| 总结: | The present article seeks to analyze the relations between the Initial and Continuing Education of Mathematics Teachers in the perspective a process of continuum, based on the assumption of the development and professional outreach of the teaching profession. This study was performed under the qualitative approach and for its development, accumulated theoretical knowledge based on bibliographical research was taken into account, as well as meaningful testimonies of participants in these two educational spaces. The discussions and reflections presented here are based on studies developed on teacher education, the initial education of mathematics teachers, the continuing education of mathematics teacher, and professional outreach. We offer excerpts from two on-going Masters research projects, providing evidence of factors that may contribute to the comprehension of professional outreach, during the initial education process or even the continuing education process of mathematics teachers.
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