PDF Summary:Critical Thinking, Logic & Problem Solving, by Bigrocks Thinking
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Have you ever wished you were a more effective thinker? Do you feel overwhelmed when presented with a problem? In Critical Thinking, Logic & Problem Solving, Bigrocks Thinking explains how you can enhance your critical thinking and problem-solving abilities to improve your learning, your work, and your personal life.
The authors provide a step-by-step method for improving your ability to think critically and solve problems. They offer tips for conducting and thinking about research and information, covering issues like source reliability and logical fallacies. They also explain how to develop and implement solutions to problems, and they provide guidance on how to structure your thinking for effective communication and powerful storytelling. In our guide, we’ll also provide tips and additional methods to implement the techniques described in the book.
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1. Identify patterns in your information. Patterns help us understand information and form arguments. For example, if you’re feeling resentful toward your partner and you don’t know why, you might notice a pattern in your relationship where your partner spends every weekend relaxing while you do all the housework.
(Shortform note: Pattern recognition is an important skill that helps us understand situations and make decisions. Some people are born with more advanced pattern recognition skills than others, but anyone can cultivate them through practice and study. Patterns occur in many different disciplines, especially art, nature, and mathematics, and studying the patterns in these fields can help you recognize patterns in other contexts. Where inductive reasoning comes in is in predicting further sequences in a pattern based on what you’ve seen already.)
2. Identify questions that need to be answered. This will tell you what type of argument or solution you need to come up with. Your question or problem should not only lead you to an answer but should also help you learn more information. For that reason, you should avoid yes or no questions, as answers to these will be simplistic and may not yield any real solutions. Additionally, use neutral language when forming your question to avoid biasing the answer. For example, asking “Why won’t my partner contribute to the housework?” will result in fewer, more biased answers than “How do I feel about the balance of labor between me and my partner?”
(Shortform note: Questions with yes or no answers or non-neutral language are types of leading questions, which means they push the answerer to a specific response rather than an organic one. Phrasings like “How satisfied were you…” and “Which thing did you like…” assume the listener had a positive experience and excludes answers that reflect negative experiences. Phrasings like “What did you think…”, “How do you feel…”, or “What are some ideas…” will give you more objective information and better guidance toward the problem you’re trying to solve.)
3. Draw conclusions. Use the information you’ve gathered to draw inferences. These inferences serve as logical foundations for the formation of your arguments. For example, based on the pattern you’ve observed and the question you’re asking about the balance of labor between you and your partner, you may conclude “I feel resentful toward my partner because I feel I do more of the housework than they do, and I would like them to do more.”
(Shortform note: The authors don’t address how to use your inferences to form your argument. Your argument is the persuasive statement you make to the opposing party to convince them to accept your claim. You would use the conclusions you formed during the analysis process to create a proposition, backed up by the evidence you’ve gathered, and present that to your audience in order to get them to agree with you. In our example, the argument you would present to your partner would be “If you do more of the housework, I will feel less resentful.”)
Step 3: Evaluate
Once you’ve formed an argument based on your analysis of your information, it’s time to test that argument and evaluate its validity. The authors recommend that you use deductive reasoning to evaluate your argument.
Deductive reasoning is the process of going from a theory to a hypothesis and testing it to see if it’s supported by evidence. For example, say you’ve used your inductive reasoning process to analyze data on how listening to classical music affects people’s moods: You notice from the data that people in a study reported feeling happy after listening to classical music. You conclude that listening to classical music makes people happy, and this is your theory.
You will then use deductive reasoning to test this theory. From your theory, you form the hypothesis that if you play classical music for someone who is sad, it will make them happier. You test this hypothesis by playing classical music for someone who is sad. If the person feels happier after listening to the music, you now have a piece of supporting evidence for your hypothesis. However, if you find that the person doesn’t feel happier after listening to classical music, you disproved your hypothesis and theory.
Replicating Your Results to Strengthen Your Hypothesis
Reproducing the results of a study to strengthen a hypothesis is an essential part of reasoning and the scientific method. Because deductive reasoning can only provide evidence for a hypothesis being true and can’t definitively prove that it’s true, it’s important to continue testing a theory even if your deductive reasoning process has provided supporting evidence.
However, sometimes the nature of a study or experiment makes it difficult or impossible to replicate. In modern science, this has led to a replication crisis in which many hypotheses can’t be tested effectively because the results of previous experiments can’t be reproduced. Consequently, hypotheses that may be true can’t become part of the scientific body of knowledge because they can’t be effectively validated.
In your own reasoning process, you may face a similar issue if you find that certain variables that you can’t control are affecting the results of your reasoning—especially since, unless you’re a scientist, you’re probably gathering your information from informal sources rather than strictly controlled experiments. While being unable to replicate the results of your reasoning doesn’t disprove your hypothesis, you should keep in mind that it hasn’t been tested thoroughly enough to prove it.
Step 4: Keep Improving
Now that you’ve used your data to form and test a hypothesis, the next step is to note things you did correctly or that made the process easier and remember them for next time. If you do this, you’ll constantly improve your critical thinking.
(Shortform note: When you first begin, you may find that this is the most difficult step for you to complete. This is because reflecting on your thinking—also known as metacognition—takes a lot of mental energy and may also take a long time. However, as you continually reflect on and refine your learning and thinking processes, this step will become easier, and eventually you may begin to do it without having to consciously think about it at all.)
Problem-Solving
Critical thinking helps you learn, understand, and form arguments. Problem-solving incorporates the process of critical thinking but is directed specifically at bridging a gap between your current state and a desired state. For example, you know you currently have a job that you don’t enjoy. Your desired state is to have a job that you do enjoy. The gap—or problem—you need to solve is how to go from having a job you don’t enjoy to having one you do enjoy.
(Shortform note: Critical thinking is only one aspect of problem-solving. Another vital one is creative thinking, which allows you to produce new solutions that may not directly arise from the information you’re thinking critically about. Like critical thinking, creative thinking can be learned and honed, but it often requires different techniques. If you’re struggling to think creatively, rather than powering through, it may help to take a break from what you’re thinking about and clear your mind, sometimes even by distracting yourself with another task or topic until creativity strikes. It can also help to change up your environment and expose yourself to new stimuli—for example, by working outdoors or taking a walk.)
There are five steps to problem-solving, which we’ll describe next.
Step 1: Identify the Problem
To solve a problem, you must first identify it. You can do this using seven basic questions that make up what the authors call the “5W2H” method (five ‘W’ questions and two ‘H’ questions):
- What? What is your current state, your desired state, and the gap between them?
- Where? What is the location of your problem?
- When? When did or does the problem occur? Is it ongoing? Will it happen again in the future?
- Who? Which people are impacted by the problem? Who caused it? Who may know more about it?
- Why? Why did the problem occur or why does it continue to occur? Why is the problem important to address?
- How? How could you solve the problem? What process should you use?
- How much or how many? How big is the problem? How much harm is it causing? How long will it take to solve?
(Shortform note: The 5W2H method is most effective when you only answer the most appropriate questions for your given situation. If your problem is that you want to buy a new video game but don’t have the money, then the “Where” question probably won’t be very useful to you. You might also need more than one answer for some of the questions. If your problem is that you think someone in your friend group is displaying toxic behavior, the “Who” question might be extra important—not only to determine who is engaging in the behavior, but also who is affected by the behavior.)
Another tool for defining your problem is what they call the SCQH (Situation, Complications, Question, and Hypothesis) framework. This method helps you analyze a problem fully to point you in the direction of possible solutions. In this method, you’ll follow four steps:
- Situation: Identify your current situation and its context.
- Complications: What things are not working about the situation? (These two steps help you identify the gap between your current state and your desired state.)
- Question: What questions do the situation and complication bring up? This will help you clarify the problem and narrow your focus.
- Hypothesis: Come up with some hypotheses that could address your questions. This leads to the next step of identifying potential solutions.
(Shortform note: The SCQH framework can be particularly helpful when working with a group to complete a project. When working in groups, there are some additional guidelines to follow to implement SCQH successfully: The Situation portion should be entirely factual, as you’re merely describing the state of things as they are. The Complications portion may be difficult to narrow down and may require some brainstorming to identify the exact problem. Questions you can ask to clarify the problem might include, What is the best course of action, How do we begin solving this problem, or What is standing in the way of implementing our solution. The Hypothesis is then an answer to the questions you’ve identified, and it should be actionable so you know what next step to take.)
Step 2: Form Solutions
Once you understand the problem you’re facing, you can begin forming solutions by first identifying potential solutions. You can use tools such as logic trees to help you identify solutions.
A logic tree is a tool that allows you to visually lay out potential solutions so you can consider them more easily. You can format the tree in whatever way works best for you, but begin by writing down your problem or question. Then, add branches that show your options and further branches that provide the details of those options, such as benefits, consequences, or other factors to consider. See the example below of a logic tree where the problem is what math class to take as an incoming college freshman, and the possible solutions are calculus, statistics, and trigonometry.
(Shortform note: Sometimes you may encounter problems that you’ve had before but find that the old solutions no longer work to fix them. Tools like logic trees can be especially helpful in these cases, as the visual aid can make it easier to understand and remember the different solutions and their characteristics. The human brain is faster at visual processing than verbal processing, so these tools facilitate faster decision-making and easier communication within groups. Other visual aids for identifying solutions include mind maps: For this, you would begin with a central idea in the middle of the page and then add thoughts as they occur to you, using lines to link them together or back to the central point.)
Step 3: Select a Solution
Once you’ve laid out your potential solutions and weighed them against each other, explain the authors, it’s time to select a solution.
One tool you can use to help you choose is a pros and cons assessment. To do this, you can list your pros and cons on a two-column chart and then rate each item based on how important it is. Once you’ve listed all your pros and cons and given them a weight rating, add up the sum for each column and then subtract the cons sum from the pros sum. If the result is a positive number, this suggests the overall benefit of the option outweighs the negatives, making it a good solution to consider.
(Shortform note: Other tools for weighing and selecting your solutions include a risk-reward assessment. As with the pros and cons assessment, you write out your potential solutions in a chart and then rate them based on how much reward they offer and how much risk they come with. Options that have a high risk score like 4 out of 5 or a low reward score like 2 out of 5 may not be worth considering and can be quickly eliminated. Another tool is a consequences table, which is similar to the pros and cons assessment except that you simply describe the consequences—positive and negative—for each option rather than assigning them a numerical value.)
Step 4: Implement Your Solution
According to the authors, it’s now time to put your solution into action. You can use the 5W2H method again to help implement your plan:
- What solution are you going to implement?
- Why is this the best solution?
- Where will it be implemented?
- When does it need to be implemented?
- Who is going to implement it?
- How will it be implemented?
- How much effort or cost will it require?
(Shortform note: You can answer these questions in whatever order works best for you and your team. Some questions may have more than one correct answer, and if you’re working as a group, “Who is going to implement it?” can be answered by assigning roles and responsibilities to various team members. One person should be in charge of facilitating the meeting to go over the plan, but roles such as project managers or record keepers should also be designated for the implementation itself. Designating roles can help your team work more productively and efficiently, and it can also improve the group’s morale.)
Step 5: Evaluate the Results
Finally, the authors advise that you evaluate the results of implementing your solution. Note what went wrong and what went well, and use that information to make better decisions in the future.
(Shortform note: To evaluate your results, consider the actions and decisions that were made, why they were made, and what the results were. Assess their effectiveness, and then consider what other results could have occurred if different decisions were made. If those alternative results seem better than the results you got, consider changing up your strategy the next time you face a similar problem.)
Communication and Storytelling
The authors also explain how to give good presentations and communicate your ideas effectively using critical thinking. They note that many people have excellent ideas but don’t understand how to structure their presentations. The authors advise you to structure your presentations logically and to use stories to persuade and inform your audience, two tactics we’ll talk about in this section. However, for any form of public speaking, they broadly recommend that you:
- Know your topic. A thorough understanding of your subject will establish credibility with your audience and help you answer questions they have.
- Know your audience. Be aware of your target audience’s demographics, interests, and beliefs, and appeal to those things to establish a bond with them.
- Make consistent eye contact. This will help you connect with your audience as well as gauge their reactions to what you’re saying.
- Ask questions of your audience. Asking questions keeps your audience engaged and focused on what you’re saying.
Further Tips on Public Speaking
Knowing your topic means not only knowing what information you’re going to give but also what objections or counterpoints might come up. You shouldn’t go into your talk with gaps in your knowledge because you assume the audience will know even less than you do.
Knowing your audience can also include knowing the type of speaking you’re doing. Different formats allow for different methods of interacting with the audience and types of language to be used. For example, a teacher in a classroom can speak directly to students one-on-one and use vocabulary terms they’re studying. If you’re a speaker on a panel at a Comic Con, you can address not only your audience but also the other members of the panel, and you can use language from popular franchises the audience will be familiar with.
Some experts suggest that eye contact is the most important thing you can practice to improve your speaking skills. It captures people’s attention, makes you look more confident, and keeps you from getting distracted.
Questions can help you at every stage of your presentation. Even before you dive into your topic, consider asking questions to break the ice like “What did you do last weekend?” It can also help to use the 5Ws to frame your questions (What, When, Where, Who, Why), or to ask reflective questions that let the audience ponder what they’ve learned so far and apply it to what they’re learning now.
Structure Your Thinking: The Pyramid Principle
According to the authors, structured thinking is key to effective communication. They recommend the pyramid principle for establishing this structure, which consists of the following three steps:
- Explain your main idea. This includes the problem you’re trying to solve and the solution you’re proposing.
- Explain your reasoning. Here you’ll let the audience in on your thought process, explaining what options you considered and why you chose your solution.
- Explain your evidence. Here you’ll give the details and facts that support the solution you chose.
(Shortform note: According to Barbara Minto, who coined the pyramid principle, the structure is effective because it mirrors the way the human brain works and presents information to the reader in the order that’s easiest for them to understand. However, she cautions that it may result in unoriginal thinking, detracting from your ability to draw new insights from the information. She also says it’s less effective for nuanced arguments that have multiple interpretations, as opposed to arguments with clear and definitive conclusions.)
How to Structure Stories
The authors place particular emphasis on storytelling, as it helps your audience understand and remember your ideas. It can also build an emotional connection, which further enhances their comprehension and retention. They recommend several ways to structure your stories depending on your goal:
To persuade others, they recommend the situation-complication-resolution approach. First you explain the situation, then the complication (the problem), and then the solution that you’re recommending to them.
(Shortform note: Another structure for persuasive storytelling is the Attention, Interest, Desire, and Action structure. This begins with an attention-grabbing statement or idea followed by another idea to retain their interest. Then you turn their attention to their desire, explaining what they can get out of what you’re saying. Finally, you provide them with a call to action as to how to achieve the desired result. Like the situation-complication-resolution approach, this method is persuasive because you end with a recommendation that your audience can act on to resolve the problem or desire you’ve brought to their attention.)
To explain information to your audience, you can use the hook-meat-payoff structure. First give your hook, where you pique their interest by letting them know what they can get out of your presentation. Follow that up with the meat, where you explain the topic you’re trying to get across to them. Finally, explain exactly how they can apply your information to their lives.
(Shortform note: This structure is great for efficiently delivering your information in easy-to-understand chunks, and the hook is a great opportunity for pulling your audience in. There are several different types of hooks you can use, the most common of which is an anecdote. Anecdotes humanize the speaker to their audience and also help the audience connect the speaker to the subject. Other options for a hook include a video, a statement of belief, a joke, or a rhetorical question. The meat should then be delivered in discrete pieces that are easy for the audience to understand, and the payoff should include a call to action.)
You can also structure your stories by breaking them into acts. One of the act structures the authors recommend is the five-act structure, or Freytag’s pyramid, which consists of:
- The exposition, which introduces the context and circumstances of the story
- The rising action, in which you describe the events leading to the conflict
- The climax, which is the high point of your plot when the conflict is greatest
- The falling action, where the conflict gets solved and the moral of the story is revealed
- The denouement, or the end of the story
(Shortform note: Some representations of Freytag’s pyramid include seven pieces: exposition, inciting incident (the event that sparks the story’s action), rising action, climax, falling action, resolution, and denouement. In this case, the falling action would refer to the events that result from the climax, the resolution would be the part where the conflict is solved, and the denouement would still be the ending. Freytag’s pyramid was originally designed for tragic dramas, and in those structures, the denouement would be replaced with a catastrophe (the hero’s lowest point, such as a death or financial ruin). Freytag’s structure is ideal for stories with a strong, conclusive ending.)
Another framework they recommend is the Pixar story framework. This framework is great for not only conveying information and ideas but also evoking emotion in your audience. You can outline a story with this framework by filling in the blanks of six sentences:
- “Once upon a time, [blank]. Every day, [blank].” These two establish the setting and context of your story.
- “Then one day, [blank].” This establishes your story’s conflict.
- “Because of that, [blank]. And because of that, [blank].” This introduces your character’s challenge and how it affects them and other characters.
- “Until finally, [blank].” This explains how the character resolved their problem.
(Shortform note: An essential element of the Pixar framework is that your hero must have a goal that carries them through the story. Someone or something has to stand in the way of the hero achieving this goal, which is the source of the story’s conflict. It should also result in a lesson or personal growth for your hero, and this lesson is an optimal place to insert your own message to the audience.)
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