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5.7 Introduction to Thinking and Problem Solving

4 min readdecember 22, 2022

Dalia Savy

Dalia Savy

Haseung Jun

Haseung Jun

Sadiyya Holsey

Sadiyya Holsey

Dalia Savy

Dalia Savy

Haseung Jun

Haseung Jun

Sadiyya Holsey

Sadiyya Holsey

So, we just went over memory, but how do we actually think and problem solve? 🤔

Problem Solving

There are two different ways by which you could solve problems:

Algorithm

An is a step by step method that guarantees to solve a particular problem. 

If you lost your phone📱, the might look like this: 

  1. Remember where you put the phone last. If you don’t, go to the next step. ⤵️

  2. Retrace your steps. If you can’t, go to the next step.⤵️

  3. Call your phone to determine the location.

Algorithms are process oriented 🔄

Heuristics 

A heuristic is also known as a “rule of thumb.” Using heuristic is a quick way to solve a problem 💨, but is usually less effective than using an (more error prone). also involve using

An example of a heuristic would be trying to find the x value that makes this equal true: 3x+6=24. You might plug in multiple x values until you determine the x value that works. 

are the opposite of algorithms and are more result oriented. We use our , schemas, prototypes, and concepts automatically when using .

How would you solve 3x624 using an algorithm?

Instead of using a heuristic and just plugging in answers till you find the right one, you could also solve this problem step by step using an . The steps may look like this:

  1. Subtract 6 on both sides: 3x=18

  2. Divide by 3 on both sides: x=6

You use a mixture of these two when taking a test and overall in everyday life activities🏃🍳.

Trial and Error

is when you try to solve a problem multiple times using multiple methods. If you try to solve a problem one time using one method, the next time you solve it, you may use a different method. This process is repeated until a solution is reached.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fbart.gif?alt=media&token=7008e518-23c6-4e5e-acd4-d3db04066038

Image Courtesy of Giphy.

How do we think?

Mental Set

A is when individuals try to solve a problem the same way all the time because it has worked in the past. However, that doesn’t mean this method is applicable to the problem at hand or will work for other people. Having a makes it harder to solve problems. Similarly, fixation is the inability to look at a problem with a different perspective.

Intuition

is colloquially known as a “gut feeling.” It is sensing something without a direct reason and basically an automatic thought💾

  • When problem-solving and making difficult decisions, our brain intuits for us.

  • As we learn and grow, our does, too. Our learned associations surface as this gut feeling that we have because of how we know the world works around us 🌎

Insight

was discovered by Wolfgang Kohler. It occurs when an individual has an all-of the sudden understanding when solving a problem or learning something. It's that light bulb💡 moment!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fzoo.gif?alt=media&token=9824522e-b6e1-479d-981e-1d01712c0fba

Image Courtesy of Giphy.

Inductive Reasoning

Reasoning from something specific to something general, which puts your thought into concepts and groups.

Deductive Reasoning

Reasoning from something general to something specific. Think of mind-maps: you have one central idea in the middle (general) and then branch out into specific ideas.

These are usually more logical 🤔

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-qsr30VS6uTpP.png?alt=media&token=e7dde749-27ee-4a2d-a706-81e892c47ccb

Image Courtesy of Kristjan Pecanac.

Creativity

Did you ever wonder how we get our and to the extent to which it exists? Being creative is having the ability to produce ideas that are valuable. That's it; we're all creative in our own way.

There are five components of 📸:

  1. —The more knowledge we have, the more ideas we build. Knowledge is the foundation of every idea that comes about.

    1. Generally, greater intelligence leads to a higher 🎭 According to the threshold theory, a certain level of intelligence is necessary for creative work. However, it's not necessary sufficient, meaning other factors play in when it comes to .

  2. —In order to be creative, you must be open-minded and see things in different ways. These skills also include being able to make connections and recognize patterns in ideas.

  3. A —Be willing to take risks, explore ideas, and try new things! 🧗

  4. —This is to be driven by your interests and the will to explore for your own satisfaction.

  5. A —All the above help fuel your , but can't exist without a supportive environment🌲

There are two different ways of thinking:

Convergent Thinking

This is the more logical way of thinking, in which we narrow the solutions to a problem till we find the best one. is used in IQ and intelligence tests.

Divergent Thinking

The more creative way of thinking! You can think of this as brainstorming and diverging into different directions of thought. Rather than finding the best solution, divergent thinkers expand the number of solutions.

Divergent thinkers have a much easier time when since they have more of an open mind to trying different solutions.

   

Key Terms to Review (17)

Algorithm

: An algorithm is a step-by-step procedure for solving a problem or accomplishing some end especially by a computer.

Convergent Thinking

: Convergent thinking is a problem-solving strategy that involves finding a single, correct answer to a problem.

Creative Environment

: A creative environment is a setting or atmosphere that fosters and encourages innovative thinking, problem-solving, and the generation of new ideas.

Creativity

: Creativity is the ability to produce new, diverse and original ideas that are also valuable or solve a problem.

Deductive Reasoning

: Deductive reasoning starts out with a general statement or hypothesis and examines the possibilities to reach a specific logical conclusion.

Divergent Thinking

: Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions.

Expertise

: Expertise refers to the comprehensive knowledge or skill in a particular area or field.

Heuristics

: Heuristics are mental shortcuts or "rules of thumb" that often involve focusing on one aspect of a complex problem and ignoring others. These strategies do not guarantee accuracy but they simplify decision-making and save time.

Imaginative Thinking Skills

: Imaginative thinking skills refer to one's ability to visualize novel situations or concepts beyond reality constraints.

Inductive Reasoning

: Inductive reasoning involves making broad generalizations from specific observations. Basically, there is data, then conclusions are drawn from the data.

Insight

: Insight is the sudden realization or understanding of a solution to a problem. It's an 'aha' moment when you suddenly see the solution without going through any conscious reasoning.

Intrinsic Motivation

: Intrinsic motivation refers to behavior driven by internal rewards such as personal satisfaction or enjoyment derived from performing an activity itself rather than for some external reward.

Intuition

: Intuition refers to understanding something immediately without conscious reasoning or analysis - it's often referred to as 'gut feeling'.

Mental Set

: A mental set is our tendency to approach situations in certain ways because that method worked in the past.

Problem Solving

: Problem solving is a cognitive process that involves identifying, analyzing, and resolving problems. It's the mental process we use to find solutions to challenges or obstacles.

Trial and Error

: Trial and error is a problem-solving strategy that involves attempting different solutions until the correct one is found.

Venturesome Personality

: A venturesome personality refers to an individual who is adventurous, willing to take risks, and open to new experiences.

5.7 Introduction to Thinking and Problem Solving

4 min readdecember 22, 2022

Dalia Savy

Dalia Savy

Haseung Jun

Haseung Jun

Sadiyya Holsey

Sadiyya Holsey

Dalia Savy

Dalia Savy

Haseung Jun

Haseung Jun

Sadiyya Holsey

Sadiyya Holsey

So, we just went over memory, but how do we actually think and problem solve? 🤔

Problem Solving

There are two different ways by which you could solve problems:

Algorithm

An is a step by step method that guarantees to solve a particular problem. 

If you lost your phone📱, the might look like this: 

  1. Remember where you put the phone last. If you don’t, go to the next step. ⤵️

  2. Retrace your steps. If you can’t, go to the next step.⤵️

  3. Call your phone to determine the location.

Algorithms are process oriented 🔄

Heuristics 

A heuristic is also known as a “rule of thumb.” Using heuristic is a quick way to solve a problem 💨, but is usually less effective than using an (more error prone). also involve using

An example of a heuristic would be trying to find the x value that makes this equal true: 3x+6=24. You might plug in multiple x values until you determine the x value that works. 

are the opposite of algorithms and are more result oriented. We use our , schemas, prototypes, and concepts automatically when using .

How would you solve 3x624 using an algorithm?

Instead of using a heuristic and just plugging in answers till you find the right one, you could also solve this problem step by step using an . The steps may look like this:

  1. Subtract 6 on both sides: 3x=18

  2. Divide by 3 on both sides: x=6

You use a mixture of these two when taking a test and overall in everyday life activities🏃🍳.

Trial and Error

is when you try to solve a problem multiple times using multiple methods. If you try to solve a problem one time using one method, the next time you solve it, you may use a different method. This process is repeated until a solution is reached.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fbart.gif?alt=media&token=7008e518-23c6-4e5e-acd4-d3db04066038

Image Courtesy of Giphy.

How do we think?

Mental Set

A is when individuals try to solve a problem the same way all the time because it has worked in the past. However, that doesn’t mean this method is applicable to the problem at hand or will work for other people. Having a makes it harder to solve problems. Similarly, fixation is the inability to look at a problem with a different perspective.

Intuition

is colloquially known as a “gut feeling.” It is sensing something without a direct reason and basically an automatic thought💾

  • When problem-solving and making difficult decisions, our brain intuits for us.

  • As we learn and grow, our does, too. Our learned associations surface as this gut feeling that we have because of how we know the world works around us 🌎

Insight

was discovered by Wolfgang Kohler. It occurs when an individual has an all-of the sudden understanding when solving a problem or learning something. It's that light bulb💡 moment!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fzoo.gif?alt=media&token=9824522e-b6e1-479d-981e-1d01712c0fba

Image Courtesy of Giphy.

Inductive Reasoning

Reasoning from something specific to something general, which puts your thought into concepts and groups.

Deductive Reasoning

Reasoning from something general to something specific. Think of mind-maps: you have one central idea in the middle (general) and then branch out into specific ideas.

These are usually more logical 🤔

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-qsr30VS6uTpP.png?alt=media&token=e7dde749-27ee-4a2d-a706-81e892c47ccb

Image Courtesy of Kristjan Pecanac.

Creativity

Did you ever wonder how we get our and to the extent to which it exists? Being creative is having the ability to produce ideas that are valuable. That's it; we're all creative in our own way.

There are five components of 📸:

  1. —The more knowledge we have, the more ideas we build. Knowledge is the foundation of every idea that comes about.

    1. Generally, greater intelligence leads to a higher 🎭 According to the threshold theory, a certain level of intelligence is necessary for creative work. However, it's not necessary sufficient, meaning other factors play in when it comes to .

  2. —In order to be creative, you must be open-minded and see things in different ways. These skills also include being able to make connections and recognize patterns in ideas.

  3. A —Be willing to take risks, explore ideas, and try new things! 🧗

  4. —This is to be driven by your interests and the will to explore for your own satisfaction.

  5. A —All the above help fuel your , but can't exist without a supportive environment🌲

There are two different ways of thinking:

Convergent Thinking

This is the more logical way of thinking, in which we narrow the solutions to a problem till we find the best one. is used in IQ and intelligence tests.

Divergent Thinking

The more creative way of thinking! You can think of this as brainstorming and diverging into different directions of thought. Rather than finding the best solution, divergent thinkers expand the number of solutions.

Divergent thinkers have a much easier time when since they have more of an open mind to trying different solutions.

   

Key Terms to Review (17)

Algorithm

: An algorithm is a step-by-step procedure for solving a problem or accomplishing some end especially by a computer.

Convergent Thinking

: Convergent thinking is a problem-solving strategy that involves finding a single, correct answer to a problem.

Creative Environment

: A creative environment is a setting or atmosphere that fosters and encourages innovative thinking, problem-solving, and the generation of new ideas.

Creativity

: Creativity is the ability to produce new, diverse and original ideas that are also valuable or solve a problem.

Deductive Reasoning

: Deductive reasoning starts out with a general statement or hypothesis and examines the possibilities to reach a specific logical conclusion.

Divergent Thinking

: Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions.

Expertise

: Expertise refers to the comprehensive knowledge or skill in a particular area or field.

Heuristics

: Heuristics are mental shortcuts or "rules of thumb" that often involve focusing on one aspect of a complex problem and ignoring others. These strategies do not guarantee accuracy but they simplify decision-making and save time.

Imaginative Thinking Skills

: Imaginative thinking skills refer to one's ability to visualize novel situations or concepts beyond reality constraints.

Inductive Reasoning

: Inductive reasoning involves making broad generalizations from specific observations. Basically, there is data, then conclusions are drawn from the data.

Insight

: Insight is the sudden realization or understanding of a solution to a problem. It's an 'aha' moment when you suddenly see the solution without going through any conscious reasoning.

Intrinsic Motivation

: Intrinsic motivation refers to behavior driven by internal rewards such as personal satisfaction or enjoyment derived from performing an activity itself rather than for some external reward.

Intuition

: Intuition refers to understanding something immediately without conscious reasoning or analysis - it's often referred to as 'gut feeling'.

Mental Set

: A mental set is our tendency to approach situations in certain ways because that method worked in the past.

Problem Solving

: Problem solving is a cognitive process that involves identifying, analyzing, and resolving problems. It's the mental process we use to find solutions to challenges or obstacles.

Trial and Error

: Trial and error is a problem-solving strategy that involves attempting different solutions until the correct one is found.

Venturesome Personality

: A venturesome personality refers to an individual who is adventurous, willing to take risks, and open to new experiences.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.