From Routine Textbook Problems to Non-Routine Teaching and Learning in Classrooms.

The paper consists of two parts. In part 1, the author reports a study of textbooks with a focus on the representation of problem types. A total of 19,711 problems from the senior secondary textbook series from two popular publishers were analyzed with a framework of seven categories of problem representation. Results indicate that over 90% of the problems are routine problems. Seeing textbooks as an important agent for interpreting the curriculum, the results indeed do not present an optimistic picture for developing students’ mathematical thinking. In Part 2, the author draws upon the results from accumulated research efforts to illustrate: (1) what were the students’ possible expectation in an examination-oriented culture influenced by routine tasks; and (2) the strategies for transforming routine problems to non-routine mathematics learning experiences based on the data of some special lessons