Thirsk Maths Tutors and Thirsk Maths Tuition

Personal Description:
I am mum to two boys, both who have flown the nest. I miss them greatly now that they are based in London but try to visit as much as I can. I love to shop and also exercise, especially pilates. Oh and I do love to cook!

Teaching Experience:
I studied at Dundee College of Education where I gained a Diploma in Primary Education. This was a three year course. I then took another Certificate in Early Years. After leaving College, I taught in both the state and private primary sector. I left teaching to have my children and then to nurse my youngest child who was quite sick for a few years. Once his health was better, I started working as a tutor from home or going to the client's house to tutor. I now tutor seven days a week. I have experience in Maths, Language, Phonics and Grammar. I also tutor children in preparation for entrance exams in to the independent sector, which includes Verbal, Non-Verbal Reasoning, Maths, Language and Spelling. The children I have tutored have all had great success, many going forward for a scholarship.
I have an online Dyslexia touch type programme which has had tremendous success. Many children, with the school's permission , come to be tutored within school hours.

Tutoring Approach:
I always believe that the child should feel comfortable with the person they are being tutored by and build up a good relationship. Tutoring is not only about helping the child to succeed but also for them to gain confidence and self belief. I have various methods of tutoring from written work, reading and oral work. I also have a computer available where we can work from. eg online games After each lesson, I give the child homework to be completed for the next lesson.

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Personal Description:
Born in London, I was educated in the UK and Hong Kong. I currently reside in Oxfordshire with my husband, where we both enjoy the outdoors in the Cotswolds.

Teaching Experience:
I have many years' experience in primary and secondary schools and home education in the UK, Hong Kong and Germany.

I teach in a school in Burford, Oxfordshire, and also provide home tuition to primary and secondary pupils.

Tutoring Approach:
To encourage your child to gain confidence and enjoy learning, I draw on my personal warmth and humour in lessons. I aim to help your child gain good exam results through:

lively engagement with your child's creative intelligence
continuous assessment and feedback of your child's progress
learning using a wide variety of resources

I believe learning comes alive through building on the child's immediate experiences and their curiosity for the world around them.

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Personal Description:
I am a friendly and approachable tutor with a huge amount of enthusiasm in the subjects I teach. I was awarded a Scholarship to a competitive independent before working towards a Masters in Biochemistry at Oxford University.

I have since worked as a Pharmaceuticals Business Analyst, as a High Yield Chemicals Industry Analyst in Investment Banking and as an Air Traffic Controller. In each case the knowledge and skills from my education have been critical. I would now like to gain the satisfaction of helping others do well in these subjects and attain their potential.

Teaching Experience:
In my industries it is critical to continue learning and passing exams, and in every role, I have always had to pass on my knowledge and understanding to others, which has been incredibly gratifying. More recently, I have enjoyed tutoring maths and other subjects to pupils locally, often to help them gain entrance to competitive schools. I also enjoy spending time teaching my son and my nieces.

Tutoring Approach:
I believe that learning should always be interesting to the pupil - inspirational even - and that the onus is on the teacher to make this the case. Learning is about being curious and asking questions; in fact I believe pupils should not be scared to ask any question, which means that learning should feel relaxed rather than formal.

Subjects should not be seen as complex but rather layers of straight forward principals that build on what the pupil already knows in an intuitive fashion. In this way, a good teacher allows understanding to grow naturally and not feel like a challenge.

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Personal Description:
I am a fully qualified Mathematics teacher currently working in an inner city secondary in Liverpool.
I graduated from the University of Liverpool with an honours degree in Mathematics and Financial Economics and have also completed a further Mathematics course at Liverpool Hope University.
My background in Mathematical education has provided me with the knowledge and skills to teach students of all ages and different abilities.
I have been tutoring for the past 12 years now, both independently and for a private agency, with a proven track record in gaining the results required by each of my students.
Full CRB available on request

Teaching Experience:
I currently work in a secondary school in the Liverpool area and I have worked in the schools for the past 12 years teaching pupils in classes, small tuition groups and on a one to one basis.
I have an extensive knowledge in preparing pupils for exams, whether it be secondary school entry exams, GCSE or A-level. This has come from working in various schools doing intervention classes, both independently and as part of my further Maths course in University.
As well as teaching in the UK I have been fortunate enough to go on a charity project to India over the summer holidays where i was able to teach in two Tibetan school, which has given me a wider perspective on teaching.

Tutoring Approach:
The first session is always used to get the know the student, find out what they want, what their strengths and weaknesses are and how we can develop these to reach our target grade/level. This is done by creating a relaxed, friendly atmosphere where the student can feel they are able to approach me with any problems or queries. By finding out the above information and creating such an atmosphere, i am then able to build their confidence and understanding in Mathematics.
I also aim to use the same approaches as i do in my classroom, where the students can see how they are doing and how to reach the next level. Regularly little assessments will take place as evidence of pupil progression.
Pupils will be encouraged to try hard and aim to reach the highest possible grade they can.

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Personal Description:
I have a PGCE in Science, a BSc(Hons) in Physics, a Ph.D ( in High Energy Physics) both from Liverpool University.
My teaching style can be described as relaxed, rigorous and mainly encouraging pupils to achieve their potential and realise their hidden talent for the subject.

Teaching Experience:
All my lessons are online via Zoom. I have taught Physics and Maths over many years both privately and as my day job as a teacher of Physics in an outstanding school.

Tutoring Approach:
My approach to tutoring can be described as relaxed, rigrous and mainly ecouraging pupils to achieve thier potential and realise their hidden talent for the subject.
All lessons are online via Zoom.

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Personal Description:
I am a very enthusiastic, focused, self-motivated, highly-disciplined, target-driven, adaptable, mobile and ambitious graduate of Microbiology and Biomedicine genuinely pursuing an outstanding, very challenging and motivational career as a Teacher, using my skills and knowledge to improve the quality of education of other people.
I am passionate about teaching and want to inspire and enhance the level of achievement of my tutees.

My strong desire is to see my tutees achieve their desired grades and conquer their fears, becoming what they aspire to be.

Teaching Experience:
I am experienced in SEN from EYFS to KS1/KS2, and also in teaching Science to KS3 to KS5. I am also well experienced in mentoring groups as well as providing one-to-one-support.

My tutoring skills have no bounds as I have also been afforded the opportunity to lecture in Microbiology and Biology.
With an ever-growing drive for excellence, I am on a perpetual route to keep up with the ever-dynamic teaching skills through CPDs and trainings in behaviour-management to all that is required to teach per excellence.

Tutoring Approach:
My belief is that everyone understands at different levels.Based on this, I personalize my teaching approach to suit the specific needs of my students. I believe that there are visual learners, kinesthetic learners and auditory learners. Therefore I have different interactive resources that can be used depending on the type of learner I am working with.

I am of the belief that if you aim higher, you can achieve anything you believe in your heart that you can do.

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Personal Description:
Fully qualified science teacher with MSc in Theoretical Physics. Teaching maths, science.

Hi, my name is Samuel-Louis. I was born and raised in London, I trained to teach at the UCL IOE and I am a fully qualified science teacher (PGCE and NQT). I have an MSc in theoretical physics and am studying for an MSc in Mathematics.

Teaching Experience:
I have been teaching science at a comprehensive school full time for the last two years and spent a few months before that tutoring a range of age groups. I have experience in teaching science and maths from KS3 to A level. I have an MSci degree in Physics from Queen Mary University of London and an MSc in Theoretical Physics from Kings College London. After passing these degrees I went on and completed my Post Graduate Certificate in Education (PGCE) with the University College London Institute of Education (UCL IOE) the worlds leading teaching establishment. I have since passed my NQT and am now a fully qualified teacher. Since training as a teacher I have worked as a science teacher in a South London Secondary Comprehensive school for the last year, where I taught all levels of science, from ages 11-19.

Tutoring Approach:
I am organised and friendly and have a lot of experience teaching all age groups. I studied for my post-graduate certificate in education (PGCE) with University College London Institute of Education (UCL IOE), the world number one centre for teacher education. I then went on to work full time teaching science in an all-girls secondary comprehensive state school in South London where I successfully completed my NQT. During this time, I was both a science teacher and a form tutor. I was responsible for ensuring that the students I taught (over 400 in total) made excellent progress and developed themselves socially, emotionally and academically.

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Personal Description:
A free initial lesson is available to help you determine if you want to continue.


I am a professional and experienced Mathematics and Physics tutor.
I have a master's degree in Theoretical and Mathematical physics from the University of Nottingham and I am currently working towards a part-time master's in Pure Mathematics at the Open University.

Teaching Experience:
I have tutored a wide range of students from primary age pupils to university students.
I have successfully tutored the following courses:
GCSE Mathematics and Physics
A-level Mathematics, Further Mathematics, and Physics
Introductory undergraduate Probability and Statistics
Cambridge STEP entrance exam.
Introductory undergraduate Physics
Mathematics for engineers and scientists
Mathematical methods for finance, accounting and economics
Linear Algebra
Vector Calculus
Calculus of Variations
Classical Mechanics
Real and Complex variables
Differential Equations & Laplace transforms
Partial Differential Equations & Fourier analysis
Please discuss with me via messaging, If you are seeking tuition on topics other than the abovementioned

Tutoring Approach:
I take a very informal, friendly and interactive approach to tutoring. I provide a positive learning environment by quickly building a rapport with my students and helping them enjoy their learning.



My Cancellations Policy
You must inform me at least 24 hours before the tuition session if you wish to cancel the session. If this notice is not provided, I may charge the full tuition. If I continually receive cancellations for sessions I may choose to terminate the private tuition

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Personal Description:
I Have worked in education for 30 years. I have been involved in Support for Learning for most of this time. I have supported many students in schools at at home and have proven experience in raising attainment.

Teaching Experience:
25 years Teaching Experience in Support for Learning in both Primary and Secondary Schools. I Have specialised in working with small groups and individual students. I have expertise in Dyslexia and devising ways in which learners can overcome barriers to learning.

Tutoring Approach:
Understand importance of building up a good working relationship. Identify learners needs and style and match teaching to their requirements. Break learning down to achievable goals and talk through targets.

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Personal Description:
I am a passionate and dedicated tutor, with a wealth of experience in both tutoring and teaching in schools, after having trained as a primary school teacher. Keeping rates really affordable for communities across Slough, Windsor and Maidenhead, I tutor pupils of all ages and abilities, to ensure that they get the best learning experience possible! P.S. I only have 2 spaces available at ONLY £20 per lesson!

Teaching Experience:
I am an experienced tutor and have worked in schools and tuition centres across Slough and Maidenhead. I have also studied Teacher Training at the University of Reading and worked as the Assistant Centre Director of Bright Young Things Tuition in Maidenhead (I am also currently writing my own teaching book based on all my experiences). I currently hold tuition sessions to the home for families across Slough, Windsor and Maidenhead, under my umbrella company.

Areas I cover are Primary, Secondary and GCSE Maths, English & Science, Early Reading & Writing and I gear children with the essential skills for the 11+ exams, including Verbal and Non-Verbal Reasoning. Some children I am currently working with and am experience with have had special educational needs like dyslexia. Additionally, I have created my own Maths & English learning resource packs, which children use for Creative Writing and Maths. I also give out homework and set tasks for pupils, which I review and mark on a weekly basis. With excellent feedback from parents, I have references that I can happily present to parents looking for lessons.

Tutoring Approach:
Parents generally find that I am a very calm and pacient tutor; I like to work at the pupil's pace and provide lots of reward, especially for the younger children (like stickers and prizes). If I find that the student needs some more help outside of my paid hourly time, I give extra time, to ensure that they have learnt the skills to the highest standard possible.

I have a lesson plan ready prior to the session, but am generally flexible in my approach to the content I teach; sometimes, the lesson focuses on helping the child with their homework or reviewing a test paper from school. To ensure learning is as enjoyable and interactive as possible, I have whiteboards that children use to brainstorm ideas or sometimes, for instance, I encourage them to use coloured card to create their own writing checklists.

As I am writing my own book based on my school, teaching experiences, my tutoring skills are derived from the wealth of experience I gained from training courses and teaching within schools.

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Personal Description:
I am a qualified teacher and experienced tutor of 16 years, previously curriculum leader of science and head of STEM, with a proven track record of securing high levels of attainment for all my students with great testimonials from previous students. I have been teaching Physics, Chemistry, Maths and Engineering since 2004 and also an examiner with AQA,OCR and Edexcel.

Teaching Experience:
I am a UK trained teacher and have been teaching physics, chemistry, maths and engineering up to A level, since 2004 in various schools in London.

Tutoring Approach:
As a qualified Scientist, my approach is to make the subjects enjoyable and convey complex concepts in a simple way. No one approach will work best for every student, and understanding how each student learns and changing my strategy to suit them is how I work.

My lessons are clear, easily digestible, based on the student's needs, developing prior knowledge, building confidence and problem solving skills whilst developing exam technique with access to practice questions.
If you find these subjects challenging or overwhelming, i'd like to hear from you because Science and Maths is only as hard as the teacher makes it.

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Personal Description:
I'm 4th year MSci Physics student at UCL. I'm great with people and as a student I know the difficult parts of the courses and can explain concepts in the simplest ways. I'm certain I can help your son/daughter achieve the grade they want at GCSE and A-Level in sciences and maths.
It's not only academic help that I can offer, I can:
- share my study tips and habits that become essential as your child moves on to higher learning
- share my up to date knowledge of what you need to do to ensure a bright future for them and secure their dream job

I have 9A*s (including all sciences and maths) and 4As at GCSE.
At A-Level I achieved 3As (Maths, Physics, Chemistry) and 1B (Further Maths)
Currently pursuing an MSci in Physics

Teaching Experience:
I have a few months of tutoring experience working with secondary school children during my A-Levels, I was selected as a physics mentor at the Liverpool Blue Coat school. I have university level teaching experience gained through tutoring my brother who is also a university physics student. I can guarantee that I will be able to deliver high quality lessons to your son/daughter if I am their tutor.

Tutoring Approach:
Often students don't understand a topic simply because the teacher hasn't put it into language the student understands. I do my best to convey ideas in clear and simple language to cut to the essence of the topic. As a current student the struggles and pitfalls of learning are very fresh so I can help someone else avoid the same issues.
I believe in STEM subjects the most important and useful way to improve is to practise a lot of questions and this will be my main method of tuition. Your child and I will discuss concepts and then apply them to concrete problems during the sessions. I will then provide some homework questions that they should attempt in their own time and will always provide complete worked solutions to all homework set by me.

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Personal Description:
I'm a friendly tutor who's a science enthusiast with a Master's degree in Mathematics, good knowledge on Physics. I'm doing my second Master's in theoretical Astrophysics at the University of Sussex now. I do art & I'm also a player of South Indian martial art called "Silambam". And I'm practicing yoga for the past 6 months.

Teaching Experience:
Over the course of time, I have tutored school students who were in need of help with their academics. I do arts and have taught that to kids. I've also been practising self defence for over a period of 9 years.

Tutoring Approach:
I can help a tutee to understand the world of mathematics/science with better liking towards the subject and to view our life with characters of morality/humanity. Free thinking and constant work will be the basic qualities of success. And I can motivate one to achieve that.

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Personal Description:
Hello there. My name is Kana. I am a person who found my passion to teaching the young kids not only their subject to score in their exam but also to have some attitude to score in their life as well.

Teaching Experience:
I am a Chemical Engineering graduate who is currently teaching for the past 6 years in an international school. I have the patience and ability to teach in a way that you will learn by understanding the subject and loving it.

Tutoring Approach:
I use daily life examples to most concepts that it is logical for you to apply the knowledge elsewhere or to understand the concepts better.

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Personal Description:
Masters and PGCE graduate from University of Cambridge. Passionate, experienced, and friendly tutor.

Hi there! My name is Jagon, and I am a passionate and experienced tutor of science at GCSE and Biology A level. I completed both my Masters and my teaching training at the University of Cambridge, which informs my practice with the most current research-based teaching strategies which leads to academic success. What makes me stand out from other tutors is that I have a talent for chunking and clarifying complex concepts into manageable pieces, making it easier for my students to understand and retain what they've learned. Whether you're struggling with a specific topic or need help with an entire subject, I'm here to help you succeed.

Teaching Experience:
Currently, I have been giving online tutoring for 5 years and am currently teaching in real-life classrooms. I am able to cater to different examination boards and learning styles.


"Tutoring with Jagon has been an experience that has aided me so much.
The lessons are always so productive and I learn so much every time. The slides that he creates are so detailed and interactive which really help me develop my understanding on the topic as well as keep me from getting distracted. Finally, he also works on past paper techniques, telling you exactly how to answer a specific question.
Overall, the lessons are great : Jagon is such a cool teacher and never makes me feel self-conscious if I get a question wrong. I love doing my lessons because I have a blast but at the same time get so much work done.
If you're looking for a biology teacher who can teach you as well as be fun, he is the best option!"
- Sophie, Year 11.

"I find the lessons very useful, and they have helped me a lot. I think you teach in a way that makes the information stick in your head. You teach the information to make us understand it but not memorise it so it is easier in exams. I find it very effective and it has helped me."
- Anna, Year 9

Tutoring Approach:
My approach to tutoring is highly personalised and focused on helping you achieve your desired marks. I believe that everyone has the potential to succeed, and I work closely with my students to identify their unique strengths and weaknesses, so that we can develop a customised learning plan that works for them. I'm patient, understanding, and committed to helping you succeed, adapting to your learning style and background.

My lessons are very much dependent on my initial assessment of the students, but usually involve discussions and activities to identify areas that need developing, explicitly teaching the material that students need help with, checking their understanding, then providing lots of opportunities to practise the content, leading to exam practice by emphasising on examination techniques.

I truly believe that everyone is capable of succeeding in their GCSEs and A level with hard work and the right guidance. I am confident that my experience and genuine passion in science will help my students grow their confidence and achieve great results. Feel free to contact me for more information, testimonials or to schedule a lesson!

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Personal Description:
I am a university academic, engineering researcher, and dedicated STEM tutor currently serving as a Research Fellow at the University of Birmingham. I hold a PhD in Mechanical Engineering from Loughborough University, an MSc (Cum Laude) from KU Leuven, and a First-Class BSc from UET Lahore, alongside formal higher education pedagogical qualifications (PGCHE) from Birmingham. Over a 15-year university career, I have progressed from Lecturer to Associate Professor, designing accredited curricula and lecturing across undergraduate and postgraduate engineering programmes.

Alongside higher education, I have spent two decades providing one-to-one tuition to over 60 students from 15+ leading UK universities, as well as secondary pupils, college students, and adult learners. For parents, I offer a dependable, reassuring, and structured partnership. I understand the anxiety that GCSE and A-Level exam preparation can cause, and I take pride in turning that pressure into genuine academic confidence, independent thinking, and top-tier results.

Top-Tier Academic Credentials: PhD (Loughborough), MSc Cum Laude (KU Leuven), BSc 1st Class (UET Lahore), and PGCHE (Birmingham).

Comprehensive Educational Scope: From GCSE and A-Level through to BTEC/Foundation pathways, undergraduate degrees, and adult career transitions.

Special Educational Needs (SEN): Experienced in providing patient, structured guidance for neurodivergent learners, including students with ADHD, dyslexia, dyscalculia, and exam anxiety.

Teaching Experience:
My teaching background covers university lecturing, laboratory leadership, and extensive one-to-one mentoring across both UK and international curricula. Having taught students across 15+ UK universities, I routinely assist undergraduates through advanced module mastery, computational modelling, and exam resit preparation. At school and college level, I provide complete, syllabus-aligned coaching for GCSE, A-Level, BTEC Level 3 Engineering, and University Foundation Year students across all major boards.

A significant part of my tuition practice involves adapting to diverse learning profiles, particularly students with Special Educational Needs (SEN). By breaking multi-step problems into visual, structured steps and maintaining a calm, unhurried pace, I ensure students with ADHD, processing differences, or executive-function challenges build strong foundations without feeling overwhelmed.

GCSE, A-Level & Further Education: Complete coverage of Mathematics, Further Maths, Physics, and Chemistry across AQA, Edexcel, OCR, and Cambridge International (CIE).

Specialist Engineering & Materials: Advanced tuition in Thermodynamics, Fluid Mechanics, Heat Transfer, Statics, Dynamics, Stress Analysis, Materials Science, and Tribology/Wear.

Higher Education & Analytical Skills: University Foundation Year coaching, Engineering Mathematics (Calculus, Linear Algebra, Differential Equations), and dissertation guidance.

Online & Adult Learning: Over a decade of interactive remote teaching (since 2016) using digital whiteboards, live derivations, and shared problem sheets for adult learners and professionals.

Tutoring Approach:
My teaching is grounded in first-principles learning-focusing on why an equation or physical law works rather than encouraging rote memorisation. When students grasp the core mechanics behind a concept, unfamiliar and difficult exam questions become approachable puzzles rather than sources of stress. I maintain a supportive, low-pressure dynamic where asking questions and making mistakes are welcomed as vital parts of the learning journey.

Subject understanding must translate cleanly into exam marks. Every lesson integrates board-specific exam technique, training students to decode command words and meet mark scheme expectations. For parents, I maintain open communication through initial diagnostic assessments, structured milestone planning, and regular progress updates aligned with upcoming school mocks.

First-Principles Mastery: Building genuine conceptual intuition so students can tackle novel, high-tariff exam problems with confidence.

Mark-Scheme Precision: Deconstructing past papers, keywords, and time-management strategies to secure every available method mark.

Parental Visibility & Feedback: Clear progress tracking, diagnostic gap identification, and homework roadmaps tailored to school exam dates.

Adaptive Delivery: Modulating between visual diagrams, practical engineering examples, and mathematical proofs to suit each student's individual learning pace.

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Personal Description:
My name is Megan, a fully qualified primary teacher and tutor in Scotland.

Teaching Experience:
I have a Bachelors of Art with Honours Professional Education (primary) with specialism in modern languages. Throughout my degree and work experience, I have taught primary school children of all ages across all primary subjects.

Tutoring Approach:
My number one priority is making lessons fun and engaging so that your child can have fun while they are learning. I am passionate about adapting my teaching for each individual child, ensuring all children are able to progress with their learning and meet their full potential.

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Personal Description:
Outside of tutoring, I enjoy photography, baking, wildlife gardening, health and fitness, including swimming and woodland walks, as well as spending time with family and friends.

I'm very proud of my daughter and three young grandchildren who also share my interests in photography, forest adventures and baking!

Since becoming a vegan, I have enjoyed creating a wide range of delicious meals which are also enjoyed by family and friends!

I am also passionate about wildlife conservation and have initiated campaigns in my local area to conserve areas of habitat for wildlife. For example, two years ago, I collaborated with local schools and councillors to stop the felling of 43 healthy trees at a historic green space in the town centre.

Teaching Experience:
I am a PGCE qualified teacher in Primary Education, specialising in Special Educational Needs, with 15 years of school teaching experience.

I chose to reduce my hours as a school teacher five years ago so that I could focus my attention on my tutoring business full time.

My main areas of expertise are English and Maths, where I can quickly diagnose a student's tuition needs and plan personalised lessons to help them to reach their learning targets.

I have taught many students with a wide range of learning needs, including learning difficulties such as dyslexia. For example, I recently tutored a boy with moderate dyslexia who was in Year 6. During this time, his confidence in his abilities in English increased significantly to such an extent that his grade increased from below to the above expected levels in Year 9.

I embrace all opportunities to keep up to date with developments in the National Curriculum by continued research in the public domain as well as attending training webinars and conferences

Since becoming a Private Tutor 20 years ago, I have helped over 1000 students to increase and exceed their grades in Maths and English Lanuage and Literature, sometimes by up to three grades.

I have also successfully coached adult learners for Functional English and Maths tests from Level 1 to Level 3, as well as students who speak English as a second language, for GCSE and IGCSE English and Maths exams.

Additionally, I tutor students in entrance test preparation skills for the 8, 11 and 13 plus exams.

I am always extremely proud of them when they exceed their predicted grades in their exams and gain entry into their chosen independent school.

Here are some recent reviews:

`Thank you Tina for helping me to take a long way in a very short time. My English was grade 2 at the beginning of the year 11. With the support from Tina, I have achieved grade 5 in both English Language and Literature. Thank you so much.`

`Tina`s teaching style allowed me to learn at my own pace and she always had a clear plan for each lesson.`

`She is patient and thought provoking, encouraging her students to `learn to learn`, rather than reproducing someone else`s ideas.`

"My daughter`s confidence in English has dramatically improved in both herself and in the classroom, thanks to Tina."

Tutoring Approach:
I would describe myself as a friendly and inspiring tutor who works with students in a calm and encouraging way.

I have been fortunate to teach in a variety of learning contexts, including nurseries, primary schools, secondary schools and colleges, which has enhanced my ability to adapt my expertise to a wide range of differing tuition needs.

I believe that by engaging with each student on a cognitive level, I am able to establish a positive rapport with them.

It is very rewardingl when I see a 'light bulb' moment happen when a student seems to glow from feeling a renewed sense of understanding and achievement.

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