Some difficulties in informal assessment in mathematics

In this theoretical paper the informal assessment practices of two experienced teachers are used as cases for generating questions about future developments in formative assessment practice. Both teachers maintain a consistent formative assessment focus on the development of their students as enquirers, and one of them supplements this with explicit self‐assessment activities. However, there are subject‐specific gaps in the ways in which they assess and describe their students and these are not addressed in widely promulgated advice about formative assessment. Questions are raised about how teachers might be supported to develop their assessment of subject‐specific behaviour. Acknowledgements Grateful thanks are due to Judy Mousley, Helen Forgasz, Helen Doerr and Deakin University, Australia, who funded the preparation of this paper through a Qualitative Learning Research Priority Initiative. Frequent discussions with Rosemary Callingham and Brian Doig took place during every stage of the writing of this paper, and it is in every sense a product of those discussions. Notes 1. I am disguising details of schools and students and use pseudonyms for the teachers and students, possibly changing genders, since some aspects of this paper could be taken to be criticisms of their work. Also, pseudonyms used in this paper do not match pseudonyms I have used elsewhere. Further details of the projects of which these findings were a part can be obtained from the author. 2. At the time there was no expectation in UK research that Garnet and other focus students needed to know she was being especially observed, and it was deemed ethical not to tell them but to ensure teachers had access to all the data so that their informal assessments would be enriched and better informed than otherwise might be the case. 3. The test had been set for the whole year group, and involved four operations on whole numbers up to three digits, decimals with up to two decimal places, and fractions with simple denominators, as well as some early algebra.