabilities of learning mathematics in this peaceful manner.