RA 101 Notes: Problem Solving and Frame of Reference
Introduction to RA 101
Course introduces problem solving and practical reasoning.
Uses the scientific method as a pattern for effective thinking.
Aims to investigate both formal and informal aspects of sound thinking.
Course Outline
Designed as an introduction to problem solving.
Teaches students how to solve problems using practical reasoning.
Uses the scientific method as a pattern for effective thinking.
Investigates formal aspects of sound thinking.
Investigates informal aspects of sound thinking.
Goals of this course
Improve thinking skills required for successful problem solving.
Increase the student’s sensitivity to subjective factors that influence decision making strategies.
Integrate these techniques into the individual's decision making process.
The personal point of view
Key elements: Frame of Reference, Values, Self-concept.
Frame of Reference
Definition: The organized body of knowledge, belief, and experience used to interpret and understand new experiences.
Includes all that one believes or knows to be true of the world.
Functions: How we sort the world out; interpret events we experience.
Frame of Reference is not complete
No one's frame of reference is totally complete or accurate.
There are vast gaps in our fund of knowledge.
We all make mistakes.
Frame of Reference: four illustrative limits
Frame of reference limits us in many ways — 4 examples.
Limit 1: Perception
Frame of reference limits perception.
Example: The problem of being tone deaf; training can change perception (e.g., daughter hears Bach concerto differently than the parent).
Limit 2: Diagnosis
Limits our ability to diagnose.
Example: People may miss problems (e.g., noises in a car while driving; doctors' diagnostic limitations).
Limit 3: Interpreting evidence
Frame of Reference limits the ability to interpret or use evidence in solving problems.
Example reference: Sherlock Holmes and determining what constitutes relevant information.
Limit 4: Acquisition of new knowledge
Limits the acquisition of new knowledge; knowledge is required to gain new knowledge (prerequisites).
False information can be worse than no information.
Medicine example: historical errors such as bloodletting or attributing influenza to meteorological events.
Essential to develop a wide, sound frame of reference; liberal education is not about political ideology.
Values
Values form a system that influences judgments and decisions.
Value judgments affect decisions and interplay with emotions.
Ethical judgments: moral judgments, ethical judgments, and value judgments are often treated as synonymous.
Issues arise in pluralistic societies; tension between freedom and security often underpins evaluative disputes.
Self Concept
The mental picture of the kind of person we believe ourselves to be.
Self Concept: contents and effects
Includes beliefs about abilities, talents, strengths, weaknesses, and the role we play in the world.
Can be helpful but may interfere with objectivity.
This is a central concept addressed in the course.
Self Concept - Objectivity
Distinction: Objectivity vs Subjectivity.
The basic difference between subjective and objective perspectives.
Everyday example: math word problems and self-perceived incompetence ("I'm no good at math"); such self-concept can lead to giving up before attempting a solution.
The Personal Perspective
Elements that comprise our personal point of view are limiting factors.
These factors constrain our ability to solve problems.
We tend to approach problem solving from a limited perspective.
Human Perspective
The reality (actuality) of human perspective is relative to viewpoint.
Question: what color is the board I’m facing? Depends on the angle of viewing.
Human Perspective: speed and motion relative to observer
How fast am I moving? The answer is relative to the observer.
To my students, I may appear to be standing still; this is a trick question.
Circumference of the Earth at the equator: about 25,000 miles.
Earth rotates in about 24 hours.
If the observer hovers above the surface without moving, they would see 25,000 miles pass in 24 hours, i.e., about
The Earth also orbits the Sun at about .
Depending on the viewer's location, the apparent speed would change.
These limitations imposed by personal points of view often cause problems in problem solving.
There is a methodology to reduce or eliminate these limitations.
Objectivity - definition
Objectivity: expressing or dealing with facts or conditions as perceived without distortion by personal feelings, prejudices, or interpretations.
Examples of usage: objective art, objective history, objective judgment, and objective test items (limited to fixed alternatives).
Objectivity: how to achieve
Question: How can objectivity be accomplished given our locked personal point of view?
Approach: start with the scientific method; the five phases of problem solving (author adds a sixth phase to be explained next lecture).
Two kinds of thinking (overview)
The material describes two kinds of thinking that are distinct yet interrelated.
These two kinds can be discussed separately but thinking is an organic whole.
The critical and creative aspects
Critical thinking and creative thinking are intertwined and often not easily distinguished in practice.
Question: Am I being creative or am I being critical? This distinction can be blurred in practice.
Critical Thinking
Definition: testing and evaluation of proposed solutions; detailed examination of the elements or structure of something.
Process: a systematic examination and evaluation of data or information; breaking data into components to uncover interrelationships; analysis.
Critical Thinking: classroom reflection
In-class exercise prompts: which activities or personalities are generally associated with critical thinking?
Discussion also asks about potential excesses of critical thinking.
Creative Thinking
Definition: the formation of possible explanations of phenomena or possible solutions to a problem; generating many possible solutions (brainstorming).
Creative Thinking: classroom reflection
Exercise prompts: identify occupations associated with creative thinking; discuss activities or personalities linked to creativity.
Discuss potential excesses of being overly creative.
Effective Thinking
Effective thinking = a combination of both creative and critical thinking.
The methods of modern science rely on both: Create and Criticize are twin watchwords.
The integration of these thinking modes will be covered in the lecture on the scientific method.
Methodological note on phases of problem solving
The course references the standard five phases of problem solving as a framework.
A sixth phase is introduced by the instructor and will be explained in the next lecture.
Introduction to RA 101
This course introduces problem-solving and practical reasoning, using the scientific method as a pattern for effective thinking. It aims to investigate both formal and informal aspects of sound thinking.
Course Outline
Designed as an introduction to problem-solving, this course teaches students how to approach and solve problems using practical reasoning. It leverages the scientific method as a template for effective thinking and investigates both the formal and informal dimensions of sound thinking.
Goals of this course
The primary goals of this course are to improve thinking skills essential for successful problem-solving, increase students' sensitivity to subjective factors that influence decision-making strategies, and ultimately integrate these techniques into one's personal decision-making process.
The personal point of view
The personal point of view is comprised of key elements: Frame of Reference, Values, and Self-concept.
Frame of Reference
Frame of Reference is defined as the organized body of knowledge, belief, and experience utilized to interpret and comprehend new experiences. It encompasses all that an individual believes or knows to be true about the world and functions by helping us sort out the world and interpret the events we experience.
Frame of Reference is not complete
No one's frame of reference is entirely complete or precisely accurate. There are significant gaps in our collective knowledge, and everyone is prone to making mistakes.
Frame of Reference: four illustrative limits
Our frame of reference invariably limits us in numerous ways, and four examples serve to illustrate these constraints.
Limit 1: Perception
The frame of reference limits perception. For instance, consider the problem of being tone-deaf; however, training can alter perception, as seen when a daughter hears a Bach concerto differently than her parent after musical education.
Limit 2: Diagnosis
Our frame of reference limits our ability to diagnose, often causing people to miss problems, such as unusual noises in a car while driving or doctors facing diagnostic limitations in their practice.
Limit 3: Interpreting evidence
The frame of reference limits one's ability to interpret or effectively use evidence in problem-solving. This concept can be exemplified by Sherlock Holmes's challenge in determining what constitutes relevant information.
Limit 4: Acquisition of new knowledge
This limit highlights that obtaining new knowledge often requires existing knowledge, serving as prerequisites. Consequently, false information can be more detrimental than no information at all. Historically, medical errors like bloodletting or attributing influenza to meteorological events demonstrate how a flawed frame of reference can impede the acquisition of sound knowledge. Thus, it is essential to cultivate a broad and robust frame of reference, emphasizing that a liberal education is not synonymous with political ideology.
Values
Values constitute a system that profoundly influences judgments and decisions, as value judgments inherently impact choices and interact with emotions. Ethical, moral, and value judgments are often treated as interchangeable. Issues frequently arise in pluralistic societies, where the tension between freedom and security often underlies evaluative disputes.
Self Concept
Self-concept is the mental picture an individual holds of the kind of person they believe themselves to be.
Self Concept: contents and effects
Self-concept includes beliefs about one's abilities, talents, strengths, weaknesses, and the role one plays in the world. While it can be helpful, it may also interfere with objectivity. This is a central concept addressed within the course.
Self Concept - Objectivity
A critical distinction exists between objectivity and subjectivity, representing the basic difference between subjective and objective perspectives. A common everyday example is encountered with math word problems, where a self-perceived incompetence (e.g., "I'm no good at math") can lead a person to give up before even attempting a solution.
The Personal Perspective
The elements that collectively form our personal point of view are inherent limiting factors, constraining our ability to effectively solve problems. As a result, we tend to approach problem-solving from an inherently limited perspective.
Human Perspective
The reality or actuality of the human perspective is relative to the viewpoint. For instance, the perceived color of a board one is facing depends entirely on the angle of viewing.
Human Perspective: speed and motion relative to observer
The question of how fast one is moving presents an answer relative to the observer. To students, an instructor may appear to be standing still; this is a trick question. Considering the Earth's circumference at the equator is approximately miles and it rotates in about hours, an observer hovering above the surface without moving would witness miles pass in hours, equating to a speed of about . Furthermore, the Earth orbits the Sun at approximately . Depending on the viewer's location, the apparent speed would change significantly. These limitations imposed by personal points of view frequently cause difficulties in problem-solving, yet there is a methodology to reduce or even eliminate these constraints.
Objectivity - definition
Objectivity is defined as expressing or dealing with facts or conditions as perceived without distortion by personal feelings, prejudices, or interpretations. Examples of its usage include objective art, objective history, objective judgment, and objective test items, which are typically limited to fixed alternatives.
Objectivity: how to achieve
Given our inherently locked personal point of view, the question arises: how can objectivity be accomplished? The approach begins with the scientific method, which encompasses five standard phases of problem-solving. The author of this course adds a sixth phase, which will be explained in the next lecture.
Two kinds of thinking (overview)
The course material describes two distinct yet interrelated kinds of thinking. Although these two kinds can be discussed separately, thinking functions as an organic whole.
The critical and creative aspects
Critical thinking and creative thinking are intrinsically intertwined and often difficult to distinguish in practical application. Consequently, the distinction between whether one is being creative or critical can often be blurred in practice.
Critical Thinking
Critical thinking is defined as the testing and evaluation of proposed solutions, involving a detailed examination of the elements or structure of something. It is a systematic examination and evaluation of data or information, breaking data into its components to reveal interrelationships through analysis. In a classroom reflection exercise, prompts often ask which activities or personalities are generally associated with critical thinking, and discussions also delve into the potential excesses of being overly critical.
Creative Thinking
Creative thinking is defined as the formation of possible explanations for phenomena or potential solutions to a problem, essentially generating many possible solutions, akin to brainstorming. During classroom reflections, exercise prompts typically ask students to identify occupations associated with creative thinking and discuss activities or personalities linked to creativity, as well as the potential excesses of being overly creative.
Effective Thinking
Effective thinking is a combination of both creative and critical thinking. The methodologies of modern science rely heavily on both, with "Create and Criticize" serving as twin watchwords. The integration of these thinking modes will be comprehensively covered in the lecture on the scientific method.
Methodological note on phases of problem solving
The course references the standard five phases of problem-solving as its foundational framework. However, a sixth phase is introduced by the instructor, and its details will be elucidated in the subsequent lecture.