Mathematics Education Review, 18, May 2006

Stephanie provides an outline of the articles in Mathematics Education Review (MER) No. 18, May 2006.

This paper describes a framework for mathematics lesson observation and the ways that this framework is being used in practice, for mathematics teaching development. The research which led to the development of the framework drew on videotapes of mathematics lessons prepared and conducted by primary PGCE students towards the end of their initial training. A grounded theory approach to data analysis led to the emergence of the framework - a ‘knowledge quartet’, with four broad dimensions, through which the mathematics-related knowledge of these teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised, and analyses a fragment of one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson.

I was attracted to write about this topic partly because I am relatively new to the world of teacher education and the call for papers encouraged people in that situation to do so, but more because I feel happy with the processes that I use to provide records of lessons that I observe. I realise as I write that rather smug statement that I am setting myself up for criticism and I look forward to reading what others have to say!

Over the years of working in teacher education, much has changed and this is reflected in how I record my observations. I offer three examples of these records one of an earlier style, these were often completed with the student, and two written after the lesson and discussion with the student, one for a strong student and one for a weaker student, to account for the standards.

This article offers a description of my practice when observing mathematics lessons. Our university report form is a blank sheet and individual tutors decide how they will record their observations. My observations are mainly descriptions with a summary table of positive aspects and things to work on, written at the beginning of the sheet but at different times in the lesson, having developed over many years.

Learning to teach is a complex process and trainees need to be provided with both theoretical and practical experiences to develop their skills. Lesson observations and feedback can play an important part in trainee’ development because they provide the opportunity to identify the current position, to discuss the place they are aiming for and strategies to ‘bridge the gap between current and intended performance’.

This account focuses on an observation method (figure 1) that has been used successfully at the University of Birmingham for trainees early in their teaching experience. It aims to record the structure of the lesson by breaking it down phases that have beginnings, middles and ends. The recording method enables trainees and observers to follow the ‘story’ of the lesson and to identify significant events that have aided or hindered the lesson.

The author works in Geography Education.

A simple statistical model was used to explore the relationship, over a five year period, between the degree results of students on a secondary mathematics PGCE course and how successful they were on the course, demonstrating that there was no relationship between the two. Implications of this are considered, both for the nature of degree courses and admissions to secondary mathematics PGCE courses.

Book review about the following 2 books:

Adey, P. and Shayer M. (1994) Really Raising Standards: Cognitive intervention and academic achievement. London: Routledge.

Shayer, M. and Adey, P. (2002), Learning Intelligence: Cognitive acceleration across the curriculum. Buckingham: Open University Press.