The committee held two workshops in 2014—on April 30 and October 2-3 in Washington, D.C.—to explore the knowledge and skills required for cyber-physical systems (CPS) work, education, and training requirements and possible approaches to retooling engineering and computer science programs and curricula to meet these needs. This chapter provides a brief summary of material presented and discussed at the workshops and during a June 26, 2014, briefing with the Jet Propulsion Laboratory (JPL) via teleconference, organized around themes chosen by the committee.
Several speakers from industry spoke about the expected demand for CPS talent. Asked how many individuals with CPS engineering knowledge Ford Motor Company needed, Craig Stephens, with Ford Research and Advanced Engineering, responded “[the] short answer is more than we can get.” Joseph Salvo, director at GE Global Research, observed that “going forward . . . almost all of our employees are going to be touched by this.”
Describing why demand for CPS talent is growing in the automotive industry, Stephens noted that while basic automobile engineering knowledge (power train, combustion, emissions, etc.) remains fundamental, automotive engineers must also be able to design, develop, and test systems that include communication and sensing technologies and
more sophisticated computer controls. These new skills are especially important in new applications such as electrification, vehicle-to-vehicle communication, active safety features, and automated or autonomous driving. Stephens noted that industry has been successful in providing the necessary training, but, looking ahead, companies like Ford hope that employees will enter with a stronger foundation in CPS. Dan Johnson, Honeywell International, Inc., cited aeronautics and aerospace as another transportation industry in which CPS play an increasingly important role. For example, numerous CPS-intensive systems—aircraft, airports, air traffic control, maintenance, passenger services, etc.—make up the air transportation environment.
Jon Williams, a system architect at John Deere, observed that the agricultural and construction equipment sector is increasingly CPS-intensive as well. For example, Deere manufactures partially and fully autonomous vehicles, provides mesh wireless and telematics links between vehicles, updates and repairs its products remotely, and is developing applications for the agronomic data that its products collect. Moreover, Williams noted, a large industrial farm today is a system of systems and requires a systems approach to developing and deploying products and services rather than the traditional focus on individual products.
John Mills, from SimuQuest, Inc., a software company that develops products that support model-based systems engineering, identified key knowledge areas that he is looking for in employees: plant modeling, algorithm design, control system design, network understanding, and engineering process. There is also a new emphasis on CPS skills, including determinism, managing timing and latency, and co-simulation. Mills noted that while Ford, GE, and Deere may have the resources to train their employees in CPS skills, a smaller company like SimuQuest has a harder time doing so.
Scott Hareland, from the medical devices firm Medtronic, Inc., discussed the increasing capability of medical devices to monitor and diagnose health conditions, be life-sustaining (pacemakers), or simply improve life through pain reduction. He noted that while today’s engineers are equipped with some of the skills needed to develop future medical devices, there are still several skills they lack.
Clas Jacobson, United Technologies Corporation, contrasted CPS and systems engineering. He noted that systems engineering is centered around four elements: requirements, architecture, model-based development, and design flows. CPS skills complement those of systems engineers, who are able to quickly build models but are unable to analyze and verify them at a system level. Individuals with CPS engineering knowledge are needed to improve quality as functionality is added to systems.
David Nichols and Daniel Dvorak, JPL, briefed the committee on the
CPS needs of JPL, which designs, builds, deploys, and operates spacecraft systems such as the Mars Science Laboratory, the Curiosity rover, and the Cassini orbiter. Jobs at JPL that require CPS skills include mission formulation dealing with autonomy requirements; engineering design at the assembly, subsystem, and system levels; design activities specifically related to autonomous control (fault management, verification and validation, and mission operations); systems engineering at all levels; and mission, software, and safety assurance. JPL tends to develop flight project engineers internally because JPL finds it hard to identify graduates who already possess all the needed CPS and other engineering skills. Indeed, about four-fifths of JPL’s science and engineering new hires are recent graduates that JPL intends to develop through hands-on project work and mentoring from senior engineers.
Several of the speakers from industry noted that engineers who deeply understand and can apply systems thinking—that is, a deep understanding of how individual parts of a system interrelate with one another and within the system as a whole—and related concepts such as abstraction and system interaction and who can carry out systems analysis using formal methods and model-based verification are in short supply. Nichols and Dvorak from JPL observed that few universities seemed to be emphasizing mission- or safety-critical systems and that hands-on project work tends to ignore properties like fault tolerance and robustness. Stephens from Ford Motor Company also noted that there is a focus on developing new functions over understanding the tools and techniques needed to test and maintain current systems. Mills pointed out that SimuQuest seeks to hire “super engineers,” individuals with knowledge in computer science and object-oriented programming; embedded software engineering; experience with hardware, firmware, drivers, BIOS, and controls systems; and plant modeling. Finding individuals with such a wide breadth of skills may seem impractical but is integral in developing new technologies.
Johnson from Honeywell underscored the importance of cybersecurity for engineers in fields like aerospace engineering, where knowledge is needed in such areas as risk management and product integrity, cryptography, and the security of network and communications protocols as well as behavioral and social aspects of security. Williams added that it was important to understand security at the system as well as component level.
Several speakers pointed to challenges working across disciplines. Hareland noted that students need to learn how to work in the cross-functional teams that are needed to build CPS, something that requires
both broad knowledge of multiple areas of expertise and excellent communication skills. Unfortunately, Hareland observed, there are countervailing trends toward very deep, narrow, and isolated work, perhaps amplified by the “publish or perish” academic culture, which often serves as a disincentive to interdisciplinary work.
Other “soft skills” were identified as important to creating well-rounded CPS engineers. Nichols and Dvorak noted, for example, that engineers sometimes fail because they simply cannot “read a room” to understand what information at what level is needed by a customer. Additionally, Williams observed that soft skills are especially important when designing for a global market. For example, the diverse regulatory, legal, and standards requirements found around the globe have significant implications for the design process. Solid technical writing and other communications skills are also essential.
Academic presenters identified what they saw as gaps in CPS education today. Sanjai Rayadurgam, Software Engineering Center, University of Minnesota, observed that although traditional undergraduate curricula cover the fundamentals of math and science, programming, and problem solving well, they do less well with applications, software engineering, and problem identification. Students are able to analyze the correctness of components but less equipped to address integration, composition, and other system-level concerns. Rayadurgam noted that students not only need to be able to verify the correctness but convince others of this correctness. Alberto Sangiovanna-Vincentelli, Department of Electrical Engineering and Computer Science, University of California, Berkeley, commented that it was far more important for students to learn design science principles than to master a particular design technique or tool suite. Janos Sztipanovits, Departments of Electrical Engineering and Computer Engineering, Vanderbilt University, discussed the need for a cross-disciplinary view of design. Sztipanovits observed that the traditional way to design starts with functional decomposition to identify major components. These components are then designed, often with a discipline-centric focus; the components are integrated; and the resulting system is subjected to testing and verification. This process often fails because interdependencies are not properly accounted for.
Douglas Adams, Department of Civil and Environmental Engineering, Vanderbilt University, suggested that project-based learning should be integral to any CPS curriculum. Students need to work on complex interdisciplinary projects that encourage systems-level thinking. Doing so requires test beds that allow for the codesign of physical and computational components that demonstrate the benefits of integrating simulation and experimentation. Sztipanovits observed that design studios, where
students can work on integrative CPS projects with multidisciplinary teams, are important.
Further discussion by workshop participants identified other skills and knowledge areas needed by a person working in CPS. These include behavior modeling, control systems, uncertainty, information management, embedded systems, embedded system design, and experience working with hardware and firmware.
CPS are only one of several current drivers of change in engineering education. Norman Fortenberry, American Society for Engineering Education, described some of the attributes expected of modern engineers: flexibility to manage rapidly evolving technologies; an ability to define as well as solve problems; skill and experience with creativity, entrepreneurship, and public policy implications; and facility with both theory and application.
Several speakers noted that engineering students increasingly seek hands-on experience early in their student careers, want to engage in meaningful work with real-world impact, and wish to be entrepreneurial. Furthermore, students tend to be motivated by societally important “grand challenges.” For example, students find large-scale projects that address real-world problems in areas like urban sustainability appealing.
Shankar Sastry, University of California, Berkeley, discussed how his institution has responded to such interests. In 2005, Berkeley started the Center for Entrepreneurship and Technology to support the prototyping of projects and a connection to businesses. The Blum Center for Developing Economies, launched in 2007, provides global field study opportunities and other international experiences. The Fung Institute for Engineering in 2010 began offering entrepreneurship opportunities via its Global Venture Lab. The Jacobs Institute for Design Innovation provides hands-on, design, and “maker” experiential learning opportunities for students and working studios for design, iteration, optimization, and commercialization.
Traditionally, students have spent the early part of their undergraduate years fulfilling basic course requirements, whereas students today, some of whom may have been building things in high school, want to continue building new things. Kevin Massey from the Defense Advanced Research Projects Agency, cautioned that students risk jumping too far ahead, not appreciating that an ability to work with plug-and-play hardware and software is not, ultimately, a substitute for foundational knowledge. Massey asked whether it is possible to develop a curriculum that blends both aspects in a way that is both immediately appealing to stu-
dents and provides them the solid educational foundation they need to be successful in their careers.
Several presentations provided examples of creating a CPS course or building CPS curricula or programs.
Edward Lee, Department of Electrical Engineering and Computer Science, University of California, Berkeley, discussed his experiences teaching a course titled “Introduction to Embedded Systems” with the goal of introducing students to the design and analysis of computational systems that interact with physical processes. Lee also noted that the traditional view of embedded systems assumes special-purpose hardware and that the chief problem is the interface between sensors and actuators and the system’s resource constraints. CPS is different—and more interesting—because of the interactions with the physical world.
The principal focus of the course was the interplay of practical design with formal models of systems, including both software components and physical dynamics, with a major emphasis on building high-confidence systems with real-time and concurrent behaviors. Traditional embedded systems classes tend to focus on building the core technical competencies to build systems. By contrast, Lee’s course also emphasized critical thinking about systems. What are the pitfalls? Where can improvements be made? Figure 1.1 compares elements of a traditional embedded systems course and a CPS-focused course.
As part of preparing for the course, Lee and coauthor Sanjit Seshia wrote a textbook titled Introduction to Embedded Systems: A Cyber-Physical Systems Approach.1 The text incorporates three distinct threads: modeling (the process of gaining deeper understanding of a system through imitation), design (the structured creation of artifacts), and analysis (the process of gaining understanding through system dissection). Material from a classical embedded systems course makes up much of the design category. The modeling side is focused on cyber-physical system modeling. Topics include modeling the physical using ordinary differential equations, combining discrete dynamics with continuous dynamics, simulation using actor models, and modeling concurrency. The analysis thread provides an introduction to formal methods. Any one of these threads
FIGURE 1.1 Elements of traditional embedded systems and CPS-focused courses. NOTE: FPGA, field-programmable gate array. SOURCE: Edward A. Lee, University of California, Berkeley.
could be the subject of a course on its own; in any introductory course, the goal is to introduce these elements and explore their interplay.
Introduction to Embedded Systems supports the threads being read concurrently and also fits nicely within a 15-week semester. Included with the text is a free laboratory manual, which was developed with support from National Instruments. Laboratory projects over the first 6 weeks cover sensors, operating-system-less programming, direct-memory mapping to interact with input/output devices, C language programming, and model-based design, culminating in a robotics challenge. A 9-week capstone project, defined by the students, follows these laboratories. Lee noted that the laboratory portions of any course can became unwieldy to manage, especially as class size grows.
Lee concluded his remarks by expressing hope that by emphasizing modeling, design, and analysis, his course could help students avoid the sort of bruteforce and over-engineering all too often used to build embedded systems today. Also, if students are to be positioned to build the systems of tomorrow, they need to understand not just today’s best practices but the weaknesses in those approaches. Lee explained, “Our view is that the field of cyber-physical systems is very young, and it would not serve our students well to leave them with the illusion that completing the course is equated to mastery of the subject.”
Tarek Abdelzaher, Department of Computer Science, University of Illinois, Urbana-Champaign, presented a conceptual CPS curriculum. Comparing a more traditional embedded systems course with a CPS-course, Abdelzaher noted that a CPS course must teach students to reason about a system (not just components) that combines interacting computational and physical components and address reliability, robustness, timeliness, performance, and stability requirements. These skills map to fundamental background knowledge in areas such as probability, control, and queuing theory and real-time systems, dynamic systems, and operating systems. Furthermore, students must be able to understand architectural trade-offs and analysis techniques and gain experience designing and implementing CPS given high-level specifications. Abdelzaher ’s proposed curriculum, including these elements and drawing on existing electrical engineering and computer science curricula, is shown in Figure 1.2.
André DeHon, University of Pennsylvania, described how Penn’s experience developing a computer engineering (CE) program might inform the development of a CPS program. At Penn, the CE program is separate from the electrical engineering (EE) and computer and information science (CIS) departments. It emphasizes embedded systems but is not exclusively CPS. The course requirements for CE include several courses offered by the EE and CIS departments together with a few new CE courses (see Figure 1.3). Several of the courses are not required for either the EE or CIS undergraduate degree but are requirements for the CE degree. As a result, although much of the coursework overlaps with that of other departments, the required coursework is quite different from that in either EE or CIS.
DeHon concluded by considering what would need to be added to the CE program to create a CPS-focused curriculum. He suggested that additional courses would be needed in linear algebra, control, design, and mechatronics or robotics.
The committee is interested not only in how one might go about establishing a CPS-focused curriculum or program, but also in how CPS knowledge currently is and might be incorporated into existing engineering programs.
FIGURE 1.2 A model for CPS curriculum. Courses highlighted in gray focus specifically on CPS, while the other courses are existing courses. SOURCE: Tarek Abdelzaher, University of Illinois, Urbana-Champaign.
FIGURE 1.3 Coursework for computer engineering (and cyber-physical systems). NOTE: RLC, resistance (R), inductance (L), and capacitance (C). SOURCE: André DeHon, University of Pennsylvania.
Jonathan How, Massachusetts Institute of Technology (MIT), discussed the need for CPS skills in aerospace engineering. He started by describing emerging applications of aerospace engineering, such as supporting wired and wireless network communications, expanding use of unmanned vehicles, commercial access to low Earth orbit, and addressing environmental and energy challenges as air travel continues to grow. How noted that MIT’s AeroAstro department has been working to identify the long-term competencies associated with these applications and build up its faculty in those areas, many of which overlap with CPS knowledge and skills. Key areas include design of aerospace vehicles; real-time aerospace information science; advanced computation methods to support design and decision-making; human-system collaboration; atmospheric science and how it informs system design; and the design, implementation, and operation of complex aerospace systems.
Cutting across these core competencies, there is a broad focus on systems. Students learn to appreciate the challenges of larger-scale “missions” and the cost, complexity, and time that must be invested in both hardware and software aspects of a system. Other cross-cutting themes include software, which has become ubiquitous in aerospace systems, and communications networks and security.
Coursework places a significant emphasis on experimental and sys-
tems design, allowing students to develop technical depth through hands-on activities.
How listed the following areas where CPS curriculum could improve:
- • Give students design problems with larger scope and cross-disciplinary mission goals, including problems that involve multiple departments and run across multiple semesters.
- • Emphasize development of communications skills.
- • Evolve the core control curriculum, which has been static for many years, to better reflect CPS fundamentals and applications.
- • Increase the emphasis on software and computing in the design process for systems taught to students.
- • Address technologies for use of multiple sensors.
- • Place greater emphasis on human-systems interaction and human factors design issues.
How concluded by underscoring that it was important not only to impart particular knowledge and develop particular skills, but also to create lifelong learners who can adapt to new technologies, tools, and problems.
Jerry Lynch, University of Michigan, discussed how CPS technologies have had significant impact on civil and environmental engineering (CEE) in applications such as intelligent transportation systems, earthquake early-warning systems, flood control, and real-time monitoring of smart buildings. CPS-rich intelligent infrastructure is an emerging and important subdiscipline of CEE. CPS technologies make it possible to detect and collect large sets of data from structures and create new opportunities to monitor and study them. CPS technologies are attracting students both because they make CEE appear more “high tech” and because they help make possible advances in two compelling applications of CEE—urban sustainability and community resiliency. In response to new technology opportunities and changing student interests, the University of Michigan has hired CPS-oriented faculty and created a new graduate program in intelligent infrastructure. Much of the faculty who participate have dual degrees in CEE and electrical and computer engineering.
Lucio Soibelman, University of Southern California, discussed the graduate program his school has created in advanced infrastructure systems. He noted that a particular challenge is teaching the necessary graduate-level computer science material to civil engineering graduates, who often lack a strong foundation in computer science.
Christopher Gill, Washington University in St. Louis, used a current
research project on structure modeling to demonstrate the importance of interdisciplinary CPS research teams. One of the project’s experiments used the response to stress of a piece of a structure in a simulation of the full structure. Such work requires knowledge and skills from computer science, computer engineering, mechanical engineering, and civil engineering. Gill also noted a conflict between what can be done and what needs to be done. Data can be provided very quickly—a millisecond interval for refreshing and delivering actuation commands—but do civil engineers need that much data? Does the physical phenomenon have such a high dynamic? Can the model provide additional detail over faster data during the time interval? In conclusion, Gill reiterated that separate disciplines have much to teach each other, and research topics that interlock with other disciplines help students develop both depth and breadth.
Several speakers addressed the related questions of how the teaching and research capacity needed to support CPS education can be built and what other resources are needed to support CPS education.
In his remarks, Christopher Gill observed that the situation with CPS today resembles the one roughly two decades ago with distributed real-time embedded systems, when knowledge and skills from the distinct areas of real-time systems, software engineering, and distributed systems had to be integrated. Support from varying organizations and agencies helped to build communities across previous boundaries, and today, with CPS knowledge spread across multiple research disciplines and educational programs, a similar integration effort is needed. Gill noted that agency coordination and investment is needed.
Jerry Lynch observed that the next generation of faculty in many areas of engineering and computer science will need a broad exposure to CPS. However, Lynch also noted that faculty members need to be deep experts in a core discipline (e.g., civil engineering) and that their preparation should reflect a balance between theory and applied research. Lynch further noted that applications for faculty positions concentrated on CPS may not have been strong because the candidates do not have the expected depth in more traditional areas. Similarly, junior faculty may find themselves in departments where the senior faculty have dissimilar backgrounds and research and teaching interests.
Several speakers stressed the value of hands-on projects. Philip Koopman, Carnegie Mellon University, noted that the tools needed to provide students with this experience must incorporate the challenges of large-scale systems and are often expensive and require frequent technology refreshes. Koopman also explained that developing problems
that represent the complexity of CPS is difficult. Projects and problems must be realistic and motivating but also incorporate domain knowledge that is accessible to students. There is a risk that problems can become overly complicated—projects must be designed with the right amount of “messy.”
In addition to recruiting faculty, universities will need to ensure that CPS is attractive to students. Several presenters reported that students tend to be attracted to courses that emphasize robotics or the Internet of things but hesitate to register for courses that specifically reference CPS.
Additionally, presenters from both industry and academia observed that large information technology (IT) firms like Facebook and Google have captured the imagination of undergraduates in a way that many CPS-intensive firms have not, even though CPS work also provides significant opportunities to innovate and have considerable real-world impact. Several asked how these opportunities can best be communicated to current and prospective students.
Although the workshop presentations and JPL briefing were largely focused on 4-year undergraduate programs and subsequent graduate programs (to some degree), some talks also touched on opportunities to introduce CPS concepts in K-12 education and supplement CPS education and training through industry-academic partnerships, internships, and online, post-graduate continuing education.
Dimitri Mavris discussed efforts in his laboratory, the Georgia Institute of Technology’s Aerospace Systems Design Laboratory (ASDL), to bridge the gap between the kinds of CPS-related research that students are typically exposed to in academia and the kinds of research carried out in industry. In the ASDL program, students are engaged for two semesters in open-ended, interdisciplinary, and large-scale projects. The problems require practical implementation of advanced methods that go beyond those needed in typical senior design problems. In one case, General Electric provided ASDL with a set of problems whose solution would require student teams with strong foundations in power technology, software, and complex system design and analysis. Five interdisciplinary teams
were created with students from electrical engineering, systems engineering (from the aerospace engineering department), and management programs. An industry representative who provided practical advice and technical feedback, and course correction as needed, advised the students.
Mavris described several challenges faced by students grappling with the inherently interdisciplinary nature of the problems. For example, systems engineering students felt they lacked sufficient expertise in electrical engineering while at the same time the EE students did not always accept the architectural work being done by the systems engineers. Over time, the students’ knowledge and appreciation of the contributions that each discipline could make to the team effort grew, as did trust and the quality of the collaboration.
Also, the teams found they had gaps in their collective knowledge in such areas as practical consideration of real power flow systems, systems engineering fundamentals, economic and market opportunity analysis, and impact of grid regulation on solution viability. Students also struggled with the business aspects of the project—overexplaining the structure and value of smart grid systems solutions and struggling with business plan development for products or services. Students also tended to rush into design activities before fully exploring alternatives.
Mavris cited several ingredients for a successful research partnership program. Both faculty and the industry partner must be very committed, and the students must be highly motivated, competitive, inventive, and articulate. Success is most likely when the industry problems are aligned with faculty expertise and research activities. The intellectual property issues inherent in working with industry will also require attention and appropriate coordination mechanisms.
Steve Anton, Tennessee Technological University, described his experience with Los Alamos National Laboratory’s Dynamics Summer School. The 9-week intensive summer program assigns a staff mentor to students and allows students to learn more about CPS and carry out research. Anton observed that some students enter the school relatively unfamiliar with CPS, and many are unfamiliar with key topics such as sensing, data acquisition, and signal processing. The students participate in week-long tutorials on sensors, controls, signal processing, and embedded systems. Students also participate in laboratory research, gaining familiarity with research practices and laboratory equipment, and develop teamwork and technical writing skills. Because it is designed to be multidisciplinary, the program works well to break down boundaries among mechanical, electrical, and computer engineers and scientists. An additional benefit to
students’ future careers in CPS is that they develop contacts in the CPS technical community.
Magnus Egerstedt, Georgia Institute of Technology, described his experiences developing and teaching a CPS-related massive open online course (MOOC). Egerstedt had taught an embedded and hybrid control systems course at the senior undergraduate level to students from electrical, computer, mechanical, and aerospace engineering and computer science and sought to provide a more solid grounding in theory as well as additional opportunities to apply that theory in practice. A stronger theoretical foundation would allow students who otherwise tended to approach difficult problems by patching the code to use more formal and systematic approaches. “Flipping the classroom” by using a MOOC to cover the theory component would maximize the classroom time available to apply the theory to robotics laboratories.
Topics for the MOOC included an introduction to controls, mobile robots, linear systems, control design, hybrid systems, navigation problems, and, finally, connecting these elements. Initial enrollment in the 2013 course was around 40,000; about 7,000 remained active at the end of the session.2 Students passing 65 percent of quizzes received a certificate of completion, and those passing 90 percent received a certificate of distinction. Egerstedt was also surprised that several of those enrolled were practicing engineers who wanted to revisit the topic.
On the practice side, Egerstedt was unhappy with the available choices for educational robots, so his team developed its own, the Quick-Bot. This robot has a differential drive, four infrared inputs, WiFi, and optical encoders and uses BeagleBone Black and Arduino computers. The cost is approximately $150 to $300. Egerstedt worked with hardware companies and online electronics providers to ensure that parts were available. Lessons were provided to help students build their own robots.
Egerstedt noted several challenges. The project was incredibly difficult, requiring three times the work of a regular class. Dividing what would normally be 90-minute lectures into very short sublectures typical of MOOCs is hard, and writing multiple-choice questions on a complex topic like control theory is incredibly difficult. Egerstedt also noted that
2 Edward Lee, University of California, Berkeley, also spoke briefly of teaching a CPS MOOC based on his embedded systems course. Offered during the summer of 2014, the course provided virtual laboratory software. The course was 6 weeks long and included 49 lectures (approximately 11 hours of video) and 6 weekly laboratory assignments. Peak enrollment was 8,767, with 2,213 submitting at least one assignment. Approximately 1,543 scored above a 0, and only 342 “passed.”
the overall design for a CPS course is challenging. For example, what are the prerequisites, what are appropriate assignments and laboratories, and how multidisciplinary should the lessons be?
Egerstedt concluded by expressing excitement about CPS as a new field and the pedagogical potential of flipped classrooms using MOOCs. There is a serious appetite for CPS content, and Egerstedt found that other schools were using his MOOC to flip their own classrooms. Egerstedt also suggested that MOOCs could be used to help students lacking prerequisite material or to supplement faculty capabilities.
Harry Cheng discussed his work in incorporating CPS into K-12 education at the University of California, Davis, Center for Integrated Computing and Science, Technology, Engineering, and Mathematics (C-STEM). C-STEM was created to close the achievement gap by broadening participation of traditionally underrepresented students in computing and STEM-related careers. C-STEM incorporates computing and robotics, two areas that touch on CPS core knowledge, into the K-12 curriculum by finding ways to use them to teach mathematics and other core subjects. The C-STEM curriculum, outlined in Figure 1.4, is accepted as part of the subject matter admission requirements of the University of California
FIGURE 1.4 C-STEM Curriculum. SOURCE: Harry H. Cheng, UC Davis Center for Integrated Computing and STEM Education (C-STEM), University of California, Davis.
system, allowing California schools to adopt the curriculum. In addition to developing the curriculum, C-STEM supports K-12 teacher development via a summer institute, academic year workshops, onsite training, and periodic conferences. Furthermore, C-STEM supports numerous robotic competitions that develop student skills and foster interest in the curriculum.