Drawing as a tool for an insight into mathematical understanding

Visual representations allow us to interpret the meanings of mathematical concepts, relationships and processes, therefore they play an important role in mathematics education. In the present study, we analysed participants’ understanding of basic mathematical concepts through drawings. Symbolic representation of mathematical concept was provided (e.g., 17 – 9) to participants and they were asked to represent the given concept through a picture. We were interested if high school students and future teachers (N = 345) adequately (in accordance with mathematical definition) depicted given mathematical concept. The data were analysed using a combination of qualitative and quantitative analyses. The results show that participants quite adequately depicted basic mathematical concepts. Less abstract concepts were depicted more accurately. It was also noted, that 4th year students, studying to teach at primary level, have performed better than others. In qualitative content analysis two themes emerged. Those themes illustrate two ways of mathematical understanding (instrumental and relational) and two types of mathematical knowledge (procedural and conceptual). The research results can serve researchers in the creation of new research instruments for measuring mathematical understanding and help teachers to find new approaches that will offer them an insight into students’ mathematical understanding.