I have been working as a professor of Computer Science at Abo Akademi University, Turku, Finland, for many years. My main research area has been on the mathematics of programming and software development, in particular on how to construct provably correct programs. During the last twenty years, I have focused on how to use the techniques developed in program correctness research for presenting mathematical arguments in a logical and transparent way, so that they are easy to understand for a middle and high school student. As part of this research, I have also applied the automatic verification techniques developed for program correctness to checking the correctness of student’s math solutions. The automatic checker that we have built goes through a student’s solution step-by-step and marks each step that was proved correct. The checker provides immediate and extremely reliable feedback for the student at the time most needed, when the student is working on a math problem.
Our techniques have been developed in a joint research at the Computer Science Departments of Abo Akademi University and University of Turku. Together with members of my research group, we have also formed a company, Four Ferries, that has turned this research into a digital learning environment for mathematics, called eMath Studio. The stand-alone automatic checking tool, eMath Checker, gives you a quick access to creating and checking solutions to your own math problems. The automatic checker works on all levels of math education, from middle school and high school to university level math.
Ralph-Johan Back