Computational and Critical Thinking Main Message Thinking like

Computational and Critical Thinking

Main Message “Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction. ” - Dr. Jeannette Wing

Computational Thinking A relatively new idea o First put forth by Dr. Jeannette Wing, Carnegie Mellon University (CMU) in 2006 o o http: //www. cs. cmu. edu/afs/cs/usr/wing/www/publi cations/Wing 06. pdf o Developed since then through presentations, workshops and other communication

Computational Thinking – for whom? q Not just computer scientists! q Dr. Wing sees this as important for q children as well as university students q everyone as well as computer scientists q Implication: we have to think about what CS material we teach K-12 as well as what is taught at the university level

Computational Thinking – about what? About people, not computers Trying to package what we, as humans, do based on what we’ve learned from 50+ years of computer science work Supplements other analytical forms of thinking (mathematical, engineering, scientific? )

Computational Thinking – involves what? q At a high level q Problem solving q Designing models, systems and solutions q Critical thinking about computational issues q More later about Critical Thinking q Understanding human behavior in regard to computing q Another place where general education matters! q Note that programming is part of this, but is certainly not the whole package

Computational Thinking – involves what? At a detailed level ◦ Abstraction – different levels of organization of concepts Example: data type and instance variable ◦ Algorithms – Decomposing a problem into sequential (and parallel) steps E. g. , sequence for a basic web request through the HTTP protocol ◦ Modeling – related to abstraction, the ability to build a representative model for a system or situation E. g. , a program to simulate the Davies Center food court

Computational Thinking – involves what? More detailed level items: ◦ Recursion – a process can be defined in terms of or “call” (programmatically) itself Example: factorial can be defined in terms of itself (how? ) ◦ Data vs. Code issue – recognizing the blurred line (and advantages and disadvantages) between represented information and represented processing E. g. , One byte can be a character, integer, part of a floating point number, or part of an instruction ◦ Planning, Searching, Scheduling, Learning, Dealing with Uncertainty E. g. , Autonomous vehicle programming

Computational Thinking – involves what? More detailed level items: ◦ Evaluating and Accomplishing Efficiency E. g. , Linear vs. Exponential time algorithms ◦ Prevention/Detection/Recovery from worst-case scenarios E. g. , Computer security ◦ Parallel Processing – activities that don’t rely on each other can be accomplished concurrently E. g. , checking values in an array to find some value ◦ Planning For Failure – building fault tolerance into systems E. g. , use of exception handling in Java, C++ to catch incorrectly formatted input

Computational Thinking – involves what? More detailed level items: ◦ Heuristic Reasoning – developing approximation functions to represent best guess and move toward solution E. g. , evaluating the quality of a position in tic-tac-toe by counting pieces plus adding value for owning certain positions (e. g. , center) ◦ Redefining Problems – e. g. , re-structuring problems by use of “reduction, embedding, transformation, or simulation” (or emulation) E. g. , modeling new hardware chips by building a software emulation of that chip before actually manufacturing it

Computational Thinking q Computational thinking is more about: q Developing conceptual skill - than just programming q Judgment and analysis - than rote application of rules q Developing ideas and concepts for problem solving - than focusing on the artifacts that those processes create q Building “virtual” systems - than just physical ones – though physical systems are a part of an overall computational system

What is Critical Thinking? Critical Thinking is the general term given to a wide range of cognitive and intellectual skills needed to: Effectively identify, analyze, and evaluate arguments. Discover and overcome personal prejudices and biases. Formulate and present convincing reasons in support of conclusions. Make reasonable, intelligent decisions about what to believe and what to do.

What is Critical Thinking? Reasoning Analyzing CRITICAL THINKING SKILLS Decision Making Evaluating Problem Solving

Universal Intellectual Standards The most significant critical (intellectual) thinking standards: Clarity Accuracy Precision Relevance Depth Breadth Logic Fairness

Clarity Could you elaborate further on that point? Could you express that point in another way? Could you give me an illustration? Could you give me an example? Clarity is the gateway standard Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Clarity Give several examples of places in the areas of computer science that we’ve discussed or that you know about where clarity could be an issue.

Accuracy q Is that really true? q How could we check that? q How could we find out if that is true? This chicken weighs over 300 pounds. A statement can be clear but not accurate Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Accuracy Think of a statement you heard recently that was clear but inaccurate.

Precision Could you give more details? Could you be more specific? Yao Ming is TALL! A statement can be both clear and accurate, but not precise Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Precision Identify a situation in which the details and specifics were important. Then identify the negative consequences that resulted because you didn’t get the details you needed to think well in the situation.

Relevance How is that connected to the question? How does that bear on the issue? I studied hard all semester, therefore I should get A+. A statement can be clear, accurate, and precise, but not relevant to the question at issue. Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Relevance Can you identify circumstances in which people tend to introduce irrelevant considerations into a discussion?

Depth How does your answer address the complexities in the question? How are you taking into account the problems in the question? Is that dealing with the most significant factors? A statement can be clear, accurate, precise, and relevant, but superficial. Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Depth Identify a problem you have experienced lately where the solution presented to the problem was superficial in nature. If decisions were based on this surface thinking, what were the consequences that followed from the decision?

Breadth Do we need to consider another point of view? Is there another way to look at this question? What would this look like from another standpoint? What would this look like from the point of view of. . . ? Headache!!! A line of reasoning may be clear, accurate, precise, relevant, and deep, but lack breadth. Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Breadth Consider the question, “Is abortion morally justified? ” Some argue yes, others argue no. Try to state and elaborate on each of these points of view in detail. Try to present each point of view in such a way that a person who actually takes that position would assess it as accurate.

Logic Does this really make sense? Does that follow from what you said? How does that follow? But before you implied X and now you are saying “not X”; how can both be true? Need to know the rules of logic. All professors are human. I am a human. Therefore, I am a professor. When the combination of thoughts are mutually supporting and make sense in combination, the thinking is "logical. “ Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Logic Remember a time when decisions at work or home seemed to be based on illogical thinking. What was the thinking in the situation that you consider to be illogical?

Fairness Critical thinking demands that our thinking be fair. Open-minded Impartial Free of distorting biases and preconceptions Fair-mindedness is an essential attribute of a Critical Thinker. Source: http: //www. fctl. ucf. edu/tresources/content/Ruland-Critical. Thinking. Standards. pdf

Fairness Think of a situation in the last several weeks where you were not fair. Try to look for situations where your behavior was selfish or self-serving and as a result, you negated another person’s desires or rights.

Practice Identify the Universal Intellectual Standards not followed in this statement. • Since we have never been visited by extraterrestrials, and have had no communication from outer space, we can safely assume that intelligent life exists only on our own planet.

Practice Identify the Universal Intellectual Standards not followed in this statement. • It is pretty obvious that smoking marijuana causes people to crave more potent drugs, like cocaine and heroin. Statistics show that almost all the people who become addicted to drugs smoked marijuana before they began using more potent drugs.

Practice Identify the Universal Intellectual Standards not followed in this statement. • The increase in violence by adolescent gangs in this country is just another result of the liberal thinking that has more sympathy for criminals than for their victims.

Practice Identify the Universal Intellectual Standards not followed in this statement. • Why are the people in this class so much better looking and intelligent than people in other introductory classes?

Practice Identify the Universal Intellectual Standards not followed in this statement. • A mother was trying to dissuade her son from marrying a girl he had met just three weeks before. The son’s response was “But I know she’s the one; the first time I saw her I began to tremble and see spots before my eyes, and I had flutters in my chest and strange sensations in my stomach. When I’m with her, I feel like I could just take off and fly. ”

Practice q Identify the Universal Intellectual Standards not followed in this statement. q I looked at several issues of the Journal of Parapsychology, a periodical that publishes research on psychic phenomena. Every article confirmed the existence of ESP, so I don’t understand why most psychologists are skeptical about it.

Barriers to Critical Thinking Five Powerful Barriers to Critical Thinking: Egocentrism Self-centered thinking self-interested thinking self-serving bias Sociocentrism Group-centered thinking Group bias Conformism Unwarranted Assumptions Beliefs that are presumed to be true without adequate evidence or justification Assumption Stereotyping Wishful Thinking Relativistic Thinking Believing that something is true because one wishes it were true. The truth is “just a matter of opinion” Relativism q Subjectivism q Cultural relativism

Critical Thinking Tools 1. Questioning 2. Mindmaps 3. Cognitive Research Trust (Co. RT)

But first, What is a Thinking Tool? A Thinking Tool is an instrument that can help us in using our minds systematically and effectively. With the use of thinking tools, the intended ideas will be arranged more systematically, clearly, and easy to be understood.

Questioning is one approach to motivate others to: Get information q Test understanding q Develop interest q Evaluate the ability of individuals towards understanding certain things. q “A person who asks questions is a person who thinks. ”’ - William Wilen

Questioning - Five Ws and H The Five W’s and H, is an H influential, inspirational and imaginative checklist (often used by journalists) to generate: Data-gathering questions, during the early stages of problem solving when you are gathering data. Idea-provoking questions (e. g. whilst brainstorming). Criteria for evaluating options. What Who Where When Why How 5 Ws H

Questioning - Bloom’s Taxonomy Synthesize Higher-Level Thinking Why? How? Evaluate Analyze Apply Lower-level Thinking Understand Remember What? Who? When? Where?

Questioning – Understand – Seek to select and organize facts and ideas, discovering the relationships between them. What is the main idea of… Retell in your on words what happened. “There are many students who are educated but few who can think out of the box. ” – Pak Lah

Questioning – Apply – Help us take knowledge or concepts learnt in one situation and apply them to other situations. How would you apply the principles of decision making when seeking a job? How do you apply this rule in your daily life?

Questioning – Analyze - To separate the entire process into component parts and understand the relation of these parts to the whole. What are the parts or features of … What evidence can you present to support… Explain the reasons why you think…

Questioning – Evaluate - to make informed judgments and decisions by determining the reliability of things. Do you agree with…? Why or why not? What criteria would you use to assess…

Questioning – Synthesize - to combine ideas and come to a conclusion. What ideas can you add to… What might happen if you combine … with …? What solution would you suggest for…

Questioning – Create - to build on other ideas and develop something new and useful. How and where is what’s been done so far not sufficient to (completely) solve the problem? What might happen if you combine … with …? What new idea can solve the problem? NOTE: this is the core of much research!

Mind Maps A mind map can be defined as a visual presentation of map the ways in which concepts can be related to one concepts another. by Tony Buzan ‘ 84

Mind Mapping • • Mind Maps form of sketching or outlining title or theme in the middle lines expand from center to resemble important ideas smaller branches expand to represent elaboration

Mind Maps

Mind Maps

Mind Maps – Why? It Helps You to: Save time as it uses only keywords (or concepts). time Understand better Increase your ability to remember by utilizing the remember seven principles of Super Memory: ◦ Visualization ◦ ◦ ◦ Association Making Things Outstanding Imagination Color Rhythm Freemind Holism Java program available at http: //freemind. sourceforge. net/wiki/index. php/Download http: //www. topicscape. com/mindmaps/

Mind Maps: When? Mind Maps are useful for: Maps Note taking (listening) taking Oral presentation (speaking) presentation Writing

Mind Maps: Note Taking Maps for Note Taking (Listening) • Tourist stops you on lower campus and asks you • • to explain route to upper campus. What is the first thing that goes through your mind? Mind map represents a map of your thinking Organize material as it makes sense to you Process of examining, sorting, and relating various words, phrases, concepts Make a map when you hear an oral presentation Note in class – can’t capture everything

Mind Maps: Oral Presentation Maps for Oral Presentation (Speaking) • Use mind map to keep your train of thought (cheat sheet) • Organize presentation around explicit mind map

Mind Maps: Writing Maps for Writing • Brainstorming is an important first step to effective writing • Mind maps help organize the disorganized • Resulting mind map can serve as blueprint for the flow of the writing

Mind Maps: How? Step 1: Draw the topic at the centre. Step 2: Add the Sub-Headings. Step 3: For each Sub-Heading, Add the Main Points and Supporting Details. Step 4: Use your Imagination (pictures/images) to make it outstanding and memorable.

Mind Maps Tips The main idea, subject or focus is crystallized in a central image. The main themes radiate from the central image as 'branches'. The branches comprise a key image or key word drawn or printed on its associated line. Topics of lesser importance are represented as 'twigs' of the relevant branch. The branches form a connected nodal structure.

Mind Maps: Example

Mind Maps: Example

Co. RT Thinking Method The essence of the Co. RT (Cognitive Research Trust) Thinking Method is to focus attention directly on different aspects of thinking and to crystallize these aspects into definite concepts and tools that can be used deliberately. It is designed to encourage students to broaden their thinking.

Co. RT Thinking Tools CAF: Consider All Factors FIP: First Important Priorities PMI: Plus, Minus, Interesting (ideas) APC: Alternatives, Possibilities, Choices OPV: Other People's Views AGO: Aims, Goals, Objectives (purpose) C&S: Consequence and Sequel

Consider All Factors Used to look as widely as possible at all the factors involved in a situation. Steps involved: List down all the factors. Consider each factor. What is the appropriate decision to be made? Example: Should the new Davies Center be located in the open green area?

First Important Priorities Choosing from a number of different possibilities and alternatives (e. g. , putting priorities in order). Steps involved: What are the important matters involved? Which is the most important one to be considered? Which one should be given priority? Example: How can we diversify campus?

Plus, Minus, Interesting Examining an idea for good, bad or interesting points, instead of immediate acceptance or rejection. Steps involved: List down all the plus points. List down all the minus points. List down all the interesting points. What is your decision after considering all the factors? Example: Should UWEC require service learning?

Alternatives, Possibilities, Choices Generating new alternatives and choices, instead of feeling confined to the obvious ones. Steps involved What are the other alternatives to overcome the problem? What are the implications incur if every step is taken? What is the best solution? Example Exams should be abolished.

Other People's Views Moving out of one’s own viewpoint to consider the points of view of all others involved in any situation. Steps involved Will this idea influence others? Other’s people opinion on this matter? Is your idea relevant before actions are taken? Example Student should be barred from the campus Internet access if they illegally download music.

Aims, Goals, Objectives Picking out and defining the objectives so as one is clear about his own aims and understanding those of others (Purpose). Steps involved: What is the AGO of the plan? Are the implementations out of the AGO? How do I make sure that the AGO is achieved? Example What is the AGO of a Liberal Arts degree?

Consequence and Sequel Considering the immediate, short (e. g. 1 - 2 years), medium (e. g. 2 - 5 year) and long term (e. g. over 5 years) consequences. Steps involved: What are the long term effects? What are the risks I have to face? To what extent the new plan would bring changes? Example: The future of distance education for computer science courses at UWEC.

3 5 5 4 2 1 3 X (cycle)

Recursive Fibonacci Code int fib(int x) { if (x == 0) return 0; else if (x == 1) return 1; else return fib(x-1)+fib(x-2); } Function call: fib(5)

Divide and Conquer

Branch and Bound Traveling Salesman Problem (TSP) - W. R. Hamilton and Thomas Kirkman Hamiltonian Cycle:

The Königsberg Bridge Problem In the 18 th century, there was a town called Königsberg. There is an island called Kneiphhof, with the two branches of the river Pregel flowing around it. There are 7 bridges--a, b, c, d, e, f, and g--crossing the two branches.

The Königsberg Bridge Problem

The Königsberg Bridge Problem R K O L

Euler Circuit Start at any node, cross a bridge ONCE and return to same node. A graph that has an Euler circuit has properties: # of ODD Vertices Implication (for a connected graph) 0 There is at least one Euler Circuit. 1 THIS IS IMPOSSIBLE! 2 There is no Euler Circuit but at least 1 Euler Path. more than 2 There are no Euler Circuits or Euler Paths.

Euler Path Start at any node, cross every bridge ONCE. An Euler Circuit IS a type of Euler Path but an Euler Path is not necessarily an Euler Circuit. The sum of the degrees of all the vertices of a graph is twice the number of edges. The number of vertices of odd degree must be even.