This theoretical essay aims at stimulating discussions on the mathematics curriculum in Brazilian high schools, through the presentation of research results that converge on the necessity of breaking the linear organizational paradigm, as illustrated by the metaphor of the bucket, building and chain links. To overcome this model, we present three other metaphors - the spiral curriculum, network curriculum and fractal curriculum. They express relatively new ways of conceiving knowledge in a postmodern perspective and influenced by complexity theory. We analyze recursion as a criterion of the organizational mathematics curriculum, contemplating what we name inter- and intra-mathematical aspects. We conclude that the mathematical content can gain more meaning when contextualized widely in other disciplines and other blocks of content and referencing issues already studied in previous series, but in new contexts and situations are more complex.
Mathematics education; Curriculum; High School; Mathematics teaching; Recursion
