Teaching Experiment Methodology for Investigating Students’ Mathematics: Theoretical Foundations and Reflections from an Exemplary Application

Abstract

In this study theoretical foundations and historical changes of the teaching experiment method, commonly conducted in the current mathematics education researches, and the features of the various teaching experiment types are explained. The teaching experiment method, first conducted in the Union of Soviet Socialist Republics in 1960s, was then divided to various types like constructivist teaching experiment emerging after 1976 and classroom teaching experiment developing in 1990s in the USA. In the Soviet type teaching experiment, it is aimed to design learning environments in which the teacher intervenes the students’ learning processes with intent to obtain prior certain learning achievements stated. The constructivist teaching experiment focuses on the design of learning environments which are appropriate with one or more students’ preknowledge and possible alternative learning processes and also aims to model their learning trajectories. In the classroom teaching experiment, in addition to individual psychological factors, social factors are also considered and it is investigated how students’ mathematical knowledge is constructed within classroom norms and social interactions. While the main elements of the teaching experiments are exploratory teaching, teaching episodes, clinical interviews, retrospective conceptual analysis and living models of the students’ mathematics, in this study the aforementioned elements are explained with relation to the writer’s experiences gained from an exemplary teaching experiment.