|
|
|
|
|
The decision to focus on Key Stages 2 and 3 was made after an initial consultation period with teachers, academics, and other stakeholders. This consultation suggested that these were areas where guidance could make a big impact as not only were schools seeking advice on adjusting to a new curriculum, there is also concern about pupils making a transition between the stages.
This report is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils’ learning, and have focused on the questions that appear to be most salient to practitioners. There are aspects of mathematics teaching not covered by this guidance. In these situations, teachers must draw on their knowledge of mathematics, professional experience and judgement, and assessment of their pupils’ knowledge and understanding.
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, and how mathematics can be most effectively taught.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Mathematical knowledge and understanding can be thought of as consisting of several components and it is quite possible for pupils to have strengths in one component and weaknesses in another. [1]
It is, therefore, important that assessment is not just used to track pupils’ learning but also provides teachers with up-to-date and accurate information about the specifics of 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 low-stakes class assessments, informal observation of pupils, or discussions with them about mathematics.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Responding to assessment |
Teachers’ knowledge of pupils’ strengths and weaknesses should inform the planning of future lessons and the focus of targeted support (see our future email focusing on Recommendation 7). 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’);
- give feedback sparingly so that it is meaningful (for example, ‘One of the angles you calculated in this problem is incorrect—can you find which one and correct it?’;
- compare 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 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. Effective feedback can be given orally; it doesn’t have to be in the form of written marking. A summary of the evidence regarding different marking approaches and their impact on workload, 'Teacher Feedback to Improve Pupil Learning' is available on the EEF website.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Addressing misconceptions |
A misconception is an understanding that leads to a ‘systematic pattern of errors’. [2] Often misconceptions are formed 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. [3]
It is important that misconceptions are uncovered and addressed rather than side-stepped or ignored. 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. [4] 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. [5]
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.
Next email #2 - 'Recommendation 2: Use manipulatives and representations'
|
|
|
|
|
|
|
|
|
|
|
|
|
|
