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).

evolutionary Biology

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 Turing Machine.

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
computational
learning differs
significantly from
other proposed
notions of
computational
thinking.

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:// ccl.northwestern.edu/netlogo/) has many available pre-built simulations, including those that model evolution albeit in a different manner than what we describe.

conclusion

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.

References

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., 2010.

2. cuny, J. finding 10,000 teachers. csta Voice, 5, 6 (2010), 1–2; http://www.csta.acm.org/communications/ sub/cstaVoice_files/csta_voice_01_2010.pdf

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 2010), 17–24.

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, Va, 2001.

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 ( [e-mail]) is an associate professor (teaching) in the computer science Department at stanford university.

Lance C. Pérez ( [e-mail]) 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 ( [e-mail]) 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.