Problem solving, exercises, and explorations in mathematics textbooks: A historical perspective

Abstract

This paper analyses the tasks proposed in several Portuguese mathematics textbooks, from the 19th to the 21st century. A look at the nature and intended purpose of these tasks raises interesting issues about school mathematics teaching and learning. Has the meaning of terms such as “problem” and “exercise” been always the same? What other terms have been used in textbooks to designate mathematics tasks? What were the reasons for the changes? The analysis of the evolution that occurred in the terminology as well as in the nature of the tasks proposed to the students provides elements to reflect about what the changes that have occurred in mathematics teaching and learning and how some changes are more apparent than real.