Investigating the interaction between defining and classifying via independent sequential tasks among pre-service teachers: the case of the triangle
摘要
This study examined the interaction between defining and classifying processes to inform the instructional design for teaching the triangle concept in teacher education programs. To address a gap in the literature regarding the effect of task sequencing on conceptual learning, this study employed independent sequential tasks focusing on the triangle concept. The study, conducted with 209 pre-service teachers, systematically analyzed the effects of defining on subsequent classifying and of classifying on subsequent defining. The findings indicate that pre-service teachers were generally successful in accurately classifying triangle examples and non-triangular non-examples, but that misclassifications were particularly concentrated in triangular non-examples. Furthermore, they frequently provided inappropriate statements when defining the triangle. It was also determined that there was no association between pre-service teachers’ defining performance and classifying performance. Whether the classifying task was administered before or after the defining task did not affect participants’ ability to construct a triangle definition containing both necessary and sufficient conditions. Performance in classifying triangle examples and non-triangular non-examples was unaffected by task sequencing, whereas performance in classifying triangular non-examples was influenced by task sequencing. These findings have implications for the instructional design for teaching the triangle concept in teacher education. Most notably, the findings suggest that reflecting on the formal definition of the triangle before the classifying task may provide a modest advantage in identifying non-intuitive non-examples of triangles.