Downloadable software and downloadable mobile applications for students, parents and teachers in the field of mathematics which provides interactive instruction, problem solving, journaling, collaborative spaces, interactive games and puzzles, and granting of rewards based upon progress and achievement by students; downloadable software and downloadable mobile applications that model, demonstrate, and visualize concepts in mathematics, and that provide analysis of data about student interactions with the software as collected by the software, and that provide reports of student performance and usage to teachers, administrators and parents