Steve Lerman

Learning Environments Using Interactive Whiteboards: New Learning Spaces or Reproduction of Old Technologies?

Interactive whiteboards (IWB) are an innovation that is gaining considerable presence in many contemporary classrooms. This paper examines the use of IWBs in mathematics classrooms. Using a productive pedagogies framework to analyse classroom videos, it is proposed that the classrooms observed used a restricted approach in their use of IWBs. It was found that they were used for quick introductions to lessons and whole class teaching. They were also teacher directed and fostered shallow learning. Through interviews with the teachers, it was found that the approaches observed were based on assumptions about learners and technology.

Students' Conceptualisations of Function Revealed through Definitions and Examples.

ABSTRACT This study aims to explore the conceptualisations of function that some students express when they are responding to fictitious students’ statements about functions. We also asked them what is meant by “function” and many voluntarily used examples in their responses. The task was developed in collaboration with teachers from two curriculum systems, England and Israel. It was given to 10 high-achieving English students from each of the years 10–13 and to 10 high-achieving Israeli students from comparable years (total of 80 students). Data analysis included identifying students’ dominant ideas for functions as expressed in their responses, and analysing the types of examples that students used to explain their responses. Differences found between the samples from the countries led to conjectures about the influence of curriculum and teaching, and in particular, about the role of word, in this case “function”, in concept image development. Whereas most students showed that they had a meaning for the word, those students whose relevant experience of earlier concepts had been organised around the word “function” generally showed stronger understanding of function as object.

Mathematical Discourse in Instruction in Large Classes

1 1 MATHEMATICAL DISCOURSE IN INSTRUCTION IN LARGE CLASSES Mike Askew University of the Witwatersrand, Johannesburg, South Africa K. (Ravi) Subramaniam Homi Bhabha Centre for Science Education, Mumbai, India Anjum Halai The Aga Khan University, Karachi, Pakistan Erlina Ronda University of the Philippines, Quezon City, Philippines Hamsa Venkat University of the Witwatersrand, Johannesburg, South Africa Jill Adler University of the Witwatersrand, Johannesburg, South Africa Steve Lerman London South Bank University, London, United Kingdom