Junior secondary students' schemata on a line reflection construction task

Abstract

This study explores junior secondary students’ schemata on a line reflection construction task, the research of which was conducted in a secondary school in Hong Kong.

The theories drawn on in this study come from the literature on theories of schemata and the corresponding knowledge embedded within, namely conceptual knowledge, manipulation and procedural knowledge. The research built on existing theories on schemata and attempted to categorize the different kinds of schemata as well as investigating the relationship between them among four junior secondary students in the construction of a line reflection task. The study also tried to find out how and why students manipulated in a line reflection construction task and the extent to which manipulation could lead learners to successfully tackle the task.

This study researched on four junior secondary students, drawing mainly on qualitative data used in the analysis, including task-based interview with the employment of think aloud method in a designed line reflection construction task, as well as study of students’ drawings. The data analysis mainly focused on three areas. First, the analysis of each of the four cases was conducted by looking into the different kinds of schemata possessed by the student informants. Second, analysis of the different knowledge (conceptual knowledge, manipulation and procedural knowledge) embedded in the schema possessed by the student informants was done. Third, synthesis was drawn upon the analysis made in an attempt to answer the research questions posed in this study.

Findings from the study confirmed the core role conceptual knowledge plays in the establishment of a learner’s schemata. Findings also revealed that different learners may possess different schemata towards the same concept such as the concept of same distance. When investigating the manipulative actions employed by student informants, it was found that there is a reciprocal relationship between a learner’s conceptual knowledge and his manipulation. This is also apparent in cases where there was a misconception in the learner’s schemata.

The research also found that students exercised manipulation very differently and these manipulative actions were largely informed by their corresponding conceptual knowledge. With regard to why they manipulated, the research revealed reasons including manipulation for exploration, manipulation for representation and manipulation for verification. Based on the observation and analysis done in the four cases, it was found that manipulation helped students in the completion of the task to different extents. Learners with weaker conceptual knowledge in line reflection benefited more from the manipulation done in the construction task.

These findings have implications for the teaching and learning of line reflection. Teachers are suggested to consider introducing using manipulative tools when approaching the teaching of line reflection, especially when they are dealing with students without rich conceptual knowledge in the area. The effectiveness of having hands-on experience implies that simply teaching definition and inviting learners to rote-learn does not necessarily lead to effective acquisition of knowledge in the Mathematics topic of line reflection.