Observing effective mathematics teaching: a review of the literature Dr Jenni Ingram Professor Pam Sammons Dr Ariel Lindorff This review examines a range of lesson observation frameworks designed for and used in the observation of teaching in mathematics. This review of existing classroom observation practices demonstrates that classroom observation frameworks can be designed and used for a variety of This includes frameworks specifically designed for international comparisons of teaching practices and teacher effectiveness, as well as those used for teaching development. This review of existing classroom observation practices demonstrates that classroom observation frameworks can be designed and used for a variety of purposes. The review has drawn on six specific frameworks. These vary in terms of whether they are mathematics-specific or not; whether their purpose is to identify the effectiveness or quality of teaching, or primarily for professional development; and the extent to which there have been studies into their reliability and validity. Important points to consider regarding frameworks for classroom observations include the following: Observations on their own are not reliable enough to make secure judgements about the quality of individual lessons for the purposes of ‘high-stakes’ judgements. Nonetheless, reliability can be improved through the use of multiple trained observers, observing a range of lessons with the same teacher, using more than one instrument; and through combining the observation data with other sources of evidence, such as student questionnaires, attainment-based measures of value-added and examples of their work during the lesson. In international studies, it is important to recognise that expert opinion may be needed to offer a clear focus for any lesson observations conducted; to ensure agreement about the main constructs to be covered and how they are measured; and to provide training to enhance the reliability and validity of the data to be used in any cross-country comparisons. Funding for this literature review was provided by the Department for Education (DfE) as part of the TALIS Video Study.