• The Mathematical Education
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• v.45 no.4 s.115
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• pp.481-491
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• 2006

Diffy is a simple mathematical puzzle that provides elementary-school students with subtraction practice. The idea appears to have originated in the late nineteenth century with E. Ducci of Itali. Thirty years ago Professor J. Copley of the University of Houston introduced the diffy game to teachers in elementary schools and it widely spreaded out. During the diffy activity we naturally guess many interesting conjectures. First, does diffy always end? Second, does the head of diffy always exist? Third, for an arbitrary given natural number n, is there any possible method to find the diffy with the given length n? In this study I give the necessary and sufficient condition for the existence of the head of diffy. Using this condition I classify all possible heads of diffy and provide an algorithm to find the diffy with any given length n. With this algorithm I find four natural numbers with diffy length 200. To ensure my numbers are correct, I make a diffy program for Mathematica and check they are correct. I suggest the diffy game is good for enlarging the mathematical thinking to all graded students, especially gifted and talented students, It will produce rational consideration and synthetic judgement.

• School Mathematics
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• v.7 no.4
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• pp.319-336
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• 2005

This study is to find the properties of Diffy activity and to investigate the problems and conjectures which could be posed in the Diffy activity. The Diffy is a simple subtracting activity. But, 1 think it is a field where the mathematical thinking can take place. I proposed some problems and conjectures which can be posed. I solved the problems using excel and the software I developed and proposed the related data. I think such problems and the data will be the good materials for elementary students and gifted to think mathematically with.

• School Mathematics
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• v.15 no.1
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• pp.121-136
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• 2013

The purpose of study was to develop distance education programs that combine the characteristics of the programs for the math gifted students. To this end, the first is to establish the standards for the development of distance programs for the math gifted students. The second is to develop the distance education programs for the elementary school math gifted students according to the program procedure models for distance education. The third is to apply the programs developed to actual distance education field and analyze the results to verify the validity of the programs. This program can increase high-level mathematical thinking power even though it is the distance education, not the face-to-face education. Second, this program make contributions to active mathematical communication through newsgroup or reflective journals. Third, the use of Diffy Game facilitates the selection of in-depth contents, which will in turn enable the development of intensive programs.