viewpoints
VDOI:10.1145/3231587 Enrico Nardelli Viewpoint Do We Really Need Computational Thinking? Considering the expression “computational thinking” as an entry point to understand why the fundamental contribution of computing to science is the shift from solving problems to having problems solved.
CONFESS UPFRONT, the title of this Viewpoint is meant to attract readers’ attention. As a com- puter scientist, I am convinced we need the concept of compu- Itational thinking, interpreted as “being able to think like a computer scientist and being able to apply this competence to every field of human endeavor.” The focus of this Viewpoint is to dis- cuss to what extent we need the expres- sion “computational thinking” (CT). The term was already known through the work of Seymour Papert,13 many com- putational scientists,5 and a recent pa- per15 clarifies both its historical devel- opment and intellectual roots. After the widely cited Communications Viewpoint by Jeannette Wing,19 and thanks to her role at NSF,6 an extensive discussion opened with hundreds of subsequent papers dissecting the expression. There is not yet a commonly agreed definition of CT—what I consider in this View- Wing discussed CT to argue it is im- Forsythe, a former ACM president and point is whether we really need a defini- portant every student is taught “how one of the founding fathers of computer tion and for which goal. a computer scientist thinks,”19 which science education in academia, in 1968 To anticipate the conclusion, we I interpret to mean it is important to wrote: “The most valuable acquisition probably need the expression as an in- teach computer science to every stu- in a scientific or technical education are strument, as a shorthand reference to dent. From this perspective, what is the general-purpose mental tools which a well-structured concept, but it might important is stressing the educational remain serviceable for a lifetime. I rate be dangerous to insist too much on it value of informatics for all students— natural language and mathematics as and to try to precisely characterize it. Wing was in line with what other well- the most important of these tools, and It should serve just as a brief explana- known scientists had said earlier; I computer science as a third.”9 Even if tion of why computer science (or infor- mention several here. both citations are not relative to a school matics, or computing: I will use these Donald Knuth, well known by math- education context, in my view they clearly terms interchangeably) is a novel and ematicians and computer scientists, in support the importance of teaching com- independent scientific subject and to 1974 wrote: “Actually, a person does not puter science in schools to all students. argue for the need of teaching infor- really understand something until he However, the wide popularity gained 10 matics in schools. can teach it to a computer.” George by CT after Wing’s Communications IMAGE BY VALLIA
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Viewpoint risks spoiling the original jor countries. Here, I discuss the three a different way of thinking, called CT” aim. Increasingly, people are consider- most relevant ones. and “learning about programming is a ing CT a new subject, somehow different In England, the national computing way to discover the rudiments of CT.” or distinct from computer science. In programmes of study,a published by the It emerges, from these three ex- the quest to identify the definition that Department of Education in September amples, that CT is not a new subject Wing did not provide, people are stress- 2013 and mandatory since school year to teach and what should be taught in ing one or other aspect (abstraction, 2014–2015, uses CT in the presented school is informatics. recursivity, problem solving, …) and in sense of what one gets by the study and But on the other side, the high num- doing so they obscure its meaning. See practice of computing. In fact, it uses it ber of papers published with CT in their V 2 5 Armoni and Denning for clear and illu- in the opening statement “A high-qual- title or abstract (the ACM Digital Library minating discussions of this issue. ity computing education equips pupils alone contains more than 400) indi- This situation becomes even more to use CT and creativity to understand cates a lot of people seem to argue (and garbled when it comes to education. and change the world” and then just even Wing seemed to agree21) that CT Speaking about teaching CT is a very two more times, in goals for Key Stage is something new and different. Some risky attitude: philosophers, rightly, ask 3 “understand several key algorithms even say “coding” (which they consider what we mean by “teaching thinking”; that reflect CT” and KS4 “develop and different from “programming”) is all mathematicians appropriately observe apply their analytic, problem-solving, you need to learn it! A discussion of that many characteristics of CT (such as design, and CT skills.” The curricu- risks related to this approach and other abstraction, recursivity, problem solv- lum never defines the term. delicate issues regarding CT appeared ing, …) are also proper of mathematics In the U.S., the “Every Student Suc- in a recent Communications column.8 (which they do not call “mathematical ceeds Act” (ESSA), approved by Congress I am convinced that considering thinking”); pedagogues ask how we can in 2015 with bipartisan support, has in- CT as something new and different is be sure CT is really effective in educa- troduced computer science among the misleading: in the long run it will do tion; teachers want to know which are “well rounded educational subjects” more harm than benefit to informatics. the methods and the tools for teaching that needs to be taught in schools “with After all, they do not teach “linguistic this new discipline and how they can the purpose of providing all students thinking” or “mathematical thinking” learn to teach it; and parents are alter- access to an enriched curriculum and in schools and they do not have “body nately happy because it appears school educational experience,” and does not of knowledge” or “assessment meth- has finally started to align itself to the contain at all the term “computational ods” for these subjects. They just teach digital society while they are also con- thinking.” In January 2016, President (and assess competences in) “English”b cerned about what will happen to their Obama launched the initiative “CS and “Mathematics.” Subsequently, the children in the future if they just learn For All” whose goal is “to empower all various linguistic (resp. mathematical) to code with the language of today. American students from kindergarten competences gained by study of Eng- I think a large part of the commu- through high school to learn computer lish (resp. Mathematics), beyond be- nity of computing scientists and edu- science and be equipped with the CT ing used in themselves, find additional cators is convinced the original Com- skills they need …”. Once again, CT is uses in other disciplines. Between CT munications Viewpoint by Wing was what you get when you have learned and computing there exists the same aiming at “start rolling the ball” and computer science. relation. Therefore, we should discuss what needs to be done is teaching in- In France, the Académie des Scienc- what to teach and how to evaluate com- formatics in schools, possibly begin- es—the highest institution represent- petences regarding informatics in pri- ning at an early age. Moreover, I am ing French scientists—published in mary/middle/secondary schools, and convinced the same people are fully May 2013 the report “L’enseignement forget about teaching and evaluating able to understand the meaning of de l’informatique en France. Il est ur- competences in CT. Wing’s expression “to think like a com- gent de ne plus attendre,” (“Teaching In summary, speaking about CT puter scientist” without the need of ex- computer science in France. Tomorrow helps people understand that: we are actly explaining it. Or, if it is absolutely can’t wait.”) recommending—for what focusing on scientific and cultural as- needed, they might agree with the regard the teaching of computer science pects of computing; we are not dealing self-referential sentence “CT is the set (“informatique”)—“teaching should with system and tools, but with principles of mental and cognitive competences start at the primary level, through ex- and methods; we are focusing on the obtained by the study and practice of posure to the notions of computer sci- core scientific concepts of computing, computer science”: the “tacit knowl- ence and algorithms, …
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Modeling a situation and specifying the ways an information-processing agent can Indeed, in looking backward to- effectively operate within it to reach an externally specified (set of) goal(s). ward how computer science was born, it is clear the cultural seeds are in the mathematicians’ quest for automatiz- thought ing theorem proving, in their efforts processes information person to unload the burden of solving prob- or processing lems onto machines. This shift in view- agent machine point, from solving problems to having problems solved is the intellectual birth specifying of informatics and is the “difference modeling effectiveness which makes a difference,”3 setting in- formatics in its own proper and unique place in the context of all sciences. The importance of the “automaton” to give to reach externally full sense to CT was also made explicitc specified goals and emphasized.1,6 I also dare to provide, for the same demonstrative purpose, a more gen- eral explanation of what CT is, which is somehow along a direction already hint- ed at by Wing,16 who clarified: “My in- terpretation of the words ‘problem’ and ‘solution’ is broad. I mean not just math- tary and useful conceptual paradigm to ematician’s answer is: “Let R be the ring ematically well-defined problems whose describe reality.7 of integer matrices; in this ring the sum solutions are completely analyzable, At this point people usually ask which of two principal left ideals is principal, for example, a proof, an algorithm, or a is this “conceptual kernel” and which ex- so let D be such that R A + R B = R D. Then program, but also real-world problems amples can we provide. This is a critical D is the greatest common right divisor whose solutions might be in the form passage to explain to people the novelty of A and B.”10 Clearly unsatisfactory for of large, complex software systems.” of informatics among scientific disci- a computer scientist, for whom a solu- Nevertheless, Wing still used the word plines and its educational value. For this tion is provided by a process computing “problem,” which conveys the meaning purpose, the formulation attributed to the answer and not by an equation defin- of something that needs to be solved. Cuny, Snyder and Wing16 is appropriate: ing the answer. I have intentionally used Since solving a problem is just “CT is the thought processes involved the word “process” instead of the more an instance of a situation where one in formulating problems and their so- usual “algorithm” to stress the fact that wants to reach a specified goal, here is lutions so that the solutions are repre- we have a “process” only when the algo- my formulation: Computational think- sented in a form that can be effectively rithm has been implemented in a suit- ing is the thought processes involved in carried out by an information-process- able “language” and an “automaton” modeling a situation and specifying the ing agent.” This is almost the same def- executes the obtained code. In such a ways an information-processing agent inition given by Aho1 “CT is the thought way three of the main pillars on which can effectively operate within it to reach processes involved in formulating computer science is based—algorithm, an externally specified (set of) goal(s).” problems so their solutions can be rep- language, and machine—are all in- (See the accompanying figure.) resented as computational steps and al- volved in characterizing the difference There are two main differences: one gorithms” and Wing acknowledges the between the viewpoints of the math- is speaking about a situation where the input received by him.20 The big issue, as ematician and the computer scientist. agent operates instead of a problem it Armoni has clearly pointed out,2 is that I therefore think that, whenever has to solve, the other is clarifying the by taking any of these as the definition of either the Cuny, Snyder, and Wing’s agent does not define by itself its overall a new discipline instead of as an expla- formulation or Aho’s one is used for (set of) goal(s) but gets it from the out- nation and trying to fully operationalize this explanatory purpose, the utmost side.d My formulation is also closer to it causes more problems than benefits. stress must be put on the involve- more recent characterizations of com- The issue of explaining in which sense ment of the information processing putation as an unbounded process.18 “the way a computer scientist thinks” agent (that is, the “automaton,” be it a is different from “the way a mathemati- machine or a person acting mechani- c Aho wrote: “An important part of this process cian thinks” is indeed an important one. cally). Without the agent and its capa- is finding appropriate models of computa- Knuth had a brilliant example in his bility to operate effectively, there is no tion with which to formulate the problem and 1974 paper, which, unfortunately, is not informatics, just mathematics, which derive its solutions.” We could say, in a some- at a level laypeople can understand. It indeed has been solving problems for what literary style, “the model is the agent is the model.” regarded the problem of finding the millennia, discovering and applying d If we allowed the agent to choose its own goals, “greatest common right divisor” of two along the way abstraction, decompo- we would leave computing and enter the realm n x n integer matrices A and B. The math- sition, recursion, and so on. of free-will entities.
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We have thus a more general ex- sidering it as a foundational discipline, 14. Polanyi, M. The Tacit Dimension. The University of 4,17 Chicago Press, 1966. planation of what CT is, covering on par with mathematics. 15. Tedre, M. and Denning, P.J. The long quest for also cases that are of high interest for computational thinking. In Proceedings of the 16th Koli Calling Conference on Computing Education Research. schools and education: simulations References (Nov. 2016), 120–129. 1. Aho, A.V. Computation and computational thinking. in other disciplines, where one has 16. The LINK. Research Notebook: Computational Ubiquity, vol.2011, issue January, Article no. 1, Thinking—What and Why?. The Magazine of Carnegie to build and manipulate a visible rep- January 2011. ACM Press. DOI: https://doi.org/ Mellon University’s School of Computer Science, 10.1145/1922681.1922682 resentation of physical laws and/or March 2011; https://bit.ly/2UTeAed 2. Armoni, M. Computer science, computational thinking, 17. Vahrenhold, J. et al. Informatics Education in Europe: natural/social phenomena (that is, to programming, coding: The anomalies of transitivity in Are We All In The Same Boat? ACM/Informatics K–12 computer science education. ACM Inroads 7, 4 Europe, NY, 2017; https://doi.org/10.1145/3106077 model a situation and explore its pos- Dec. 2015), 24–27. 18. van Leeuwen, J. and Wiedermann, J. Computation as sible evolution) rather than to solve 3. Bateson, G. Form, substance and difference. In Steps to an unbounded process. Theoretical Computer Science an Ecology of Mind. University of Chicago Press, 1972. 429, (2012), 202–212. a problem. Simulation is a very pow- 4. Caspersen, M.E. et al. Informatics for All: The 19. Wing, J. Computational thinking, Commun. ACM 49, 3 erful tool to improve understanding Strategy. ACM/Informatics Europe, NY, 2017; (Mar. 2006), 33–35. https://doi.org/10.1145/3185594 20. Wing, J. Computational thinking benefit society. and computing is unique in its capa- 5. Denning, P.J. Computational thinking in science. Social Issues in Computing blog, January 2014; American Scientist 105, (Jan.–Feb. 2017); 13–17. https://bit.ly/2SOnisk bility of making concrete the abstract 6. Denning, P. Remaining trouble spots with 2 21. Wing, J. Computational thinking and thinking about models defined by a simulation. In computational thinking. Commun. ACM 60, 6 (June computing, Philosophical Transactions of The Royal 2017), 33–39. Society A366, 37 (2008): 3717–3725. addition, we have a formulation that 7. Denning, P.J. and Rosenbloom, P.S. Computing: The can be used to explain why mathemat- fourth great domain of science. Commun. ACM 52, 9 ics or other sciences are not enough (Sept. 2009), 27–29. Enrico Nardelli ([email protected]) is a 8. Denning, P.J., Tedre, M., and Yongpradit, P. Full Professor in Informatics in the Department of for these purposes. Misconceptions about computer science. Commun. Mathematics at the University of Rome “Tor Vergata,” ACM 60, 3 (Mar. 2017), 31–33. Italy. He is currently the president of Informatics Europe, In such a way informatics can more 9. Forsythe, G.E. What to do till the computer scientist the association representing the academic and research clearly explain its dual role12 both as a comes. The American Mathematical Monthly 75, (May Informatics community in Europe. 1968), 454–462; https://bit.ly/2S19xXo fundamental scientific subject, with its 10. Knuth, D.E. Computer science and its relation to own independent set of concepts, and mathematics. The American Mathematical Monthly Discussions with Mehdi Jazayeri, Jan van Leeuwen, 81, 4 (Apr. 1974), 323–343; https://bit.ly/2ErRMMU Michael Lodi, Simone Martini, and Guido Proietti have been as a discipline of transversal value, pro- 11. Lodi, M., Martini, S., and Nardelli, E. Abbiamo davvero useful to focus ideas and improve presentation; comments viding methods contributing to a bet- bisogno del pensiero computazionale? Mondo Digitale from referees have also been greatly helpful. Many of the 72 (Nov. 2017), AICA, Milan; https://bit.ly/2CLJcr5 ideas first presented in this Viewpoint have been further 7 ter understanding of other disciplines. 12. Nardelli, E. Informatica nella scuola: disciplina developed by the author in subsequent papers since fondamentale e trasversale, ovvero “di cosa parliamo this material was reviewed, revised, and accepted for This latter role of computing is also of quando parliamo di pensiero computazionale.” publication in early 2017. particular importance for its introduc- Scienze e Ricerche Magazine (Apr. 2017), 36-40; https://bit.ly/2GqszFk tion as a regular subject in schools, and 13. Papert, S. Mindstorms: Children, Computers, and can constitute a solid argument for con- Powerful Ideas. Basic Books, 1980. Copyright held by author.
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