Thinking & Language Study Guide

Fundamental Components of Thinking

• Definition of Thinking: Thinking involves the following cognitive processes:     * Manipulating Information: The act of processing and organizing data within the mind.     * Forming Concepts: Creating mental categories for information.     * Reasoning: Applying logic to reach conclusions.     * Decision-making: Choosing between various alternatives or courses of action.     * Problem-solving: Finding solutions to difficult or complex issues.     * Critical Thought: Objective analysis and evaluation of an issue in order to form a judgment.

Models of Concept Formation

• Concept: These are defined as mental categories used to group objects, events, and characteristics.     * Example: The concept of "pets" describes a category of domesticated animals.
• Classical Model: This model posits that defining properties are assigned to all members of a category without exception.     * Example: The concept of a triangle requires that the object has exactly $3$ sides.
• Prototype Model: This model suggests that characteristic properties are used to create a mental representation of the "ideal member" of a specific concept.     * Example: When considering the concept of a "bird," a person might use a robin as their prototype (an ideal representation) whereas a penguin, despite being a bird, is further from the prototype because it lacks common characteristic properties like flight.

Reasoning and Thought Patterns

• Inductive Reasoning: This involves reasoning from the specific to the general.     * Conclusions are drawn about all members of a group based on observing only a few members of that group.     * Certainty: These conclusions are never entirely certain.
• Deductive Reasoning: This involves reasoning from the general to the specific.     * This process involves learning when general rules apply to specific instances and when they do not.
• Convergent Thinking: This type of thinking is directed toward finding exactly one correct solution to a problem.     * Example: Solving an algebra problem.
• Divergent Thinking: This is utilized for problems that have no single correct solution. It requires a flexible and inventive approach to generate multiple possibilities.     * Example: Thinking of $50$ different uses for a brick.

Factors Influencing Decision-Making

• Confirmation Bias: The cognitive tendency to look for evidence that supports a pre-existing belief while simultaneously ignoring or overlooking evidence that would disprove that belief.
• Representativeness Heuristic: A mental shortcut by which a new situation is judged based on how much it resembles a stereotypical model or prototype already existing in the mind.
• Availability Heuristic: A mental shortcut where a judgment or decision is based on the information that is most easily retrieved from memory at that moment.
• Framing: This refers to the specific phrasing or presentation of information used to influence decisions and judgments.

Problem-Solving Strategies: Algorithms vs. Heuristics

• Algorithms: Problem-solving methods that guarantee a correct solution if followed correctly.     * The user does not necessarily need to understand the underlying rule to reach the solution.     * Examples: Mathematical formulae; the spelling rule "I before E except after C."
• Heuristics: Mental "rules of thumb" that help simplify and solve problems.     * Unlike algorithms, they do not guarantee a correct solution.     * These are primarily used when facing ambiguous problems.
• Effective Problem-Solving: Proficiency occurs when an individual knows exactly when to apply algorithms and when to apply heuristics.

Heuristic Problem Examples

• The Candle Problem: How would you mount a candle on a wall so that it won't drip wax on a table or a floor while it is burning?
• The Nine-Dot Problem: An arrangement of dots is presented; the task is to connect all the dots using only $4$ straight lines without lifting the pencil from the paper.
• The Six-Matchstick Problem: Arrange $6$ matchsticks of equal length to create exactly $4$ equilateral triangles, where each side of the triangles is exactly one matchstick long.
• Anagram Problem: Deciphering the scrambled letters "ce_bi" to find the word involves deciding whether to use a systematic algorithm or a heuristic shortcut.

Obstacles to Effective Problem-Solving

• Mental Sets: A tendency to perceive and approach problems in specific, habitual ways based on past experience.
• Functional Fixedness: The tendency to assign a single, fixed function to an object that we have learned to use in one particular way, preventing us from seeing alternative uses.
• Belief Perseverance: Clinging to one's initial conceptions even after the evidence or basis on which those conceptions were formed has been thoroughly discredited.
• Overconfidence: The tendency to overestimate the accuracy of our personal beliefs and judgments.

Five General Heuristics for Problem-Solving

• Trial and Error: Systematically eliminating possible solutions one by one until the correct one is found.     * Constraint: This is only useful if the number of possible solutions is limited.     * Example: Trying every key on a keychain to find which one unlocks a specific garage door.
• Hill Climbing: Starting with the given information (the "base of the hill") and moving steadily toward the solution (the "peak") without ever moving backward.     * Example: Taking a multiple-choice test by answering from memory first, then crossing off incorrect answers, and finally making an intelligent guess.
• Subgoals: Breaking a complex, complicated problem into smaller, more manageable pieces.     * Example: Writing a $10$-page term paper by breaking it into steps: introduction, position description, providing evidence, drawing conclusions, and bibliography.     * Sample Problem: Transporting $3$ Hobbits and $3$ Orcs across a river in a boat that holds only $2$ creatures, ensuring Orcs never outnumber Hobbits on either bank.
• Means-End Analysis: A combination of hill climbing and subgoals.     * The solver periodically evaluates if the chosen means are actually moving them closer to the desired end goal.     * Example: Driving toward a landmark without specific directions; the driver may start one course but change direction if they realize they aren't getting closer.
• Working Backward: Starting from the desired goal and working back to the conditions that lead to it.     * Example 1: Buying clothes on a budget by starting with a fixed amount of cash (e.g., a $100$ dollar bill) rather than a credit card.     * Example 2: Detectives solving a crime by starting at the crime scene and tracing the steps of the criminal backward.

Language and Communication

• Human Language: A flexible system of symbols that enables humans to communicate ideas, thoughts, and feelings.
• Animal vs. Human Communication:     * Nonhuman (Animal): Communication occurs primarily through signs, which are global statements about the animal's current state (e.g., alarm, distress, hostility). Animals typically do not signal the cause of their state.     * Human: Language is semantic, meaning it is meaningful. Humans exchange detailed info regarding objects, feelings, and ideas, including abstract concepts that exist only in the imagination.
• Noam Chomsky’s Theory: In $1957$, the linguist Noam Chomsky argued that human babies are born with an innate capacity to learn language. He proposed an unspecified biological structure called the Language Acquisition Device (LAD) that permits this learning.

Developmental Stages of Language in Children

• At Birth: Communication is primarily through crying.
• 2 Months: Infants begin to "coo."
• 4 to 6 Months: Babbling begins; infants soon incorporate intonation into their babbles.
• 1 Year: Children enter the "one-word stage."     * Holophrases: Single-word sentences used to convey complex meanings, often naming objects.
• 2 Years: Children start using possessive words and forming sentences of $2$ or $3$ words.     * Telegraphic Stage: Speech that omits verb endings and auxiliary verbs (e.g., "Daddy go").
• 3 Years: Children have grasped basic language rules, and their sentences become more structurally complete.
• 5 Years: Vocabulary is greatly expanded. Children construct sentences that are $6$ to $8$ words long. Sentence structure is complex, conversational skills improve, and the foundations of adult language are established.
• Critical Period: A specific window of time in which a child must be exposed to language for language learning to proceed normally.

The Structure of Language

• Phonemes: The basic units of spoken language that indicate a change in meaning.     * The English language contains approximately $45$ phonemes.     * Example: The different starting consonants in the words "dog," "fog," and "log."
• Morphemes: The smallest units of meaning within a language. These include small words as well as prefixes and suffixes.
• Grammar: The overarching system of rules for combining phonemes, morphemes, words, and sentences to communicate.
• Syntax: A subgroup of grammar that specifically governs the rules for how words are combined to form correct sentences.     * Example of Poor Syntax: "Hit Sally car the."