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4 Summaries of Individual Presentations 4.1 COMPUTATIONAL THINKING AND SCIENTIFIC VISUALIZATION 4.1.1 Questions Addressed • What are the relevant lessons learned and best practices for improv- ing computational thinking in K-12 education? • What are examples of computational thinking and how, if at all, does computational thinking vary by discipline at the K-12 level? • What exposures and experiences contribute to developing compu- tational thinking in the disciplines? • How do computers and programming fit into computational thinking? • What are plausible paths and activities for teaching the most important computational thinking concepts? Presenters: Robert Tinker, Concord Consortium Mitch Resnick, Massachusetts Institute of Technology John Jungck, Beloit College, BioQUEST Idit Caperton, World Wide Workshop Committee respondent: Uri Wilensky 65

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66 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING 4.1.2 Robert Tinker, Concord Consortium The Concord Consortium is a non-profit research and technology development group that focuses on applying technology to improve learning at different grades. Robert Tinker, the founder of the Concord Consortium, argued that computational efforts in K-12 should be inte - grated around a science focus rather than a focus on either mathematics or engineering. Elaborating on this argument, he suggested that computational think- ing offers an alternative new way of finding out about the world, which is important for citizenship, for future work, and for professionals of all types. Nevertheless, he believes that neither the computer science community nor the education community has yet clearly articulated the essence of computational thinking. As usually presented, computational thinking involves abstractions upon abstractions, which are difficult to make concrete. At the core of computational thinking, Tinker argued, is the ability to break big problems into smaller problems until one can automate the solutions of those smaller problems for rapid response. (It is for this rea - son that Tinker believes that engineering is not an appropriate integrating focus for attempts to teach computational thinking—engineering taught at the K-12 level is not particularly amenable to decomposition.) This core, he argued, indicates a possible route for introducing computational thinking into K-12 education. Tinker’s view is that science is the right focus because modern science often uses computational models that are based on scientific principles and whose use depends on visualizations. Understanding these models requires computational thinking—scientific models and visualizations allow students to visualize the computations that are going on in near real time. Tinker noted that students learn better by seeing models and inter- acting with them, and that by exploring the model in a spirit of inquiry, they learn about the science in the model in much the same way that scientists learn about nature by using the scientific method. He argued that students can learn complicated, deep concepts this way rather than through the more “off-putting” and often confusing approach of formal- istic equations. Tinker proposed an approach across the K-12 curriculum that uses simple models of scientific concepts such as temperature, light, and force to teach computational thinking. A progression of concepts could start in early elementary grades with basic ideas such as “there are numbers associated with things you observe.” (See Figure 2.1.) In later grades, stu - dents might manipulate and refine models to reflect more sophisticated understanding of the concepts represented in the models. Finally, in high

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67 SUMMARIES OF INDIVIDUAL PRESENTATIONS school, a student might be able to select, modify, and apply both hardware and software models as a key part of an extended investigation. Tinker suggested that the following learning progression could fit into the K-12 curriculum, improve science teaching and learning, and introduce important aspects of computational thinking: 1. There are numeric values associated with every object and their interactions. 2. These values change over time. 3. These changes can be modeled. 4. Models involve lots of simple steps defined by simple rules (e.g., the molecular dance). 5. Models can be tested to find their range of applicability. 6. You can make models. 7. Many other applications of computers share the same features. When asked whether students perform better when learning through computational modeling and visualization as opposed to a more tra- ditional approach, he replied that such a distinction is not particularly important. Rather than worry whether one method is better than the other, Tinker pointed out that it is a good outcome if a teacher has an additional tool in his or her arsenal to teach a complicated concept. Tinker noted that because students begin as concrete thinkers, it remains a challenge to identify the age or grade level at which children can handle abstraction. As an example, he said that although he has worked with second graders by hooking up a probe to measure tempera- ture, it is only at fourth grade that students demonstrate reliable results of learning and comprehension with such methods. According to Tinker, students involved in a very tightly packed K-12 curriculum do not have the time to master programming in order to manipulate models. Rather, he recommends a programming environ- ment such as NetLogo or AgentSheets partially populated with general tools, but still needing interconnection and “tuning,” that were designed to focus users on the concepts represented rather than on the details of programming. Another option is to use an existing piece of software in which the student can manipulate important parameters. 4.1.3 Mitch Resnick, Massachusetts Institute of Technology Mitch Resnick of the MIT Media Lab said that computational think- ers must be able to use computational media to create, build, and invent solutions to problems. He framed this approach in terms of students being able to express themselves and their ideas in computational terms, and

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68 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING emphasized that indeed this should be part of the motivation to learn computational thinking. “When young people learn about language, we don’t just teach them linguistics or grammar; we let them express them - selves. We want a similar thing with computational thinking.” Moreover, he argued, most people work better on things they care about and that are meaningful to them, and so embedding the study of abstraction in concrete activity helps to make it meaningful and understandable. Resnick pointed out that for students to express themselves meaning- fully with computational media, they need to learn new concepts as well as develop new capacities. He argued that computer science classes often overemphasize computational thinking concepts (such as recursion) at the expense of helping students develop computational thinking capaci - ties for design and social cooperation. Computational concepts include concepts such as conditionals, processes, synchronization, and recursion. Design capacities deal with skills like prototyping, abstracting, modu - larizing, and debugging. Social-cooperative capacities include sharing, collaborating, remixing, and crowd-sourcing. These social-cooperative capacities are becoming increasingly important as new computing and networking technologies open up new possibilities for widespread coop - eration. Resnick’s computational environment of choice for supporting com - putational expression is Scratch. The MIT Media Lab developed Scratch and a companion online community to help engage people in creative learning experiences and to support the development of computational thinking. Scratch is a graphical programming language, giving the user the ability to build programs by snapping together graphical blocks that control the actions of different dynamic actors on a screen. (Such an approach to program construction enables users to avoid issues of syn - tax and other details that often distract users from the critical processes of designing, creating, and inventing. Resnick believes this construction process serves an important grounding function for learning abstract computational concepts, making concepts more concrete and understand- able.) Scratch also facilitates social cooperation by making it very easy for a user to share his or her design with others for comment and feedback. (See Figure 2.2.) Resnick provided several examples emphasizing the role of expres - sion through construction and social cooperation from one particular member of the Scratch online community who goes by the username MyRedNeptune. MyRedNeptune was a young student from Moscow and joined the Scratch online community shortly after it went live in 2007. “One of the first projects that she created,” Resnick said, “was a type of interactive greeting card for the holidays.” Each time a person clicked

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69 SUMMARIES OF INDIVIDUAL PRESENTATIONS on one of the reindeer, it would begin playing “We Wish You a Merry Christmas” on a musical instrument in concert with the other animated reindeer. Creating the card required modularization and synchronization, as well as a number of core computational concepts. Next, MyRedNeptune began offering her consulting services to develop animated characters upon request. Another community member requested that she develop a cheetah for a project. Resnick continued, “She went to the National Geographic website and she found a video of a cheetah. She used that to help guide the graphic of an animation that she developed, and then someone else used her graphic and integrated it into her project.” When yet another community member requested that she show how she developed her animations, she began to develop tutorials in Scratch on how to program animated characters. One of her first tutorials was on how to animate a bird to make its wings flap back and forth. Later she was asked to participate in an international collaboration with five or six other kids in three different countries. Working together, they developed a type of adventure video game, with each child working on different parts of the activity. Resnick noted: “I think you can see from these examples how MyRedNeptune developed as a computational thinker, learning to think creatively, reason systematically, and work collaboratively.” Scratch is used both inside and outside formal school curricula. Ini - tially used in homes, after-school centers, community centers, and muse - ums, it is now moving into the schools and is being used today to teach basic concepts in university-level introductory computer science classes in a number of universities. Resnick shared that “one thing we’ve seen is that different kids have different trajectories. Some will spend a lot of time continuing to work on the same types of projects, over and over. You might think that they are stuck, but there’s a lot of things happening in their minds, and suddenly they’ll start working on new types of projects and ideas.” Resnick and his colleagues are working on many new initiatives to support the development of computational thinking through Scratch, including an online community (called ScratchEd) specifically for teachers who are helping students learn with Scratch. 4.1.4 John Jungck, Beloit College, BioQUEST John Jungck and his collaborators founded the BioQUEST Curricu - lum Consortium 24 years ago to bring computation and mathematics into the undergraduate biology curriculum. Jungck noted that although there are many reasons for using computation in biology education, the rationale he presented at the workshop focused on the power of visual -

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70 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING ization in a biological context. He noted the evolution of paradigms for scientific investigation from empirical (experiment, observation) to theo - retical (models, theoretical generalizations) to computational (simulation) to data exploration and e-science (collection of data on a massive scale: exploration facilitated by theory, mathematics, statistics, and computer science). In this context, biology education needs to provide students with ways of understanding biological data—environmental data and genomic data, for example—that is multivariate, multidimensional, and multicausal and that exists at multiple scales in enormous volume (tera - bytes of data per day). The philosophy of BioQUEST rests on three pillars: • Students take an active role in posing problems to examine, much as a scientist has to learn to pose good problems. Good problems must be appealing, have significance, and be feasible to address. • Students solve problems iteratively. They must learn to appreciate the nature of scientific hypotheses as answers as well as to develop heu- ristics for achieving closure to scientific problems. • Students must persuade their peers that a solution is useful and or valid, a process that mirrors the role of publication and extensive peer review in biological research. The primary challenge for learning in accordance with this philoso - phy is that in focusing on the student as problem-poser, teachers lose much of the control they traditionally have over the learning process. Stu- dents engaging in self-directed collaborative processes may make some teachers uncomfortable. Furthermore, students in this environment may have more technical skill than their teachers, and so peer review from other classmates may be more important than teacher feedback as far as advancing learning. Jungck briefly described a number of BioQUEST projects. For exam- ple, one project sought to develop student facility with the idea of biologi- cal modeling with equations. For this purpose, the Biological ESTEEM project (ESTEEM stands for Excel Simulations and Tools for Exploratory Experiential Mathematics) seeks to provide students with a mathemati - cal vocabulary for describing common modeling concepts (e.g., linear, exponential, and logistic growth1). Another BioQUEST project (BEDROCK) focuses on bioinformatics. The BEDROCK project requires students to use a supercomputer tool 1 The Biological ESTEEM Collection, website, BioQUEST Curriculum Consortium, http:// bioquest.org/esteem/index.php. Last accessed February 7, 2011.

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71 SUMMARIES OF INDIVIDUAL PRESENTATIONS called Biology Workbench,2 which allows biologists to search many popu- lar protein and nucleic acid sequence databases. Database searching is integrated with access to a wide variety of analysis and modeling tools. Students can align multiple sequences of a particular gene from different organisms onto one three-dimensional structure and see the evolutionary conservation involved; they can thus relate the comparative biology of sequences to structure, function, and phylogeny. Yet another project is BIRDD (Beagle Investigations Return with Dar- winian Data), whose goal is to provide a variety of resources related to evolutionary research. Labs are rare in courses dealing with evolu - tion, largely because evolutionary phenomena involve temporal and geographic scales that make it difficult for instructors to develop labs comparable to those in biochemistry, physiology, or behavior. BIRDD addresses this problem by providing raw data (e.g., bird songs, sequence data, rainfall, breeding sites, and so on) and pedagogical ideas to help instructors structure appropriate pedagogical experiences for their stu- dents. BIRDD helps students generate questions and look at, for instance, whether character displacement happens when the species co-occur or when they inhabit different islands. To illustrate the special relationship between biology on one hand and mathematics and computation on the other, Jungck noted 10 equations that have driven substantial amounts of biological research and for which numerous educational materials have been developed:3 1. Fisher’s fundamental theorem of natural selection, 2. Cormack-Hounsfield computer assisted tomography, 3. Genetic mapping (units = morgans; the Haldane function), 4. Fitch-Margoliash little maximum parsimony algorithm (Penny and Hendy—Molecular Phylogenetic Trees—Bioinformatics), 5. Lotka-Volterra interspecific competition logistic equations, 6. Hodgkin-Huxley equations for neural axon membrane potential, 7. Michaelis-Menten equation for enzyme kinetics (Jacob and Monod), 8. Allometry (e.g., MacArthur-Wilson species area law and conservation), 9. Hypothesis testing (e.g., Luria-Delbrück fluctuation test), and 10. Crick-Griffith-Orgel comma-free coding theory. 2 BEDROCK (Bioinformatics Education Dissemination: Reaching Out, Connecting, and Knitting-together), website, BioQUEST Curriculum Consortium, http://bioquest.org/ bedrock/about.php. Last accessed February 7, 2011. 3 John Jungck, 1997, “Ten Equations That Changed Biology: Mathematics in Problem- Solving Biology Curricula,” Bioscience 23(1):11-36.

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72 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING He also noted that the typical biology textbook contains only a hand- ful of equations, and even those are linear equations, and expressed his surprise that biological visualizations, important as they are to the way biologists think about the world, are not accompanied by the tools needed to interpret different kinds of multivariate, multidimensional biological data. Finally, Jungck discussed the Visible Human Explorer (VHE). Accord- ing to the VHE website,4 the VHE is an experimental user interface for browsing the National Library of Medicine’s (NLM’s) Visible Human data set, which is based on two digitized cadavers in the National Institutes of Health Visible Human data set. The interface allows users to browse a miniature Visible Human volume, locate images of interest, and auto - matically retrieve desired full-resolution images from the NLM archive. Jungck concluded by noting that computers and computation have transformed biology. He noted a quote from Michael Levitt (a structural biologist at Stanford) that “computers have changed biology forever, even if most biologists don’t yet realize it.” Educationally, he stressed the work of di Sessa, Parnafes, and others who emphasize the impor- tance of engaging students in constructing, revising, inventing, inspect - ing, critiquing, and using rich visualizations for promoting conceptual understanding. 4.1.5 Idit Caperton, World Wide Workshop, Globaloria Idit Caperton described Globaloria as a platform, a transformative social media learning network, with a comprehensive hybrid course (online/in class) for playing and making games. It includes a customiz - able curriculum, community-developed resources, tools, tutorials, and expert support. Students and educators learn how to create their own web games, produce wikis, publish rich-media blogs, and openly share and exchange ideas, game code, questions, and progress using the lat- est learning methods and digital communication technology. Globaloria is a project-based learning environment for stimulating computational creativity as well as inventiveness in youth and educators as a necessary skill for the 21st century. Computational projects are built around a range of topics, such as health, climate, alternative energy, civics, mathematics, biology, social studies, and literature. The World Wide Workshop’s innovative R&D and pedagogical approaches to platforms and tools for cultivating computational think - 4 Human Visible Explorer, website, Human Computer Interaction Lab, University of Maryland, http://www.cs.umd.edu/hcil/visible-human/vhe.shtml. Last accessed Febru - ary 7, 2011.

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73 SUMMARIES OF INDIVIDUAL PRESENTATIONS ing and computational inventiveness have roots in Caperton’s MIT and Harvard research, and in educational theories about the value of project- based, multidisciplinary, innovative and creative learning (of any subject) through software design and programming.5 Caperton also described Globaloria as a customizable textbook com- prising three main units. An introductory or “getting started” unit pro- vides students with the opportunity to establish their own project spaces on the wiki network and to review existing games’ operation and their codes. A following unit is “game design,” in which students design an original game about a complex topic (in science, math, health, civics) and a social issue that matters to them. Students come up with an idea, assemble teams, do research, build and videotape their paper prototypes, and construct a concept and a demonstration that they present, both physically and online via web conferencing. Using Flash text and drawing and animation techniques, they program an interactive demonstration of their game concepts. A third unit is “game development,” in which stu - dents develop their game concepts and demonstrations into a complete, interactive game. Each unit contains a structured set of learning topics, as well as projects and assignments structured to help students create critical parts for their own original game. Globaloria seeks to impart to students six contemporary learning abilities: the ability to imagine, design, prototype, and program an edu - cational game, wiki, or sim; the ability to use project management skills in developing programmable wiki systems in a Web 2.0 environment; the ability to produce animated media, programming, publishing, and dis - tributing interactive purposeful digital media in social networks; the abil- ity to learn in a social constructionist manner and to participate actively in the public exchanges of ideas and artifacts; the ability to undertake information-based learning, search, and exploration as they relate to the abilities above; and the ability to surf websites and use web applications thoughtfully as they relate to the earlier abilities enumerated. Caperton argued that these abilities go beyond the typical media literacy skills, since they emphasize a bundle of complex and sophisticated construc - tionist digital literacies and involve longer-term engagement (students are required to use Globaloria daily, over two semesters, for a minimum of 100-150 hours6). The Globaloria approach emphasizes constructionist collaboration 5 The canonical examples of such research are Idit Caperton, 1991, Children Designers, and Idit Caperton and Seymour Papert, 1991, Constructionism, both published by Ablex, Norwood, New Jersey 6 Caperton recommended repeating the use of Globaloria year after year for greater effects on computational thinking in learners.

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74 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING within a transparent community. Participants in the community—teach- ers, students, staff, and game teams—maintain public blogs as design journals, share resources, and publish completed games on the commu- nity wiki. They can also submit created games for competitions or for publishing on the school’s Globaloria network. Caperton suggested that it is possible to learn any subject and to master complex topics or social issues by creating functional, representa- tional, educational multimodal computer games involving that subject’s content. She provided “10 design principles for implementation ‘The Globaloria Way.’” For example, developing educational games requires students to spend significant time, engaging daily on personally chosen projects involving open-ended and creative design tasks. A transparent and collaborative studio environment facilitates the sharing of work and provides many opportunities for social expression and discussion about game projects. Students thus learn through four modes simultaneously: (1) through design and teaching, (2) through peer-to-peer interactions, (3) through co-learning with teachers (and also from watching the teach- ers themselves learn), and (4) from online research and consultation with other experts (just-in-time learning) via pre-scheduled web conferencing and a help desk. (See Figure 2.3.) The basic technology underlying the Globaloria platform is open- source MediaWiki with customized MediaWiki extensions, PHP, MySQL, Tumblr, Blogger and multiple Google tools. Students learn to program their games much like professionals in the real world using Adobe Flash Actionscript. The World Wide Workshop Foundation’s team (creators of Globaloria) chose Flash for students’ programming for a number of reasons, including: • They themselves are expert developers in Flash; • Flash provides a wide variety of tools, such as interfaces and video tutorials, to support users and thus can support a range of skill levels from novice to professional; • Flash’s capability is present on many websites and in simulations and media devices; • Flash is an industry professional standard in game development and multimedia programming, and so proficiency in Flash is likely to help provide students with internships and job opportunities in the future. Finally, Caperton described research she and colleagues conducted on the impact of implementing models of Globaloria for fostering com - putational thinking and inventiveness among low-income rural students and low-income minority urban schoolchildren: (1) Model 1 in 45 schools throughout the public school system in 20 counties in the state of West

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75 SUMMARIES OF INDIVIDUAL PRESENTATIONS Virginia, where 1,300 students in rural middle schools, high schools, community colleges, and alternative education institutions participated with 55 educators in 2010 for credit and a grade; and (2) Model 2 within a charter middle school system in East Austin, Texas, where every student in that school took Globaloria once a day for 90 minutes for the entire school year. She provided an overview of selected research results7 and shared video case studies.8 Caperton argued that these were powerful demonstrations of plausible paths and activities for teaching compu- tational thinking concepts to low-income rural and urban students of underserved communities. 4.2 COMPUTATIONAL THINKING AND TECHNOLOGY 4.2.1 Questions Addressed • What are the relevant lessons learned and best practices for improv- ing computational thinking in K-12 education? • What are examples of computational thinking and how, if at all, does computational thinking vary by discipline at the K-12 level? • What exposures and experiences contribute to developing compu- tational thinking in the disciplines? • How do computers and programming fit into computational thinking? • What are plausible paths and activities for teaching the most important computational thinking concepts? Presenters: Robert Panoff, Shodor Education Foundation Stephen Uzzo, New York Hall of Science Jill Denner, Education, Training, Research Associates Committee respondent: Yasmin Kafai 4.2.2 Robert Panoff, Shodor Education Foundation Robert M. Panoff, founder and executive director of the Shodor Education Foundation, is a proponent of teaching computational think - ing through computational science. At the same time, he stresses the 7 For more information see www.WorldWideWorkshop.org/reports. Last accessed Febru - ary 7, 2011. 8 For more information see www.worldwideworkshop.org/programs/globaloria/vftf. Last accessed February 7, 2011.

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122 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING ing ideal gases in physics. In particular, he noted that the laws of ideal gases traditionally entail equations such as the Maxwell Boltzmann dis - tribution and the relationship between pressure and volume. Blikstein offered an alternative restructuration based on computational thinking that represents a gas as a collection of molecules moving in a gas cham - ber governed by a simple rule: a molecule will move forward until or unless it bumps into another molecule or wall, at which point it will bounce back. This simple rule applied in this agent-based model results in aggregate behavior of the collection of gas molecules that is identical to that described by the formal gas law equations. Blikstein asserted that the computational representation of the gas laws is simpler and easier to learn than are the equations. He also described how to reformulate a number of complex con- cepts from undergraduate-level materials science. Blikstein noted that students in traditional introductory materials science courses encounter new equations at a very rapid rate (one new equation every 150 seconds, not counting intermediate steps in a derivation). It is often that many dif - ferent equations and models are needed to develop an understanding of a particular concept. These equations must be combined and manipulated to arrive at the final result. Blikstein argued that an agent-based approach helps students to explore these complex and intertwined concepts more easily, and further that the rules and mechanisms governing the behavior of individual atoms can be used to understand a number of different crystal phenom- ena in materials science, such as growth, solidification, diffusion, and so on. An example of a relevant mechanism might be for molecules to “look around and see if they are surrounded by different neighbors or equal neighbors” and then cluster or disperse “based on their neighborhood.” Similarly, solidification follows a comparable process except that an “atom in the liquid is kind of going around and looking for solid neighbors where it can attach itself.” Blikstein also described some of the challenges in assessing and giv - ing objective feedback on open-ended projects with varying levels of com- plexity and explanatory power. These challenges included the following: • How do we go about looking at various artifacts and understand- ing what students are doing? • How do we assess the relative levels of complexity of the artifacts? • How do we use assessment to provide feedback to students to improve their models as well as their understanding of concepts? Blikstein described several tools to facilitate assessment—rubrics and maps, coding patterns over time, and representational shifts.

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123 SUMMARIES OF INDIVIDUAL PRESENTATIONS • Rubrics and maps. Based on the actual code that students generate, maps can be created that track the programming steps and decisions stu- dents were making. These maps capture many dimensions of students’ decision making, such as how they define the system, how they define the rules of the system, how they define what the agents are doing, and so on. From these large maps, it is possible to categorize the rules embedded in the system and assess the sophistication of the rules. Evaluators can check each map to see if a student used various affordances of the programming language. For example, is this student using collisions? Is this student using neighborhood checking? Agents moving? Agents seeking agent clusters, walls, or energy? Blikstein argued that the greater the number of affordances appearing in a map, the more sophisticated the underlying model is likely to be, although this measure is not absolute and in many respects depends on the phenomenon being modeled. • Coding patterns over time. Such patterns document how a student’s code changes over time (e.g., what is added or deleted, what is found each time compilation is attempted). For example, one can count the number of characters in a program submitted for compilation. Some students— typically novice students—exhibit a pattern in which the code is more or less constant for several compilations but then jumps significantly in size. For other students (typically more expert students), there are fewer large increases in code size—code size increases more or less linearly over time. Blikstein asserted that such knowledge can be exploited to help tailor the most effective way to give feedback to different kinds of students. • Representational shifts. Changes in how a student represents or depicts physical phenomena can indicate differences in the level of sophis- tication of his or her understanding. For example, Blikstein compared two groups of students, one that had been exposed to computational model- ing and one that had not. Each group was asked to sketch the process involved in a scientific phenomenon different from the one they were modeling, such as the impact of a change in temperature. The students with computational modeling experience drew and described a mecha- nism showing the behavior of the atoms as the temperature changed. Students who were not exposed to the activity instead drew a graphical curve showing the aggregate behavior of the atoms as the temperature changed. 4.6.3 Christina Schwarz, Michigan State University Christina Schwarz, an associate professor in the College of Educa- tion at Michigan State University, described her work with elementary and middle school students using scientific modeling and practices. The MoDeLS (Modeling Designs for Learning Science) project works

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124 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING to involve students in science through the use, revision, and creation of models. Although not explicitly focused on computational models, some of her work, Schwarz believes, may apply to the ongoing dialog about computational thinking. In the context of her work, a model is an abstract, simplified repre - sentation of some phenomenon which could include but is not limited to computational representations. Models also include physical models and diagrammatic models. Modeling involves constructing a representation that embodies aspects of theory or evidence; evaluating that representa- tion or testing it against empirical evidence and scientific theory; using it to illustrate, predict, and explain; and revising the representation. Schwarz and her colleagues believe that the underlying concepts of modeling are powerful for sense-making and for communication in science. She further noted an overlap between modeling practice and computational thinking, particularly the ideas of abstracting and decom - posing systems, testing the model against actual data, and so on. Schwarz argued that models can make important aspects of science accessible by helping students to understand invisible processes, mecha - nisms, and components in phenomena. Models promote both subject- matter and epistemological understanding, and they develop systems thinking skills. Most importantly, models can generate predictions and explanations for scientific phenomena. Schwarz walked through a generic MoDeLS curriculum sequence that would be given to students. The first step is for the researchers to provide some sort of anchoring phenomenon in a scientific context. For example, a fifth grade unit starts with a question like, Would you drink liquid that collected in a solar still?, and continues, “You can’t test it, you don’t want to drink it, because you might get sick, so you have to design an initial model that you can use to begin thinking through what is going on.” The unit then provides some discussion about the nature and purpose of models. Such dialog is essential to abstracting knowledge for transfer to other kinds of systems and contexts, and to motivate and support the kinds of skills and habits of mind essential to computational thinking. The third element of the unit is an investigation of the subject phe - nomenon through data gathering and students’ testing of their models. Students evaluate their models and discuss the criteria for evaluation. Evaluation is thus another strategy for teasing out modeling practice and scientific thinking. Last, the unit introduces scientific ideas that students can use to revise their models again. Here, students often use visual, diagrammatic models and computer simulations in different ways. Students may look at simulations and then use some of those ideas from the simulations in their diagrammatic models. Model design, revision, and analysis occur in

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125 SUMMARIES OF INDIVIDUAL PRESENTATIONS the context of a small scientific learning community (i.e., their classmates). The students debate data and concepts, as well as evaluate and peer- review each other’s work. Finally, students develop a consensus model at the end of the unit and explore applying the model developed to other contexts that they care about. Schwarz noted that different science disciplines use different aspects of modeling to explore scientific phenomena. For example, flow diagrams and process diagrams might be most appropriate for modeling relation - ships between components of a biological system. Most of the MoDeLS effort focuses on various aspects of physical science, but the group is looking at exploring modeling in other areas. Schwarz uses a four-level learning progression to guide the interpre- tation of student activities. This progression is continually revised and improved based on their assessment outcomes. • Level I focuses on students’ reflections on their existing practices of modeling around the idea that children often begin modeling practice by drawing literal illustrations but have yet to really grasp the purpose of or use for models. • Level II characterizes student use of models and shows that stu- dents are constructing and using models to illustrate and explain to an audience how phenomena occur. Although students at Level II are still somewhat literal, they are moving closer to the use of abstraction. • Level III is even more sophisticated, as students move farther along the literal-to-abstract scale closer to the abstract end of the spectrum. • Level IV students are constructing and using models spontane- ously in a range of domains to help their thinking and problem solving. For example, students might be prompted to consider, before they test their model, how the world would behave. Schwarz argued that this fourth level is most similar to the types of modeling a computer scientist would do. Schwarz also commented on assessment. Specifically, she noted that her assessments seek evidence in student work of engagement in modeling: • Around different content knowledge for which students did not receive explicit instruction—to determine what aspects of modeling prac - tices might be used across contexts. • By applying their models to familiar and less familiar contexts. Schwarz described an example in which a student noted that she was actually applying the condensation and evaporation model to simple experiences at home like boiling water.

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126 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING • Mapping between representations and the real world, as illustrated by students’ application of their models in a specific context. • Evaluating and revising their models for items like relevancy or saliency, evidentiary support, communicative power, and so on. Schwarz and her colleagues use a variety of tools to obtain such evi - dence. Although there is some use of written pre-test and post-test items involving scientific modeling, they also use reflective interviews with students and in-person or videotaped observations of in-class student interactions. These qualitative instruments are designed to probe content that was both explicitly and not explicitly taught to examine transfer to other disciplines and the time evolution of student modeling practices and thinking. Nevertheless, she was aware that their assessment efforts had a num- ber of limitations. For example, many young students often see modeling and scientific thinking as a school-only activity that is unrelated to daily life rather than thinking of models as tools useful for their own purposes. Although they understand in principle the notion of evaluating each others’ models according to relevant objective criteria, in practice they sometimes fail to do so in the classroom environment, instead deferring to the classmate they like better or the classmate who is the loudest. Students also sometimes focus on the external audience when com- municating through a model; that is, they may formulate their comments and responses based on what they think their teachers want to hear and what they think are “correct” answers, rather than what they themselves think. Last, Schwarz noted that pedagogical constraints often result from the curricular and learning approaches determined by the various schools. As an example, Schwarz explained that in one school, the state-wide curriculum mandated that before fifth grade, science teachers are not to discuss phenomena at the cellular or atomic level because they are invis - ible. In response, Schwarz and her colleagues developed a special unit on evaporation and condensation that was actually an attempt to bridge the project’s elementary learning goals to a particular state guideline prohibit- ing discussion of atoms. 4.6.4 Mike Clancy, University of California, Berkeley Mike Clancy, from the Department of Computer Science at the Uni- versity of California, Berkeley, addressed the topic of assessment for intro- ductory programming classes. His top-level goals for students could be characterized as knowing when given aspects of computational thinking

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127 SUMMARIES OF INDIVIDUAL PRESENTATIONS are applicable, when they are not applicable, and how these aspects are applied when they are applicable. Clancy described two complementary approaches that are useful in assessment and evaluation. The first approach is based on case studies. A case study is an expert solution to a problem that is accompanied by a narrative of how that solution came to be. The expert, who may be a faculty member or a teaching assistant, provides a solution that addresses questions like why one approach to solving the problem was chosen over another and how problems originating in the first implementation of a solution were fixed (debugged). Case studies are intended to make the expert’s thinking visible to expose his or her design and development decisions. They demonstrate how abstract concepts are manifest in specific situations. They encourage reflection and self-monitoring, and they support collaborative learning and emphasize links among various problem solutions. A typical problem might be to find the number of days spanned by two dates in the same year. (This problem arises in the third week of Berkeley’s introductory programming course for non-majors, at which point they have been exposed to conditional programming structures such as “ifs” and how to deal with data but have not yet encountered recursion.) One approach splits the solution into three situations—those in which the dates occur in the same month, those in which the dates occur in con- secutive months, and those in which the dates are further apart. The first two situations are relatively easy to address, but the third is harder. Spe - cifically, the solution for the third case depends on whether the months involved (including the intervening months, if any) have 28, 29, 30, or 31 days. Sometimes it is possible to kludge a solution when the dates are about 2 months apart, but if they are any further apart, a more systematic approach is needed. At this point, the expert is faced with the question of crafting a solu - tion to the third case that builds on the work already invested in crafting a solution to the first two cases. If one realizes that the day-span com- putation is essentially a subtraction of one date from another, a sensible approach is to change the representation of the dates involved into things that are easier to subtract—specifically, the date in month-day format is transformed into the number of days past January 1 for the year. Using this idea, that is, finding a uniform representation for dates, students are then asked to address a number of related problems, such as computing the difference between two heights, finding the number of Saturdays spanned by two dates, and finding the number of days between dates in different centuries. In practice, their task is to under- stand the original solution (for the problem of computing the number of

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128 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING days between two dates in the same year) well enough so that they can modify the approach accordingly. This case study also includes a debugging exercise; debugging is of course another key aspect of computational thinking. Imagine that the day-span program has been accidentally modified (e.g., one word is changed). Given the change in the output of the program as a starting point, students are asked to figure out what was changed and how to fix the problem. The second approach used for assessment and evaluation involves lab-centric instruction, which emphasizes hands-on lab hours supervised by a teaching assistant rather than lecture and discussion. This instruction entails a variety of traditional programming tasks, such as writing, modi - fying, and analyzing a program. But because there is more lab time than in most lecture/discussion courses, the course also has room for a number of embedded assessment activities. For example, a lab period often starts with a quiz, and it provides opportunities for self-tests. “Gated collabo - rations” enable instructors to pose a question to students, and after any given student answers, s/he sees the answers of his or her lab mates. In this environment, lab instructors can monitor most of what the stu- dents 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. The result is that instructors can nip confusion and misconceptions in the bud rather than having to wait for them to be revealed in some later venue. 4.6.5 Derek Briggs, University of Colorado, Boulder Derek Briggs of the School of Education at the University of Colo- rado, Boulder, began by suggesting several questions that he believed should guide any assessment of computational thinking. His first ques - tion is, What is being assessed? A prerequisite for assessment is a common understanding of the important constructs and concepts of the topic being assessed. In the case of computational thinking, Briggs noted a lack of consensus on its essential elements and commented that even if one isn’t willing to put down a thorough definition of what constitutes computa - tional thinking, there has to be some common ground on the topic. What are the important elements? Second, he argued for clarity about why the topic is being assessed. Briggs identified several possible reasons for assessing student under- standing of a subject: • Evaluating a program. If a pedagogical activity purports to promote

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129 SUMMARIES OF INDIVIDUAL PRESENTATIONS student learning, the students involved in the activity must be assessed to see if the claimed learning indeed took place. • Grading of students. In graded courses, a student’s understanding of a topic often relates to the grade s/he receives. • Diagnosing a student’s understanding of a subject in detail. Pinpoint- ing a student’s misunderstanding of a particular subject-matter point provides feedback to a teacher about how to direct his or her pedagogi - cal efforts to address that particular misunderstanding. For this particu- lar application, multiple concepts of learning progression are helpful. A learning progression can be regarded as an ordered description of a specific student’s understanding of a given concept as that student learns more about it; a description of successively more sophisticated under- standing of a concept or ways of reasoning in a content domain; and also an ordered description of a typical student’s understanding of a given concept as students learn more about it. • Developing a better intellectual understanding of a subject. It sometimes happens that an attempt to assess a student’s understanding of a subject demonstrates that the expert’s understanding of the subject is incomplete, and it is through the act of developing an instrument, and developing questions for students that are intended to elicit information about the subject, that the expert gains insight as to what it is that the expert really meant. Third, an instrument for the assessment must be appropriate to the purpose of the assessment. For example, if the purpose of the assessment is to grade students, an instrument may need only to record the percent- age of correct answers provided by a student. However, if the purpose of the assessment is to diagnose a student’s misunderstandings, the instru - ment must be constructed in a way that sheds light on the specific nature of those misunderstandings. Briggs also noted that diagnosing student misunderstandings does not necessarily entail open-ended interactions with students—carefully designed multiple-choice items can provide diagnostic information that is as meaningful as or more meaningful than that obtained through open-ended interviews. Finally, Briggs argued for the importance of validating an instru- ment, contrasting the notion of validity to the notion of reliability. A valid instrument is one that accurately reflects a student’s knowledge of the specific concepts of interest (i.e., what the investigator really wishes to assess), whereas reliability is concerned with the consistency with which an instrument can produce a given measure. He further noted that low reliability of an instrument was not necessarily problematic in the context of formative evaluations for real-time informing of in-class pedagogy or group-level comparisons.

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130 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING 4.6.6 Cathy Lachapelle, Museum of Science, Engineering is Elementary Project Cathy Lachapelle, director of research and evaluation for the Engi- neering is Elementary (EiE) project at the Museum of Science, discussed her assessment and evaluation experiences with that project. EiE is a cur- riculum development and improvement effort that develops engineering guides and activities for children in grades 1-5. Assessments of EiE activities are focused on what students learn and measure specific learning objectives.46 Lachapelle noted that there is no existing standard “yardstick” against which to assess student learning about engineering. Thus, assessment efforts compare progress toward learning objectives in an EiE activity group to progress among students in a control group. Lachapelle suggested that a variety of methods are available for assessing student learning, depending on the purpose of the assessment: • Class observation that focuses on collecting qualitative data. Such data include information obtained from helping the teacher implement EiE, interviewing students to try to understand their attitudes with respect to the learning objectives, and observing how they perform against the learning objectives. To illustrate, Lachapelle noted that one of the learn - ing objectives is to be able to reason from a model and understand that a model is representing something in the real world. During class obser- vation, assessors talk to the teacher and students to see if the students are grasping the concept. (They might also point out different ways to structure the lessons so that students better understand the learning objec- tives.) A degree of uniformity in data collection is obtained by using the same standards and criteria in each observation. • Embedded assessments, which are often used by teachers to understand the pedagogical impact they are having on students as they go along. Embed- ded assessment can be as simple as examining individual student perfor- mance on a particular worksheet, so that a teacher can better understand which students need more help, whether he or she should give clearer instructions, and so on. • Paper-and-pencil assessments, which are very difficult to construct but provide an excellent source of feedback. EiE typically uses these paper-and- pencil assessments for summative evaluation. A great deal of work is involved in constructing assessments and testing them, piloting them, checking them for reliability, and then using them with hundreds of 46 Not all investigation of student learning requires such objectives—specifically, some research is useful for understanding what students know in general and what they can do on average.

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131 SUMMARIES OF INDIVIDUAL PRESENTATIONS students. For example, developing multiple-choice questions that yield insight into student thinking is sometimes problematic. Lachapelle and her colleagues often ask students how they would answer a question, and unusual or incorrect student answers become alternative choices for answering the question. For example, Lachapelle said, “We asked kids what is the function of leaves in a plant and the kids said, to make food. We would say well why did you choose that answer? And they said because they make salad. You have learned that things are not always as they might seem or as you might expect.” Ultimately, they discarded that particular question. • Performance assessments, which can be used either by teachers for their own understanding of what their students are learning (in formative evalua - tion) or by the curriculum development team as a summative evaluation of what students learned. This type of testing is also time- and resource-intensive because the assessment must be administered and scored. EiE uses this type of assessment in the final project design exercise. Speaking more broadly, Lachapelle addressed formative and sum- mative evaluations in the EiE project. All work products require regular evaluation, including teacher guides, student exercises and activities, the learning goals, and teacher professional development materials and activities. As is usually the case, formative evaluation is used to inform the development and improvement of products and processes. In the EiE con- text, formative evaluations seek evidence of growth in students’ under- standing and skills as stated in EiE learning objectives, determine the age-appropriateness of lessons and activities, and examine the ease of use of lessons and materials. Formative evaluation for EiE usually relies on feedback from teachers and students. Therefore, it is critical that research- ers make sure that the lines of communication are open and that feedback received is considered in light of the project’s set evaluation criteria. Lachapelle explained that if a researcher receives feedback that the project was great but too troublesome to clean up afterward or the standard for an activity was that a teacher be able to manage the activity the following year without any support staff, the activity would be revised accordingly. The purpose of summative evaluation is to provide evidence to EiE stakeholders, including funders, school districts, teachers, and parents, that implementation of specific EiE activity is worthwhile. Robert Panoff was particularly struck by this concept of “being worthwhile” and argued that this concept is a key factor in terms of scaling, adoptability, and moti- vation for using the materials or the exercises. Lachapelle stated that one criterion for this type of evaluation is to show improved learning of target concepts among students as compared to a control group of students. The

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132 PEDAGOGICAL ASPECTS OF COMPUTATIONAL THINKING control group consists of students in a comparable classroom taught the same science and engineering topics but not with EiE curriculum materi - als and tools. In the ideal scenario, EiE has a large pool of teachers from which part are admitted to the EiE project and the other part remain as control groups. This process does not always work because of constraints of funding and time. Another example criterion is that teachers express increased efficacy and interest in teaching engineering to their students. Randomized, controlled studies with external evaluators are the pre- ferred method for evaluating and comparing efforts in education, said Lachapelle. NSF, for example, prefers this approach when seeking sum- mative assessments in projects it funds. Unfortunately this type of assess - ment is very expensive to execute because there is usually a need for a fairly large number of students in order to randomize whole classrooms into different testing groups. Also external evaluators are an added cost and bear their own pros and cons. Although external evaluators are likely to be more objective in their assessments, they do not have the advantage of an ongoing relationship with the teachers, administrators, and students whom they are engaging and thus may miss subtleties that more familiar evaluators might observe. In her discussion, Lachapelle cautioned that assessments and evalu - ations of computational thinking activities and materials require clearly specified learning objectives, which in turn require some community con- sensus regarding the content of computational thinking—that is, what is it that the community wants children at various ages to know (from early elementary school to college)? In the EiE context, some learning objectives include being able to identify a process, to explain what a process is in an engineering context, and to explain why the order of steps in a process is important. She also argued that the learning objectives should align with psycho- logical and developmental learning progressions, since doing so provides some guidance over time as to where students should be at each stage. Thus, learning objectives are and should be the object of research and design. She noted that EiE does extensive literature searches and local interviews with kids before beginning the design of each of its units in order to learn more about what kids know. For example, for a unit on sinking and floating, developers would do a literature search and then interview local students by asking them things like, “Do you know what it means to float?,” “Do you understand why things float?,” and so on. Finally, Lachapelle commented that their assessments are also designed to address student attitudes toward science and engineering. Broadly speaking, these assessments indicate that girls tend be interested in engineering things when framed as helping to improve people’s lives and boys tend to be interested in engineering things when framed in terms of constructing engineering artifacts.