Beliefs About Mathematics, Its Teaching, and Learning: Contrast Between Pre-service and In-service Teachers

The present research inquired about beliefs of in-service and pre-service mathematics teachers as well as the analysis and comparison between the beliefs that they declare, argue, and reflect in their lessons plans, and the use of those beliefs in their practical exercises. Five pre-service teachers studying a Bachelor’s in Mathematics, and three in-service teachers who were Ph.D. candidates in Mathematics Education participated in the study. A multiple case study was carried out using mixed methods. Closed questionnaires, semi-structured interviews, and lesson plans were used as instruments for information collection. The obtained data show how participants have been structuring their beliefs. Moreover, it was possible to determine that in-service teachers have more firm beliefs which were evidenced in their classroom proposals, whereas pre-service teachers have more tentative beliefs that, in general, do not align with what is evidenced through their lesson planners. The training received at the undergraduate and postgraduate levels has permeated the formation of participants’ beliefs which can be evidenced in the obtained results. Some implications and suggestions for initial and continuous education programs for mathematics teachers and future research suggestions are presented.