As interest grows in learning math concepts in fields like data science and machine learning, it is becoming more important to help broad audiences engage with math notation. In this paper, we explore how authoring tools can help authors better style and label formulas to support their readability. We introduce a markup language for augmenting formulas called FFL, or "Formula Formatting Language," which aims to lower the threshold to stylize and diagram formulas. The language is designed to be concise, writable, readable, and integrable into web-based document authoring environments. It was developed with an accompanying runtime that supports live application of augmentations to formulas. Our lab study shows that FFL improves the speed and ease of editing augmentation markup, and the readability of augmentation markup compared to baseline LaTeX tools. These results clarify the role tooling can play in supporting the explanation of math notation.
Inferential statistics are typically reported using p-values (NHST) or confidence intervals on effect sizes (estimation). This is done using a range of styles, but some readers have preferences about how statistics should be presented and others have limited familiarity with alternatives. We propose a system to interactively translate statistical reporting styles in existing documents, allowing readers to switch between interval estimates, p-values, and standardized effect sizes, all using textual and graphical reports that are dynamic and user customizable. Forty years of CHI papers are examined. Using only the information reported in scientific documents, equations are derived and validated on simulated datasets to show that conversions between p-values and confidence intervals are accurate. The system helps readers interpret statistics in a familiar style, compare reports that use different styles, and even validate the correctness of reports. Code and data: https://osf.io/x4ue7
https://doi.org/10.1145/3586183.3606762
We introduce Augmented Math, a machine learning-based approach to authoring AR explorable explanations by augmenting static math textbooks without programming. To augment a static document, our system first extracts mathematical formulas and figures from a given document using optical character recognition (OCR) and computer vision. By binding and manipulating these extracted contents, the user can see the interactive animation overlaid onto the document through mobile AR interfaces. This empowers non-technical users, such as teachers or students, to transform existing math textbooks and handouts into on-demand and personalized explorable explanations. To design our system, we first analyzed existing explorable math explanations to identify common design strategies. Based on the findings, we developed a set of augmentation techniques that can be automatically generated based on the extracted content, which are 1) dynamic values, 2) interactive figures, 3) relationship highlights, 4) concrete examples, and 5) step-by-step hints. To evaluate our system, we conduct two user studies: preliminary user testing and expert interviews. The study results confirm that our system allows more engaging experiences for learning math concepts.
https://doi.org/10.1145/3586183.3606827
Weaving is a fabrication process that is grounded in mathematics and engineering: from the binary, matrix-like nature of the pattern drafts weavers have used for centuries, to the punch card programming of the first Jacquard looms. This intersection of disciplines provides an opportunity to ground abstract mathematical concepts in a concrete and embodied art, viewing this textile art through the lens of engineering. Currently, available looms are not optimized to take advantage of this opportunity to increase mathematics learning by providing hands-on interdisciplinary learning in collegiate classrooms. In this work, we present SPEERLoom: an open-source, robotic Jacquard loom kit designed to be a tool for interweaving cloth fabrication, mathematics, and engineering to support interdisciplinary learning in the classroom. We discuss the design requirements and subsequent design of SPEERLoom. We also present the results of a pilot study in a post-secondary class finding that SPEERLoom supports hands-on, interdisciplinary learning of math, engineering, and textiles.
https://doi.org/10.1145/3586183.3606724
Domain-specific languages (DSLs) for visualization aim to facilitate visualization creation by providing abstractions that offload implementation and execution details from users to the system layer. Therefore, DSLs often execute user-defined specifications by transforming them into intermediate representations (IRs) in successive lowering operations. However, DSL-specified visualizations can be difficult to profile and, hence, optimize due to the layered abstractions. To better understand visualization profiling workflows and challenges, we conduct formative interviews with visualization engineers who use Vega in production. Vega is a popular visualization DSL that transforms specifications into dataflow graphs, which are then executed to render visualization primitives. Our formative interviews reveal that current developer tools are ill-suited for visualization profiling since they are disconnected from the semantics of Vega's specification and its IRs at runtime. To address this gap, we introduce VegaProf, the first performance profiler for Vega visualizations. VegaProf instruments the Vega library by associating a declarative specification with its compilation and execution. Integrated into a Vega code playground, VegaProf coordinates visual performance inspection at three abstraction levels: function, dataflow graph, and visualization specification. We evaluate VegaProf through use cases and feedback from visualization engineers as well as original developers of the Vega library. Our results suggest that VegaProf makes visualization profiling more tractable and actionable by enabling users to interactively probe time performance across layered abstractions of Vega. Furthermore, we distill recommendations from our findings and advocate for co-designing visualization DSLs together with their introspection tools.
https://doi.org/10.1145/3586183.3606790
Search and information retrieval systems are becoming more expressive in interpreting user queries beyond the traditional weighted bag-of-words model of document retrieval. For example, searching for a flight status or a game score returns a dynamically generated response along with supporting, pre-authored documents contextually relevant to the query. In this paper, we extend this hybrid search paradigm to data repositories that contain curated data sources and visualization content. We introduce a semantic search interface, OLIO, that provides a hybrid set of results comprising both auto-generated visualization responses and pre-authored charts to blend analytical question-answering with content discovery search goals. We specifically explore three search scenarios - question-and-answering, exploratory search, and design search over data repositories. The interface also provides faceted search support for users to refine and filter the conventional best-first search results based on parameters such as author name, time, and chart type. A preliminary user evaluation of the system demonstrates that OLIO's interface and the hybrid search paradigm collectively afford greater expressivity in how users discover insights and visualization content in data repositories.
https://doi.org/10.1145/3586183.3606806