Abstract:

Math expressions play a significant role in STEM education. With the science e-books becoming widespread recently, there is a high demand for retrieving math contents. Searching algorithms for math expressions are more complex than those for natural languages because the layout of the characters is different due to their two-dimensionality of the descriptions. In this study, a web-based application for retrieving math expressions is proposed, based on a pattern-matching algorithm. What the presenter is pursuing recently is to build a synthetic math learning environment with this math IR (Information Retrieval) system as its core technology. The introduction of one of the applications is the main topic of this article, which is, finding math formulas and annotating where they are used in the course of the transformation of math expressions. This helps learners find math formulas in math contents and understand how transformations of math expressions are made with the provided annotation indicating the underlying math formulas.

The educational benefits of introducing this feature can be broadly divided into the following two aspects:
1. Facilitation of learner autonomy through personalization.
By providing annotations that show how the transformation is performed, learners can learn by themselves without the help of a teacher. In addition, the personalization function that utilizes the information collected from the learner's learning history accelerates autonomous learning.
2. LA (learning analytics)-based education and learning optimization.
Since this function records the learner's learning history, it is possible to grasp the degree of understanding from the behavior during the learning activity. For example, it is likely that the part where the annotation function is used is not well understood, or the formula used for the transformation is unfamiliar to the learner if the learner attempts to retrieve afterwards with the name of math formula shown. Sharing such data among learners also allows for statistical extraction of mathematical transformations.

The annotating function extracts MathML differences between mathematical expressions of left- and right-hand side of the equation and checks the existence of the formula in DB. The conventional annotating function, however, does not succeed in matching when the target mathematical expression is transformed algebraically of the stored pattern. To cope with this, we applied Wolfram Alpha API that allows you to perform mathematical transformations and present functions of Wolfram | Alpha into the Web. First, conventional matching is performed. Then, a new array is created that collects only the mathematical formulas for which the matching is not successful. The mathematical expression in the array is transformed using the API and the matching process is performed again. After updating the flags for the mathematical expressions that have been successfully matched, the mathematical expression data are restored to the original data, and the mathematical expressions with flags for matching success are highlighted and the name of the corresponding mathematical formula is presented.

In the future, our study group plans to conduct experiments to show how this tool can help users retrieve math expressions they seek and study mathematics, and understand provided learning materials. It is also desirable to implement the applications to evaluate the usefulness of the proposed system.

Keywords:

STEM education, Search Engine, Mathematical Expressions, Annotation of Underlying Math Formula, Algebraic Transformations