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Maths Switched On

The Complete Maths Solution For Bright But Struggling Learners
"R's maths teacher was hugely complimentary about your work with R (and quite emotional about his Common Entrance result!) today, as was his science teacher who noted the dramatic improvement in R’s ability after your sessions.

"R is the only non-scholarship student to win the headmasters academic endeavour award! Your ears must be constantly burning with the amount of times I sing your praises to everyone!"

More on R's mathematical journey

Some imaginative and creative individuals find it difficult to do maths.

The sequential thinking required to be good at maths – a subject in which there is always one right answer – does not always come easily to artistic, lateral or explorative thinkers. Frequently, difficulty with maths (dyscalculia) is accompanied with issues around telling the time, managing time, and/or personal organisation.

Many traditional approaches to maths require a great deal of memorisation of data such as times tables, without their necessarily having been understood. Frequently, individuals who struggle with mathematical thinking also struggle with rote memorisation. This can result in stress, anxiety, and damage to the person's self-esteem.


Typically, these same individuals also have marked strengths. They may excel in creative, artisic activities; be talented in sport; and be good at picturing or visualising in general. Their imagination, not their memory, is their strongest learning tool. When they can picture what they are learning and re-create it for themselves, the thing being learnt becomes part of who they are.

For these individuals, maths should not be memorised; it needs to be memorable.
Claire Tuthill.jpg

Claire has a degree in Mathematics and Education from Cambridge University and has been teaching Mathematics for over 30 years. She has taught children aged 5-18 across every year group in school in prep and senior schools. She has run three Mathematics departments

in independent Preparatory schools in London, Oxfordshire and Malvern.


Claire is a published author, an independent Maths consultant and is currently working for the ISEB. She has attended courses at The Hornsby Centre and with Unicorn Maths in London to help her develop an understanding of Dyscalculia and Dyslexia.

More about Claire

From Maths Failure To Maths Success: Your Team Of Two Experts

Richard Whitehead: Maths Dyslexia And Dyscalculia

Richard is author of "Why Tyrannosaurus But Not If: The Dyslexic Blueprint For The Future of Education."  He is a former SENCo in a leading British private secondary school and a Patoss-accredited Specialist SpLD Teacher Assessor.

Claire Tuthill: Maths Tutoring and Exam Preparation


Richard is Director of Davis Learning Foundation and specialises in the Davis Maths Mastery Programme, a leading solution for dyslexic and dyscalculic individuals devised by Ronald Davis, author of "The Gift of Dyslexia".

Richard also conducts Davis programmes for individuals with dyslexia, dyspraxia, ADHD and autism, as well as presenting workshops on the Davis methods.

More about Richard

From 22% to 65% in 4 months: R.'s journey from Dyscalculia to Common Entrance Success
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R's mother contacted Richard at the end of January 2022. As a Year 8 pupil, he was struggling badly in almost all areas of maths. He was experiencing a crisis of self-confidence and significant symptoms of anxiety.

In February, R.'s took a mock Common Entrance examination, in which he scored 22%. There was a real fear that he would not pass Common Entrance in a few months' time.

In March, R. was diagnosed with dyscalculia by a local educational psychologist.

In April, Richard gave R. an intensive, one-to-one Davis Maths Mastery Programme. R. quickly responded to the techniques, growing rapidly in confidence and achieving more and more correct answers to more and more difficult questions. Richard then handed R.  back to Claire for targeted Common Entrance preparation, communicating closely over his needs.

In May-June, R. took Common Entrance, passing it with 65%.

Inspired by R's success, Richard and Claire decided to form a longer-term partnership to help other struggling mathematicians in a similar way.

The Davis Maths Mastery Programme — with Richard
“The Davis Maths Mastery course matched the pace my child need to learn. I witnessed my son grasp concepts with speed and clarity, growing in confidence and excitement to learn more. Maths very quickly became his favourite subject.

"We were both blown away by how quickly years of lost of learning were set in a foundation which became easy to build upon.”
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Some individuals do not respond to remedial maths interventions, however well thought out and skilfully devised.


Because key foundation pieces are missing. These need to be put in place before any mathematics teaching is attempted.

Typically, these pieces are:

  • a relaxed, consistent focus. Individuals who struggle with maths often experience mental "glitching" as they attempt to solve mathematical problems. This will cause what are often branded "careless" mistakes, leaving the individual frustrated and confused about their abilities;

  • the ability to "picture" quantities and mathematical processes.

  • difficulty with mathematical thinking. Creative individuals often excel at associative, out-of-the-box thinking but struggle with linear and sequential logic.

The Davis Maths Mastery Programme employs a unique combination of tailored mental focusing tools,  creative concept exploration, and real-world experiences of how quantities can change, to put these missing pieces in place.

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Once the individual is able to focus consistently and is starting to think "like a mathematician", a series of creative exercises quickly establish confidence and certainty in counting, adding, subtracting, multiplying, dividing — with whole numbers as well as with decimals and fractions.


A uniquely creative approach to the most common words used in maths story problems helps the individual clearly to visualise what the problem means, and what mathematics it requires.

And right at the end, pencil-and-paper training is provided in column addition and subtraction, long multiplication and division — with whole numbers and decimals.

Bespoke Maths Tutoring — With Claire

Building on the visualisation of number concepts developed in The Davis Program. Claire utilises visual techniques to build understanding of number operations, algebra, shape and space. Other areas of maths can be addressed as needed. This develops confidence and pupils start to make links between the various concepts in Mathematics. This can help prepare pupils for entrance examinations at 11+ and 13+, GCSE, or for school examinations. She can also be a point of contact for any Maths questions via email or Teams outside lessons.


Alongside their improved results, Claire's pupils experience increased confidence, enhanced ability to make links between various concepts in Maths, and greater independence at using online sources to find the correct method for the mathematical task in hand.

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The Davis Maths Mastery programme and Bespoke Maths Tutoring are separate and distinct programmes which are provided in their own distinct contexts, on separate schedules, and with separate fees.

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