Many of the problems experienced in Primary school will continue into Secondary school. These will often be exacerbated by a more formal approach and a change in surroundings and ethos. We should be aware of the strong influence of, and need for, consistency in many aspects of learning. When collecting the data for my standardised test (see, More Trouble with Maths, 2nd edition, 2017, Routledge) I recorded a dip in achievement levels across the whole sample at age 12 years, a dip that seemed to be overcome by 13 years.

I noticed with my students, all severely dyslexic, that any work that is not constantly refreshed is often lost. This is just one reason why it is so important to revisit the pre-requisite knowledge and skills for any new topic. For example, a sound understanding of the four operations (add, subtract, multiply and divide) is an essential pre-requisite for algebra. One of the basic cognitive (thinking) skills for algebra is the ability to generalise and see patterns. That was a key skill for young children and just one illustration of the need to take interventions back to the basics, even if just for a brief refresher.

Topics such as word problems and fractions become more prevalent at secondary level. These present many children with overwhelming challenges and withdrawal is the most likely coping strategy. Students will often choose not to answer a question rather than get it wrong. The classroom ethos is critically important to minimise this behaviour.

Note: It may be helpful to read the previous section, irrespective of your age

There are some reasons that might interfere with parents helping their children with maths. These include the parent's own anxieties and insecurities about maths or that the methods used in schools now are different to those used when they were in school or that some children do not want to 'see' their parents as teachers.

One of the practices I try to encourage in schools regarding homework is that pupils are given the homework before the lesson ends so that they can try the first two questions. This will help teachers identify the pupils who are likely to fail in the task. Again, I refer to the research that found that getting something wrong in the first stages of learning is harmful to future attempts to get it correct. Speed of working is a common problem so parents may have to be advocates (as is so often necessary) and ask the school to set fewer examples for their child, again without drawing attention to different treatment.

Creating the right environment for doing homework is often important. Children who are easily distracted may benefit from what Americans call a 'vanilla environment'.

Beware of setting expectations. This is a very complex skill, often simplified to 'Do your best'. If pupils do their best, they do not want to achieve low scores. If parents under expect, for example, 'It doesn't matter, I was never any good at maths', then they facilitate failure. I like the ungrammatical phrase, 'unanxious expectations'.

There is a danger of creating learned helplessness if failures, however small, are not managed. I have long been an advocate of attributional style (by Martin Seligman) and used it with great success in my school (see, Burden, 2005, 'Dyslexia and Self-concept')

One of the biggest issues I have found, both from working with dyslexic and dyscalculic children and my research is withdrawal. At the classroom worksheet level, this is revealed as a 'no answer'. If the pupil predicts failure then they will not commit to paper. The lack of engagement, of risk taking is, of course, a major barrier to learning.

Feed-back, obviously, has a significant impact on attitude. This can be as simple as a mark, 1/10, a comment, 'You are not trying' or a facial expression or tone of voice. Teaching is an incredibly complex and skilled activity and involves as much about the affective (emotional) domain as it is about cognition.

There is a questionnaire on maths anxiety in 'More Trouble with Maths' (Chinn, 2017) which can help identify some of the main issues. Although (Western) social attitudes to maths condone poor abilities with maths, the reality for young people now is that career options will be dramatically reduced if they fail to achieve an acceptable qualification/examination result in maths. Peer pressure can be a significant factor at this age and can work at two extremes (and in between). There may be pressure not to be good, which could be seen as 'geeky' or pressure to be correct, quick and high achieving.

One of the most useful strategies is the appropriate use of the question, 'How did you work that out?' or 'Can you tell me how you did that?' Listening to the pupil is so important and informative. There is currently a great interest in meta-cognition, which is 'thinking about how you are thinking', for example, when seeing 99, some students are literal and see just that number as an isolated piece of information rather than seeing 99 as 1 less than 100. So much in education depends on effective communication, teacher to pupil and pupil to teacher.

Pupils may not know all the times table facts, but they do tend to know the 1x, 2x, 5x and 10x facts. This can be the cause of failures when doing calculations rather than the concept that is being tested. I find that error patterns are very illustrative for teachers. It takes a reaction from, 'Wrong' to 'Here is where you made the mistake'. Error patterns can be used to reveal misconceptions.

The questions that generate a 'No answer' response from the pupil are also a guide to the problems and perceptions of the pupil. The 'No answer' response is an emotional issue and may come to be the dominant behaviour, the pupil no longer engages with any maths.

Being pro-actively aware of students' short term and working memories can help maintain their engagement in maths. For example, to address stm problems, repeat a question or a chunk of information, break the information down into stm appropriate chunks. As a real-life example, notice how the 16 digit credit card numbers are broken down into chunks of 4 digits.

Working memory influences much of maths, especially mental arithmetic. For example, if the question involves four steps to achieve a solution and the pupil's working memory can only handle three steps, then he will fail. Thus, the failure may not be conceptual, but a consequence of poor working memory. It is worth noting that reversing any sequence of procedure challenges working memory.

It is rare to see visual images and maths manipulatives used a secondary level. The appropriate use of these can help in teaching pupils to understand maths topics. They can link the maths vocabulary to the symbols and to the procedures and enhance conceptual understanding. For example, cutting (dividing) squares of paper can show what fractions mean. Cutting a square into three equal parts shows it being divided into three thirds. Combining this with the symbols, 1/3, shows that the / means division, the 3 means 3 equal parts and that the 1 shows that this is 1 of 3 equal parts. As recommended for use with younger pupils, it may continue to be of help to children who are unable to organise their work on paper, for example, to line up columns of numbers, to use squared paper where the squares are sized to suit the individual. As with any accommodation, the pupil and peers must not perceive this as treating them specially and giving them an advantage.

- R. Ashlock (2010) 'Error Patterns in Computation' 10th edn Pearson
- Chinn, S. (2017) 'The Trouble with Maths' 3rd edn. Routledge
- Chinn, S. and Ashcroft, R. (2017) 'Maths and Dyslexia and Dyscalculia: A Teaching Handbook' 4th edn. Wiley
- Henderson, A. (2012) 'Dyslexia, Dyscalculia and Mathematics: A Practical Guide' 2nd edn. Taylor and Francis
- www.mathsexplained.co.uk (tutorials that address topics in a visual and non-age specific way)