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2
Key Points Expressed by
Presenters and Discussants
2.1 PERSPECTIVES ON COMPUTATIONAL
THINKING AND COMPUTATIONAL THINKERS
Workshop participants extended the discussion started at the first
workshop concerning the nature of computational thinking and compu-
tational thinkers. In offering one perspective, Peter Henderson, formerly
chair of the Department of Computer Science and Software Engineering
at Butler University, described computational thinking as generalized
problem solving with constraints. He argued that almost every problem-
solving activity involves computation of some kind. For Henderson, a
toolsmith metaphor is a convenient means for characterizing the elements
of computer science and also computational thinking—computer science
offers sophisticated tools that strengthen problem solving. Henderson
illustrated his point using an example from Thomas the Tank Engine—a
series for preschool students. In one situation, Thomas is pulling two cars,
one red and one green. They are on a track with a siding (connected on
both sides), and the problem is to reverse the order of the two cars. This
problem engages students in using a computational algorithm at a very
early age.
Matthew Stone, a computational linguist at the Rutgers Universi-
ty’s Department of Computer Science and Center for Cognitive Science,
argued that core ideas of computational thinking arise in many domains
independent of computer technology. Stone pointed out the universality
of computational thinking in the context of Jacquard looms that control
the weaving of patterns, algorithmic approaches to choosing the grocery
6
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
checkout line with the shortest wait time, and representation of corre-
spondences between symbols and the physical world such as between
online banking and money.
Robert M. Panoff, founder and executive director of the Shodor Edu -
cation Foundation, Inc., illustrated the generality of computational think -
ing by identifying three fundamental ideas that ground computational
thinking:
• What you have now is what you had before plus what has changed.
That is, Xnew = Xold + change in X.
• I am the average of my neighbors; that is, add up a bunch of num-
bers and divide by the number of numbers. This is the essence of solving
Laplace’s equation.
• When two entities interact with each other, one of the entities
acquires with some probability a property that the other entity already
had. For example, if the two entities are people and the property is a wal -
let, there is some probability of a crime—an example found in criminol -
ogy. If the entities are trees and the property is being on fire, there is some
probability that the tree not on fire will become a tree that is on fire—an
example from forest management. If the entities are particles and the
property is momentum, there is some probability that one particle will
acquire some of the momentum of the other particle—an example often
found in physics.
Ursula Wolz, associate professor of computer science and interactive
multimedia at the College of New Jersey, noted that concepts of com -
putational thinking permeate journalism. The similarities stem from the
reliance of both fields on language. Languages can be natural as found in
journalism or formal as found in computer science. Both formal and infor-
mal languages involve access to information, aggregation of data, and
synthesis of information. Concepts of reliability, privacy, accuracy, and
logical consistency are essential to both formal and informal languages.
Both involve knowledge representation (e.g., determining the appropri -
ate granularity for reporting a story or taking data) and abstraction from
cases.
2.2 ACTIVITIES OF COMPUTATIONAL THINKING
Workshop participants extended the discussion of activities associ -
ated with computational thinking that had been initiated at the first work-
shop. During the second workshop participants focused on educationally
relevant activities.
Robert Tinker, founder of the Concord Consortium, argued that the
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8 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
core of computational thinking is to break big problems into smaller prob-
lems that lend themselves to efficient, automated solutions. This approach
can be implemented using realistic situations as well as visualizations.
Tinker advocated introducing computational thinking in science for sev -
eral reasons. Modern science regularly relies on computational models
that are based on scientific principles and are illustrated using visualiza -
tions. For example, scientists explore visualizations of new proteins or of
new theoretical accounts of tectonic plate movements.
Consulting scientist Walter Allan and outreach education coordina-
tor Jeri Erickson, at ScienceWorks for ME of the Foundation for Blood
Research, echoed this point. They argued that the ability to construct rules
to specify the behavior of an agent is important to computational think -
ing. These rules might implement a scientific principle.
Tinker said that he favors exposing students to computational think -
ing in the context of scientific models and visualizations that depict phe -
nomena in a realistic time sequence. Examples include visualizations of
chemical interactions using software such as Molecular Workbench;1 of
force and motion; and of plate tectonics. Students can interact with these
visualizations, explore their behavior and limitations, and learn about
the science represented in the model. This approach is consistent with
the way scientists learn from visualizations and also resonates with the
ways that scientists explore the natural world using the scientific method.
Mitch Resnick, professor of learning research at the MIT Media Lab,
said that the ability to use computational media to create, build, and
invent solutions to problems is central to computational thinking. He
argued that computational thinkers can express themselves and their
ideas in computational terms. He explained that meaningful expression
requires developing both concepts and capacities. He pointed out that
capacities for design and social cooperation are often neglected in school.
Yet the capacity to design solutions has become more important as the
world has increased in complexity. Students need the capacity to design
solutions to personal problems such as determining energy-efficient home
heating solutions. Students also have to be able to communicate their
designs to others and to benefit from the expertise of multiple partici-
pants. As a result, students need a way to design solutions that are rich
enough to cope with complexity and interactivity in a manner often asso -
ciated with computational expression. And the design environment needs
to support social cooperation in constructing meaningful expressions.
Advances of these kinds are synergistic—computing technology itself
opens up new possibilities for widespread cooperation.
1 The Molecular Workbench is available at “Molecular Workbench,” website, Concord
Consortium, http://mw.concord.org/modeler/index.html. Last accessed February 7, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
Supporting Resnick’s emphasis on social cooperation, Jill Denner—a
developmental psychologist with Education, Training, Research (ETR)
Associates—noted that students program differently in pairs than by
themselves. She found that students in pairs spent more time doing pro-
gramming and housekeeping tasks (e.g., saving and testing their code)
than did individuals working alone. She observed that most students
find programming in pairs highly motivating. When they collaborate stu -
dents need to develop the ability to communicate concepts. Similarly, Idit
Caperton, founder of the World Wide Workshop,2 described the supports
in the Globaloria approach for collaboration and community. Globaloria
participants develop original games and publish them on a community
Wiki. Participants in the Globaloria community—teachers, students, staff,
and teams—all maintain public blogs as design journals, share resources,
and build on the products of their peers.
Danny Edelson, director of the National Geographic Society’s Geo-
Literacy Program, argued that systems thinking is an essential activity of
computational thinking. Edelson drew insight from his work in promot -
ing geo-literacy. He noted that geo-literacy calls for a systems view of the
world—an understanding of the world as a set of interconnected human
social systems and physical environmental systems—and that computa-
tional thinking about complex problems calls for a similar understanding.
Jim Slotta, a professor at the University of Toronto’s Ontario Institute
for Studies in Education, echoed the point that understanding complex
systems requires computational thinking. He mentioned a Web-based
Inquiry Science Environment (WISE)3 unit that uses scientific visualiza-
tions of global climate change to engage students in reasoning about how
their own activities affect the accumulation of carbon dioxide. He noted
that the visualizations were designed by Robert Tinker using NetLogo, a
language created by Uri Wilensky.
2.3 CONTEXTS FOR COMPUTATIONAL THINKING
Most workshop participants echoed the notion articulated in the first
workshop that the power of computational thinking is best realized in
conjunction with some domain-specific content. Thus, to understand the
human genome, individuals need to combine computational thinking and
concepts in genetics. The diversity of possible contexts in which compu -
tational thinking applies illustrates its power. Computational thinking
2 Globaloria is available at “Globaloria,” website, World Wide Workshop, http://www.
worldwideworkshop.org/programs/globaloria. Last accessed February 7, 2011.
3 “Web-based Inquiry Science Environment,” website, University of California, Berkeley,
http://WISE.berkeley.edu. Last accessed February 7, 2011.
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10 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
occurs in a vast array of domains. Developing expertise in computational
thinking involves learning to recognize its application and use across
domains.
2.3.1 Everyday Life
Many participants provided examples of the use of computational
thinking in everyday situations. Troubleshooting devices such as comput-
ers, cell phones, and digital cameras involves knowing how to return to
a known state (typically by turning the device off and restarting) or test
boundary conditions (such as interactions between two applications).
Joyce Malyn-Smith, strategic director of the Workforce and Human
Development Program for the Education Development Center, Inc., noted
that today’s youth carry their technological learning environment con -
tinuously in the form of cell phones, computers, and gaming devices.
Schools are finding ways to engage students in using their devices to
advance learning such as by having them take digital photos for science
projects. After school, students bring their devices to community-based
programs where they can engage in science inquiry and to museums
where they play with exhibits. Taylor Martin, an associate professor of
education at the University of Texas at Austin, supported this point,
arguing that schools and after-school programs can exploit computational
tools such as Facebook.
Lou Gross, at the University of Tennessee and also director of the
National Institute for Mathematical and Biological Synthesis, emphasized
the value of incorporating a computational worldview into the everyday
experiences of students. To illustrate, Gross described an everyday prob-
lem—how to pick a checkout line at a grocery store. Gross asked partici-
pants to generate parameters that might affect one’s decision. Workshop
participants suggested line length, the presence or absence of a bagger,
someone writing a check, the number of items in a person’s cart, and
whether the line is an express line. Gross pointed out that high school
students often include the presence or absence of someone cute in the
checkout line, thus illustrating the point that the criteria for decision mak-
ing depend on the nature of the model involved and its purpose.
2.3.2 Games and Gaming
A number of participants described game playing and game develop-
ment as activities well suited to developing computational thinking. They
stressed the importance of games that involve domain-specific ideas such
as simulations of political situations.
Jill Denner argued that the programming of computer games connects
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11
KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
to computational thinking in several ways. Computer games provide a
context for the modeling of abstractions. For example, students might
program a model of their make-believe world, create variables and new
methods, and think at multiple levels of abstraction. They might consider
how a player will interact with the game or conceptualize the goal of the
game.
Idit Caperton argued that it is possible to learn any subject and to
master complex topics or social issues by creating functional, represen-
tational, educational multimodal computer games in that domain. The
Globaloria environment supports the collaborative development of games
and also provides an opportunity for students to play each others’ games.
For example, Globaloria provides a unit on game design, in which stu-
dents design an original game about a complex topic (science, math,
health, civics) and a social issue that matters to them. Students come up
with an idea, assemble teams, and do research. Another Globaloria unit
focuses on game development: students develop original game concepts,
create prototypes, and produce a complete, playable interactive game.
Each unit contains a structured set of learning topics, and each topic
contains projects and assignments for students to complete. Assignments
scaffold4 students to create critical parts of their own games.
2.3.3 Science
Robert Tinker advocated the use of simple models of physical phe-
nomena such as temperature, light, and force to teach computational
thinking. He described activities in which students use temperature
probes to capture data and use graphing programs to develop a model
to explain their data. A student makes progress by manipulating and
refining the model to reflect increasingly sophisticated understanding of
the scientific concepts. The student learns both about the physics of the
phenomena and about computational thinking.
John Jungck, at Beloit College and also founder of the BioQUEST Cur-
4 According to Susanne P. Lajoie, 2005, “Extending the Scaffolding Metaphor,” Instructional
Science 33:541-557 (https://www.tlu.ee/~kpata/haridustehnoloogiaTLU/scaffoldinglajoie.
pdf; last accessed May 20, 2011). “The term ‘scaffolding’ was used by Jerome Bruner (Wood
et al., 1976) to describe the process in which a child or novice could be assisted to achieve a
task that they may not be able to achieve if unassisted, until they are able to perform the task
on their own. This definition was influenced by Vygotsky’s (1978) conception of the zone
of proximal development which is ‘the distance between the actual developmental level
as determined by independent problem solving and the level of potential development as
determined through problem solving under adult guidance or in collaboration with more
capable peers’ (p. 86). The implication is that individuals have learning potential that can be
reached with scaffolding provided by tutors, parents, teachers, and peers.”
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12 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
riculum Consortium, explained the interconnections between computa -
tional thinking and biology and described activities that engage students
in linking the two. He pointed out that modern biology is essentially
an information science. Today, biological data—environmental data and
genomic data, for example—is multivariate, multidimensional, and mul -
ticausal, and it exists at multiple scales in enormous volume (increasing
at terabytes of data per day). He noted that in BioQUEST,5 students pose
original problems, iteratively apply computational thinking to solve those
problems, and persuade their peers that their solution is useful and valid.
For example, in one activity students pose problems about evolution-
ary similarities among genes. Using powerful databases they can align
multiple sequences of the same gene from different organisms onto one
three-dimensional structure. They iteratively refine their representation
to illustrate evolutionary conservation across organisms. They use their
representation to clarify the comparative biology of sequences in terms of
structure, function, and phylogeny.
Walter Allan and Jeri Erickson described computational thinking in
ecology and environmental science using a modeling approach. Using
simulations to address topics found in the curriculum, they created activi-
ties to help students understand complex systems. For example, their
Runaway Runoff simulation called for students to conduct experiments
on phosphorus pollution using a simulated lake ecosystem.6 This simu-
lation depicts a lake ecosystem, with fish, zooplankton, and algae that
are visible to students as well as bacteria that are invisible to students.
Students conduct experiments to develop a food web for the ecosystem.
They examine the contents of the digestive tracts of the trout and zoo -
plankton to see how changes in phosphorus affect the populations in the
lake and the concentration of dissolved oxygen. They predict the impact
of increasing levels of phosphorus on the different populations of fish
and zooplankton.
Allan and Erickson explained that the activity scaffolds students to
follow a cognitive pattern. This pattern features the same iterative refine -
ment approach described by Jungck. Students start by making a predic -
tion about how a system works. They use a simulation for testing, tinker-
ing, and playing. They record their observations, refine their model of
how the system works, and make further predictions. They summarize
their findings in essays or posters that describe how runoff affects lake
5 BioQUEST Curriculum Consortium is available at “BioQUEST,” website, BioQUEST
Curriculum Consortium, http://bioquest.org/. Last accessed February 7, 2011.
6 A sample student worksheet from the project can be seen at “Runaway Runoff Exercise
1: Who’s Who,” Worksheet, available at http://simbio.com/files/EBME_WSExamples/
RunawayRunoff_WkSh1_example.pdf. Last accessed February 7, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
ecology. These artifacts show that the students learn to make fairly sophis-
ticated models of the lake ecosystem.
Allan and Erickson also described how they implemented this pattern
in the “Program a Bunny” environment. In this environment, the bunny
is an agent that the student programs to find and eat carrots in a field.
The environment is probabilistic, so that carrots are not always located
in the same places in the field. A program for a successful bunny must
account for the randomness in the bunny’s environment. Students can test
different programming strategies in a number of increasingly complex
scenarios and refine their program. The initial “out of the box” solution
is, by design, inadequate for bunny success. Thus, students must learn
to modify the program. Modification of the program initiates a cognitive
cycle similar to that of the Runaway Runoff simulation involving iterative
refinement. The student observes the bunny’s success in finding carrots,
develops a model of how the program works, and then thinks of another
modification that is intended to further improve the bunny’s performance.
Lou Gross illustrated ways to use environmental science as a platform
for computational thinking. Beginning with an aerial image of Wash-
ington, D.C., from Google Earth, students are asked, How would you
describe this image? After listing typical topographic features such as
buildings, roads, and trees, students eventually describe the image by
saying how much of the image is this color or that color, how much is
made up of buildings, how much of roads, and so on. Gross described
these observations as the basis for describing the image as a vector where
the components consist of the fraction of the image that is of each type.
One interpretation of this vector is that it represents a probability distribu-
tion of the landscape for a discrete number of components. Students are
scaffolded to realize that spatial aspects of the image are not included in
the vector description. They explore how some large-scale temporal varia-
tions (such as the growth of cities) could be captured by a time-varying
vector. This activity prepares students to use prepackaged software to
take advantage of computational methods for looking at change across a
landscape, e.g., coupling between an image, a dynamically changing vec-
tor, in this case a bar graph, and then an overall descriptor.
Danny Edelson showed how geography and earth science involve
computational thinking. Edelson described some of the issues that arise
for students learning to understand geographic data:
• Continuous versus discrete data sets. Students learn about the issues
in transforming a map from a continuous representation to a map repre -
sented in discrete pixels or cells. They can articulate all the positive and
negative implications of each representation and learn how the represen -
tation affects the results of their data analysis.
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14 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
• Color representations of temperature. Students explore the implica-
tions of using color to represent temperature on a map. For example,
although it makes physical sense to subtract two temperatures (e.g., Janu-
ary’s temperature from July’s temperature), it does not make much sense
to subtract yellow from red. Color representations on the map cannot be
manipulated in the same way as the underlying physical parameters.
To resolve the paradox, students need to realize that temperature maps
consist of regular arrays of numerical data. They can be transformed into
colors, but their underlying mathematical character is maintained.
• Boolean operations. Boolean operations are key analytic tools for
interpreting maps. Students gain insight into Boolean operations by test -
ing and refining solutions to problems. For example, to analyze geo-
graphic data students might be asked to find counties in the United States
whose African American population exceeds the Caucasian population.
• Spatial relationships as specifications of sets. In working with geo-
graphic data, a student might want to find the intersection of two regions
on a map, where the regions are specified according to some nonspatial
criteria. Managing such operations intellectually calls for thinking about
them as combinations in one sense and as spatial entities in another sense.
• Satisfaction of multiple constraints in problem solving. Students might
be asked to locate a power plant in areas that are both accessible to rail -
road transportation and close to large bodies of water. Students learn how
to use logic tools to locate specific geographic features.
Robert Panoff advocated teaching computational thinking through
computational science, in part because this approach develops metacog -
nitive skills or the ability to monitor understanding of computational
results. Panoff drew on quantitative reasoning and multiscale modeling
to illustrate various anomalies in how people conceptualize quantity.
Examples include:
• Inconsistent and faulty intuitions about numbers. Many people believe
that two-fifths (2/5) is a small number, whereas 40 percent feels like a
large number to them. Panoff noted that one metropolitan police depart-
ment assigned more officers to patrols on Friday and Saturday night
because a careful analysis of the data showed that just under 30 percent
of car break-ins were on either a Friday or a Saturday night. Since 2/7 is
29 percent, the frequency of car break-ins was actually consistent across
weekdays and weekends!
• Representations of numbers in computational media. In principle, the
arithmetic expression given by 355/113 – 101/113 – 101/113 – 101/113 –
52/113 should equal zero. But when the expression is evaluated on most
calculators, a non-zero result is obtained. Because most students realize
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
that “something’s not right” when they are confronted with this expres -
sion, such a realization can be the beginning of a serious exploration of
how numbers are represented in a computer.
• Interpretation of orders of magnitude. Panoff noted that many people
have difficulty recognizing the degree of precision necessary to make
an inference. He illustrated the point by asking what a student needs to
know in order to answer the question, How much bigger is Earth than
Pluto? An obvious way to approach this problem is to perform Internet
searches for the mass of Earth and the mass of Pluto. But an Internet
search for the mass of Earth generates 20 or 30 different values, which
have a spread of several percent. How does one know which value to use
or how to proceed? Here context matters—why is one asking the ques -
tion about relative sizes? If the question relates to how big an object has
to be in order to be a planet, then in the absence of a formal definition
of “planet,” one needs to know only that the ratio MEarth/MPluto is on the
order of a few hundred—and a difference of “several percent” is simply
irrelevant to knowing which value of MEarth to use.
2.3.4 Engineering
Christine Cunningham, vice president at the Museum of Science,
Boston, described engineering as a focus of computational thinking for
elementary education. Echoing discussions from the first computational
thinking workshop, she pointed to intellectual parallels between com -
putational thinking and solving engineering problems. Cunningham
stressed that understanding engineering habits of mind and mental pro-
cesses is an important goal of elementary science. She illustrated how
these habits of mind require important aspects of computational thinking.
Cunningham identified 20 topics that are commonly covered in elemen-
tary science programs, paired each with an engineering specialty, and
illustrated the pairing with a particular technological device or process.
For example, environmental engineering can be introduced using water
filtration devices to help students understand the human impacts on the
water cycle. In another example, a solar cooker can illustrate principles of
energy and connect to sustainable engineering.
2.3.5 Journalism
Ursula Wolz described the use of the language arts and journalism as
a vehicle for exploring computational thinking. She argued that insights
into computational thinking can come from comparing the precision of
computer languages to the challenges of precise communication in jour-
nalism using natural language. Journalism involves principled storytell -
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16 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
ing and information dissemination. Journalism students are constructors
of aggregated content (rather than just consumers). To produce a story,
students must inquire, create, build, invent, iterate on the account, polish,
and publish. Wolz emphasized that students iterate on defining the prob-
lem, researching it, drafting a solution, and testing it. They copy edit and
fact check. In the end, they publish and get more feedback. All of these
same notions arise in other instances of computational thinking.
2.3.6 Abstracting Problem Solving from Specific Contexts
Given the diversity of contexts discussed and even the diversity of
problems within a single context, a number of workshop participants
discussed the use of computational thinking across contexts or topics.
For instance, several noted that individuals were likely to need different
(though overlapping) sets of computational thinking skills. Thus, physi -
cians need to learn how to use visualization tools, as do teachers. Joyce
Mayln-Smith of the Education Development Center suggested that the
computational thinking abilities needed by users of information technol -
ogy tools and applications are different from those needed by producers
or developers of such tools and applications. Consequently, the pedagogi-
cal approaches needed for developing these skills must be suited to the
goal.
Michelle Williams, assistant professor of science education at Michi -
gan State University, made a similar point, arguing for helping students
and their teachers recognize that the computational thinking skills they
use to make sense of representations of scientific knowledge work for
multiple representations. Williams showed how a WISE project can scaf -
fold students to use computational thinking skills as they engage with a
number of computer-based representations. In her project students used
simulations of mitosis to understand phases of cell division, and Punnett
squares to determine the genotypes and phenotypes of different genera -
tions of plants, and they interacted with the Audrey’s Garden animation 7
to make distinctions between inherited and acquired traits.
7 See “Case of Audrey,” website, Exploring Younger Children’s Understanding of Hered -
ity, http://education.msu.edu/research/projects/nsf-heredity/curriculum.html. Last ac-
cessed March 14, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
they are doing integration. Panoff’s philosophy here is to help students
break a big problem into smaller problems and let the computer do the
small parts—a process that helps to empower students. Taylor Martin
argued that educators could see this approach as being a “sneaky” way
to get students to use computational reasoning. Once engaged, students
continue to use computational thinking and even begin to see its applica -
tions across contexts.
As a point of departure for considering learning progressions, Joyce
Malyn-Smith proposed a sequence:
• Grades K-4, to focus on computational thinking literacy, career
awareness, and computational thinking skills for learning. An overarch-
ing theme in this time frame might be the lesson that learning is cumu-
lative—a student can learn more by building on something he or she
already knows.
• Grades 5-8, to continue to address computational thinking literacy
but add career exploration and learning about computational thinking
skills for various careers in science, technology, engineering, and math -
ematics (STEM). This exploratory phase would offer students an oppor-
tunity to test their interest in various careers.
• High school, a final preparatory phase, to prepare students to have
the credentials to be able to keep doors open so that they can move into
computing careers and careers in other STEM fields in which computa-
tional thinking will give them really strong opportunities.
Others, including Panoff, Allan and Erickson, and Denner, proposed
looking at a learning progression for the development of computational
thinking by applying the use-modify-create continuum over and over
again. For example, a student first runs a model to see what happens.
Then she may modify it by moving a slider bar, or two or three slider bars.
And then she may change the number of slider bars. Finally, she writes a
model that calls for the use of slider bars to change parameters. By iterat -
ing on this pattern, the student gains progressively more capabilities in
the area of computational thinking.
Peter Henderson would start with computational thinking activi-
ties involving pattern recognition and naming in pre-K, although for
the first several years, the term would not be introduced explicitly. Only
later would the notion of computational thinking be explored as such. In
this sequence, traditional mathematics, discrete mathematics, and logical
reasoning are taught at all grade levels. This has important implications
for high school, where an advanced placement (AP) course in discrete
mathematics would replace the current AP course in computer science. A
freshman discrete mathematics sequence would be introduced, similar to
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26 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
that currently present for calculus. This approach would allow students
to link mathematics and science following the traditional engineering
educational model. This model emphasizes the connections across the
science and math foundations of the disciplines (e.g., physics, chemistry,
calculus). Clancy pointed out that this approach could also apply in col -
lege course sequences.
2.6 ASSESSMENTS FOR COMPUTATIONAL THINKING
Many workshop participants stressed the importance of student eval-
uation for pedagogical purposes. For example, Christine Cunningham
pointed out that both teachers and students in the Museum of Science’s
Engineering is Elementary project pay much more attention to material
when student understanding of such material will be evaluated. She cau -
tioned that narrow goals for evaluation are counterproductive. Students
and teachers need to appreciate the links among topics, and goals for
courses need to acknowledge these dependencies. If students and teachers
know that an evaluation will involve student knowledge of, for example,
looping, they proceed to learn and teach looping. However, if teachers
and students realize that an evaluation will involve student knowledge
of program design, and knowledge of looping helps students understand
program design, both students and teachers are more likely to connect
looping and program design.
To evaluate the connections and interdependencies in computational
thinking in introductory programming courses, Mike Clancy uses a case
study approach and lab-centric instruction. A case study is a worked-out
solution accompanied by a narrative of how the solution was identi-
fied. The narrative discusses design tradeoffs, evidence for alternatives,
methods for testing the solution, debugging, and other issues such as
optimizing. Students respond to questions that require them to consider
new alternatives, critique design choices, develop test suites, and interpret
results of tests conducted by others.
Lab-centric instruction emphasizes hands-on lab hours supervised
by a teaching assistant rather than lecture and discussion. But because
there is more lab time than in most lecture/discussion courses, the course
has room for a number of embedded assessment activities. Lab instruc-
tors can also monitor most of what the students are doing, and have a
window into much of their thinking and not just their finished work.
Thus lab instructors can notice confusion when it occurs and address it
immediately to provide targeted tutoring. Clancy reported that students
in lab-centric courses are less likely to drop the course, possibly because
their confusions are caught before they become too burdensome.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
2.7 TEACHERS AND COMPUTATIONAL THINKING
Teaching computational thinking requires both knowledge of the dis-
cipline and skill in teaching when students collaborate to solve complex
problems (sometimes referred to as pedagogical content knowledge). John
Jungck argued that the primary challenge for teachers of computational
thinking is placing student interests at the center of problem posing. In
courses where students pose and solve problems teachers lose much of
the control they traditionally have over the learning process and may
become uncomfortable. They need new skills to guide individual learn-
ers. Supporting students engaging in self-directed collaborative processes
requires an ability to diagnose difficulties and give hints rather than sup -
plying solutions. Designing effective assignments is also challenging, but
many programs such as BioQUEST offer excellent options.
Michelle Williams stressed that to be effective, teachers have to under-
stand where students are starting. Further, teachers need to determine
the types of understandings that students must have to be successful and
to design new ideas or computational activities to provoke students to
engage in computational thinking.
Jungck noted that students in some cases may have more techni-
cal skills than their teachers in the area of using computers. Williams
pointed out that teachers often find ways to make individual students
class “experts” on troubleshooting the operating system or accessing
online materials to take advantage of available technical skills. Williams
also noted that teachers need professional development to become pro-
ficient in teaching computational thinking. In her work she found that
teachers followed a learning progression, becoming more proficient over
time in using technology and guiding students with inquiry questions.
Thus teachers of computational thinking may well be called on to assume
new and unfamiliar roles in the classroom and need support to become
proficient in performing these roles.
Cunningham argued for the importance of building on what teachers
know or feel comfortable doing. It is well known that many elementary
school teachers are uncomfortable with science because of their limited
preparation in this area. Cunningham argued that engineering (and pre -
sumably computational thinking) is even more terrifying. To build on
what teachers know, Cunningham and colleagues begin their professional
development by connecting exercises in literacy—an illustrated storybook
for children—with engineering. The story has significant engineering
content, but it is presented as a reading exercise so that teachers can use
established skills to lead their classes. Students receive a very general
introduction to engineering and to some computational thinking concepts
from the book. The book provides context for the hands-on engineering
activities that the kids will be doing in their classes.
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28 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
2.7.1 Professional Development and Other
Needs for Teacher Support
Participants described a number of alternative views concerning
methods and models for professional development. Cunningham sug -
gested starting small. Teachers tend to be more willing to invest a couple
of class periods to experiment with a new concept, rather than an entire
school semester or year. The success of one individual teacher with a
particular concept or topic can catalyze others, as his or her students tell
their friends about an interesting new experience in class. Other teachers
also hear about such a program and often want to try it themselves. These
efforts build grassroots support for change.
Jim Slotta agreed that teachers are more willing to use materials for
a short period to see if their students benefit from a particular approach.
He described the experience of the Technology-Enhanced Learning in
Science (TELS) center, where teachers first used a 1-week unit featuring
visualizations. He also noted that asking teachers to identify the topics
for professional development was effective. Initially teachers asked for
help with the technology. These issues were resolved, and the teachers
then asked for guidance on using inquiry questions. Next teachers asked
for help with using visualizations. Successful professional development
involved making videos of varied teaching practices and conducting a
dialog where teachers discussed the alternatives and identified a set of
best practices.
Jill Denner reported a number of challenges in promoting computa-
tional thinking in middle school. These included mundane issues such as
difficulties with hardware and software and with Internet access, consis-
tent with the comments of Slotta. Taylor Martin emphasized that access
to computers and provision of technical support are important, stressing
that computers are the tool students will use in the workplace. Teaching
computation without them is not really preparing students for the real
world. Many schools lack access to computers or only have productivity
tools like word processing rather than the computational environments
mentioned in the workshop (e.g., WISE, Scratch, or Globaloria).
Several participants emphasized the importance of combining profes-
sional development with solid curricular materials. Because precollege
teachers are often inexperienced with the subject matter of engineering,
teaching materials have to be explicit and clear. Cunningham argued that
when learning objectives drive the experiences embedded in curricular
units, objectives need to be very explicit and specific rather than high-
level and abstract. She argued that learning objectives should also be few
in number and relatively narrow so that a high degree of student success
is possible. She suggested that the materials provide ways of specifically
assessing the scope and extent of student mastery and comprehension.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
Cunningham and colleagues have found that hands-on experiences
are particularly important for young learners. They have fielded many
requests to replace physically manipulative experiences in handling
objects with a click-and-drag interface on the computer that students can
use to connect objects on the screen. But knowledge about the physical
world that teachers take for granted cannot be assumed in students. For
example, students don’t necessarily know that a fuzzy pompom will pick
up pollen better than a smooth marble. In fact, that fact is engineering
knowledge, and it’s “common sense” only if one has real-world experi -
ence with pompoms and marbles.
Experience with the physical world varies across populations.
Cunningham reported that many students, including especially girls and
underrepresented minorities, lack cultural experiences that illustrate the
value of learning about engineering or the benefits of advances in engi -
neering. She and her colleagues use hands-on materials as well as story-
books that bring these ideas to life.
Williams reported on her experience working with precollege teach-
ers. She stressed the importance of engaging teachers in reviewing student
work. She has found it valuable to have teachers use the scoring rubrics
developed by the curriculum designers. She observed that teachers can
make big gains in the sophistication of their teaching by making changes
based on the gaps in their students’ knowledge.
2.7.2 Teachers and Career Awareness
Joyce Malyn-Smith pointed out that teachers can play an important
role in helping students make connections between what they know and
what they are learning. Teachers can encourage students to connect the
new ideas to activities they would like to perform either in the present
or in the future. Teachers can help students understand the connection
between computational thinking and future earning power. Malyn-Smith
said that students often have understanding of details about compu-
tational thinking from their areas of interest but lack the historical and
cultural frameworks for placing such information in context. Teachers
can help students to validate what they know and to understand how it
is important and how it relates to what they are learning in class.
Williams added that instructional materials that connect to personally
relevant problems can help teachers make connections between science
and students’ ideas. Questions such as determining the origin of one’s eye
color or distinguishing among possible ways to reduce the accumulation
of greenhouse gases stimulate exciting conversations between students
and teachers.
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30 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
2.8 LEARNING CONTEXTS AND COMPUTATIONAL THINKING
Workshop participants contrasted formal, informal, and ubiquitous
learning contexts. They noted that computational thinking may fit better
in some contexts than others.
2.8.1 Aligning with Standards
Several presenters stressed the challenges posed by a tightly packed
curriculum that does not necessarily stress abstract thinking skills but
that could provide a framework for integrating curricular content. Cun -
ningham underscored the importance of integrating the new material—in
this case, engineering—with what schools are already teaching. Successful
integration can show how the new material contributes to understanding.
Arguing for new material as a primary focus, however, is not likely to
succeed because of preexisting curriculum demands.
Cunningham noted the importance of articulating how new content
and skills in the Engineering is Elementary project connect to existing
educational standards. Such connections could include, for example, core
concepts of technology such as systems, processes, feedback, controls,
and optimization; the design process as a purposeful method of planning
practical solutions to problems; inclusion in the design process of such
factors as the desired elements and features of a product or system or the
limits that are placed on the design; and the need for troubleshooting.
Paulo Blikstein of Stanford University noted that often typical instruc-
tion is oriented toward declarative knowledge, whereas computational
thinking is oriented toward procedural knowledge. In this view, declara -
tive knowledge provides content (and is essential to particular fields or
careers), whereas computational thinking is most useful for integrating
and building connections in the midst of such knowledge. Those accus-
tomed to thinking primarily in terms of declarative knowledge may find
it difficult to appreciate educational themes oriented toward procedural
knowledge.
Allan and Erikson reported that the development effort for the Eco -
ScienceWorks10 project approached the use of programming instrumen-
tally. Downplaying the use of programming was a response to the devel -
opers’ concern that some teachers might rebel because the Maine learning
standards did not mention programming. They feared that they would
have a hard time justifying spending scarce classroom time on program -
10 EcoScienceWorks is available at “EcoScienceWorks: Exploring and Modeling Ecosystems
Using Information Technology (IT),” website, Foundation for Blood Research, http://www.
fbr.org/swksweb/esw.html. Last accessed March 14, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
ming, even if focusing explicitly on programming might have significant
educational value.
Robert Tinker observed that students involved in a very tightly
packed K-12 curriculum do not have the time to master programming.
His preferred approach is thus to use a programming environment such
as NetLogo11 or AgentSheets12 that allows users to focus on the concepts
represented rather than on the details of programming. Janet Kolodner of
the Georgia Institute of Technology noted that another option is the use of
powerful software suites in which the student can manipulate important
parameters.
Several participants noted that learning about engineering or compu -
tational thinking may meet teacher goals that are not necessarily based
in educational standards but are expected outcomes for students. For
example, Cunningham observed that many elementary school teachers
want to find ways to help their students work together in teams. Persuad-
ing students to work together, to respect each other, and to communicate
what they’re doing is something that many teachers want to accomplish
at the beginning of each year, because learning to work in groups is a
skill elementary teachers are expected to develop in their young pupils.
Educational activities that call for collaboration can often be an important
part of such persuasion.
2.8.2 Out-of-School Computational Thinking
Given the issues relating to introducing computational thinking into
schools, a number of workshop participants pointed to out-of-school
venues as providing significant opportunities for exposure to computa -
tional thinking. In out-of-school venues, students have the time to engage
in complex projects that are needed to nurture computational thinking.
Malyn-Smith noted that learners need opportunities for thoughtful,
reflective engagement with phenomena—not just a “drive-by” experi -
ence. Teachers in Malyn-Smith’s program are encouraged to think broadly
about the knowledge base that students are developing in all of their
activities, not just those provided in program settings. Teachers also
engage in conversations with students about their interests and what they
are learning in other settings, such as in museums, in watching television
and listening to the radio, by playing games, and through what they’re
doing with their friends.
11 NetLogo is available at “NetLogo.com,” website, Northwestern University, http://ccl.
northwestern.edu/netlogo/. Last accessed March 14, 2011.
12 AgentSheets is available at “AgentSheets, Inc.,” website, AgentSheets, Inc., http://
www.agentsheets.com/index.html. Last accessed March 14, 2011.
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32 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
Out-of-school environments can provide curricular flexibility, appro-
priate staff capacity, infrastructure access, and access to effective pro-
grams, Malyn-Smith explained. This is especially valuable in rural areas.
These interrelated challenges have constrained many previous educational
innovations, and computational thinking is no different, she argued. For
example, although nearly every middle school student learns from the
textbook that trees help mitigate pollution, students in an after-school
program can have a chance to go further, using modeling tools to map the
trees in their school yard and to record relevant data on species, health,
growing conditions, and the like.13 Students can use automated models to
calculate the benefits of the trees in terms of pollution removal and runoff
mitigation, and they can model alternative growth scenarios as they either
“plant” new trees, let the existing trees continue to grow, or remove the
trees for expanded parking. Re-running the model leverages the power of
automation to quickly adjust the underlying parameters and see what the
impacts are. This iterative process just doesn’t fit in a curriculum packed
with hundreds of discrete topics that are connected loosely at best. Time
allocations that allow for depth and complexity are possible in these pro-
grams. Schools have to provide this type of time allocation as part of the
culture change needed for computational thinking to take root.
Stephen Uzzo promotes computational thinking as a way to help
future scientists cope with the transformational effect of data-rich science.
New York Hall of Science activities entail developing exhibits, implement-
ing them, and then evaluating them for pedagogical efficacy in conveying
the relevant concepts to students.
For example, Uzzo discussed a project developed cooperatively with
the School of Library and Information Science (SLIS) at Indiana Univer-
sity. The SLIS macroscope helps to identify patterns, trends, and outliers
in very-large-scale static or streaming data sets. The macroscope is an
expandable and integrated set of applications that scientists can use to
share scientific data sets and algorithms and to assemble them into work-
flows. Macroscopes continuously evolve as scientists add and upgrade
existing plug-ins and remove obsolete ones to arrive at a set that is truly
relevant for their work. This project requires little or no help from com -
puter scientists.
Uzzo argued for a new generation of science students who know
what it means to be an e-scientist, taking advantage of online data. He
suggested that informal learning institutions may be in the best position
13 This example is further elaborated in ITEST Small Group on Computational Thinking,
2010, Computational Thinking for Youth, Newton, Mass.: Education Development Center.
Available at http://itestlrc.edc.org/resources/computational-thinking-youth-white-paper.
Last accessed May 20, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
to advance the cause of e-science. Specifically, he said that informal sci-
ence institutions have an opportunity to integrate computational think -
ing in a broad range of science activities. These institutions are in a good
position to conduct learning research on computational thinking and to
integrate such research into professional development and curriculum
development for K-12 formal education.
2.9 RESEARCH AND UNANSWERED QUESTIONS
REGARDING COMPUTATIONAL THINKING
The first workshop report identified five open questions that at
least some participants in that workshop believed were worth further
exploration:
1. What is the structure of computational thinking?
2. How can a computational thinker be recognized?
3. What is the connection between technology and computational
thinking?
4. What is the best pedagogy for promoting computational thinking?
5. What is the proper institutional role of the computer science com-
munity with respect to computational thinking?
Several of these questions were discussed in the second workshop:
question 2 is related to the discussion of student assessment (Section
2.6); question 3 is addressed in Section 2.9.2; and responding to ques -
tion 4 is implicitly the purpose of Sections 2.3 and 2.4. In addition,
participants in the second workshop raised additional issues that are
described below.
2.9.1 The Importance of a Process for
Defining Computational Thinking
As noted above, the first workshop identified the structure of compu-
tational thinking as an important open question. A number of participants
in this second workshop amplified this observation by pointing to the
importance of a process for defining computational thinking.
For example, Joyce Malyn-Smith argued that the field needs a rigor-
ous and valid way of bringing people together and figuring out what
computational thinking is. It is necessary to have consistency because
not everyone understands what computational thinking is about, or they
see it only through their own lens. Absent a rigorous process for defining
computational thinking, efforts to promulgate computational thinking in
the curriculum will lack credibility. Whatever else it may be, computa -
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34 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING
tional thinking in the curriculum cannot be just a bunch of examples that
are placed into the curriculum at the discretion of individual teachers.
2.9.2 The Role of Technology
Elaborating on the first workshop’s question regarding the connection
between technology and computational thinking, Malyn-Smith identified
two research questions. First, to what degree and in what ways does the
technology expertise of youth contribute to their computational thinking?
A related second question is, How and to what degree can the use of tech-
nological tools and systems and processes facilitate transfer of learning in
STEM careers and in the sciences?
2.9.3 The Need for Interoperability
Al Aho noted that “the software world of today is largely a Tower
of Babel, with lots of incompatible infrastructures and a lot of expense
regarding who pays, who collects the data, who maintains the data, who
maintains and evolves the software.” Stephen Uzzo said this was espe-
cially true in an e-science environment in which data is produced in
prodigious quantities and there is a premium on making large data sets
available to researchers reliably and promptly. In this view, computational
thinking efforts would be facilitated by interoperability between applica -
tions used by researchers, and it must provide easy-to-use tools for pro -
cessing, manipulating, and combining multiple data types.
Jim Slotta echoed these points when he observed that content from
most platforms is not portable across platforms. Further, the environ -
ment of a given platform is generally unable to interact with other
applications that are running on the machine. To address some of these
limitations, Slotta and his team engaged with the computer science
department to develop a new open-source architecture called SAIL
(Scalable Architecture for Interactive Learning) for content display and
manipulation that separates the various layers of the learning environ -
ment (and in particular the content and the user interface) wherever
possible.
SAIL has been used in a number of other science education efforts
as well. For example, SAIL is an integral element of the Science Created
by You (SCY) project of the European Union.14 SCY is a large project that
provides a flexible, open-ended learning environment for adolescents.
Within this environment—called SCY Lab—students engage in personally
14 This discussion of SCY includes material found at “Science Created by You,” website,
http://www.scy-net.eu/. Last accessed February 7, 2011.
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KEY POINTS EXPRESSED BY PRESENTERS AND DISCUSSANTS
meaningful learning activities that can be completed through constructive
and productive learning. Examples of such learning activities include
browsing for information, generating a hypothesis, and distributing tasks.
Slotta has also developed a technology framework called SAIL
SmartSpace (S3) to support a complex orchestration of people, materials,
resources, groups, conditions, and so on. This framework can be regarded
as a “smart classroom” infrastructure that facilitates cooperative learning
in a milieu of physical and semantic spaces. From a technical standpoint,
S3 supports aggregating, filtering, and representing information on vari -
ous devices and displays (e.g., handheld devices, laptop computers); loca-
tional dependencies (i.e., allowing different things to happen depending
on the physical location of a student); interactive learning objects; and an
intelligent agent framework. The S3 environment is highly customizable
and supports the coordination of people, activities, and materials with
real-time sensitivity to inputs from students.
2.9.4 The Need for a Career Framework
Joyce Malyn-Smith contended that for computational thinking to get
traction in the K-12 education community, it needs to be connected to
frameworks and standards that are already implemented nationwide. An
analysis of the Information Technology Career Cluster Initative’s model,
for example, provides a way to organize a hierarchy of skills and knowl-
edge that can be repurposed to support the integration of computational
thinking in the K-12 arena. At the most basic level, this information tech -
nology skills framework calls for literacy and the ability to use com-
mon technology applications. Further up the hierarchy is fluency with
information technology, which involves core knowledge and skill sets
of technology-enabled workers employed in any industry sector. At the
highest level of this model are the skill sets necessary for information
technology producer or developer careers—those that involve the design,
development, support, and management of hardware, software, multime-
dia, systems integration, and services. In short, individuals engaged in
different activities are likely to need different (though overlapping) sets
of technology skills.
