Hisashi Yokota

Length and denominators of Egyptian fractions II

Abstract An algorithm which yields a short Egyptian fraction expansion in which the denominators stay small is given.

On a problem of Erdős and Graham

Abstract Let m(l)= min {n 1 : 1 = Σ i=1 l 1 n i ,n 1 2 1 } , where the minimum ranges over all sets {ni} of positive integers. Then there exists an increasing sequence of integers {lk} such that m(l k ) l k ≦ ( log log l k ) 3 which improves Erdős and Grahams result m(l k ) l k ≦ ( log l k ) 2 .

Mobile Adaptive Tutoring System with Formative Assessment

Smartphones and tablets are becoming major learning tools in higher education. But developing educational software for smart phones and tablets based on iOS, Android, and Windows operating systems are time consuming task. Since smart phones and tablets are equipped with the web browsers, instead of developing educational software for all different operating systems, it is only necessary to develop educational web application. This way, all the effort for developing educational software can be concentrated on how to evaluate learner’s level of understanding. In this paper, how to generate a formative assessment using educator’s knowledge structure map and how to implement it as an web application is shown.

On Mathematics Software Equipped with Adaptive Tutor System

In this article, we describe how an educators’ knowledge structure map is utilized to assess a knowledge state of a learner in college mathematics courses such as calculus and linear algebra. We also describe how an adaptive tutoring system is implemented into our mathematics learning software JCALC using the relative distance and the knowledge score.

On development of a problem based learning system for linear algebra with simple input method

Learning how to express a matrix using a keyboard inputs requires a lot of time for most of college students. Therefore, for a problem based learning system for linear algebra to be accessible for college students, it is inevitable to develop a simple method for expressing matrices. Studying the two most widely used input methods for expressing matrices, a simpler input method for expressing matrices is obtained. Furthermore, using this input method and educator’s knowledge structure as a concept map, a problem based learning system for linear algebra which is capable of assessing students’ knowledge structure and skill is developed.

On Development of an Adaptive Tutoring System for Calculus Learning

One‐on‐one tutoring is known to be an effective model for learning calculus. Therefore, implementing one‐on‐one tutoring system into calculus learning software is a natural thing to do. The purpose of this article is to describe how to diagnose a students’ knowledge structure about calculus without asking many questions and to show how an adaptive tutoring system is implemented into our calculus learning software JCALC.