images to 3D objects. Finally, students
develop a further ability to abstract. As
part of the creation of a single 3D object,
say a chair, the students are then challenged to place many chairs in a room.
They need to be able to recognize that
representing a 3D chair consists of two
parts: the relative coordinates of each of
the parts of the chair, and the absolute
location of one part (say the bottom-right corner of the front-right leg).
The second example involves the teaching of evolution using computational
learning. Our vision is of a 3D visualization system that could simulate evolution. A student could specify an organism, with primitive appendages (arms,
legs, joints, and other attributes) to accomplish locomotion. Then, by providing an environment, the student could
run the simulation to watch how the
organism’s ability to move evolves over
time as a function of its current locomotion capability coupled with the impact of that organism’s environment.
Students could change the appendages and/or the environment to observe
how such changes lead to a difference
in the organism’s evolution over time.
In computer science terms, this example is similar to passing a program and
an initial state as input to a Universal
Such a simulation allows the student to work interactively with the
computer program. The student learns
both from the impact of the changes
she makes to the initial configuration
of the organism and to the initial environment (which will lead to the organism evolving the ability to move
differently) as well as by the ability to
observe the simulation/visualization
as it is running. In science, researchers
have found that visualization is central
to increasing conceptual understanding and prompting the formation of
dynamic mental models of particulate
matter and processes (see 5, 7, 9, 12). Visualization and computer interaction
through animation allow students to
engage more in the cognitive process,
and to select and organize more relevant information for problem-solving. 7
Computer animations incorporated
into interactive simulations offer the
user a chance to manipulate variables
to observe the effect on the system’s
this model for
behavior (see 9, 10, 13).
While we know of no tool that provides the exact support/simulation we
are describing, there are several available visualization systems that can
simulate/model the world. Two of these
systems have helped to shape our vision
of the above-mentioned simulation:
The 3D visualization system, Fram-sticks ( www.framsticks.com) can be
used for modeling evolution, and the
2D simulation system, NetLogo (http://
many available pre-built simulations,
including those that model evolution
albeit in a different manner than what
Most papers we’ve seen on compu-
tational thinking represent attempts
at repackaging computing science
concepts, especially in the form of al-
gorithmic thinking and introductory
programming, sometimes in other do-
mains. Though this may be useful in
some contexts, it is unlikely such a sim-
ple approach will have significant im-
pact on student learning—of computer
science or other disciplines—in the
K– 12 setting. The proposed model of
computational learning combines the-
ories of learning with the computer’s
superiority in dealing with complexity
and variability and its ability to present
results using modalities that appeal to
the learner in order to enhance student
learning and understanding. We believe
that computational learning can be
framed within various theories of learn-
ing, where the computer plays a similar
role as Vygotsky’s More Knowledgeable
Other (though the computer obviously
cannot think at a higher level than the
student), 11 or even fits within Newell
and Simon’s Information Processing
Theory framework. 8 Our hope is that by
considering our model of computation-
al learning, we can better educate and
prepare teachers to benefit from com-
puting in and outside the classroom,
and that approaches and computing
tools can be identified and built to im-
prove K– 12 student STEM learning.
1. committee for the Workshops on computational
thinking, national research council. Report of a
Workshop on the Scope and Nature of Computational
Thinking. national academies press, Washington, D.c.,
2. cuny, J. finding 10,000 teachers. csta Voice, 5, 6
(2010), 1–2; http://www.csta.acm.org/communications/
3. cutler, r. and Hutton, m. Digitizing data: computational
thinking for middle school students through computer
graphics. In Proceedings of the 31st Annual Conference
of the European Association for Computer Graphics EG
2010—Education Papers. (norrköping, sweden, may
4. Denning, p. Beyond computational thinking. Commun.
ACM 52, 6 (June 2009), 28–30.
5. gilbert, J.K., Justi, r., and aksela, m. the visualization
of models: a metacognitive competence in the learning
of chemistry. paper presented at the 4th annual
meeting of the european science education research
association, noordwijkerhout, the netherlands, 2003.
6. margolis, J. et al. Stuck in the Shallow End: Education,
Race, and Computing. the mIt press, 2008.
7. national science foundation. molecular visualization
in science education. report from the molecular
visualization in science education workshop. ncsa
access center, national science foundation, arlington,
8. newell, a., and simon, H.a. Human Problem Solving.
prentice-Hall, englewood cliffs, nJ, 1972.
9. rotbain, y., marbach-ad, g., and stavy, r. using a
computer animation to teach high school molecular
biology. Journal of Science Education and Technology
17 (2008), 49–58.
10. sewell r., stevens, r., and Lewis, D. multimedia
computer technology as a tool for teaching and
assessment of biological science. Journal of Biological
Education 29 (1995), 27–32.
11. Vygotsky, L.s. Mind and Society: The Development of
Higher Mental Processes. Harvard university press,
cambridge, ma, 1978.
12. Williamson V.m. and abraham, m.r. the effects of
computer animation on the particulate mental models
of college chemistry students. Journal of Research in
Science Teaching 32 (1995), 522–534.
13. Windschitl, m.a. a practical guide for incorporating
computer-based simulations into science instruction.
The American Biology Teacher 60 (1998), 92–97.
14. Wing, J.m. computational thinking. Commun. ACM 49,
3 (mar. 2006), 33–35.
15. Wing, J.m. computational thinking and thinking about
computing. Philosophical Transactions of the Royal
Society A, 366 (2008), 3717–3725.
Stephen Cooper ( email@example.com) is an associate
professor (teaching) in the computer science Department
at stanford university.
Lance C. Pérez ( firstname.lastname@example.org) is an associate professor
in the Department of electrical engineering at the
university of nebraska-Lincoln where he also holds the
position of associate Vice chancellor for academic affairs.
Daphne Rainey ( email@example.com) is a biologist
currently serving in a temporary assignment as a program
director at nsf’s Division of undergraduate education
within its education and Human resources Directorate.
copyright held by author.