Computational thinking and thinking about computing

Abstract

Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing.

Full text

Computational thinking and thinking
about computing
BYJEANNETTE M. WING*
Computer Science Department, Carnegie Mellon University,
Pittsburgh, PA 15213, USA
Computational thinking will influence everyone in every field of endeavour. This vision
poses a new educational challenge for our society, especially for our children. In thinking
about computing, we need to be attuned to the three drivers of our field: science,
technology and society. Accelerating technological advances and monumental societal
demands force us to revisit the most basic scientific questions of computing.
Keywords: computational thinking; abstraction; automation; computing;
computable; intelligence
1. Computational thinking
Computational thinking is taking an approach to solving problems, designing
systems and understanding human behaviour that draws on concepts fundamental
to computing
1
(Wing 2006).
Computational thinking is a kind of analytical thinking. It shares with
mathematical thinking in the general ways in which we might approach solving a
problem. It shares with engineering thinking in the general ways in which we
might approach designing and evaluating a large, complex system that operates
within the constraints of the real world. It shares with scientific thinking in the
general ways in which we might approach understanding computability,
intelligence, the mind and human behaviour.
(a)Computing: abstraction and automation
The essence of computational thinking is abstraction. In computing, we abstract
notions beyond the physical dimensions of time and space. Our abstractions are
extremely general because they are symbolic, where numeric abstractions are just a
special case.
In two ways, our abstractions tend to be richer and more complex than those in
the mathematical and physical sciences. First, our abstractions do not necessarily
enjoy the clean, elegant or easily definable algebraic properties of mathematical
Phil. Trans. R. Soc. A (2008) 366, 3717–3725
doi:10.1098/rsta.2008.0118
Published online 31 July 2008
One contribution of 19 to a Discussion Meeting Issue ‘From computers to ubiquitous computing,
by 2020’.
*wing@cs.cmu.edu
1
By ‘computing’ I mean very broadly the field encompassing computer science, computer
engineering, communications, information science and information technology.
3717 This journal is q2008 The Royal Society

abstractions, such as real numbers or sets, of the physical world. For example, a
stack of elements is a common abstract data type used in computing. We would not
think ‘to add’ two stacks as we would two integers. An algorithm is an abstraction
of a step-by-step procedure for taking input and producing some desired output.
What does it mean ‘to interleave’ two algorithms, perhaps for efficient parallel
processing? A programming language is an abstraction of a set of strings each of
which when interpreted effects some computation. What does it mean ‘to combine’
two programming languages? These kinds of combinators are themselves
abstractions that take careful thought, perhaps an entire research agenda, to
define. Second, because our abstractions are ultimately implemented to work
within the constraints of the physical world, we have to worry about edge cases and
failure cases. What happens when the disk is full or the server is not responding?
What happens when a program encounters at run-time an error that should have
been caught at compile time? How do we get a robot to move down a hallway
without bumping into people?
In working with rich abstractions, defining the ‘right’ abstraction is critical.
The abstraction process—deciding what details we need to highlight and what
details we can ignore—underlies computational thinking.
The abstraction process introduces layers. In computing, we work simul-
taneously with at least two, usually more, layers of abstraction: the layer of interest
and the layer below; or the layer of interest and the layer above. Well-defined
interfaces between layers enable us to build large, complex systems. Given the
application programming interface (API) of a software component, a user need not
know the details of the component’s implementation to know how to interact with
it, and an implementer need not know who all the component’s potential users
might be in order to implement it correctly. The layered architecture of the
Internet, in particular the ‘thin waist’ Internet protocol layer, supports both the
incorporation of new computing devices and networking technology at the bottom
and the addition of new, unforeseen applications at the top.
In working with layers of abstraction, we necessarily keep in mind the
relationship between each pair of layers, be it defined via an abstraction function,
a simulation relation, a transformation or a more general kind of mapping. We
use these mappings in showing the observable equivalence between an abstract
state machine and one of its possible refinements, in proving the correctness of an
implementation with respect to a specification and in compiling a program
written in a high-level language to more efficient machine code.
And so the nuts and bolts in computational thinking are defining abstractions,
working with multiple layers of abstraction and understanding the relationships
among the different layers. Abstractions are the ‘mental’ tools of computing.
The power of our ‘mental’ tools is amplified by the power of our ‘metal’ tools.
Computing is the automation of our abstractions. We operate by mechanizing our
abstractions, abstraction layers and their relationships. Mechanization is possible
due to our precise and exacting notations and models. Automation implies the need
for some kind of computer to interpret the abstractions. The most obvious kind
of computer is a machine, i.e. a physical
2
device with processing, storage and
2
The obvious physical devices are the mechanical or electrical of today. I also mean to include the
physical devices of tomorrow, e.g. nano and quantum computers; and even the biological devices of
tomorrow, e.g. organic, DNA and molecular computers, as well (cf. §2a).
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communication capabilities. Yes, a computer could be a machine, but more subtly it
could be a human. Humans process information; humans compute. In other words,
computational thinking does not require a machine. Moreover, when we consider the
combination of a human and a machine as a computer, we can exploit the combined
processing power of a human with that of a machine. For example, humans are still
better than machines at parsing and interpreting images; on the other hand,
machines are much better at executing certain kinds of instructions far more quickly
than humans and processing datasets far larger than a human can handle.
Operationally, computing is concerned with answering ‘How would I get a
computer to solve this problem?’ where the computer could be a machine, a human,
the combination of a machine and a human, or recursively, the combination (e.g. a
network) of such computers. Implicit in answering this question is our identifying
appropriate abstractions and choosing the appropriate kind of computer for the
task. Unfortunately, it is all too easy to answer this question by not thinking very
hard about defining the right abstraction and then choosing a machine with lots of
horsepower to solve the problem using brute force. Computational thinking can
offer more than this simple use of mechanical computers.
(b)Computational thinking everywhere
‘Computational thinking is influencing research in nearly all disciplines, both in
the sciences and the humanities’ (Bundy 2007). Evidence of computational
thinking’s influence on other fields abounds: computational thinking is transform-
ing statistics, where with machine learning the automation of Bayesian methods
and the use of probabilistic graphical models make it possible to identify patterns
and anomalies in voluminous datasets as diverse as astronomical maps, functional
magnetic resonance imaging scans, credit card purchases and grocery store receipts
(e.g. Machine Learning Department 2008). Computational thinking is transforming
biology, first with the shotgun sequencing algorithm accelerating our ability to
sequence the human genome, and now with our abstractions representing dynamic
processes found in nature, from the cell cycle to protein folding (e.g. Fisher &
Henzinger 2007). Computational thinking is transforming economics, spawning a
new field of computational microeconomics, with applications such as advertise-
ment placement, online auctions, reputation services and even finding optimal
donors for n-way kidney exchange (Abraham et al.2007).
In other fields, computational thinking is still at the stage of simple
computational thinking: spending days’ worth of machine cycles to solve
problems. Many sciences and engineering disciplines rely on enormous computer
simulations of mathematical models of physical processes found in nature.
Aerospace relies on being able to simulate an entire aircraft or space mission. The
geosciences dare to want to simulate the Earth, from its inner core to its surface
to the Sun. In the humanities and the arts, digital libraries of books, collections
and artefacts create opportunities through computational methods such as data
mining and data federation to discover new trends, patterns and links in our
understanding and appreciation of humankind.
Looking to the future, deeper computational thinking—through the choice of
cleverer or more sophisticated abstractions—may enable scientists and engineers
to model and analyse their systems on a scale orders of magnitude greater than
they are able to handle today. Through the use of abstraction layers, e.g.
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hierarchical decomposition, we look forward to when we can: model systems at
multiple time scales and at multiple resolutions of the three space dimensions;
model the interactions of these many complex systems to identify conditions for
tipping points and emergent behaviour; increase the number of parameters and
sets of initial conditions in these models; play these models backwards and
forwards in time; and validate these models against ground truth.
Deeper computational thinking will help us not only to model more and more
complex systems, but also to analyse the massive amounts of data we collect and
generate. Through deployment of distributed sensor nets, routine use of
monitoring and surveillance systems, the prevalence of digital cameras on
mobile (cell) phones, digitizing the world’s information, running simulations of
models of complex systems, and so on, we will be collecting and generating more
and more data to analyse. It will be through computational thinking—
abstractions for representing and processing the data—that we will be able to
extract the knowledge buried within or spread throughout the data. There is an
open feedback loop: this knowledge, piquing our curiosity, will lead us to ask new
questions that require collection of more data; and this knowledge will help us to
fine-tune our simulation models, thereby generating even more data.
Vision no. 1. I envision that computational thinking will be instrumental to
new discovery and innovation in all fields of endeavour.
(c)Computational thinking for everyone
If computational thinking will be used everywhere, then it will touch everyone
directly or indirectly. This raises an educational challenge. If computational
thinking is added to the repertoire of thinking abilities, then how and when
should people learn this kind of thinking and how and when should we teach it?
Let us assume that the trend of using computational thinking in research in all
fields is already happening, thereby already influencing the training of graduate
students. Let us further assume that universities have already begun to
incorporate computational thinking in their undergraduate curricula, thereby
recognizing how the next generation will have to be able to think in order to
succeed in modern society. Thus, let us focus this question at the elementary
through high school levels of education. In fact, if we wanted to ensure a common
and solid basis of understanding and applying computational thinking for all,
then this learning should best be done in the early years of childhood.
I pose the following as a challenge to the computer science, learning sciences
and education communities.
Challenge no. 1. What are effective ways of learning (teaching) computational
thinking by (to) children?
This question raises even more fundamental questions:
What are the elemental concepts of computational thinking? Educators in
computing have answered and continue to answer this question by creating
courses, typically for first-year undergraduates, that focus on the principles
of computing rather than just on computer programming skills. As the field of
computing continues to mature, it is worth revisiting this question again, with a
specific focus on earlier years.
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Moreover, it is worth revisiting this question in collaboration with scholars in
learning science and education. For example, what, if any, computational
thinking concepts are as innate to human cognition as is the mathematical
concept of numbers? Human vision is parallel processing. What tasks do we most
naturally do or learn to do in parallel versus sequentially? Children experience
notions of infinity and recursion through mathematics and language; naming and
teaching these fundamental concepts early on in formal learning settings would
provide powerful building blocks for computational thinking.
What would be an effective ordering of concepts in teaching children as their
learning ability progresses over the years? By analogy, we teach numbers to
children in kindergarten (when they are 5 years old), algebra in junior high (12
years old) and calculus in senior high (18 years old). There may be many possible
ways to structure the progression of computational thinking concepts; which is
the most effective for which kind of learner?
How best should we integrate the tool with teaching the concepts? Here and
henceforth, let ‘the tool’ mean the computing machine (a particular ‘metal’ tool
of §1a). Our field of computing is in a unique situation since not only are there
computational concepts to teach but also there is a tool to teach. This tool
provides some challenges and opportunities.
One challenge is that we do not want the tool to get in the way of
understanding the concepts. We also do not want people just to be able to use the
tool but not have learned the concepts (a case in point: using a calculator versus
understanding arithmetic). Worse, we do not want people to come away thinking
they understand the concepts because they are adept at using the tool. A second
challenge is that we want to track the learning of how to use the tool with the
order of learning of concepts. At what point do we introduce each of the powerful
capabilities of a computing machine? At what point do we expose children to the
intricacies of how the machine works? These questions are analogous to choosing
the right abstraction where now the criteria are defined by learning ability.
One opportunity is that we can use the tool to reinforce the concepts we teach.
Computing is cool: it is all about making abstractions come alive! Through
effective visualization and animation, even at early grades we can viscerally show
the difference between a polynomial-time algorithm and an exponential-time one
or show that a tree is a special kind of graph; in later grades through acquiring
programming skills, students can automate their own abstractions. Indeed, this
tool can be useful for reinforcing not just computational thinking concepts but
also concepts in other fields. A second opportunity is that most children today
are facile with the mechanics of using the tool and are not afraid to explore and
play with it. We can take advantage of the routine exposure children have to
computational devices at home and in school today.
Given this last observation, we should also explore informal as well as
formal learning. Learning takes place in many ways and outside the classroom:
children teach each other; learn from parents and family; learn at home, in
museums and in libraries; and learn through hobbies, surfing the Web and
life experiences.
Vision no. 2. I envision that computational thinking will be an integral part of
childhood education.
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Caveat. There are many cultural, economic, political and social barriers in realiz-
ing this vision, especially in countries where the education system is not centrally
controlled. Striving towards this vision could still yield worthwhile benefits.
2. Thinking about computing
The field of computing is driven by scientific questions, technological innovation
and societal demands. I remind us of this point for two reasons. First, in our field,
we are often so swept up by our technological advances or societal expectations
that we forget that there are deep scientific questions that underlie our field.
Second, for others outside of computing, it is important to explain that the
weight of each, and moreover the combination of our three drivers—science,
technology and society—make our field unique, indeed distinctive from other
sciences, mathematics and engineering. Why not celebrate this distinction?
Moreover, as shown by the bidirectional arrows in figure 1, there is wonderful
interplay—push and pull—among these three drivers: in the usual loop, scientific
discovery feeds technological innovation, which feeds new societal applications;
in the reverse direction, new technology inspires new creative societal uses, which
may demand new scientific discovery. An example of how society demands new
science: the spread of our own computing and communications machinery, from
mega-data centres of tens of thousands of servers to billions of mobile phones,
requires new advances in science to use energy more efficiently. An example of
how society demands new technology: the desire for higher fidelity and more
realistic virtual environments is straining our network capability for real-time
simultaneous transmission of multiple multimedia (audio, video and text) data
streams. Another example of technology pull is how a fundamental social desire
to express one’s identity and connect with likeminded others led to the unantici-
pated and rapid rise of social networks, such as Facebook, MySpace and
YouTube, which in turn added a new industry to our economy.
Our field most naturally anticipates technology trends and embraces the
demands and expectations of society, so let us start with the technology drivers,
then societal, and then scientific.
(a)Technology drivers
Beginning at the computing substrate level, we are predicting the end of
Moore’s law within the next 10–15 years (Engadget 2006). The immediate
consequence for silicon-based technology is the production of multi-core
technologyscience
society
Figure 1. Three drivers of computing: science, technology and society.
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architecture machines; the challenge is understanding how to program them to
use their parallel processing capability effectively.
Beyond silicon, we look at nanocomputing, biocomputing and even quantum
computing. In some sense they have already arrived. Nano is here: IBM (2006)
announced that its researchers had built the first complete integrated circuit
around a single carbon nanotube molecule. Bio is here: Adleman (1994) solved
the seven-point Hamiltonian path problem with DNA computing; Benenson et al.
(2004) described in Nature the construction of a DNA computer. We are now
building molecular machines. Quantum is coming? The Swiss (Messmer 2007)
use quantum cryptography to secure ballots in their elections. The design of
nanocomputers and bio-inspired computers must already take into consideration
quantum effects (e.g. Heller et al. 2005).
At the device level, Strukov et al.(2008)announced that they can create a
memristor (Chua 1971), the missing fourth element along with the resistor,
capacitor and inductor. At larger scales, we see a growing use of mobile phones,
radio frequency identification tags, sensors, actuators and robots. Our automobiles
are laced with embedded computers: a BMW is ‘now actually a network of
computers’ (Economist 2007).
In terms of data, we are drowning in data (cf. §1b). Sensors are everywhere,
storage is cheap and we are in a constant state of information overload.
In terms of communication, Web 3.0 or the Semantic Web is an active area of
research. We will see more sophisticated virtual worlds; Second Life is today’s
Mosaic. The scientists and engineers of tomorrow will conduct their work
through virtual organizations, facilitating international collaboration.
In terms of far-reaching technological machines, people aspire to build machines
that model the human brain. The IBM and EPFL’s Blue Brain Project (2005) aims
to create a biologically accurate, functional model of the brain. The start-up
company Numenta (2005) is building a software platform for intelligent computing
modelled after the human neocortex.
These are just a few technology trends of today; it will be interesting to read this
section of this paper in 10 years to see where we were and how far we will have gone.
(b)Societal drivers
The success of our information technology, including computers and communi-
cations, has raised society’s expectations of us. People now demand availability,
24 hours per day, every day, 100 per cent reliability, 100 per cent connectivity,
instantaneous response, the ability to store anything and everything forever, andthe
ability for anyone to access anything from anywhere at any time.
The classes of users of our technology are not limited to scientists and
engineers. Rather, our users are young and old, able and disabled, rich and poor,
literate and illiterate.
Our technology must also support a range in the number of users: from
individual to groups to populations to the global society. Individuals want highly
personalized devices and services; search companies realize this desire by
tracking our queries and personalizing the advertisements we see. Cliques of
friends lead to larger acquaintance networks such as LinkedIn or social networks
such as Facebook. Different populations may use information and networking
technology to preserve their cultural heritage.
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The Internet and the World Wide Web together is a great equalizer. On the other
hand, there remain scientific and technical challenges regarding accountability,
anonymity, identity management and privacy.
Challenge no. 2. How do we make our technology and the wealth of our
applications accessible to all? How do we balance openness with privacy?
(c)Science drivers
Wing (2008) presented five ‘deep questions in computing’, as a way to remind
ourselves that there are scientific challenges that underlie our individual research
pursuits or innovations in technology. I repeat this set (i.e. no ordering implied)
of questions for the sake of completeness in this paper. This set is meant to be a
starting point, with new questions added by the entire community.
— Does P equal NP?
— What is computable?
— What is intelligence?
— What is information?
— (How) can we build complex systems simply?
Closing question. Given (i) the philosophy of §1a, which says that computa-
tional thinking is informed by our desire to automate abstractions, where the
computer can be human and/or machine, and (ii) the technological trends
outlined in §2a, which test the adequacy of Shannon’s information theory and the
Turing machine as the fundamental model of computation, we might even ask
the most basic question of all: what is a computer?
I thank the many people who read my Communications of the ACM March 2006 viewpoint or
heard me speak about computational thinking. The outpouring of support from everyone has been
gratifying. I also thank my colleagues at Carnegie Mellon and Microsoft Research who early on
supported my vision to make computational thinking commonplace, and my colleagues at the
National Science Foundation who have helped sharpen and deepen the ideas behind this vision.
This article was based on work partially supported by the National Science Foundation, while
working at the Foundation. Any opinion, finding and conclusions or recommendations expressed
in this material are those of the author and do not necessarily reflect the views of the National
Science Foundation.
References
Abraham, D., Blum, A. & Sandholm, T. 2007 Clearing algorithms for barter exchange markets:
enabling nationwide kidney exchanges. In Proc. 8th ACM Conf. on Electronic Commerce,
pp. 295–304. New York, NY: Association for Computing Machinery.
Adleman, L. M. 1994 Molecular computation of solutions to combinatorial problems. Science 266,
1021–1024. (doi:10.1126/science.7973651)
Benenson, Y., Gil, B., Ben-Dor, U., Adar, R. & Shapiro, E. 2004 An autonomous molecular
computer for logical control of gene expression. Nature 429, 423–429. (doi:10.1038/nature02551)
Blue Brain Project 2005 See http://bluebrain.epfl.ch/.
Bundy, A. 2007 Computational thinking is pervasive. J. Scient. Pract. Comput. 1, 67–69.
Chua, L. 1971 Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519.
J. M. Wing3724
Phil. Trans. R. Soc. A (2008)

Economist 2007 Quote from R. Achatz, Seimens, from ‘Revving up’. The Economist, 11 October
2007.
Engadget 2006 See http://www.engadget.com/2007/09/19/gordon-moore-predicts-end-to-moores-
law-in-10-years/.
Fisher, J. & Henzinger, T. A. 2007 Executable cell biology. Nat. Biotechnol. 25, 1239–1249. (doi:10.
1038/nbt1356)
Heller, M. J., Sullivan, B. & Dehling, D. 2005 Fabrication of photonic transfer DNA–quantum dot
nanostructures. In Technical Proc. 2005 NSTI Nanotechnology Conference and Trade Show,
vol. 1, ch. 12, pp. 769–772.
IBM 2006 See http://domino.watson.ibm.com/comm/pr.nsf/pages/news.20060324_carbonnano-
tube.html.
Machine Learning Department 2008 Research projects home page, Carnegie Mellon University. See
http://www.ml.cmu.edu/research/index.html.
Messmer, E. 2007 Quantum cryptography to secure ballots in Swiss election. Network World,11
October 2007. See http://www.networkworld.com/news/2007/101007-quantum-cryptography-
secure-ballots.html.
Numenta 2005 See http://www.numenta.com.
Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. 2008 The missing memristor found.
Nature 453, 80–83. (doi:10.1038/nature06932)
Wing, J. M. 2006 Computational thinking. Commun. ACM 49, 33–35.
Wing, J. M. 2008 Five deep questions in computing. Commun. ACM 51, 58–60. (doi:10.1145/
1327452.1327479)
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