Final answer:
The nine dot problem and the glass problem illustrate functional fixedness, a type of cognitive bias. Overcoming functional fixedness is essential for effective problem-solving, as demonstrated by the classic candle problem and the real-world Apollo 13 incident.
Step-by-step explanation:
The nine dot problem and the glass problem illustrate functional fixedness, a cognitive bias that limits a person to using an object only in the way it is traditionally used. The concept of functional fixedness can significantly affect problem-solving capabilities. Duncker's candle problem is a classic example, where individuals had to overcome functional fixedness by thinking of a box not just as a container for thumbtacks but as a potential candle holder. Similarly, the Apollo 13 incident showcased NASA engineers overcoming functional fixedness to save the lives of astronauts by improvising a solution with materials aboard the spacecraft.
Research by German & Barrett (2005) also contributes to our understanding of functional fixedness across different cultures, highlighting that this cognitive bias is not limited to industrialized nations. Whether in day-to-day life or in unusual and high-pressure situations, recognizing and overcoming functional fixedness can be critical to successful problem-solving.