Structure Editing of Handwritten Mathematics

Abstract

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 flexible 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, definition and redefinition of operators in runtime, gesture's editor, and handwritten 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.

A calculational approach to path-based properties of the Eisenstein–Stern and Stern–Brocot trees via matrix algebra

“…We plan to continue this effort not only by trying to find more properties of the Stern-Brocot, Eisenstein-Stern, and Bird trees, but also by investigating whether other areas of mathematics can be made more calculational. We are also building software tools that can help us write calculational proofs in a more reliable way; as an example, we are currently extending the structure editor described in [23] to support automated verification of handwritten calculational proofs. The following lemma is used in the proof of Lemma 2.…”