computational thinking is informational thinking

Computational Thinking is Informational Thinking

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Computational Thinking is

Informational ThinkingGreg Michaelson

School of Mathematical & Computer SciencesHeriot-Watt University

[email protected]://www.macs.hw.ac.uk/~greg

21/11/2012

mailto:[email protected]


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Models

• we make models of the world to:– understand it– change it in predictable

ways

Columbus Globeshttp://www.maps2anywhere.com/Globes/columbus_world_globes_01.htm

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Programs and models

• a program:– maps the abstractions of

a conceptual model

model

world brain

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Programs and models


a conceptual model – onto the concrete

behaviours of a physical computer

model

program

world brain

computer

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http://openclipart.org/detail/34531/tango-computer-by-warszawianka


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Programs and models


a conceptual model – onto the concrete

behaviours of a physical computer

– so the behaviour of the program on the computer tells us about the world

• computing

model

programprediction

world brain

computer

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http://openclipart.org/detail/34531/tango-computer-by-warszawianka


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How do we...?

• make models?– solve problems

• realise models as programs?– write programs– programming

Then a miracle occurs...http://www.sciencecartoonsplus.com/pages/gallery.php

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Discourse & method

• should we separate out:– problem solving– model making– programming?

• are they inextricably linked?

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Discourse & method

• we need languages/notations to:– solve problems– make models– write programs

• should these be the same or different?

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Computing Science?

• academic discipline• underpins all ICT– model making– tool building

• theory & practice of computation– making models of reality from information structures

& algorithms– animating models on computers

• programming bridges models and computers21/11/2012


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Computing Science?

• is programming the “new Latin”?

• should we teach all students to program?

Observer 1/4/1221/11/2012


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Computing Science?

• NO!• we need to teach all

students to think:– first characterise

problem– then choose technology

• how to characterise problems? THINK!

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Computational thinking

• modern approach to problem solving

• draws heavily on insights from Computing Science

• very widely applicable• not about programming

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http://chomskyscolorlessgreenideas.blogspot.co.uk/

2009/09/chinese-room.html


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Computing triangle

ICT Computing Science

Computational Thinking

social needs

tools

problemssolutions

praxis

concepts

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• homage to:– N. Wirth, Algorithms + Data Structures = Programs,

Prentice-Hall, 1973• information + computations = solutions– how do we know when the problem is solved?– what information is relevant to solving the problem?– how must the information change for the problem to be

solved?– what computation(s) should we perform on the

information to reach the solution?

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• hardest part is characterising the problem• two standard approaches:– ask someone else...– look for a similar problem you already know how to

solve• what makes problems similar?– similar information + computations

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• four core techniques;– decomposition– pattern recognition– pattern generalisation/abstraction– algorithm design

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Decomposition

• identify the information needed to solve problem

• break the problem up into smaller sub-problems

• identify the sub-information needed to solve sub-problems http://www.lostateminor.com/2012/03/14/if-stonehenge-came-with-ikea-

instructions/

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Pattern recognition• look for patterns amongst problems

– have I seen a problem like this before?– how is this problem different?

• look for patterns in the information– how is the information structured?– are there useful relationships within the

information?– have I seem information organised like

this before?– how is this information different?

http://www.moneymatterstome.co.uk/interactive-workshops/writingcheque.htm

http://en.wikipedia.org/wiki/Bank_statement

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Pattern generalisation/abstraction

• what is the general case for my problem?– what doesn’t change in how sub-

problems are organised?– what does change?

• what is the general organisation of the information?– what doesn’t change in structure?– what information does change?

http://www.learndirect.co.uk/campaigns/worth-learning/managing-money/understanding-bank-statement/

http://en.wikipedia.org/wiki/Bank_statement

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Algorithm design

• what is the sequence of steps from the initial information to the problem being solved?

• how are sub-problems connected?

• how does the information change between steps? Mug design – Le Chat Noir Boutique

http://www.lechatnoirboutique.com/proddetail.php?prod=FSFPTS

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Applying computational thinking

• what does this mean for practical teaching?

• where to begin?• are familiar approaches

useful?• can we retrofit

computational thinking to what we do already...?

An armillary sphere and discussion by R. W. Seale, in A New Geographical Dictionary,"

published by J. Coote, London, 1760 *http://www.columbia.edu/itc/mealac/pritchett/00routesdata/17

00_1799/compendia/coote/sphere.jpg21/11/2012


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Current approaches

• programming language oriented– full strength language– pedagogic or full strength subset– functional/logic – object oriented– pseudo code – language independent

• simple to complex– stepwise refinement– structured programming– iterative prototyping

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Current approaches

• components– modular programming– algorithms– data structures– types– classes– libraries

• design– flowcharts – data flow– entity relationship – UML

• use case• class diagrams• structure diagrams• sequence diagrams• state machines

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Current approaches

• fashions change• too many possibilities• none work easily beyond simple cases• all have a strong focus on the final program• programming not hard when you know how to solve

the problem...• ...except for vagaries of specific language syntax &

semantics & tools– get in the way of problem solving & model making

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Forget the past...!

• familiar approaches useful – at end of problem solving to realise solution– with more advanced classes when basic

computational concepts understood• need to focus on problem without worrying about

how to implement solution• key is to characterise information & computations• start with information, not computations

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Characterising information

• information = base/atomic elements + structure• NB not type, class etc – programming concepts– used to represent/implement problem

information

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• base/atomic elements– things!

• at simplest, represented as symbols– sequences of characters– unitary entities that are meaningful– e.g. words, numbers

• elements may be composite– made up of sub-elements– structured

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• information structures– sequences: before/after, unordered/ordered– tables: rows & columns of contents– arrays: index & contents– record: fields & contents– lists: head & tail values – trees: value & branches – graphs: nodes & arcs

• NB not data structures: programming concept

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• structures have equivalences– table == array of records of row/column contents– array == list of index/value records– list == array of records of head & tail

• for some problems, base elements in structures are themselves structures

• where to begin...?• back to Computing Science...?

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Thinking about information

• start in real world!• look at lots of concrete

examples:– parked cars– numbered houses– supermarket queue– English v Scottish

bank queue– shopping list

– receipt– bill– account statement– itinerary– diary– calendar– invitation list– address book– seating diagram

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– shop catalogue– library catalogue– family tree– cladistic tree– decision tree– underground map– road map– lottery ticket– betting slip

– sports league table– mobile contacts– browser favourites– social media friends– eBook downloads– digital photo album– digital music library– music play list

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• use concrete problem scenarios:• typically, how to find specific information in

structure• start from scratch• try to characterise scenario’s:– elements– structures

• don’t yet introduce named structures• do this intuitively

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• ask if information is:– simple or composite– linear or grid or branching or cyclical– unordered or ordered– fixed or changeable:• content• size• shape

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• ask how to access elements– why do you want to access elements– which elements do you want to access– how does why/which affect access– where to start access– how to continue access– how to know if successful/unsuccessful– what to do if unsuccessful

• then ask how to add/delete/modify elements

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• next, compare apparently disparate structures• ask what:– changes– stays the same

• look for similarities in: – concrete detail– gross structure, ignoring elements– access/update/add/delete

• use comparisons to draw out named structures

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• finally develop notion of abstract data type (ADT)• operations to:– construct new, empty structure– add to structure– find in structure– change contents– delete from structure

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From information to computation

• abstract data type defines base operations– like the verbs of a language

• computations structure these operations into algorithms

• try to make structure of computation follow structure of information

• not yet programming...

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• go back to scenarios• computation solves problems by changing old

information into new information• in the scenario, explore sequences of information

change

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• typically want to:– traverse structure• visit each element once• continue visit until some condition is met

– do something to each element– accumulate intermediate information

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Structure traversal

• bounded iteration– from first to last element– notion of next element

• unbounded iteration– continues while some condition holds

• how to start/continue/end iteration...?

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Structure traversal

• bounded recursion– base case• at end of structure so return final value

– recursion case• do something with current element • recurse on rest of structure

• how to start/end/continue recursion...?

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Accumulate information

• need to keep track of intermediate stages in computation– different positions in structure– partial results from computations

• variable– general name/value association– change association with new value from

computation, often using old value• use variable to manage stages of traversal...

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Do something to element

• change element• how to identify element?– position in structure associated with a value– position often found via structure name– position is like a compound variable

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How to decide what to do

• often want to change element regardless of its properties

• may only want to change element if it satisfies certain criteria– choice/condition

• may want to change what to do next depending on element properties

• use choice to manage stages of traversal...

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Characterising the computation

• finally explore if computation is necessarily:– iterative, or could it be recursive?– sequential, or could it be concurrent?– linear, or could it be backtracking?– deterministic, could it be non-deterministic?– bounded, or could it be unbounded?

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But...

• need to describe information and computation in a consistent manner

• so why not just use a programming language?– programming is motivating– seeing things work early on is motivating

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But...

• so, use practical programming alongside problem solving!

• but...– choice of language affects what can be described– programming language fine detail gets in way of

fundamental concepts– simple small scale intuitive techniques don’t scale to

realistic problems• for problem solving, use a neutral notation

– e.g. pseudo code

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Conclusions

• focus on problem solving not programming• CT = decomposition + abstraction + patterns +

algorithms• solution = information + computation• let information structure the computation• start with concrete instances• use CT to:

– ask good questions– find well kent information structures– guide computation design

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Conclusions

• CT is a framework not a recipe• CT components overlap and

interact• maybe classic CT over-

emphasises computation at expense of information?

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http://affordablehousinginstitute.org/blogs/us/page/251


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Activity

1. choose two very different scenarios from the following list:– parked cars– numbered houses– supermarket queue– English v Scottish bank

queue– shopping list– receipt

– bill– account statement– itinerary– diary– calendar– invitation list– address book– seating diagram– shop catalogue

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Activity

– library catalogue– family tree– cladistic tree– decision tree– underground map– road map– lottery ticket– betting slip

– sports league table– mobile contacts– browser favourites– social media friends– eBook downloads– digital photo album– digital music library– music play list

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Activity

2. choose one information structure from the following list:• sequence: before/after,

unordered/ordered• table: rows & columns of

contents• array: index & contents• record: fields & contents• list: head & tail values • tree: value & branches • graph: nodes & arcs

3. explain how to represent both scenarios from 1. using the information structure from 2.

This is well suited for use as an activity for a pair of people.

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Resources

Jeanette Wing, `Computational Thinking’, Communications of the ACM, Vol 49, No. 3, pp 33-35, March 2006

http://www.cs.cmu.edu/~wing/publications/Wing06.pdfGoogle, `Exploring Computational Thinking’http://www.google.com/edu/computational-thinking/Pat Phillips, `Computational Thinking: A Problem

Solving Tool for Every Classroom’ , CSTA/Microsofthttp://education.sdsc.edu/resources/CompThinking.pdf21/11/2012

http://www.cs.cmu.edu/~wing/publications/Wing06.pdf

http://www.cs.cmu.edu/~wing/publications/Wing06.pdf

http://www.google.com/edu/computational-thinking/

http://www.google.com/edu/computational-thinking/

http://education.sdsc.edu/resources/CompThinking.pdf

http://education.sdsc.edu/resources/CompThinking.pdf

computational thinking is informational thinking

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