Tetsuo Fukui

Development and Evaluation of a Web-Based Drill System to Master Basic Math Formulae Using a New Interactive Math Input Method

We present a web-based drill system named DIGITAL-WORK which assists learners in mastering some basic formulae using a new interactive math input method. This method enables users to format any mathematical expression in WYSIWYG by converting from colloquial style strings in fuzzy mathematical notation. The purpose of this study is to investigate whether students can smoothly learn basic math formulae with our drill system. In this paper, we report the results from a field survey that was conducted in an actual remedial math class of 20 junior high school students. The results of our survey showed that 85% of them found this system to be more fun than learning on paper.

Predictive Algorithm for Converting Linear Strings to General Mathematical Formulae

Standard input methods for entering mathematical expressions on digital devices are cumbersome. Our goal is to develop an intelligent mathematical input method that allows users to input mathematical expressions using colloquial linear strings. This paper presents the evaluation of an improved predictive algorithm for converting linear strings into general mathematical formulae. The results of our evaluation show that the prediction accuracy of the top ten ranking for our method is 85.2%.

Evaluation of a Predictive Algorithm for Converting Linear Strings to Mathematical Formulae for an Input Method

Recently, some computer-aided assessment CAA systems are able to assess learners answers using mathematical expressions. However, the standard input method for mathematics is cumbersome for novice learners. In 2011, the last author Fukui proposed a new mathematical input method similar to the ones used for inputting Japanese characters in many systems. This method allows users to input mathematical expressions using colloquial-style mathematical string. However, users must convert each element contained in the colloquial-style mathematical string. In this study, we propose a predictive algorithm for converting the whole mathematical formulae.

Intelligent Editor for Authoring Educational Materials in Mathematics e-Learning Systems.

E-learning systems for mathematics, such as STACK, Maple T.A., and MATH ON WEB that are able to assess answers using mathematical expressions, have been used for mathematics education at universities. The means for inputting mathematical expressions using current interfaces in these mathematics e-Learning systems are cumbersome not only for students entering their answers, but also for teachers authoring educational materials. In most editing software, teachers need to enter mathematical expressions according to LaTeX-style or computer algebra system-style. This exerts a heavy toll on teachers who have never used these systems. For general use of these systems, it is important to improve the means for entering mathematical expressions. In this study, we developed an intelligent editor for authoring educational materials in mathematics e-Learning systems by implementing a mathematical input interface, named MathTOUCH. This interface allows users to enter the desired mathematical expressions through predictive conversion that converts obscure linear strings presented in a colloquial-style into suitable formats. The results of our previous investigation show that MathTOUCH allows higher level of performance than the standard interfaces. Therefore, the proposed editor is expected to overcome the problem of inputting mathematical expressions in e-learning systems for mathematics education.

Effective Use of Math E-Learning with Questions Specification

MATH ON WEB, STACK, and Maple T.A. are the prominent mathematics e-learning systems used in Japan. They can assess answers containing mathematical content freely written by students as opposed to only answers to multiple-choice questions. However, there are two major challenges while using these systems: inconvenience in inputting answers and heavy content-development workload. We have developed two math input interfaces, MathTOUCH and FlickMath, using which students can easily input mathematical expressions. The interfaces were developed as part of a project aimed at accelerating the spread of math e-learning systems using a question-sharing environment among heterogeneous systems such as MATH ON WEB and Maple T.A. Further, they form a part of mathematics e-learning question specification (‘MeLQS’) system, which is currently being developed in our project to realise this objective. We would like to emphasize the importance of building a common base, ‘MeLQS’, for creating questions in math e-learning.

Algorithm for Predicting Mathematical Formulae from Linear Strings for Mathematical Inputs

Recently, computer-aided assessment (CAA) systems have been used for mathematics education, with some CAA systems capable of assessing learners’ answers using mathematical expressions. However, the standard input method for mathematics education systems is cumbersome for novice learners. In 2011, we proposed a new mathematical input method that allowed users to input mathematical expressions through an interactive conversion of mathematical expressions from colloquial-style linear strings in WYSIWYG. In this study, we propose a predictive algorithm to improve the input efficiency of this conversion process by using machine learning to determine the score parameters with a structured perceptron similar to natural language processing. In our experimental evaluation, with a training dataset comprising 700 formulae, the prediction accuracy was 96.2% for the top ten ranking by stable score parameter learning; this accuracy is sufficient for a mathematical input interface system.