Discovery Of Formulas Research Articles

Students’ Combinatorial Thinking Processes in Solving Mathematics Problem

Combinatorial thinking is a way of thinking in solving combinatory problems. Combinatory problems are one of the difficult problems for students to solve. This study aims to analyses students’ combinatorial thinking processes in solving problems. Given two combinatory problems that consist of problems with multiplication rule and combination. The Problems were given to two 11th grade senior-high school students. The results obtained were that there was a tendency for male Participants to do the two different ways which are direct counting and using diagram. The female participants did the work with one way which is direct counting. On more complex issues, namely about combination, students' thinking models go through stages of set of outcomes. From this research, it is expected that combinatory material learning is emphasized on the discovery of formulas by students themselves inductively, especially deductively. So that in this case the students interpret the combinatory formula more.

High order formulas with second derivatives for the numerical integration of stiff ordinary differential equations

A class of multistep formulas using second derivatives was studied and searched for stiffly stable formulas with order of accuracy p = k + 2, where k is the step-number. The search led to the discovery of formulas with k as high as 11 and with better stability regions as compared with existing methods of the same kind.

Sum Squares On A Geoboard

Introduction, difference tables, discovery of formulas— all motivated by this intriguing use of the geoboard.