This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…

A well-documented curricular gap exists in L2 pedagogy between the introductory courses, focusing mainly on language, and advanced courses, focusing mainly on literary content. Intermediate learners, despite their proficiency, generally have difficulty in bridging this gap, as it requires a shift from decoding to interpreting and analyzing texts.…

A primary goal of instruction is to prepare learners to transfer their knowledge and skills to new contexts, but how far this transfer goes is an open question. In the research reported here, we seek to explain a case of transfer through examining the processes by which a conceptual representation used to reason about complex systems was…

The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…