Mind map as a tool to assess conceptual understanding of mathematics: The case with the four centres of a triangle

Assessment is a major concern in education. Despite the general acceptance that mathematics teaching is to achieve mathematical understanding on the part of the learners, there is always the problem with the extent to which the assessment tools can serve learning and teaching to this end. The notion of assessment for learning suggests broader assessment concerns instead of a practical solution to the problem, especially when the assessment practice is much dominated by the public examination such as Hong Kong Diploma of Secondary Education examination. Taking as an example the four centres of a triangle (each as the result of a concurrent set of special lines in the triangle), this study reviews the problems related to this topic set in the mathematics textbooks and DSE examination. On the other hand, this study also investigates the concepts possibly related to the four centres of a triangle. Through the analysis of a collection of mind maps drawn by 57 Secondary 3 students on the lines in a triangle, the use of mind maps as an alternative assessment tool to assess the conceptual understanding is explored. It is concluded that mind map grants an accessible means of assessment of and for the learning of mathematics if we are concerned more with a network of interrelated concepts and procedures than with a collection of isolated facts and methods of solution to typical questions