This qualitative case study examined similarities and differences between circle geometric proof development tasks set up in the Malawian Grade 11 mathematics textbook, and those that are set up and implemented by teachers in the classroom. Data generation included analysing the content of circle geometry proof tasks from the mathematics textbook…

First order knowledge and understanding, relating to the "stuff" of history, is, of course, absolutely fundamental to the development of children's historical knowledge and understanding. However, as Frances Blow shows, in a contribution to a series of articles exploring second order concepts in history published in Teaching History by…

Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) "embodied objects" or Lakoff and Nunez's (2000) "mathematical idea…

This study reports on our steps toward achieving a conceptually coherent and empirically validated learning progression for carbon cycling in socio-ecological systems. It describes an iterative process of designing and analyzing assessment and interview data from students in upper elementary through high school. The product of our development…

The aim of this paper was to describe the changes in one student's ideas about force and one-dimensional motion concepts and portray the relevant metaconceptual processes that she engaged in during the implementation of metaconceptual teaching interventions. Metaconceptual processes involves metacognitive processes that are directly acting on or…