Geoffrey Herman

Seth Poulsen, Shubhang Kulkarni, Geoffrey Herman et al.

Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing solution quality feedback to students. This is done by computing the edit distance from a student's submission to some predefined set of solutions. In this work, we propose an algorithm for the edit distance problem that significantly outperforms the baseline procedure of exhaustively enumerating over the entire search space. Our algorithm relies on a reduction to the minimum vertex cover problem. We benchmark our algorithm on thousands of student submissions from multiple courses, showing that the baseline algorithm is intractable, and that our proposed algorithm is critical to enable classroom deployment. Our new algorithm has also been used for problems in many other domains where the solution space can be modeled as a DAG, including but not limited to Parsons Problems for writing code, helping students understand packet ordering in networking protocols, and helping students sketch solution steps for physics problems. Integrated into multiple learning management systems, the algorithm serves thousands of students each year.

Seth Poulsen, Mahesh Viswanathan, Geoffrey L. Herman et al.

Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback on how they are doing with their proofs. When constructing a problem, the instructor specifies the dependency graph of the lines of the proof, so that any correct arrangement of the lines can receive full credit. This innovation can improve assessment tools by increasing the types of questions we can ask students about proofs, and can give greater access to proof knowledge by increasing the amount that students can learn on their own with the help of a computer.

Alan T. Sherman, Geoffrey L. Herman, Linda Oliva et al.

We reflect on our ongoing journey in the educational Cybersecurity Assessment Tools (CATS) Project to create two concept inventories for cybersecurity. We identify key steps in this journey and important questions we faced. We explain the decisions we made and discuss the consequences of those decisions, highlighting what worked well and what might have gone better. The CATS Project is creating and validating two concept inventories---conceptual tests of understanding---that can be used to measure the effectiveness of various approaches to teaching and learning cybersecurity. The Cybersecurity Concept Inventory (CCI) is for students who have recently completed any first course in cybersecurity; the Cybersecurity Curriculum Assessment (CCA) is for students who have recently completed an undergraduate major or track in cybersecurity. Each assessment tool comprises 25 multiple-choice questions (MCQs) of various difficulties that target the same five core concepts, but the CCA assumes greater technical background. Key steps include defining project scope, identifying the core concepts, uncovering student misconceptions, creating scenarios, drafting question stems, developing distractor answer choices, generating educational materials, performing expert reviews, recruiting student subjects, organizing workshops, building community acceptance, forming a team and nurturing collaboration, adopting tools, and obtaining and using funding. Creating effective MCQs is difficult and time-consuming, and cybersecurity presents special challenges. Because cybersecurity issues are often subtle, where the adversarial model and details matter greatly, it is challenging to construct MCQs for which there is exactly one best but non-obvious answer. We hope that our experiences and lessons learned may help others create more effective concept inventories and assessments in STEM.

Travis Scheponik, Enis Golaszewski, Geoffrey Herman et al.

We present and analyze results from a pilot study that explores how crowdsourcing can be used in the process of generating distractors (incorrect answer choices) in multiple-choice concept inventories (conceptual tests of understanding). To our knowledge, we are the first to propose and study this approach. Using Amazon Mechanical Turk, we collected approximately 180 open-ended responses to several question stems from the Cybersecurity Concept Inventory of the Cybersecurity Assessment Tools Project and from the Digital Logic Concept Inventory. We generated preliminary distractors by filtering responses, grouping similar responses, selecting the four most frequent groups, and refining a representative distractor for each of these groups. We analyzed our data in two ways. First, we compared the responses and resulting distractors with those from the aforementioned inventories. Second, we obtained feedback from Amazon Mechanical Turk on the resulting new draft test items (including distractors) from additional subjects. Challenges in using crowdsourcing include controlling the selection of subjects and filtering out responses that do not reflect genuine effort. Despite these challenges, our results suggest that crowdsourcing can be a very useful tool in generating effective distractors (attractive to subjects who do not understand the targeted concept). Our results also suggest that this method is faster, easier, and cheaper than is the traditional method of having one or more experts draft distractors, and building on talk-aloud interviews with subjects to uncover their misconceptions. Our results are significant because generating effective distractors is one of the most difficult steps in creating multiple-choice assessments.

Alan T. Sherman, Linda Oliva, Enis Golaszewski et al.

For two days in February 2018, 17 cybersecurity educators and professionals from government and industry met in a "hackathon" to refine existing draft multiple-choice test items, and to create new ones, for a Cybersecurity Concept Inventory (CCI) and Cybersecurity Curriculum Assessment (CCA) being developed as part of the Cybersecurity Assessment Tools (CATS) Project. We report on the results of the CATS Hackathon, discussing the methods we used to develop test items, highlighting the evolution of a sample test item through this process, and offering suggestions to others who may wish to organize similar hackathons. Each test item embodies a scenario, question stem, and five answer choices. During the Hackathon, participants organized into teams to (1) Generate new scenarios and question stems, (2) Extend CCI items into CCA items, and generate new answer choices for new scenarios and stems, and (3) Review and refine draft CCA test items. The CATS Project provides rigorous evidence-based instruments for assessing and evaluating educational practices; these instruments can help identify pedagogies and content that are effective in teaching cybersecurity. The CCI measures how well students understand basic concepts in cybersecurity---especially adversarial thinking---after a first course in the field. The CCA measures how well students understand core concepts after completing a full cybersecurity curriculum.

Alan T. Sherman, Linda Oliva, David DeLatte et al.

We report on the status of our Cybersecurity Assessment Tools (CATS) project that is creating and validating a concept inventory for cybersecurity, which assesses the quality of instruction of any first course in cybersecurity. In fall 2014, we carried out a Delphi process that identified core concepts of cybersecurity. In spring 2016, we interviewed twenty-six students to uncover their understandings and misconceptions about these concepts. In fall 2016, we generated our first assessment tool--a draft Cybersecurity Concept Inventory (CCI), comprising approximately thirty multiple-choice questions. Each question targets a concept; incorrect answers are based on observed misconceptions from the interviews. This year we are validating the draft CCI using cognitive interviews, expert reviews, and psychometric testing. In this paper, we highlight our progress to date in developing the CCI. The CATS project provides infrastructure for a rigorous evidence-based improvement of cybersecurity education. The CCI permits comparisons of different instructional methods by assessing how well students learned the core concepts of the field (especially adversarial thinking), where instructional methods refer to how material is taught (e.g., lab-based, case-studies, collaborative, competitions, gaming). Specifically, the CCI is a tool that will enable researchers to scientifically quantify and measure the effect of their approaches to, and interventions in, cybersecurity education.