The Future of Education

We, as 11th grade students, conducted a mathematical exploration about the infinite sum of the reciprocals of hexagonal numbers. In our study, we obtained the infinite sum which converged to ln2 by using a further calculus covering differentiation, different methods of integration, Maclaurin series and some tests for convergence of series. What makes our study special is almost all the mathematics we used in our study is beyond the National Curriculum. From the aspect of mathematics education, our claim in this research is the positive effects of studying further mathematics beyond the curriculum at high school level. Students who are following the curriculum are competing with each other in the same track however the students who uses further mathematics beyond the curriculum have got a head start over the others. Learning mathematics beyond the curriculum which isn’t included in the national programs helps students to gain a better vision and intuition over mathematics. Usually, in math education, teachers apply a differentiation in their classes for the competitive students. But this differentiation remains in dealing with challenging problems or a more detailed vision of the same topic. Moreover, further mathematics can be taught by means of flipped classroom activities which is supported by teacher’s private tutoring out of class hours. The further calculus we learned during out of class hours covers the first year of university mathematics and we managed to understand and apply the mathematics we learned to another field of mathematics. That’s why we claim, students who are able to understand a further calculus and who aims to be engineer or mathematician must learn these topics in high school. This will motivate the students and let them to taste the power of mathematics before they start their university career.

Keywords: Math Education, Differentiation, Hexagonal Numbers, Convergence;