Communications of the ACM

transformers were a new focal phenomenon covered by no other field. They also argued that “algorithmic thinking”—a process of designing a series of machine instructions to drive a computational solution to a problem—distinguishes computer science from other fields.

In 1974, Donald Knuth said that expressing an algorithm is a form of teaching (to a dumb machine) that leads to a deep understanding of a problem; learning an algorithmic approach aids in understanding concepts of all kinds in many fields.

In 1979, Edsger Dijkstra wrote about the computational habits of mind he learned to help him program well: 9 separation of concerns; effective use of abstraction; design and use of notations tailored to one’s manipulative needs; and avoiding combinatorially exploding case analyses.

Seymour Papert may have been the first to use the term computational thinking in 1980, when in his book Mindstorms he described a mental skill children develop from practicing programming. 24, 25

In 1982, Ken Wilson received a No-
bel prize in physics for developing
computational models that produced
startling new discoveries about phase
changes in materials. He went on a
campaign to win recognition and re-
spect for computational science. He ar-
gued that all scientific disciplines had
very tough problems—“grand chal-
lenges”—that would yield to massive
computation. 33 He and other vision-
aries used the term “computational
science” for the emerging branches
of science that used computation as
their primary method. They saw com-
putation as a new paradigm of sci-
ence, complementing the traditional
paradigms of theory and experiment.
Some of them used the term “com-
putational thinking” for the thought
processes in doing computational
science—designing, testing, and us-
ing computational models to make
discoveries and advance science. They
launched a political movement to se-
cure funding for computational sci-
ence research, culminating in the High
Performance Communication and
Computing (HPCC) Act passed in 1991
by the U.S. Congress. Computer scien-
tists were slow to join the movement,
The current surge of interest in
computational thinking began in
2006 under the leadership of Jean-
nette Wing.35–37 While an NSF assis-
tant director for CISE, she catalyzed
a discussion around computational
thinking and mobilized resources to
bring it into K– 12 schools. Although
I supported the goal of bringing com-
puter science to more schools, I took
issue with the claim of some enthusi-
asts that computational thinking was
a new way to define computing. 7 The
formulations of computational think-
ing at the time emphasized extensions
of object-oriented thinking to soft-
ware development and simulation—a
narrow view the field. Moreover, the
term had been so widely used in sci-
ence and mathematics that it no lon-
ger described something unique to the
computing field.

In 2011, on the eve of Alan Turing’s
100th birthday, Al Aho wrote a signifi-
cant essay on the meaning of compu-
tational thinking2 for a symposium
on computation in ACM Ubiquity. 5 He
said: “Abstractions called computation-
al models are at the heart of computa-
tion and computational thinking. Com-
putation is a process that is defined in
terms of an underlying model of com-
putation and computational thinking
is the thought processes involved in for-
mulating problems so their solutions
can be represented as computational
steps and algorithms.” 2, a
a Aho’s definition Aho’s definition was noted by
Wing in 201035 and is used as the definition of
computational thinking by K12cs.org.

Aho emphasized at great length the importance of computational models. When we design an algorithm we are designing a way to control any machine that implements the model, in order that the machine produces a desired effect in the world. Early examples of models for computational machines were Turing machines, neural networks, and logic reduction machines, and, recently, deep earning neural networks for artificial intelligence and data analytics. However, computational models are found in all fields. The Wilson renormalization model is an example in physics, the Born-Oppenheimer approximation is an example in chemistry, and the CRISPR model is an example from biology. Aho says further, “[With new prob-lems], we discover that we do not always have the appropriate models to devise solutions. In these cases, computational thinking becomes a research activity that includes inventing appropriate new models of computation.” 2

As an example, Aho points out that in computational biology there is a big effort to find computational models for the behavior of cells and their DNA. The search for computational models pervades all of computational science. Aho’s insight that computational thinking relies on computational models is very important and has been missed by many proponents.

Aho’s term computational model is not insular to computer science—it refers to any model in any field that represents or simulates computation. I noted several examples above. Moreover, his definition captures the spirit of computational thinking expressed over 60 years of computer science and 30 years of computational science.b It also captures the spirit of computational thinking in other fields such as humanities, law, and medicine.

This short survey of history reveals two major sources of ambiguity in the post-2006 definitions of computational thinking. One is the absence of any mention of computational models. This is a mistake: we engage with abstraction, decomposition, data repre- b I was an active researcher in the computational sciences field during the 1980s and 1990s and can attest that his definition captures what the computational scientists of the day said they were doing.