Developing teacher subject knowledge
How do I evaluate the level of subject knowledge of my colleagues?
How can I work with colleagues to develop subject knowledge?
What resources can help to support teachers’ subject knowledge?
How can we develop knowledge of the Key Stage 3 curriculum in order to prepare children for the L6 tests?
Things to think about
Weaknesses in teachers’ subject knowledge were an impediment to effective assessment because the teachers were not able to anticipate misconceptions or spot fundamental errors and use them to enhance pupils’ understanding. These weaknesses also affected the quality of questioning.
Mathematics: made to measure, (Ofsted 2012, p. 36)
High attaining pupils require greater challenge in lessons: many primary teachers need stronger subject knowledge to do this well.
Mathematics: understanding the score, (Ofsted 2009, p. 3)
One of the characteristics of excellent teachers is their ability to respond quickly and appropriately to what their pupils are saying and doing. This might be about being able to work out quickly why a child has made a mistake so that the way the teacher then responds helps the child learn. Or it might be about seeing ways in which children can be further challenged, perhaps by making links with other aspects of mathematics or by asking questions that effectively probe children’s understanding more deeply. Without secure subject knowledge it is hard, if not impossible, to do this.
This can be a particular challenge with high attaining children in Years 5 and 6 where some teachers may feel insecure in their own mathematical knowledge and understanding, especially with topics recognised as being harder to teach, such as fractions, decimals and percentages or ratio and proportion.
What does research tell us?
The influential research paper by Askew et al (1997), Effective Teachers of Numeracy, indicated one reason why strong subject knowledge is essential. They suggested that one of the characteristics of more effective teachers was the way they helped children see the connections between different mathematical concepts, for example the links between multiplication tables, equivalent fractions, ratio and proportion. Teachers with weaker subject knowledge may well not see these links, and this then needs to be a focus for CPD.
In their book Developing Primary Mathematics Learning Rowland et al (2009) develop the idea of ‘contingency’. This is characterised by the ‘unplanned-for or unexpected responses that a child may give in a lesson’ and ‘how teachers may respond to them’. Such moments can give real insight into children’s understanding and can be the prompt for rich learning, but teachers’ ability to respond quickly and appropriately is reliant on the depth of their subject knowledge.
Harder mathematics topics
There is evidence to suggest that children’s ability to do harder mathematics topics is a good predictor of their future success in the subject at secondary school. Siegler et al identified links between the ability of 10 to 12-year old children in fractions and division and their success in mathematics five or six years later. They argued that strong conceptual understanding of fractions is needed in order to develop understanding of secondary school topics such as algebra. This research indicates the importance of excellent teaching of harder topics in the primary curriculum, and this in turn is dependent in part on the quality of teachers’ subject knowledge. Read more about this research here .
Nunes et al (2006) have explored in some depth children’s understandings of fractions, and their report Fractions: difficult but crucial in mathematics learning gives valuable insight into aspects of learning fractions that teachers will find insightful.
Implications for the use of the Year 6 Level 6 tests
Preparing children for the L6 tests requires teachers to develop their knowledge and understanding of the Key Stage 3 mathematics curriculum. The authors of Investigation of Key Stage 2 Level 6 Tests (Coldwell et al, 2013) found that many primary teachers lacked confidence in their knowledge of this, and few had actually assessed children as being at L6 through on-going teacher assessment. Secure subject knowledge therefore is needed both to teach high attaining Year 6 children successfully and to develop accurate assessment of these children, which in turn can lead to more accurate identification of which children to enter for the test.
Secondary schools consulted in the study expressed concerns that high attaining Y6 children might experience a narrow version of the Key Stage 3 curriculum, and some questioned the value of getting Y6 children to L6 as a result. But where links between primary schools and secondary mathematics departments were already strong, these issues were seen as less significant.
This indicates the value of investing time and energy in developing such links with, for example, colleagues able to spend time in each other’s schools. This could also help Y6 teachers develop their confidence to teach L6 mathematics. Only a minority of the schools in the Coldwell et al study identified that they had strengths in relation to the teaching of mathematics, which suggests that most primary schools have a staff training need in this area.
Working with colleagues
Establishing a strong sense of trust with colleagues is essential in order to help colleagues develop their subject knowledge. Try to make discussion about subject knowledge a regular part of staff discussion and encourage colleagues to talk about their own understanding of mathematics and how they teach different topics, especially more challenging topics.
Ideas for staff meetings
One way to do this is to get colleagues to work together on parts of the Mathematics Content Knowledge Self-evaluation Tools (the Self-evaluation Tools help teachers to check their understanding of the mathematics they are teaching and to explore ideas on how to develop their practice). This can encourage them to talk about areas of mathematics they feel less secure with in a non-threatening way, and from this it will be possible to identify where you need to focus support and further training.
In particular, use parts of the Key Stage 3 Self-evaluation Tools to help colleagues develop confidence in their teaching of Level 6 topics.
You could also use the L5 and L6 APP descriptors to develop colleagues’ understandings of the differences between these two levels. Share ideas about teaching activities that would allow high attaining Y6 children to explore L6 mathematics. Invite a teacher from your local secondary school to join you for this discussion in order to develop a wider range of ideas.
You could ask colleagues to read a research paper such as the one by Nunes et al (2006) on fractions, and then use this as the basis for a discussion about the extent to which the scheme of work gives opportunities for children to develop rich conceptual understanding of this topic. This would allow colleagues to identify aspects of their own subject knowledge that needs developing.
Another possible prompt for discussion between colleagues would be entries on the Mathemapedia such as Adding makes bigger or Oblong or rectangle?
Other ways of working
Investigate the possibility of colleagues spending time in the local secondary school in order to develop an understanding of the Key Stage 3 mathematics curriculum, and invite mathematics teachers from the secondary school to spend time in your school. This is likely to have most impact if it is part of a long term programme of developing primary/secondary liaison, so discuss this with your senior leadership team.
Resources to use
The Self-evaluation Tools can be used by individuals or groups to develop subject knowledge. The Key Stage 3 and 4 subject knowledge self evaluation tools are a useful resource for teachers to develop their understanding of mathematics topics in later years and key stages.
The Primary Magazine has a regular series (Maths to share - CPD for your school) about running CPD sessions on specific mathematics topics. Use ones which cover some of the more challenging mathematics topics such as:
The Primary Online CPD Module is a rich resource which aims to develop teachers’ understanding of the connections between different mathematics topics.
NRICH has guidance on how to teach more difficult topics, such as Ratio and Proportion or Probability.
There is a range of articles on mathematics topics available here. You could use these to prompt discussion about subject knowledge with colleagues.
Teachers TV videos are another rich resource to use with colleagues. For example, in Decimals Forever, Jonny Heeley works with a group of high attaining Year 6 children on developing their understanding of decimals. In Polygons he works with a similar group developing their understanding of geometrical properties.
Departmental workshops are intended for mathematics departments in secondary schools, but they contain much that is useful for any primary teacher who wants to learn more about Key Stage 3 mathematics. Year 5 and 6 teachers would find them useful in order to develop a better sense of what their children will be moving on to in secondary school.
Askew, M., Brown, M., Rhodes, V., Johnson, D. and Wiliam, D. (1997) Effective Teachers of Numeracy: Report of a study carried out for the Teacher Training Agency. London: School of Education, King’s College.
Coldwell, M., Willis, B. & McCaig, C. (2013) Investigation of Key Stage 2 Level 6 Tests. Centre for Education and Inclusion Research & Sheffield Hallam University.
Nunes, T., Bryant, P., Hurry, J. & Pretzlik, U. Fractions: Difficult but Crucial in Mathematics Learning. London: TLRP.
Ofsted (2009) Mathematics: understanding the score – Improving practice in mathematics (primary).
Ofsted (2012) Mathematics: made to measure.
Rowland, T., Turner, F., Thwaites, A. & Huckstep, P. (2009) Developing Primary Mathematics Learning. London: Sage.