Algorithmic problems are problems where the solution involves —possibly implicitly— the design of an algorithm. Algorithmic problem solving is about the formulation and solution of such problems.
Over the last forty years, the unprecedented scale of programming problems, and the consequent demands on precision and concision have forced computing scientists to hone their algorithmic problem solving skills to a very fine degree. Even so, and although much of mathematics is algorithmic by nature, the skills needed to formulate and solve algorithmic problems do not form an integral part of mathematics education.
As part of my PhD, I have developed educational material supporting the use of an algorithmic and calculational approach to school mathematics. Some of that material is in the form of teaching scenarios, which are fully worked out solutions to algorithmic problems together with “method sheets” —detailed guidelines on the principles captured by the problem, how the problem is tackled, and how it is solved. Although they can be used directly by the student, they are primarily written for the teacher and they are designed to promote self-discovery by the students.
The teaching scenarios currently available are: