Using simple concepts that middle and high school students should be able to grasp, including “clock face arithmetic,” the standard multiplication table, and adding the digits of a number together, more abstract concepts such as modular arithmetic and cyclic groups may be introduced at an early stage in the students’ mathematical career. We find this approach to be organic and appealing to most students, encouraging them to think in different ways about familiar objects, and we encourage educators to test the concepts in their own classrooms.
Goel, Sudhir and Ault, Shaun V.
"Introducing Abstract Mathematics through Digit Sums and Cyclic Patterns,"
Georgia Journal of Science, Vol. 74, No. 2, Article 20.
Available at: http://digitalcommons.gaacademy.org/gjs/vol74/iss2/20