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.

本研究询问在职和职前数学教师的信念，以及他们在课程计划中声明，争论和反映的信念与在实践中使用这些信念之间的分析和比较。五名在职数学教师学习数学学士学位，三名在职教师为博士学位。数学教育的候选人参加了这项研究。使用混合方法进行了多案例研究。封闭式问卷，半结构式访谈和课程计划被用作信息收集的工具。获得的数据显示了参与者如何构建自己的信念。此外，有可能确定在职教师的信念更加坚定，这在他们的课堂建议中得到了证明，而职前教师则具有更初步的信念，即总体上讲与他们的课程计划者所证明的观点不一致。在本科和研究生阶段接受的培训已经渗透了参与者的信念，这可以从获得的结果中得到证明。提出了一些对数学教师的初步和继续教育计划的启示和建议，以及未来的研究建议。