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Mathematics Problem Solving Skills

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Problem Solving Skill: Visualization



It isn't easy for all of us to visualize things. Some of us do our mental work more with words than with images. Anyone, however, can get better at visualization with practice. The payoff is more creative and sometimes quicker solutions to problems.

Suppose you operate a gas station. In your mind, you visualize a customer coming into your lot and pulling up to the pump. You get inside the head of that customer and try to see things as he does. Suddenly, your nice vision of him pulling up to get gas is intruded on by another car that is in his way. Maybe you need more gas pumps? Or perhaps a better design for incoming traffic flow?

The idea here is to visualize as clearly as you can. With enough clarity and detail, your unconscious mind can begin to play with the images, and to suggest solutions, or point out things you haven't yet noticed consciously. There is always a lot going on below consciousness, and this is a way to access that part of your thinking.

Suppose the problem you want to solve is that you live in a too-tiny crowded apartment. It is time to put your problem solving skills to work, so you visualize your apartment, and see yourself being hemmed in by the stuff in it. Then you start to play with the image, and imagine that the apartment is empty. It doesn't seem so tiny now, so you get the idea that owning fewer things could be a partial solution. Storing things more efficiently in the closets might also open up some space.

Perhaps at some point in your visualization you feel too enclosed in your crowded apartment, and you see yourself leaving, perhaps climbing up the stairs to the open roof. This gets you thinking about what it means to "live" in a place. If you just use the apartment for eating and sleeping, and carry a few essentials with you always, you can "live" in the small space only part-time, and spend more time in open spaces, whether roofs, parks, or coffee shops.

Another thing that you accomplish with visualization is the directing of your attention. Knowing how to direct your attention is another powerful problem solving skill.

Problem Solving Skill: Directing Attention

I once noticed that people are essentially decent to each other. I pointed this out to a friend who immediately argued that people are essentially rude to each other. Who was right? Well, I'm not sure that "decent" and "rude" can be defined with enough preciseness to even study the issue scientifically. But the more important point here is why we differed so much in our views.

The answer to that question is relatively simple. I was looking around for examples of decency, and so I found them - and probably missed seeing many examples of rudeness. My friend habitually directed his attention to people's rudeness, and was certainly not noticing many of the real examples of decency. The ways in which we direct our attention dramatically affect what we see and believe.

Now, to use this phenomenon as one of our problem solving skills, we just need to direct our attention to possible solutions. Consider a simple problem: backpacker's tents get too hot in the sun. The tent designer or backpacker can start to think about cooling, and look for examples of it. He is now directing his attention, so his unconscious mind will go to work looking for anything inside his mind or outside that is related.

He notices an air conditioning unit, but the machinery isn't practical for carrying while hiking. He gets cool as he walks in the shade, and becomes aware of this because his attention is directed. Immediately he considers that a tent pitched in the shade will be cooler. This is not a new idea, and isn't always practical, but then he wonders if a lightweight tarp would shade the tent enough. A possibility.

Water spills from his drink onto his arm and he notices the cooling effect of the evaporation. This reminds him of a book he once read about how before refrigeration people would put food in a box covered with a wet cloth, and the evaporation would keep the interior of the box as much as fifteen degrees cooler than the outside air. Could the same thing be true if a thin cloth were draped over a tent and kept wet? There might be a new product here.

We all have had the experience of seeing more of whatever we direct our attention towards. Just start looking for red cars, and you'll suddenly realize there are more than you thought. To use this to solve problems, though, be careful to direct your attention to possible solutions, and not to more problems. Focusing on all the reasons you can't start a business, for example, will only make matters worse. Better to start noticing all the ways in which others have started businesses.

Finally, how do you develop these problem solving skills? This part is simple. Visualization and directing one's attention are skills we already have. To develop them further, we need only use them repeatedly.
Mathematics Problem Solving Skills
Relationships are an integral part of our lives. Most of our daily routine activities and various other important decisions of life not only revolve around them, but also are influenced by them. Hence, it becomes all the more necessary to put in all the required effort to maintain harmonious relationships and nurture them. This helps to strengthen the family bonds. However, being human beings, we have our individuality, each with a different mindset and unique nature and hence, a right to form our own opinions. These opinions very often differ widely from those of our near-and-dear ones. All this consequently gives rise to quarrels, arguments and conflicts. This is all the more prevalent in relationships like that of husband and wife or parents and children.

Marital discord may be the result of various factors, the most common issues being disagreements over kids, household expenses, dissatisfaction of sexual desires, religious concerns, adjustment problems with in-laws, and a wide communication gap. Although, mild disagreements can prove to be a healthy boost to a relationship, on the other hand, frequent problems and fights over a period of time tend to leave a negative impact on the family and eventually, only weaken the family ties. A problem arising every now and then does not allow you to experience marital bliss. It means that if a couple cant solve the problem amicably, they wont be able to enjoy the kind of marital ties that they really want to.

A couple has to compulsorily learn to solve problems together since no marriage is perfect and no relationship is devoid of problems. They need to become skilled at negotiating situations so that both of them can come to agreeable terms. Husbands and wives are meant to be pillars of strengthen and provide each other with support during trying times. They are supposed to complement each other and not contradict. Hence, when confronted with problems, couples should turn to each other for help; rather turn than against each other. Problems in any relationship are like a vicious cycle, one leading on to another and in turn aggravating the situation even more. It is human nature to become frustrated and panicky during such circumstances and find a reason to blame your spouse for the problem.

Undoubtedly, irritation and depression caused due to problems tend to intensify situations all the more, resulting in clashes rather than providing a suitable solution to the problems. But this does not mean that nothing can be done to solve problems together. By learning to manage situations in a mature manner, you can reduce the fights in your marriage. Begin by making improvements in your attitude, since it is your behavior that determines your actions. Then, both of you can work together by trying to focus on finding feasible and viable solutions to the problems. This way, you will have two minds working to solve the problems, which means better results in the shortest time. The secret to marital harmony lies in using the skills of your spouse to your benefit and making up for your drawbacks with them.
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