Abstract:

Learning definitions and theorems have an important role in mathematics education. The way how students learn definitions and theorems could influence the quality of their mathematical knowledge, their problem solving competence and their mathematics teaching. It also shows if they apply deep learning (for example, they use critical reflection on the definition or theorem, they find examples from everyday life for the new notion, etc.) or surface learning (they memorize the definition or theorem). The aim of this paper is to study how pre-service primary school teachers learn mathematical definitions and theorems. The data was collected using an online questionnaire and quantitative data analysis was made. The results show that almost one quarter of the students memorize the definitions. Three quarters try to connect the new notion, if possible, to everyday life and to illustrate it. Three quarters of the students try to find examples for the new notion but only few are thinking on contra-examples. Less than one third of the students analyze the definition to see if all of the properties given are necessary. As regarding formulas or theorems, one third of the students only memorize it, half of the students learn how to find the formula/theorem. Taking in consideration that these students will teach mathematics, the percentage of those only memorizing is quite high. The research results highlight the importance of teaching students how to learn mathematical notions and properties.

Keywords:

Mathematics Education, deep learning, surface learning, learning definitions, learning theorems.