In the study presented, as we report in this paper, we describe our theoretical and practical consideration to engage first-year pre-service teachers in proving activities in the context of a transition-to-proof course. We investigated how students argued to verify a claim of elementary number theory on entering university and compared the results…

The study of mathematics at the university level requires logical thinking and strong mathematical skills. Contemporary first-year students are not prepared for these demands and end up failing their courses. This study aims to present an instrument for enhancing mathematics teaching and promoting learning with understanding in higher education by…

This paper explores ideas of language as a cognitive tool and the role of gesture in expressing children's interests and levels of knowledge. The context is a group of three-year-old children who participate in a weekly music session with a trained musician. The authors present drawings from photographs of children's hands and interpret them,…

The purpose of this article is twofold. The first objective is to update the traditional craft of education by revising the folk theory of mind that underpins such traditions. This is necessary if we are to develop a new learning science as the cornerstone for the renewal of the education enterprise. The second objective is to highlight the need…