How lower-secondary pupils approach and perceive understanding mathematics

Abstract

Mathematics requires deep thinking. It may be educationally beneficial if pupils are aware of their own shortcomings in understanding. We investigated how pupils of lower-secondary schools in Prague perceive their understanding mathematics, with a particular focus on whether they have distinctive attitudes towards the quality of their understanding. In the first, quantitative stage, a diagnostic test of surface knowledge and a questionnaire about mathematical understanding were developed and administrated. Using a factor analysis, t-tests and methods of descriptive statistics, we created indices of understanding and ascertained that the respondents were often mixing various levels of depth of their understanding mathematics. The quality of a pupil’s understanding was also influenced by many latent factors, including strategic approach to learning, volition to remember facts, ability to solve tasks independently, perfectionism, and also, to some extent, the parental view of mathematics. In the second stage of the research, some individual semi-structured interviews were conducted to illustrate and validate the results. The findings of the study highlight the need to raise pupils’ awareness of the quality of their mathematical understanding, since it may influence their willingness to deepen their knowledge in mathematics and subsequently their school performance.