- To analyse teacher knowledge of error analysis we developed an instrument with six criteria and compiled evidence of its usability as an analytical tool. This we did as part of our work with 62 mathematics teachers over a three-year period in the Data Informed Practice Improvement Project (DIPIP, see more below). Our central aim in developing the instrument was to detect variation and associations between and within the different aspects of teacher knowledge related to mathematical error analysis. With this in mind, we investigated the following research questions:

- Knowledge of errors can be shown to incorporate both the substantive and syntactic dimensions of teacher subject matter knowledge. Following the famous work of Schwab (1978) and Shulman (1986), Rowland and Turner (2008) propose the following definition of the substantive and syntactic dimensions of teacher subject matter knowledge:

- Particular to the field of mathematics education, Hill and Ball (2009) see analysing learners’ errors as one of the four mathematical tasks of teaching ‘that recur across different curriculum materials or approaches to instruction’ (p. 70). Peng and Luo (2009) and Peng (2010) argue that the process of error analysis includes four steps: identifying, addressing, diagnosing and correcting errors. In South Africa, Adler (2005) sees teachers’ knowledge of error analysis as a component of what she calls mathematics for teaching. She asks:

- Under the first domain, common content knowledge, we map aspects related to the recognition of whether a learner’s answer is correct or not. Teachers need to recognise and be able to explain the crucial steps needed to get to the correct answer, the sequence of the steps and their conceptual links. Because this knowledge underlies recognition of error, we include it under content knowledge. This analysis gives rise to two criteria in this domain:

- Under the third domain, knowledge of content and students, we map aspects related to teachers’ mathematical perspective of errors, typical of learners of different ages and social contexts in specific mathematical topics. This knowledge includes common misconceptions of specific topics (Olivier, 1996) or learners’ levels of development in representing a mathematical construct (e.g. Van Hiele levels of geometric thinking, Burger & Shaughnessy, 1986). From the point of view of error analysis, this knowledge domain involves teachers explaining specific mathematical content primarily from the perspective of how learners typically learn the topic or ‘the mistakes or misconceptions that commonly arise during the process of learning the topic’ (Hill et al. 2008:375). The knowledge of this domain enables teachers to explain and provide a rationale for the way the learners were reasoning when they produced the error. Since it is focused on learners’ reasoning, this aspect of teacher knowledge of errors includes the ability to provide multiple explanations of the error. Because contexts of learning (such as age and social background) affect understanding and because in some topics the learning develops through initial misconceptions, teachers will need to develop a repertoire of explanations, with a view to addressing differences in the classroom. We included three further criteria under this domain:

- Teachers sometimes explain why learners make mathematical errors by appealing to everyday experiences that learners draw on and confuse with the mathematical context of the question. Drawing on the work of Walkerdine (1982), Taylor (2001) cautions that: