Say one person in a boardroom comes up with brilliant ideas--new ways of doing things, innovative approaches, fresh concepts--but the CEO at the head of the table constantly dismisses them. Fairly shortly, everyone in the room will stop bringing new ideas to the table; eventually, they will stop trying to find creative solutions and original ideas altogether. Even new people brought into the group will fear flexing their creativity.
Creating new ideas means challenging all assumptions and thinking productively by looking at things in as many different ways as possible. Typically, we think reproductively--that is, on the basis of similar problems encountered in the past. When confronted with a new problem, we fixate on something in our past that worked before, exclude all othe approaches, and work within a clearly defined direction toward the solution of the problem.
In contrast, creative thinkers confronted with a problem ask, "How many different ways can I look at it? How can I rethink the way I see it? How many different ways can I solve it?" They don't ask, "What have I been taught by someone else about how to solve this?" They tend to come up with many different responses, some of which are unconventional and possibly unique.
With productive thinking, we generate as many alternative approaches as we can, considering both the least obvious and the most likely. This willingness to explore all approaches is essential. Someone once asked Einstein what the difference was between him and the average person. He said that, if you asked the average person to find a needle in the haystack, the person would stop when he or she found a needle. He, on the other hand, would tear through the entire haystack looking for all the possible needles.
Whenever Nobel Prize winner Richard Feynman was stuck on a problem, he would invent new thinking strategies. He felt his secret was his ability to disregard how past thinkers thought about problems and would invent new ways to think instead. If something didn't work, he would look at it several different ways until he found a way that moved his imagination. He was wonderfully productive. He could do in 10 minutes something that might take the average physicist a year.
Feynman proposed teaching productive thinking in our schools instead of reproductive thinking. He believed that the successful mathematician is an inventor of new ways of thinking in given situations. Even if the old ways are well known, he believed it is usually better to invent your own way or a new way than to apply what is already known.
For example, the addition problem 29 + 3 is considered a third-grade problem because it requires the advanced technique of carrying. Feynman pointed out that a first grader could handle it by counting in sequence 30, 31, 32. A child could mark numbers on a line and count off the spaces--a method useful in understanding measurements and fractions. Children can write larger numbers in columns and carry sums larger than 10, or use fingers or algebra for other, seemingly more complicated problems (e.g., 2 times what plus 3 is 7?). Feynman encouraged teaching people to figure out how to think about problems many different ways using trial and error.
Reproductive thinking is rigid thinking. This is why we often fail when confronted with a new problem that is similar to past experiences only in superficial ways but is different from previously encountered problems in its deep structure. Interpreting such problems through the prism of past experience leads to setbacks and stagnation. When Univac first developed a computer, for example, company managers refused to talk to business people because they said the computer had no business applications. Then along came IBM. IBM managers themselves once said that, according to their past experiences in the computer market, there was virtually no market for the personal computer. In fact, they said they were absolutely certain there were no more than five or six people in the entire world who had need for a personal computer. …