Exercise (mathematics)

Stephen Leacock described this type:[1] A distinction between an exercise and a mathematical problem was made by Alan H. Schoenfeld:[2] He advocated setting challenges: A similar sentiment was expressed by Marvin Bittinger when he prepared the second edition[3] of his textbook: The zone of proximal development for each student, or cohort of students, sets exercises at a level of difficulty that challenges but does not frustrate them.

Some comments in the preface of a calculus textbook[4] show the central place of exercises in the book: This text includes "Functions and Graphs in Applications" (Ch 0.6) which is fourteen pages of preparation for word problems.

At the Russian School of Mathematics, students begin multi-step problems as early as the first grade, learning to build on previous results to progress towards the solution.

The Book on Numbers and Computation and the Nine Chapters on the Mathematical Art include exercises that are exemplars of linear algebra.

[11] In about 980 Al-Sijzi wrote his Ways of Making Easy the Derivation of Geometrical Figures, which was translated and published by Jan Hogendijk in 1996.

Recorde was writing mainly for those who were teaching themselves, scholars who would have no one to check their answers to the exercises.In Europe before 1900, the science of graphical perspective framed geometrical exercises.

Felix Klein described preparation for the entrance examination of École Polytechnique as[17] Sylvestre Lacroix was a gifted teacher and expositor.

In 1816 he wrote Essays on Teaching in General, and on Mathematics Teaching in Particular which emphasized the need to exercise and test: Andrew Warwick has drawn attention to the historical question of exercises: In reporting Mathematical tripos examinations instituted at Cambridge University, he notes Explaining the relationship of examination and exercise, he writes Explaining how the reform took root, Warwick wrote: Warwick reports that in Germany, Franz Ernst Neumann about the same time "developed a common system of graded exercises that introduced student to a hierarchy of essential mathematical skills and techniques, and ...began to construct his own problem sets through which his students could learn their craft.