Constructivist learning theories have become the dominant ideology in educational circles, in part, because there is a primacy on the agential individual with its definite identity. However, precisely because "to construct" is a "transitive" verb, it occludes the fact that in learning and development, we come to know something new, that is, something unknown before and therefore something that could not be anticipated. The related concepts of "surprise," "astonishment," and "admiration" refer to phenomena through which the person acknowledges the encounter with the absolutely new, the alien, the unanticipated; and the person acknowledges "having been affected" something unknown before, an experience that transcends agency and manifests the passivity that comes with the encounter of the unknown. In this study, teaching for "astonishment" is presented and discussed as an alternative way of thinking about mathematics learning.