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We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time. 

It is known that timely and personalized feedback is vital to the learning process, and because of increasing enroll- ment, instructors can find it harder to provide that feedback. Learning analytics presents a solution to this problem. The growth in popularity of online education systems better enables learning analytics by providing additional educational data. This work focuses on the analysis of students’ incorrect short answers and their pathways to correct solutions. By considering student submissions as sequences, this work uses a dimension called “distance” which can be used to predict how far off a student’s incorrect answer is from a correct one. This distance metric can be used for recognizing students who may need help, understanding which concepts students struggle with, evaluating assessment questions, and improving multiple-choice answers. This paper discusses the methods, relevant learning scenarios, and applications of the learning analytics system. It features the results and analysis of a usability test conducted on 56 faculty members. 

Understanding the thought processes of students as they progress from initial (incorrect) answers toward correct answers is a challenge for instructors, both in this pandemic and beyond. This paper presents a general network visualization learning analytics system that helps instructors to view a sequence of answers input by students in a way that makes student learning progressions apparent. The system allows instructors to study individual and group learning at various levels of granularity. The paper illustrates how the visualization system is employed to analyze student responses collected through an intervention. The intervention is BeginToReason, an online tool that helps students learn and use symbolic reasoning-reasoning about code behavior through abstract values instead of concrete inputs. The specific focus is analysis of tool-collected student responses as they perform reasoning activities on code involving conditional statements. Student learning is analyzed using the visualization system and a post-test. Visual analytics highlights include instances where students producing one set of incorrect answers initially perform better than a different set and instances where student thought processes do not cluster well. Post-test data analysis provides a measure of student ability to apply what they have learned and their holistic understanding.