카탈란수와 관련된 수학영재 교수·학습자료의 개발 및 적용

Abstract

Abstract

I have done some research on the Catalan numbers through several domestic papers. It was a fantastic story. It was Eugene Charles Catalan (1814-1894) that mentioned the Catalan numbers for the first time. H.D. Grossman (1950) made the formula that matched the ballot problem to the Catalan numbers. M.T.L. Bizley (1954) proved Grossman's formula. Johann Cigler(2002) found out the Hankel determinants of the Catalan numbers. Richard Stanley(2009) showed lots of examples of for Catalan numbers. W.-G. Jo (1998) introduced the Catalan numbers, and explained the basic idea of ​​the proof of Catalan numbers. S.-W. Kim(1999) studied the Noncrossing division and q-Catalan numbers. S.-K. Lee, G.-Y. Jeong(2007) developed teaching and learning materials for gifted students of math related to the "exploration of Catalan numbers". We can make the students feel the excitement and fun with math and get a positive reaction to math. And we will provide basic materials and worksheets.

The main purpose of this paper is to explore a variety of methods which can be expressed as Catalan numbers and develop teaching and learning Materials for gifted students.