The values required for a problem solver: Curiosity, Perseverance, Determination and Imagination.
Curiosity to ask: “How can I solve this problem?”, “what if I try this?” “How does this/that work?”
Perseverance to keep trying different things and searching for the answer determined that there is an answer. Perseverance requires time to work on things and it is important to determine at the outset that you will achieve your goal.
Imagination is very important because it enables new solutions to problems that might never have been attempted or seen before.
To solve problems requires the right tools and enough time. Students should know or learn that problems are solved by persevering and continuing to work on a problem, determined that they can solve the problem.
Students that I work with often get confused and discouraged in settings where other students solve the problem quicker than they are able to. Students often confuse good problem solving skills and experience with out and out intelligence. I’ve seen several instances where very bright individuals didn’t feel like they were as good as somebody else in class because they were working along somebody with more experience. Some individuals are more intelligent than others. A more intelligent person can come to an answer faster but, given enough time, anybody can come to an answer with enough perseverance.
Intelligence is BrainPower... Power is how fast WORK(force*distance) can be done.
Brain work = How big of a problem * how many parts of the problem
Brain work = problem solving * tasks
In school I encountered many individuals that I felt were clearly smarter than me. A few of these would sleep through class and miss tests. I went to class, did my homework (even though it took longer) and would pass the tests. Through hard work, determination, and follow through I have achieved nearly everything I have wanted in my career so far. Intelligence is a gift, working hard is a choice, both are required to succeed.
I, personally, would just wait until somebody else solved questions asked in class. The important thing is for students to have the opportunity to work on problems long enough to solve the problems. One of the difficulties I had with school was timelines. I still have a lot of problem being put on the spot and asked to figure something out. This time isn’t unbounded in the real world as there are real deadlines to meet. The timeline I discovered I needed was on the order of a day but this day also involved a lot of wasted time staring at walls.
In college I would work long hours to solve the same problem that friends could sit down and do in 30 minutes. It took longer for me because I have difficulties concentrating and also I had an accumulated weakness in math application and understanding. I didn’t understand how to apply the math taught in math classes to the engineering problems being taught in engineering classes.
I was taught math through disjointed building blocks. Each unit was new and didn’t seem to build on the previous unit. There was no real connection for using the building blocks to solve problems. Math was essentially re-taught or had to be relearned for use in engineering and physics environments. Teaching math through an engineering or physics environment with hands on problems would have solidified the concept and connection for me.
I would encounter a calculus symbol and skip the section or stare at the problem for a long time because I wasn’t confident that I knew how to do the problem properly. I learned that I could go to the teaching assistant for the class or classmates and have them check my work. It was important that I had already tried and understood what I didn’t understand instead of simply giving up. Homework that built upon the previous answer was very frustrating because I couldn’t skip a step and come back to it.
As a student when I would try to apply things learned in class they would break. This caused me to feel like I wasn’t being shown the whole story, and had difficulty believing that something worked the way shown in class. I feel it’s important to show students where to get materials so that they can go home and buy the same materials to create things they are interested in. Instructables.com is amazing for instructions and material references.
Confidence is important for perseverance because you personally know that you have the ability to accomplish things. Confidence is built by successfully solving problems on your own. Building student confidence by working through building blocks is important, but the building blocks must be put into context and used together.
Follow through; doing the best you can with everything given to you. How well you handle small tasks shows that you will take care with larger opportunities. There have been many projects where I wasn’t doing what I wanted to be doing, but it was my job to complete them. I have been amazed time and again how doing the best I could, with everything given to me, has provided valuable experience that I never expected later on in life.
The amount of effort put into a project is directly proportional to the reward received at the end. The reward might not be the one that you are hoping for, but knowledge and experience is a reward in and of itself. Every experience of your entire life is something that you can draw from. You are the only person in the entire world with your experience set and this makes you unique.