Visualizing the concept images of students on numbers with combined SOM-ward clustering analysis

Abstract

The purpose of the study is to perform a less-dimensional visualization process for the purpose of determining the images of the students on the concept of number. The Ward clustering analysis combined with the self-organizing map (SOM) was used for this purpose. The conceptual understanding tool, which consisted of the open-ended question "write the first ten things you remember when the term number is mentioned" to the study group, which consisted of 212 fifth grade students. The analysis results showed that students mostly explained the concept of number by associating with mathematics and other sciences with the terms like "addition, subtraction, division, multiplication, fraction, share, equation, cluster, angle, square, rectangle, plus, minus, shape, operation, step, graphics, value, equal, equals", which are related with "operations-calculations" and "mathematical terms". The students mostly established relations with mathematical side of the number. At the end of the study, the dataset obtained from the conceptual understanding tool was used for training the SOM, and a visualization approach that revealed the images of the students on number concept was recommended.