The objective of this study was to learn about the conceptualizations of creativity and innovation of future mathematics teachers in secondary education; for this purpose, a questionnaire with open-ended questions was applied to a convenience sample of the student population in the seventh semester of a normal school in Guanajuato, Mexico. The lexicon incorporated into the students’ discourse was analysed in three semantic fields: innovation, creativity and creative environment. They identify innovation with improvements and modifications generated from something existing, while creativity is for them a new idea that arises from the imagination, a “capacity” that develops. Among the ideal characteristics of a creative environment, they highlight “freedom”, “tranquillity”, “respect”, “tolerance”, “materials” and “technology”. Most find differences between creativity and innovation, the former being a condition for the latter, in which they see an operative character (something that is done), and optional in creativity (something that is imagined). Regarding practice, they express “positive”, “favourable”, “inspiring” and “empowering” experiences, although some express unfulfilled expectations, or find them impracticable in the daily task. It is concluded that future mathematics teachers find contradictions between reality and the teachings received at school; although they consider it important to create and innovate in their field, they reveal difficulties in incorporating these concepts in educational action.
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