The EEF (Education Endowment Foundation) published a report with eight recommendations to improve outcomes in maths for 7-14-year-olds (KS2 and KS3). In this series of blog posts, starting on ‘World Maths Day’ we summarise the report.
Background to the report
The report was published in 2018 based on an evidence review commissioned by the EEF. It was in response to a consultation with teachers, academics and education authorities that highlighted the issues with maths education. This consultation suggested areas, where guidance could make a big impact in the new curriculum, but also as pupils, transitioned between the stages.
This report intended to provide a comprehensive guide to mathematics teaching. There were recommendations so that schools could make a significant difference to pupils’ learning.
The focus is on improving the quality of teaching. Excellent maths teaching requires good content knowledge, but this is not sufficient. Excellent teachers also know the ways in which pupils learn mathematics and the difficulties they are likely to encounter. They know how mathematics can be most effectively taught.
Strategy One – Using Maths Assessments
Mathematical knowledge and understanding are made of several components. It is quite possible for pupils to have strengths in one area and weaknesses in another.
It is, therefore, important that teacher use assessment to track pupils’ learning but also to gather up-to-date and accurate information about what pupils do and do not know. This information allows teachers to adapt their teaching so it builds on pupils’ existing knowledge, addresses their weaknesses, and focuses on the next steps that they need in order to make progress.
Formal tests can be useful here, although assessment can also be based on evidence from class observations, informal observation of pupils, or discussions with them.
Teachers’ knowledge of pupils’ strengths and weaknesses should inform the planning of future lessons and the focus of targeted support.
Teachers may also need to try a different approach if it appears that what they tried the first time did not work.
Effective feedback will be an important element of teachers’ responses to assessment information. Consider the following characteristics of effective feedback:
- be specific, accurate, and clear (for example, ‘You are now factorising numbers efficiently, by taking out larger factors earlier on’, rather than, ‘Your factorising is getting better’);
- meaningful feedback (for example, ‘One of the angles you calculated in this problem is incorrect—can you find which one and correct it?’;
- comparison with what a pupil is doing right now with what they have done wrong before (for example, ‘Your rounding of your final answers is much more accurate than it used to be’);
- encourage and support any further effort by helping pupils identify things that are hard and require extra attention (for example, ‘You need to put extra effort into checking that your final answer makes sense and is a reasonable size’);
- provide guidance to pupils on how to respond to teachers’ comments, and give them time to do so; and
- provide specific guidance on how to improve rather than just telling pupils when they are incorrect (for example, ‘When you are unsure about adding and subtracting numbers, try placing them on a number line’, rather than ‘Your answer should be -3 not 3’).
Feedback needs to be efficient.
Schools should be careful that their desire to provide effective feedback does not lead to onerous marking policies and a heavy teacher workload. Teachers can give effective feedback orally; it doesn’t have to be in the form of written marking.
Misconceptions in Maths
A misconception is an understanding that leads to a ‘systematic pattern of errors’. Often student form misconceptions when knowledge has been applied outside of the context in which it is useful. For example, the ‘multiplication makes bigger, division makes smaller’ conception applies to positive, whole numbers greater than 1. However, when subsequent mathematical concepts appear (for example, numbers less than or equal to 1), this conception, extended beyond its useful context, becomes a misconception.
It is important that teachers uncover misconceptions rather than ignore them. Pupils will often defend their misconceptions, especially if they are based on sound, albeit limited, ideas.
In this situation, teachers could think about how a misconception might have arisen and explore with pupils the ’partial truth’ that it is built on and the circumstances where it no longer applies. Counter-examples can be effective in challenging pupils’ belief in a misconception. However, pupils may need time and teacher support to develop richer and more robust conceptions.
Knowledge of the common errors and misconceptions in mathematics can be invaluable when designing and responding to assessment, as well as for predicting the difficulties learners are likely to encounter in advance.
Teachers with knowledge of the common misconceptions can plan lessons to address potential misconceptions before they arise, for example, by comparing examples to non-examples when teaching new concepts. A non-example is something that is not an example of the concept.