1,162 research outputs found
A reappraisal of online mathematics teaching using LaTeX
The mathematics language LaTeX is often seen outside of academic circles as a legacy technology that is awkward to use. MathML - a verbose language designed for data-exchange, and to be written and understood by machines - is sometimes by contrast seen as something that will aid online mathematics and lack of browser support for it bemoaned. However LaTeX can already do many of the things that MathML might promise. LaTeX is here proposed as a language from which small fragments, with concise syntax, can be used by people to easily create and share mathematical expressions online. The capability to embed fragments of LaTeX code in online discussions is described here and its impact on a group of educators and learners evaluated. Here LaTeX is posited as a useful tool for facilitating asynchronous, online, collaborative learning of mathematics
Discovering real-world usage scenarios for a multimodal math search interface
To use math expressions in search, current search engines require knowing expression names or using a structure editor or string encoding (e.g., LaTeX) to enter expressions. This is unfortunate for people who are not math experts, as this can lead to an intention gap between the math query they wish to express, and what the interface will allow. min is a search interface that supports drawing expressions on a canvas using a mouse/touch, keyboard and images. We designed a user study to examine how the multimodal interface of min changes search behavior for mathematical non-experts, and discover real-world usage scenarios. Participants demonstrated increased use of math expressions in queries when using min. There was little difference in task success reported by participants using min vs. text-based search, but the majority of participants appreciated the multimodal input, and identified real-world scenarios in which they would like to use systems like min
Technologies for engineering education
Within any discipline, teaching involves a distinctive relationship between content, pedagogical approaches and the use of technologies. In engineering education, the content includes mathematical symbolic and diagrammatic forms, traditionally taught using handwritten and talk-based approaches which have not been easily accommodated by keyboard-centric digital technologies. In 2012, a pilot project involving staff in the AUT School of Engineering was initiated to explore the use of digital pen-enabled technologies. This paper reviews educational research supporting the use of these technologies in an engineering education context and reports on findings from the project. The paper also discusses ways of integrating digital pen-enabled technologies with other developments in educational technology to enhance traditional pedagogical approaches to the teaching of engineering, and to facilitate progressive development of transformative approaches
Structure Editing of Handwritten Mathematics: Improving the Computer Support for the Calculational Method
We present a structure editor that aims to facilitate the presentation and manipulation of handwritten mathematical expressions. The editor is oriented to the calculational mathematics involved in algorithmic problem solving and it provides features that allow reliable structure manipulation of mathematical formulae, as well as ļ¬exible and interactive presentations. We describe some of its most important features, including the use of gestures to manipulate algebraic formulae, the structured selection of expressions, deļ¬nition and redeļ¬- nition of operators in runtime, gestureās editor, and handwrit- ten templates. The editor is made available in the form of a C# class library which can be easily used to extend existing tools. For example, we have extended Classroom Presenter,a tool for ink-based teaching presentations and classroom interaction. We have tested and evaluated the editor with target users. The results obtained seem to indicate that the software is usable, suitable for its purpose and a valuable contribution to teaching and learning algorithmic problem solving.(undefined
Introducing Handwriting into a Multimodal LATEX Formula Editor
Handwriting has been shown to be a useful input modality for math. However, math recognizers are imperfect, especially when recognizing complex expressions. Instead of improving the recognizer itself, we explore ways to best visualize the recognizer\u27s output to help the user fix recognition mistakes more efficiently. To do this, we propose changes to the visual editing operations in MathDeck, a math-aware search engine and formula editor, as well as the addition of an n-best list of results for each symbol in the recognizer\u27s output. We present two experiments to help us find good ways to help users fix errors in the recognizer, and to test whether these changes help novices input formulas more efficiently than they would if they did not have handwriting as an input modality. In the first experiment, users had the option to fix errors with an in-place drop-down menu of alternate symbols, a side symbol correction panel, or by typing the symbols themselves or dragging them from a symbol palette. In our experiment, most users preferred to fix the errors manually by typing the correct symbols or using the symbol palette. In the second experiment, participants entered formulas using handwriting and/or LaTeX. We found evidence that suggests that novices can input formulas faster when they have access to handwriting, but experts still do better when they can just type LaTeX
Developing studentsā strategies for problem solving in mathematics: the role of pre-designed āsample student workā
This paper describes a design strategy that is intended to foster self and peer assessment and develop studentsā ability to compare alternative problem solving strategies in mathematics lessons. This involves giving students, after they themselves have tackled a problem, simulated āsample student workā to discuss and critique. We describe the potential uses of this strategy and the issues that have arisen during trials in both US and UK classrooms. We consider how this approach has the potential to develop metacognitive acts in which students reflect on their own decisions and planning actions during mathematical problem solving
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