Isle of Benbecula Maths Tutors and Isle of Benbecula Maths Tuition

Personal Description:
I'm a very approachable person who interacts well with students of all ages. Most would say that I have a positive outlook on life and always leave a positive impact on those I meet. I'm friendly, down to earth and honest. My philosophy is that studies don't have to be boring, and I always use my career as a teacher/tutor as testament to this.

I enjoy a variety of different things such as arts, culture and cuisine. My hobbies include drawing comic strips, magna, anime and playing electric bass. I am open minded and welcome students of any age, race, background and culture as an honour for me to teach.

Teaching Experience:
Over 19 years experience teaching and tutoring in and out of classrooms. I have taught both in the UK and abroad. I am one of the few teachers in London who is able to teach Mathematics, English Language, English Literature and the three respective Sciences to A* at GCSE.

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School/Classroom references available
Tuition references available

Tutoring Approach:
Each student is different, and I feel it an insult to my students' integrity to tell them how to revise when first meeting them. Through my experience teaching, there is no right way to study, but there are a variety of 'better' ways to make the best grades for each person's potential.

Many students approach me frustrated that they often don't achieve the same calibre as their peers despite the hours they put in. Often it is due to the fact that they aren't their peers and a different approach to revision and homework is required. I believe in working smart before working hard.

We'll tailor a program as a team, and prioritise it factorising your: current ablities, time proximity, and scope of subjects you'd like to cover.

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Personal Description:
Extensive experience teaching secondary school Mathematics (KS3/4) and striving towards being a specialist for A-level Mathematics (KS5).

I offer online tuition with an emphasis on the students' needs. I'm flexible on approach and will gladly cater to your technological specifications. Meaning, you will not require the best microphone, webcam, feng shui background or even the fastest bandwidth to maintain an improving grade. So long as you have a pencil, paper and an inquisitive mind that is set on learning, you will walk away from our sessions academically fulfilled.

My aim is to boost your self-esteem around the subject of Mathematics. As the tutor, it is my duty to listen to you and diagnose the root of your trouble. I will forever do my utmost to openly exhibit the array of techniques Mathematics has to offer us in order to equip you with enough confidence to speak up and ask, "hey, can you help me with this, please?"

Step-by-step we will learn how to overcome and begin to finish the race at our own pace.

Teaching Experience:
My experience in education has been learnt from the ground up. Each role that I have been honoured to fulfil has blessed me with a unique insight that support roles provide; the focus has always been about the individual.

Every child comes to school wanting to learn. Creating lessons that are engaging and modified not only for their academic level but also for their interests commands respect. Using Mathematics that mirrors their world is a guaranteed method to inspire motivation for the apathetic and manage behaviour for the unruly.

Teaching is a skill that is built with time and I am proud in my ability to engage young students as presentable maturity is so repeatedly demanded.

2021 - PGCE Secondary Mathematics
2018 - 2021 Private Tutor, Mathematics
2017 - 2018 Learning Assistant, Woodfield
2014 - 2017 Maths Intervention Tutor, HGAED
2011 - 2014 Teaching Supervisor, KUMON

Tutoring Approach:
"But I very much believe that anyone can learn anything, as long as it is explained clearly enough" ~Raffi Grinberg, Real Analysis Lifesaver

In the age of online learning, explaining clearly enough is a nuanced task especially when it comes to Mathematics. I have always tailored my delivery to suit the needs of the student. The soft skills required to pick up on the preferred learning methods of each student is an ability I pride myself in. The topics covered in Mathematics for most school curriculums do not differ drastically. But what does have a lasting impression for those who hold any apprehension towards the subject is making the lesson intrinsically derived from their passions. Because Mathematics is everywhere. It is up to us educators to enlighten and embolden their world with how much Mathematics is involved in their innate interests. This wonder of discovery awaits every student. No matter how they regard their perceived natural ability towards numeracy.

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Personal Description:
If you needed a doctor, dentist or lawyer then you would want someone who was fully qualified and very experienced. So don't settle for anything less when you need a tutor. To get the best out of your tutoring, and hence the exam grades you want, make sure that you are getting the following:

1. Someone who will sit beside you and teach you in person. If the covid-19 pandemic has taught us anything then it has taught us that online tutoring can't hold a candle to having a teacher in the same room as you.

2. Insist on someone who is a qualified teacher. Just because someone has passed a few exams themselves doesn't mean that they will be able to teach their subject well. That's precisely why we have teacher training, to help people learn how best to convey that knowledge to others.

3. Insist on someone with plenty of experience. Practice may not make perfect, but it usually does make one a lot better, and this is often the case in teaching.

4. It's very important that a tutor knows their subjects very well and really enjoys them. Without both of these they are never going to be a good teacher.

Let's see how I measure up to these criteria. Well, I only teach in person, and from my home. On several occasions I have been offered online work, but always refused it, as I really do believe that I would be offering students a much inferior service. I have a Joint Honours B.Sc. in chemistry and physics, and for my PGCE my main subject was mathematics, and my secondary subject was physics. So I am well qualified in all the subjects that I offer: maths, further mathematics, chemistry and physics. My PGCE is from the University of Leeds, which has a very good reputation for its teacher training. I also have many years classroom and tutoring experience. As for knowing and enjoying my subjects, those who come to me for tutoring can see my large collection of maths, chemistry and physics books. I have also had a subscription to Scientific American for decades. I read maths and science for fun. Maybe that's why I gave up a very lucrative career as a software engineer to become a teacher. This is also why usually I only offer tutoring at A-level or equivalent, because I particularly enjoy teaching at this level. However, I am currently accepting a limited number of Y11 Higher Level Maths GCSE students.

Students studying maths might also be interested to know that I have written books about the best graphics calculators and also the Classwiz. So it's very likely that I'll be able to show you how to use your calculator much more effectively, which could save you time and mistakes in your exam.

Over the years many students, and their parents, have been very happy with my tutoring. Perhaps you will be too.

Please also note that I ONLY TUTOR FROM MY HOME: no exceptions. Among other reasons, this allows me to teach many more students, some of whom have been known to travel a considerable distance in order to get the right tutor.

Teaching Experience:
Let me be very frank. In the UK teaching in most schools is much less enjoyable than in many other countries. Behaviour, and what the school is prepared to spend on a teacher are often major issues. For students who genuinely want to learn this has serious implications. How qualified and experienced a teacher is may not be be a school's main recruitment criteria. Foremost may be their cost. A well qualified and experienced teacher will cost significantly more than a much younger one, so many older teachers' applications are often passed over. Also much greater weight may be given to classroom "management" skills, rather than the ability to teach ones subject.

Most of my time teaching in the classroom has been spent abroad, with a lot of it in private schools. For these schools neither behaviour nor salary is a major issue, so they recruit and retain teachers based on how well they can teach their subjects. This is the environment in which I have done my many years of classroom teaching. My years in the classroom have been spent in schools where ones teaching ability is paramount.

In regard to tutoring, this has been my main source of income for the past ten years, and most of this time has been spent teaching A-level, or the equivalent. It's probably fair to say that I spend many more hours teaching A-level than most classroom teachers, and as such I know what most students need, and where they are likely to experience difficulties.

Among the schools whose students I have recently tutored are: Ashmole Academy, Dame Alice Owen`s School, Enfield County School, Enfield Grammar School, Highlands School, Hockerill Anglo-European College, Princess Helena College, Southgate School, St. Michael`s Catholic Grammar School, The Latymer School, The Royal Masonic School for Girls, and Woodhouse College.

Tutoring Approach:
I believe that when it comes to teaching I know my subjects very well. So you don't have to tell me in advance what you require help with. If you come to me for tutoring you will be able to ask me, on the fly, about any maths, physics or chemistry that you are having problems with, and I would expect to give you good help immediately.

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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'm a MSc construction project management student and had my Bsc in Statistics.

Teaching Experience:
I've been a tutor on mathematics for more than ten years.

Tutoring Approach:
Breaking down problems in the simplest methodlogical approach is the best way I use in making my students understand complex calculations like Differentiations, integrations, probabilities, algebra, e.t.c

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Personal Description:
In October 2014 I graduated from Imperial College London, where I spent 4 years studying for my Masters Degree in MSci Mathematics. I have a big passion for learning and this is a trait I want to be able to pass on to other children. Currently, I am working as an Analytic Consultant in Birmingham, which helps to demonstrate the strong analytical and communication skills that I possess.

Teaching Experience:
During Secondary School I ran a Maths Club once a week where I set problems and puzzles for all students. Furthermore, I was a Chess Coach teaching chess to primary school children and in Imperial College I held sessions with 1st Year students aiding their transition between school and university.

Thus, I have had experience teaching a wide range of ages and abilities, which will help me to adapt my approach based on the student.

Tutoring Approach:
As a tutor I aim to pass on my passion for Mathematics onto my students, developing their understanding and appreciation for the subject. In my opinion this is the best way to learn as ideas become easier to remember and concepts become quicker to grasp, which will transpose into better grades and examination performances.

Overall, I bring an enthusiastic and approachable atmosphere to my sessions, where students are not afraid to ask questions. This will enhance their learning experience and again improve exam results.

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Personal Description:
I've over 13 years teaching experience. I teach KS3, GCSE & A level students. I'm currently working in tuition centre and also doing private tutoring.
I've BEng (Hons) in electrical & electronic engineering degree from London South Bank University.

I was a good science student. My favourite subjects are always Maths, Science, Physics, Computer/IT. I always achieved 95% + mark in math since my school term to Degree level. I also always got good marks in Physics and computing.

I love to teach student who is interested learning. I know the trick to let enjoy learning to make sure my student is enjoying learning and understanding what i'm trying to teach.

I'm happy to teach online (skype). If the student does know how to set up skype, i will visit your home and will set up skype and will show my student how to use it. A part from my tuition hour, if there is extra hour needs i'm happy to provide extra hours in tuition.

Teaching Experience:
I have been teaching GCSE and A level students in Physics, Chemistry and Maths. Student was able to develop their skills and achieved A*/9.
Some student set up their target for B but i changed their target for A/A* and they were able to achieve that grade.

Tutoring Approach:
If you live too far from me and traveling is not possible then i would prefer to teach on online to save time both side. Parent don't need to waste time to drop or pick up their children. I can record the teaching session if parents want to see what their children learning. They can see straight way what their children is learning.

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Personal Description:
My name is Marcia, and I am a PhD student in biomedical engineering. My project uses mathematical modelling to determine the optimal conditions for in vitro testing of new therapeutic agents. This project combines techniques and principles from mathematics, biology, physics and engineering. I received a studentship from the EPSRC to fund my studies. I am also a graduate with an MEng degree in Biomedical Engineering, awarded with first-class honours, from the University of Glasgow. I have a passion for mathematics and the sciences, and have always excelled in these subjects. My final year project for my MEng degree combined my skills in maths, physics and biology, and was based on the mathematical modelling of antibody drug therapy. I believe especially in encouraging young women and girls to find enjoyment and fulfilment from STEM subjects, although of course, boys are also welcome! I received three different scholarships during my undergraduate degree: the Allan Glen Scholarship, the William Wilson Scott Scholarship, and a scholarship through the Women's Engineering Society.

Teaching Experience:
I have been tutoring for 8 years and have worked with young people ranging from primary school age up to advanced higher pupils. I have also worked as a tutor in an Engineering Mathematics tutorial for first-year engineering students at the University of Glasgow. Finally, I participated in and received accreditation for my involvement in a university-run initiative, where I visited a local secondary school to assist students preparing for their Advanced Higher Physics coursework and examinations.

Tutoring Approach:
I believe that the key to learning mathematics and the sciences is in a relaxed and enjoyable approach. I am very patient and quick to find the best approach for each individual learner. I believe that no two individuals learn in the same way; therefore, it is of great importance to be flexible in my approach. It is my belief that mathematics and the sciences are best learned through the practice of problems. Still, I feel that it is crucial to first work through, with the student, how I personally would approach solving a particular class of problem to provide the student with a model by which to base their understanding. I am able to provide exam-style questions as well as handwritten notes. I believe it is essential to ensure that the tutee knows that they can ask any question without judgment. There are no "silly questions" - only things the student does not yet know or understand.

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Personal Description:
I am an enthusiastic tutor who has a degree and NVQ level 5 in Youth and Community Worker with 11 years post qualifying experience educating hundreds young people informally and outside of the classroom in groups and 1-2-1 in all sorts of different locations. I have a Level 3 teaching and assessment qualification. I have very good Maths and English having used them to study to degree level and in Youth Work Management. I have an active interest and knowledge in History, Geography and Religious Education having studied them to A-Level meaning that I am very knowledgeable in each of those subjects. I am a highly competent musician and sports person with Grade 5 in piano and music theory and having coached Football, Badminton, Tennis, Chess, Table Tennis.

My greatest skills are in building professional relationships, communication, building self-confidence and social skills, developing motivation and this is what I have been doing for over 15 years for hundreds of young people that I have met as a Youth Worker.

Teaching Experience:
I have over 15 years informally educating young people through qualifications and certifications.
I have over 9 years experience of teaching youth work and assessing it.
I am a Functional Skills tutor at Level 1 and 2 in English and Maths.

Tutoring Approach:
My approach is student centred - focused on the students strengths and development points and work alongside the student to build confidence and trust so that the student can excel. My style is quite relaxed yet challenging for the student so that the student engages and to increase the students enjoyment and understanding of the material and why they are learning it. My approach is very thought through and meticulous, carefully considering: personality and learning styles as well as the preferences of the student. I provide a lot of explanation and am able to explain things in many different ways.

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Personal Description:
I'm a statistician and scientist to trade and a father of two children.
I have taught many pupils (mainly Higher, Advanced Higher, or A level when I did my PhD in England).
Because I am employed and have a family, I like to teach just one pupil per year
I teach Higher or Advanced Higher level because I prefer that level of maths and also I enjoy teaching that level of pupil.

Teaching Experience:
I've tutored maths to many pupils over the past 30 years and within my work, I teach statistics to adults.

Tutoring Approach:
1. I always urge pupils to LEARN the rules (the maths rules). People think this is odd because the rules are often given at the front of the exam paper. I do this because I believe learning helps with knowing what tools are available and because I think it helps understanding.
2. I encourage pupils to decide what topic they want to cover in advance of the lesson so that we cover what THEY think they find difficult
3. As well as explaining the concepts and getting the pupil to practice relevant questions I also, as we approach May, give advice on exam preparation and technique.

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Personal Description:
Experienced Tutor (GCSE, IB/A-level and Degree) with 3 degrees obtained with scholarships in Science and Engineering at a top European institute, currently teaching Maths & Science at MathysicsTutor Kingston.

It has been satisfying to be able to help students and career changers to lift the grades, raise the confidence and discover the joy of learning through private tuition journey.

Besides tutoring, I am a Geoscientist with more than 10 years of experience in research and operation. As a Geoscientist, I combine advanced Maths, Physics and Geology in order to discover oil and gas within the earth.

The skills and experiences that I have acquired in the energy industry have enabled me to bring to students not only the knowledge and essential skills such as creative thinking, critical thinking and problem solving in the academic context but also the experience of applying those skills to the real-world problems in the science and engineering sector.

I was a teaching assistant during my academic years. Since graduating from IFP School in 2009, I have tutored people in my social circle. Since 2016, I have tutored students and career changers at various levels and from a variety of backgrounds.

Teaching Experience:
I have experience of private tutoring GCSE, IB & A-level and University students from a variety of backgrounds with a firm knowledge of the optimal motivating and engaging approaches for each age group, with great satisfaction rate.

My private tutoring methods have enabled many pupils to successfully get into a variety of top schools listed below. I am able to assist students in boosting their confidence, reaching their full potentials and stretching their abilities whilst maintaining high academic performances.
In addition, my private tutoring style is aimed at building problem solving skills, improving accuracy and speed, providing remedial work for those struggling as well as making study interesting and engaging.

40% of my students come from referral.

I have tutored university students from Imperial College, Edinburgh, SOAS, Kingston, Leeds and City universities in Maths, Geology, GIS and research/dissertation preparation.

My GCSE & IB/A-level students have come from following schools among others:

King's College School Wimbledon
Whitgift School Croydon
Tiffin School Surbiton
Tiffin Girls Kingston
ACS Cobham
Kingston College
Kingston Grammar
Hampton School
Sutton Grammar
Esher college
Coombe School New Malden
Surbiton High school
Wimbledon High school
Lady Eleanor Holles Hampton
Box Hill School Dorking
Royal Russell School Croydon
Nonsuch High School Cheam
Grey Court School Richmond
Twyford Church of England High School Acton
Royal Grammar School Guildford
Esher High School
Ursuline High School Wimbledon
Whitgift School Croydon
Latimer school Hmmersmith
St Dominic`s Sixth Form College Harrow
Notting Hill and Ealing High School
International School of London Ealing
Moulsford Preparatory School Oxfordshire
St John's Beaumont School Windsor

Tutoring Approach:
Every student is different and that is why private tutoring approach must be tailored to each individual. Upon discussion with students and their parents, I offer a customised SMART tuition plan: Specific, Measurable, Attainable, Realistic and Timely.

Core part of my private tutoring approach is to go over each topic to ensure thorough understanding of the concepts which is followed by variety of questions to consolidate the learning.

Assignments and homework are an integral part of my private tutoring approach as key to success is effective practice.

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Personal Description:
I am an 18 year old A level student attending Tiffin Boys Grammar School. I have experience tutoring, having managed to get all 3 of my previous students to get an 8+ grade in their maths GCSE. Maths has been a passion of mine which I plan to carry on at university and I believe this is evident in my tutoring where I try and keep an enjoyable vibe with the students. I am confident to answer any questions and I have as much experience as anyone with the new GCSE syllabus having sat it myself. I create an enthusiastic learning atmosphere in which the student can feel free to express their ideas, but I also encourage students to set themselves very high standards.

Teaching Experience:
I have tutored many students one-to-one, all aged from 10 (sitting their 11+ exams for grammar schools) all the way through to GCSEs. I found the process of tutoring rewarding and always try to tailor my tutoring sessions to the student's needs. I have advanced and centralised knowledge on maths up until this level and stay punctual and regular with the sessions.

Tutoring Approach:
My approach is to baseline the student's academic level based on which set they are in or previous exam attainment and plan the most efficient way to tutor them. Then I plan to plug any gaps in their knowledge through rigorously going over the content before working through exam questions. I would expect the student to provide the topic they would like to go over before the lesson so that I can prepare the lesson before hand.

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Personal Description:
I am an engineer from a top engineering college and worked at several leading organisations thereafter. My love for quantitative and analytical subjects brought me to London School of Economics (LSE) where I am pursuing a specialisation in Applied Development Economics.

Teaching Experience:
I have taught mathematics and economics to school students since past 3 years. I have also taught undergrad students during my engineering education.

Tutoring Approach:
I love mathematics. I can make someone understand the problem in simple and fun way by giving practical examples. I believe in building on basic skill set repeatedly to master the advance concepts. More you play with maths more you start learning it. My approach is to first build student's confidence in mathematics by inculcating a love for the subject. I am a strong believer in learning by doing.

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Personal Description:
I tutor in mathematics and science (Chemistry and Physics) GCSE (foundation and higher tiers) and to A-level.

I have undertaken chemical research at university and in industry and have also worked as an Environmental Chemist/Consultant advising and training on contaminated land risk assessment, remediation and verification.

I have bachelors and masters degrees in Chemistry from Birmingham University. I am a Chartered Scientist (CSci), a Chartered Chemist (CChem), a Fellow or the Royal Society of Chemistry (FRSC), a Specialist in Land Condition (SiLC) and a Suitably Qualified Person (SQP) under the UK planning National Quality Mark Scheme (NQMS).

I have an enhanced DBS certificate for inspection as required.

Teaching Experience:
I help younger people as a private tutor towards GCSE and A-levels in Chemistry, Physics and Mathematics (Pure and Mechanics) - either in person or on;ine.

I help students with attaining the grades they need to continue their studies into the 6th form or for entry into their chosen University to study subjects such as mechanical engineering, aerospace engineering, medicine, pharmacy, dentistry, chemistry, biomedical sciences, etc. Testimonials are available on request.

I have also mentored graduates on their path to becoming chartered with the Royal Society of Chemistry, the Chartered Institution of Water and Environmental Management (CIWEM) and SiLC.

Tutoring Approach:
I provide strategies to help students manage the stresses of exams. This includes time management in exams and methods to maximise marks in exams in such a way to give the student confidence during any given paper.

Primarily, I undertake one-to-one tuition either in person or online. I enjoy working to improve their understanding and learning - giving them confidence to tackle the various aspects of the subject matter with confidence and efficiency.

I focus on their weaker areas of any given subject whilst reinforcing the aspects where they are already comfortable.

If needed I can tutor groups of students when necessary. Please get in touch to make the necessary arrangements.

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Personal Description:
My name is Edwin. I am originally from the United States and have lived in Scotland since 2016.

I enjoy working with children and helping them reach their potential. As a university student, I first discovered my interest in teaching by volunteering in my mother's preschool. And since then, I have worked with children in varying capacities. Outside of teaching, I was a volunteer youth counsellor for five years and a volunteer youth basketball coach for four years.

Teaching Experience:
I am a newly qualified Primary Teacher in Scotland, currently working as a supply teacher. I have experience teaching at all levels of primary education in a variety of school settings.

As a doctoral candidate, I worked as a Graduate Teaching Assistant (GTA) at the University of Glasgow. In this capacity, I led seminars and helped students plan their essays, which I later marked.

I also used to work as a substitute teacher and after school coordinator in the United States, working primarily with early level students.

Tutoring Approach:
As a teacher and a tutor, I build positive relationships by being both professional and approachable.

Understanding their prior learning is important for creating challenging lessons which engage and motivate my students. Furthermore, I stay up-to-date with educational initiatives and learning strategies.

Pupil welfare must always be the first and foremost consideration, and I strive to teach to their needs and in the style which best benefits them.

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Personal Description:
I hold a B.Tech in Mechanical Engineering with QTS and PGCE from the University of Birmingham. My background in engineering has provided me with a strong foundation in Physics, Mathematics, and Chemistry, and I am passionate about sharing this knowledge with students. I am dedicated to helping students build confidence and achieve their academic goals through personalized support and structured learning.

Teaching Experience:
I have experience tutoring students in Physics, Mathematics, and Chemistry at both KS3 and GCSE and A Levels. My focus has been on creating a supportive and engaging environment where students feel comfortable asking questions and exploring challenging topics. While completing my teaching qualifications, I have gained practical classroom experience, developing and delivering lessons that cater to different learning styles and abilities.

Tutoring Approach:
My tutoring style is student-centered, focusing on understanding each individual's strengths and areas for improvement. I tailor my lessons to meet the specific needs of the student, using a combination of theoretical explanations, practical examples, and problem-solving exercises. I aim to make learning interactive and enjoyable, ensuring that complex concepts are broken down into manageable steps. My goal is to build the student's confidence and foster a deeper understanding of the subject matter.

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Personal Description:
I have always had a profound love of literature and language, and every career decision I have made has revolved around that. After several years teaching English at a boarding school near Oxford, I have returned to London to be closer to theatre and to pursue a few creative projects alongside much private tutoring.

Teaching Experience:
I taught English full-time 2015-23, most recently for seven years at Radley College, a top boarding school near Oxford. I was also Head of UCAS there, where I personally checked and sent about 800 UCAS applications, so I can advise on Personal Statement for all types of degree, not just English.

Tutoring Approach:
I balance rigour with a pastoral approach: I want students to be on top of the detail but I am always happy to zoom out to the bigger picture and explain the value of why we are doing this or that.

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Personal Description:
I believe that a good understanding of Maths and Physics is a key skill with benefits in so many aspects of life. Having seen first hand how studying STEM at higher level can lead to an exciting and rewarding career I'm keen to pass on my knowledge and my enthusiasm for the subject.

Teaching Experience:
Currently I work as an Aerospace Engineer in fast jet development, I have tutored informally for siblings and friends in the past at GCSE level. I was previously offered a job as a secondary Physics teacher although I did not end up accepting the position.

Tutoring Approach:
As with any subject, everyone learns in different ways- however I believe this is especially true of STEM subjects as often key scientific concepts can be tricky to understand at first. I always aim to be able to teach a concept/idea in a few different ways and use tools such as visualisation of problems with diagrams and animations to illustrate a point. Most importantly I believe in using real world examples, as without them it can sometimes be hard to understand why we are learning these things, and can make the problem feel more approachable/familiar.

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