As K-12 schools incorporate computer science, one of the challenges they face is preparing teachers to teach their first CS course. Survey responses were collected from teachers each day of a week long professional development, and then at a follow up session near the end of their first semester of implementation. In this paper we discuss teacher responses from their implementation of CS Makers in their middle school classrooms. The professional development sessions used a curriculum developed in our NSF INCLUDES supported CS Makers course with micro:bit hardware. We found that most of the teachers were out of their fields, many were told to teach the class, rather than requesting it, and all had positive results with students.

It is a widely held belief among computer science researchers that studying computer science enhances critical thinking, problem solving, and creativity; and it should be a part of the K-12 classrooms. Our home state has joined other states in mandating the latter. Issues of curriculum development, teacher preparation, pre-service and in-service training, funding and logistics, are all important. Over several years, we have developed a novel approach to using computer programming to explicitly teach mathematical generalization and abstraction. In this study, we applied this instructional model to pre-service elementary teachers (PSETs). PSETs participated in four days of explicit instruction where students wrote mini programs designed to push them towards generalization of statistics concepts found in the elementary classroom. Along with instruction, PSETs were given information regarding the important contributions of computer science and abstraction in their future elementary classrooms. Results showed that PSETs did show improvement in conceptual understanding and also showed that some of the teachers were initially unconvinced that the curriculum was relevant to them or to their future classrooms. The instruction improved PSET attitude and showed that training to meet new computer science (CS) standards in K-6 can and should address this reluctance.

Computer science and math education researchers have long believed that a symbiotic relationship exists between their disciplines [7]. In fact, in its early days, computer science education programs were often co-located in a math department. Stenger et al. [13] developed an instructional treatment that uses computer programming as an explicit method for teaching abstraction and generalization in the STEM classroom. This instructional strategy uses computer programming to explore the essential characteristics of a mathematical concept and to push learners to advance in levels of abstraction. In this study, results are shown from a professional learning session using computer programming activities, mathematical arguments, and programming on an S2 robot to push middle and high school computer science, math, and science teachers (N=25) to improve their level of generalization over area expansion of a triangle with respect to the expansion of the sides of the triangle. The programming activities served as a laboratory to expose and explain what happened in the minds of learners as they explored and learned to generalize this geometry concept. The researchers used an initial genetic decomposition to evaluate the learner's level of abstraction. Follow up interviews were conducted with 6 participants. The analysis, using APOS as a framework, categorized mathematical behaviors at the Action, Process or Object level. The data demonstrated how computer programming activities influenced teachers' mental images and pushed them to higher levels of abstraction.

Compromising IoT devices to build botnets and disrupt critical infrastructure is an existential threat. Refrigerators, washing machines, DVRs, security cameras, and other consumer goods are high value targets for attackers due to inherent security weaknesses, a lack of consumer security awareness, and an absence of market forces or regulatory requirements to motivate IoT security. As a result of the deficiencies, attackers have quickly assembled large scale botnets of IoT devices to disable Internet infrastructure and deny access to dominant web properties with near impunity. IoT malware is often transmitted from host to host similar to how biological viruses spread in populations. Both biological viruses and computer malware may exhibit epidemic characteristics when spreading in populations of vulnerable hosts. Vaccines are used to stimulate resistance to biological viruses by inoculating a sufficient number of hosts in the vulnerable population to limit the spread of the biological virus and prevent epidemics. Inoculation programs may be viewed as a human instigated epidemic that spreads a vaccine in order to mitigate the damage from a biological virus. In this paper we propose a technique to create an inoculation epidemic for IoT devices using a novel variation of a SIS epidemic model and show experimental results that indicate utility of the approach.

Botnets compromised of IoT devices have been on the rise recently with attacks originating from compromised refrigerators, DVRs, security cameras, and other consumer networking equipment. Most owners of these devices are neither security aware or motivated to secure their IoT devices. Manufacturers of these devices are not currently motivated by market forces or regulatory requirements to improve the security of their products. At 7: 00 a. m. on October 21st of 2016 the Mirai IoT botnet launched a DDoS attack against Dyn, a major DNS provider. The attacking hosts generated 1.2 terabits of malicious traffic forcing Dyn off the Internet for hours. This was the second high profile attack by the Mirai botnet. Noted security blogger Brian Krebs' site was the target of the first high profile Mirai attack on September 20, 2016. As a result of the publicity the source code for the botnet was published in early October. We have reviewed the source code and devised a tactic that will use the same compromise vector as the Mirai botnet to catalog vulnerable IoT devices and motivate operators to address their poor security practices. In this paper we discuss our approach and show experimental results that indicate feasibility.

ion and generalization are critical skills for navigation through the computer science and mathematics curriculum. Any effort to improve instruction should take into consideration how students learn. It is widely believed that teaching proof writing as a solitary activity may not provide students the building blocks to become proficient in reasoning about mathematical concepts. Stylianides claims that the four essential components of ‘reasoning-and-proving‘ are ‘identifying patterns, making conjectures, providing non-proof arguments and providing proofs‘ (Stylianides, 2008). Jenkins, et al., developed an explicit approach to teaching abstraction and generalization that considers the mental processes by which abstract concepts are acquired and utilized (2012). In developing the instructional treatment, close attention was paid to the theory of learning called APOS theory (Dubinsky, 1984). APOS is an acronym that stands for Action, Process, Object, and Schema. Each level denotes a cognitive classification of the learner's conception. APOS theory is an outgrowth of Piaget's theory of Reflective Abstraction (Piaget, 1971). As a constructivist theory, the basic tenet of APOS theory is that an individual's understanding of a mathematical topic develops through reflecting on problems and their solutions in a social context and constructing or reconstructing certain mental structures, then organizing these mental structures into schemas to use in dealing with problem situations. Specifically, in APOS theory, the process of reflective abstraction is the key to cognitive construction of logico-mathematical concepts (Dubinsky & McDonald, 2001, Beth & Piaget, 1966). Programming as a Vehicle for Building Abstraction in the Mind of the Learner Researchers in APOS theory have long employed computer programming as a means to teach undergraduate mathematics. In numerous studies, spanning several countries, and applied to a spectrum of mathematical topics, APOS theory has been applied to the use of computer experiences to encourage the construction of mental processes that lead to mathematical concepts (Asiala et al., 1998, Weller et al., 2008). The computer treatments have consistently yielded an increase in likelihood that students acquired the desired concepts. It is a commonly held belief among this substantial group of researchers that computer constructions are an intermediary between concrete objects and abstract entities (Dubinksy, 1997, Asiala et al., 1998). Instructional Treatment: Building Mental Structures with Computer Programming Applying this theoretical framework, an instructional treatment was developed using computer programs to push students to build the mental frameworks for abstraction and generalization. This instructional treatment consists of four stages as shown in Figure 1. In the first stage essential characteristics (ESS) of a problem are identified. Next, mini programs (PROG) are written to explore the essential characteristics. General expressions (GEN) are found in the programs. Participants are taught to write these generalizations as mathematical statements. Further exploration with computer programs (PROG) leads to more generalizations, and general expressions (GEN) are collected as participants conjecture about relationships between concepts. Participants are taught to write convincing arguments (CA) for some of the conjectures, using the general expressions (GEN). Figure 1. The four stages of the instructional treatment

Traditional L2 VPNs such as Frame Relay and ATM offer private network service over shared infrastructure. These services are customarily provided on leased-lines or dedicated circuit-switched backbones. Customers of network service providers regard these traditional services as a secure and reliable method to interconnect geographically dispersed sites. However, these services are being rapidly replaced by service providers with MPLS L3 VPNs running over IP based networks. Customers expect MPLS VPNs to provide the same level of privacy as traditional L2 VPNs. The MPLS L3 VPN architecture has been shown to be secure if and only if the MPLS infrastructure is correctly configured. In this paper we examine how misconfigurations of the MPLS architecture may lead to privacy violations and demonstrate the MINA algorithm is capable of discovering when the MPLS network is misconfigured.

Students have difficulty with concepts that require mathematical reasoning such as abstraction and generalization. Efforts to improve instruction often do not take into consideration how students learn. Often times the unintentional expectation communicated to the student is to mimic the behavior of the teacher. A more fruitful approach may be to consider the mental processes by which abstract concepts are acquired.

In this paper we explore CS students' perception of the relationship between computer science and mathematics. It is widely accepted by educators and researchers that the study of mathematics is an essential part of the CS curriculum. We were surprised to discover that many of our CS students believed that no relationship or dependence exists between computer science and mathematics. We establish that many of our CS undergraduates do not believe that mathematical reasoning and problem solving skills are necessary for success in computer science. Furthermore, we will show that this anti-symbiotic stereotype is harmful to student's success in computer science.

This paper describes a design for an immediate immersion of computational thinking into current high school math classrooms in Alabama. Most schools in our region have eliminated computer science classes from the curriculum. Alabama has an existing state initiative to improve mathematics, science and technology education in K-12. The Alabama Math, Science, and Technology Initiative (AMSTI) emphasizes learning by doing, with hands-on, activity based instruction. We have developed an instructional treatment that uses strategically designed computer exercises to push students to form the mental foundation necessary for abstraction and generalization. We selected popular problems from the AMSTI mathematics curriculum and applied our instructional design. The first step we took in implementing our plan for reintroducing computational thinking into the secondary schools was to conduct a workshop for math education leaders. This training was sponsored and supported by AMSTI. Results from the workshop included demonstrating to a select group of math education leaders that computer programming could be easily integrated with the AMSTI math curriculum and could be used to meet the educational goals of the initiative and the educators.

Connecting geographically dispersed sites by layer two virtual private networks is a widely deployed, cost effective, and reliable technology. The key feature of layer two virtual private networks is confidentiality. However, L2 VPNs are being rapidly replaced by layer three virtual networks as common carriers expand the roles of their shared IP networks. The recent increase of interest in L3 virtual networks has led to renewed interest and new questions concerning their privacy.We designate virtual network nodes that are undesirable as extrinsic. In this paper we propose a novel algorithm, Message Induced Network Appraisal (MINA), for detecting the presence of extrinsic nodes in virtual networks. MINA is inspired by Kleinberg's HITS algorithm for ranking web pages. The generalization of a HITS derived algorithm to detecting the presence of extrinsic nodes in virtual networks is novel.Our MINA algorithm constructs the communication graph induced by message exchange, scores the participating nodes to identify mutual nodes, and detects the presence of extrinsic nodes. Using the MINA algorithm, network users are presented with a useful indicator about the confidentiality of their L3 virtual network. In this paper we describe MINA and demonstrate that our method reliably detects the presence of extrinsic nodes in L3 virtual networks.

Virtual networks continue to increase in popularity as a technique to implement confidential communications over a shared network infrastructure. The retirement of legacy layer 2 virtual networks, widespread availability of common carrier TCP/IP networks, and migration to layer 3 virtual network technologies has resulted in the inability to determine if undesirable nodes are connected to a virtual network. A method for classifying the members of a virtual network into communities is of significant interest to researchers seeking solutions to this problem. We propose a community detection methodology inspired by Kleinberg's HITS algorithm for web topic searches. The application of a HITS derived algorithm to community detection in virtual networks is novel. Our method reliably detects the presence of active communities in the virtual network and identifies community members in the common set of nodes.

This study explores undergraduates’ understanding of direct variation before and after instruction using computer programming to teach generalization over the concept. Based on an initial genetic decomposition for direct variation, the four math/CS researchers developed a research design that included lessons featuring computer programming and mathematical proof writing activities. This study shares results from an application of the instructional research design to N=33 undergraduates interested in teaching. Lessons were from a secondary education math methods course. Follow up interviews were conducted with seven participants. The analysis, using APOS as a framework, categorized mathematical behaviors at the Action, Process or Object level. The study identified obstacles that may have prevented progression through deeper levels of understanding such as deficient prerequisite skills and an affinity for routine algebraic manipulation rather than considering underlying relationships. The student data demonstrated how computer programming activities influenced undergraduates’ mental images.