Kilsyth Physics Tutors and Kilsyth Physics Tuition

Personal Description:
I am an Independent Educational Consultant specialising in Dyslexic Disorders. I have been a private tutor for many years and have tutored over 200 students. I have worked with many gifted children and those also who find education a challenge. I specialise in special needs especially dyslexia and Autism. After training as a teacher and the a medical doctor I find that my interest has remained in the education field and so am now to begin training as an Educational Psychologist with the Institute of Education, University of London.

Teaching Experience:
Over 20 years teaching experience with 18 years specialising in special needs. Over 10 years an an Independent Education Consultant specialising in Dyslexia. I am able to offer tuition to students with ADHD, ADD, and Autistic spectrum disorders. I also have a child with dyslexia and Autism so understand the domestic side to these conditions as well as the educational.

Tutoring Approach:
My general approach to teaching is to enhance individual skills by providing an individual programme for the student. This allows the student to learn independently instead of the learning associated within schools of one size fits all. Unfortunately, this does not work with many children who need a structured individualised approach. I also work within the "We find this subject a challenge, not an impossibility" field; that is to say everything is positive concerning the tuition, and everyone can learn, its just they have not been taught in a way that they personally understand. This is especially apparent with the dyslexic student.

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Personal Description:
I have a dual background in Electrical Engineering and Psychology and retired in 2007 after 20 years as a University lecturer. At different stages in my career I have taught telecommunications engineering, computer programming, software engineering, artificial intelligence and psychology. For relaxation I listen to jazz and blues.

Teaching Experience:
I have been tutoring students since March 2008 and am able to offer maths, physics and ICT from primary up to 'A' level, and general science (biology, chemistry, and physics) up to GCSE level. I have taught GCE A-level Maths, Further Maths and Physics with a number of students who have obtained places at Oxbridge/ Russell Group Universities to study Engineering, Maths, Medicine and Economics. A number of my tutees have been following courses in IGCSE Maths or Science or the IB in Maths or Physics. I have also taught students with Statements of Special Educational Need who have succeeded in obtaining qualifications in Functional Skills in Maths, English and Science. I am familiar with the 11+ exam requirements of Bromley, Bexley, and Kent education authorities and have assisted a number of pupils with their preparation for the exam. (In the absence of this category in the Subject list, my fee for 11+ preparation is 24/hour and for 13+ (Common Entrance) 26/hour.). At postgraduate level I can advise on research methods and statistics.

I am a chartered psychologist and can carry out educational and psychological assessments of both children and adults who are experiencing learning or language difficulties (however, I do not undertake remedial teaching).

Tutoring Approach:
PLEASE NOTE: FROM JANUARY 2019, I WILL NO LONGER BE OFFERING IN-PERSON LESSONS BUT CAN PROVIDE LESSONS VIA SKYPE OR (PREFERABLY) ZOOM ON EITHER WEEKDAYS OR WEEKENDS

I consider it important to assess the student's needs, strengths, and weaknesses carefully at the outset in order to develop a set of goals based on this assessment. I aim to provide well-structured and clearly presented instruction, which if the pupil is able and well-motivated will generally lead to progress. If the pupil is poorly motivated and/or has acquired unhelpful learning habits then we may need to vary the approach in order to re-engage their interest and/or find a level at which they can perform successfully, and then build on this accomplishment.

If required, I can provide references from past and present clients. I also offer a free first lesson so that the student has the opportunity to experience my style/approach before committing themselves to further lessons.

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Personal Description:
Here is a little bit about myself: I enjoy reading, watching television and playing cricket.

I am 55 years old and live in Redhill, Surrey. I am able to tutor the following subjects:

A' Level Mathematics, GCSE Mathematics, KS3 Mathematics, KS2 Mathematics, A`Level Economics and GCSE Physics.


I am available any day of the week, daytime as well evenings.

Before the first lesson is scheduled, I will pay to you in full for the cost of purchasing my contact details. As for the first lesson, if for whatever reason your child is unhappy with my tutoring style within the first 20 minutes, we will stop the lesson straight away and I will not ask any payment for it. This way you will not pay a penny for anything you are uncertain about.

Here is a testimonial from a parent of a child that I tutor:

A great tutor and always strives on making sure the student understands the topics. He teaches my son GCSE Maths and my son has improved since working with him.

He is very approachable and communicates well both with my son and with myself. I`m glad I found this website.

Teaching Experience:
I have more than twenty years of teaching experience, which includes one-to-one tutoring as well as school, college and university teaching.

Tutoring Approach:
I feel very passionately about learning. Mathematics in particular is a challenging subject, but with hard work, patience and a willingness to learn from my mistakes, I have found it very rewarding. It is this same lesson I have learned which I would like to continue to convey to students.

A great emphasis is placed on helping students truly understand the subject material, rather than tutoring them to simply pass exams. My aim is to impart transferable skills beyond the field of studying, whether it be in the work place or students` personal lives. Encouragement is given to students to ask any questions that are concerning them.

Rather than spoon-feed them information, I interact with them by asking them to justify answers to follow-up questions I ask, and hence lead them to the solution as a result of their efforts.

My teaching style is such that I am able to empathise with students with respect to any learning and developmental issues which they may need support with. To achieve this goal, special consideration is given to identifying particular learning weaknesses and providing multiple approaches to learning which best suit the need of the student. This in turn makes the primary learning objective of understanding and advancement achievable as well as an enjoyable and productive experience.

Students are encouraged to chart their progress with my guidance by recording their assessment of specific topics throughout the year. This in turn would give them confidence leading up to their exams.

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Personal Description:
I am currently working in a Pharmaceutical company as research scientist. Teaching is my hobby and the knowledge I gained so far from my education and experience, I am sure I can teach students from the basic level to pro and make them ready to pursue their future goals.

I have two master degrees from the UK, one in Drug design and discovery from Salford University, and the other in Pharmaceutical analysis from Kingston University. I am also a graduate pharmacist from India.

I have more than nine years of rich experience in Pharmaceutical Industries working in Analytical department, which has helped me a lot developing and applying my science and maths knowledge in real life.

The level of my work is much higher than what I offer to teach and this is the advantageous for students because I can explain them everything in-depth with real world examples.

I also offer a trial class where I can focus on any subject area and you can see how I teach students.

Please get in touch for any queries. Thanks.

Teaching Experience:
I have taught maths, chemistry and physics at higher secondary levels.

Tutoring Approach:
1. Firstly I like student to feel comfortable while learning any topic. I make them more communicative and encourage asking question at any point if he/she is not able to grasp things.
2. I would like to know the level of understanding of the student which will help me deciding where and how to start teaching.
3. I always focus on scope of learning any topic or subject so that students can have a clear idea about why they need to learn that particular subject and how it is going to help them in future. I believe the subjects are not there just to learn and give exams, but for how they can be useful in their personal and professional life.

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Personal Description:
Maths for English, Russian and Polish speakers
English for Polish and Russian speakers
Polish for English and Russian speakers

I am a qualified teacher (formerly KS5 Co-ordinator & IB Subject and GCSE Curriculum Lead for Maths) and a private tutor with more than 15 years of experience teaching maths at all levels from Secondary through to GCSE and A-levels or equivalents. The great majority of my students have achieved or exceeded their goals and passed their examinations. I speak all three languages (English, Polish, and Russian) fluently and am a qualified translator, so I can teach in any of them for your convenience.

I am a Polish native speaker who has lived in the UK for many years. I offer Polish language lessons for English and Russian speakers as well as English lessons for Polish and Russian speakers. I offer typical tuition focused on learning from the basics as well as conversation-oriented classes for more advanced students.

I will be happy to help you as well. Prices vary from £30 to £40 per hour depending on the level required, location, and the number of hours. Additional information is available upon request.

Teaching Experience:
approx. 15 years

Tutoring Approach:
Based on individual assessment of each person's circumstances.

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Personal Description:
My Profile:

Graduated from Leeds University in Genetics and have a deep passion for science. After leaving University, I have worked in the Computing and IT industry to Project Manager level, mainly for large blue chip financial companies such as General Accident (now Aviva), Standard Life, Bank of Scotland, GE Corporate and others. In 2004 I decided to return to my original love of science and gained a PGCE teaching qualification to teach science.

It is my aim to transfer my passion and love for science to my students as well as an understanding of the subject in order to enable them to AIM HIGHER and ace their exams.

Building on my science qualification, I gained a PGCE teaching qualification from Huddersfield University to become a qualified teacher of science in 2005. Following the successful completion of the PGCE, I rapidly achieved the position of Programme Manager and gained extensive experience of teaching Biology, Chemistry, Physics, BTEC Applied Sciences (Medical Science, Forensic Science, Health and Social Care), Access to Nursing, Access for Medical Professionals and Foundation Degree (Biology). The teaching experience has been in schools, Sixth Form Colleges and Further Education Colleges in Warrington, Leeds and Manchester.

Teaching Experience:
Building on my science qualification, I gained a PGCE teaching qualification from Huddersfield University to become a qualified teacher of science in 2005. Following the successful completion of the PGCE, I rapidly achieved the position of Programme Manager and gained extensive experience of teaching Biology, Chemistry, Physics, BTEC Applied Sciences (Medical Science, Forensic Science, Health and Social Care), Access to Nursing, Access for Medical Professionals and Foundation Degree (Biology). The teaching experience has been in schools, Sixth Form Colleges and Further Education Colleges in Warrington, Leeds and Manchester.

I have been providing select 1 to 1 private tuition in all areas including English, Biology, Chemistry, Maths, Media Studies and Physics.

I am able to tutor from primary, secondary (including entrance exams) through GCSE, A Levels, BTEC (Level 2 and Level 3) and Adult Foundation Degree level.

Tutoring Approach:
The tutor is the expert in subject knowledge and learning but it is the tutee who has the paramount role in their own education and excelling in their subjects. I firmly believe that the role of a tutor is that of a catalyst and the child's role in their own learning is of greater importance. I aim to guide the tutee to learn in a structured manner that so that the child does not waste their time jumping from topic to topic, randomly browsing a bit here and a bit there, as often happens. To do that, as tutor, I will facilitate their learning on a 1 to 1 basis so that they may gain a deeper and greater depth of knowledge of the subject. I will provide the subject knowledge expertise and transfer my knowledge to the tutee in a manner and at a level that is appropriate to the tutee but pushing them beyond their limits to the next stage. To achieve that grade "A*" a GCSE tutee should be able to understand basic AS Level material. For an A Level tutee to achieve the highest grades at A Level they should be able to cope with University first year material with ease. It is my aim to enable my tutees to achieve these goals.

I will work to improve the child's self esteem, self belief and confidence in their ability to do well. As a trained hypnotherapist I am particularly qualified to boost a child's self-esteem. Once the tutee is confident in their subject knowledge, then we will work on exam techniques and exam practice in order to enable the tutee to ace the exams and significantly improve their grades.

I will work with each tutee on an individual basis and adjust the tuition lessons to their needs. There is no standard one size fits all model with me. Homework will be set to enable the subject matter to be reinforced with some self-learning at home. Exam practice will be key to enable the tutee to become proficient in their exams and achieve the highest grades. Exam technique contributes significantly towards exam success. We will always work to enable the tutee to AIM HIGHER.

I am also able to guide sixth formers with their UCAS applications and personal statements.

At all times parents will be involved with the learning of their child so that they may guide and support their child's education and monitor progress. Parental involvement is also a major factor in the child's success.

For the science lessons my aim is to include as much practical work as is possible, where this is feasible in a tuition setting, keeping safety of the child of paramount importance.

If your child is quiet and shy or is in a mediocre class or is just coasting along or is struggling to achieve the grades required to get into the University course of their choice, whether it is Medicine, Dentistry, Pharmacology, Engineering, Computing, Optometry or other science course, then tuition with myself will enable them to boost their grades and give them the advantage that they need. Honest school teachers will tell you that it is the noisy and disruptive pupils that get their attention, whereas the quite shy hardworking pupils tend to get neglected. Busy school teachers just do not have the time or energy to devote to helping their quieter or weaker pupils and it is these pupils that especially benefit from extra personal tuition. On the other hand a brighter pupil may be so far ahead of his or her peers that the teacher is just not able to give them the attention they need. A good tutor will help guide tutees who want to learn to get ahead and avoid becoming disinterested or bored. Why leave it to chance?

It is never too early to start boosting a child's education. For primary school children it is important that they get a good start to their education and do not lag behind. A tuition boost will enable them to get into a better school or a higher stream set so that they do not have to struggle or get left behind when the come to do their GCSE and A Levels.

I also have experience of vocational courses such as the BTEC and Applied Science courses and I am able to provide the additional guidance and support required to ensure that your child achieves Distinctions rather than passes in their assignments. It is not my policy to do the tutee's coursework for them but to help, guide and support their research and provide constructive feedback.

Tutees will be required to complete all assessments and homework on time in advance of the relevant lesson.

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Personal Description:
I have retired from school/ college teaching, I am a Physics graduate, qualified science teacher, with 21 years teaching experience. I am able to teach all 3 sciences and maths at GCSE level, and Physics to A Level. I have tutored for many years and have some experience with high level autistic students and considerable experience with dyslexic and dyspraxic and other students that require an extra bit of help.

Please note GCSE rates are £36ph
A level rates remain at £36ph.

Please note that when I can come to you there will be a travel charge of £2 per mile travelled.

Teaching Experience:
2019-2021 Theale Green p/t
2013 -2021 All Hallows 6th Form & School p/t
2011-2013 Farnborough 6th Form College
2005-2011 Bearwood College
2004-2005 Reading Blue Coats School
2002-2004 Shiplake College

Tutoring Approach:
Every student is different and so my approach is to assess the problems/difficulties and with heaps of encouragement build confidence through increasing success. I am very adept at inventing mini practicals in order to develop interest and enthusiasm.

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Personal Description:
I am a qualified and professional tutor, who is passionate about science and research and hope to transfer my knowledge and passion to my students. I provide resource materials and practice books matching to the curriculum and student level to gradually upgrade the performance of the learner.

I have a two postgraduate qualifications in Orthopaedic Engineering and in Materials Enginnering. I have a degree in Biomedical Materials Science. I am a keen researcher in this field. One of my research paper has been the europes best editors pick in a reputable journal (Journal of Non-Crystalline Solids).

My lessons are well planned and tailored to individual student requirements. I develop students` full potential by agreeing on appropriate targets with students and the parents. The progress of the students is monitored through tests and subject understanding to achieve better results. I use a regular record sheet to inform about progress and results of the students to the parents.

Teaching Experience:
I have worked as a science teacher and a department Supervisor at a London tuition center. I have taught GCSE Science , Maths and A Level Chemistry to number of students as a home tutor in the past seven years. Most of them have achieved excellent results.

Tutoring Approach:
Lessons are well planned and they are tailored to individual students' requirement.

I provide tests resource materials and practice books matching to the curriculum and student level to gradually upgrade the performance of the learner.

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Personal Description:
I am a Chemistry Teacher in a Secondary School where I teach Chemistry from year 7 to year 11. I can help students to practice exam skills and revision techniques.

I am also an Italian native speaker, so I can teach Italian at any level. I am also able to help with French from Primary to KS4.

I like helping others, so I enjoy helping students to achieve good grades.

Teaching Experience:
I am a Science Teacher in a Secondary School.

I have a PGCE in Secondary Science - Chemistry, and a PhD in Chemical Engineering.

Regarding teaching languages, I am an Italian native speaker and I am also fluent in French.

Tutoring Approach:
I like to be systematic without being too severe. I like to establish a good relationship with the students, based on a reciprocal respect.

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Personal Description:
Hello my name is Dorian and I am applying for uk-tutor to be a pesonnal tutor. I teach mathematics(up to gcse Level), physics(up to gcse level) and french(up to A-Level).My method of teaching is based on the exercise. Indeed I ask the pupil to show me the lesson that he did with his teacher at school and then I put hi; in front of an exercise and after he has finished I correct him and tell him the mistake he needs to avoid in s tests day.

Teaching Experience:
I used to teach in a youth center when I was in France

Tutoring Approach:
Tutoring is a good experience with people. This job allow to have an acknowledge in speaking to others. It allows us to share experience about our educations with pupils and ect..

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Personal Description:
Hi! I am a PhD student at the University of East Anglia in Environmental Sciences.
Previous to this, I was a research assistant working in climate change fields at the University of Cambridge and completed a masters degree in Animal Science

In my spare time, I enjoy cooking, sports and playing the piano.

Teaching Experience:
5 previous tutees.
Cambridge University Undergraduate Supervisor for over 15 final year undergraduates.
Demonstrator (Large group teaching) for Undergraduate to Masters Level at the University of East Anglia

Tutoring Approach:
I am happy to adapt tutoring to suit you! I want to help students not just be able to learn the subject but also understand and appreciate it. I understand that not everyone has the same learning style so am keen for trying out lots of techniques.

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Personal Description:
I am an outstanding science teacher/tutor with 17 years of classroom and online teaching experience. I am a qualified teacher, AQA examiner and a Specialist Leader of Education training science teachers. I love all things science with a particular love for chemistry.
During lessons I specialise in building confidence alongside exam technique and developing subject knowledge. My lessons are fun, engaging and relevant to everyday life as well as being tailored to achieving and succeeding in exams. Independent work and homework will be set to assess prior knowledge and next steps.

Teaching Experience:
Over the past 17 years I have taught and tutored science to school-based and home educated students in KS2, KS3, at GCSE and A` Level. At GCSE I have experience teaching AQA, OCR, Edexcel and BTEC science courses and at A` Level AQA, OCR and Salters chemistry specifications. I am an AQA GCSE examiner.
I also currently train science teachers and deliver courses to support improvement in science teaching across Yorkshire.

Tutoring Approach:
I specialise in building confidence alongside developing subject knowledge. My lessons are fun, engaging and relevant to everyday life as well as being tailored to achieving and succeeding in exams. Independent work and homework will be set to assess prior knowledge and next steps.

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Personal Description:
I am a PhD student at the University of Manchester researching materials for applications to nuclear fusion. I am deeply passionate about my subject, although I understand that it's not everyone's cup of tea! I try my hardest to help my students increase their confidence, enjoyment of the subject and, of course, their grades.

Teaching Experience:
I have been an online tutor since October 2019 and have seen some of my students make 3 grades progress in 3 months. I have worked with a variety of exam boards including international qualifications.

Tutoring Approach:
I try to keep my sessions relatively relaxed as I strongly believe that the best way to learn is when you feel most comfortable. As a fellow student, I can relate to my students and offer them some advice about their studies outside of the classroom. I leave the content of my sessions up to the student to decide, but a typical session would feature a discussion of the content followed by applying the relevant skills through exam practice.

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Personal Description:
Having gotten straight A stars at GCSE and A-levels I definitely know the best way to revise and study to achieve the best grades. I am a medical student in the UK and I currently am part of 3 tutoring companies which are all reputable companies which allow me to gain sufficient experience. I am a caring, compassionate and knowledgeable tutor to all my students and have been tutoring for the last couple of years, I feel teetering is a way for myself to connect with students at a level to help them reach their academic goals. I am a fun person and a self disciplined tutor that can also teach your child to fall in love with academics and push them to their limits in their academic work.

Teaching Experience:
I have ample amounts of teaching experience starting from teaching at my local tuition centre when I was in year 12, I then decided in university to start teaching online and have been teaching for about almost a year at a number of different tutoring agencies and teacher in companies I teach a load of different subjects from stem subjects such as Biology, chemistry, physics, English and maths. In these tutoring agencies I teach a range of kids from age 13 to 18 from academic subjects to entrance exam preparation for medical school in the entrance exams and the interviews.

Tutoring Approach:
My approach to teetering is a very a structured but relaxed way to ensure the child is comfortable enough with the teaching and a lesson. I first try to examine the student and get a sense of what their strengths and weaknesses are in a particular subject or ask them what they are struggling with in school. Then I tried to get as many resources and lessons to be able to teach them in a way and explain in a way that they can understand using diagrams pictures and any other resources. Finally I think this is the most crucial part of learning is practice questions whether it be the entrance exams or subjects I will give them past paper questions for them to work on.

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Personal Description:
Hi, I'm Harry, a dedicated and experienced tutor with a passion for helping students unlock their full academic potential. I specialize in Maths and Science at the GCSE level and have a proven track record of supporting students to build confidence, improve their understanding, and achieve their target grades. Whether you're looking for help with exam preparation or ongoing support with schoolwork, I'm here to provide clear explanations, tailored lessons, and encouragement every step of the way.

Teaching Experience:
I began tutoring during my A-Levels, assisting GCSE students with their understanding of Chemistry. Helping students develop towards a deeper understanding of the subject is what inspired me to start tutoring more. I continued tutoring during my time at university, whilst also participating in a mentor programme where I would assist younger students with coursework, practical and theory questions.

My teaching approach centres on tailoring material to each individual student, as there is no 'one-size-fits-all' approach to learning. Each student has their own strengths and weaknesses, which mY lessons would be built around. From there, I can prioritise tackling problems that they might be having with certain skills and aim to further improve their strengths, whilst maintaining an appropriate level of challenge across skills.

Before the lessons, I like to establish with each student what goals they want to reach. It's a useful icebreaker, but also allows me to determine what they want to get out of the teaching, whether this is boosting their confidence or excelling at exams. This way we can identify what the focus point is, and plan the lessons around that.

Tutoring Approach:
Making sure the lessons are interactive is another of my top priorities, as I believe that mixing the content up to keep the student engaged helps them to learn a lot faster. Once a student is confident with the subject, I get them started on past papers, as applying the knowledge in this way is better reflective of actual exam conditions.

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Personal Description:
Hi!
I'm Necdet and am a student of Boğaziçi University's teaching physics program. I have successfully completed the first year without failing any of my lesson and getting a GPA of 2.42. I am a Turkish Cypriot and I am quite familiar to the GCSE and A-level curriculum. Apart from my academic background I'd like to address couple more stuff I have in my life. First off I have to state that I love learning and teaching new stuff, and also I believe teaching is the older brother of learning; as you can not say that you have learned something deeply if you are unable to teach it to someone that does not know it; like I play chess and have been the 6th table player of my municipality's chess team. Even though I have attended many many games with that team I was not aware of the fact that thinking simple would actually be a benefit in any game, and I realized this when last year I have aided an association's chess team in stars category as an educator. When working with youngsters that are looking at the game much simpler than you do, you have to match their energy and try to predict what obstacles may get in their way, and I believe this working experience improved me quite a bit in that matter. There are couple more sports that I am into and have been a part of, I have listed them in my CV and I do not want to make this message too long and boring so I am stopping here:))

Thank you for your time and I am looking forward to hearing from you!!!

Necdet

Teaching Experience:
I am actively working in a private tutoring association for more than 2 years and also I have given many private lessons from grade 4 all the way up to adults.

Tutoring Approach:
Tutoring is not only a job for me, but also a way to stay active in life and become more energetic. Being with and tutoring youngsters boost my confidence in our future!!

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Personal Description:
Current Secondary Science Teacher specialising in Physics and Biology, Master of Education from Cambridge University alongside PGCE and 14 year's experience both in the UK and abroad in both private and UK state schools.

I have held a variety of positions from Classroom Teacher up to Head of Department but with a young family I have stepped back from management for the time being. I teach at a local state school in North Tyneside.

Teaching Experience:
14 years teaching both in the UK along with 4 years teaching abroad. I am qualified to teach all sciences to GCSE and Physics and Biology to A-Level. I have worked with classes from 32 down to 1-2-1 tuition with significant value added to pupils from all levels of ability.

Tutoring Approach:
As different pupils learn in different ways I am happy to tailor my teaching style to fit the needs of the student. I work to ensure that there is understanding of the topic alongside just knowing the facts. I am up to date on current paedagogical research which I use to ensure that I am able to give the best to my students.

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Personal Description:
I have always been incredibly passionate about learning as much as possible and I want to instil this in others.
I have high scores on my GCSEs and AS Mathematics and I am currently studying Mathematics at University.
I am a very friendly, outgoing person who enjoys teaching thoroughly.

I genuinely love what I do.

Teaching Experience:
I have been teaching since my sister was learning to talk but I first started as a private tutor at age 14. I was lucky enough to teach a class of 30 girls just after I did my GCSEs at age 17, and from there I went on to start my own business.

I worked for myself as a private maths tutor for 3 years before working at London School or Science and Technology and I am now back to private tutoring.

Tutoring Approach:
My teaching style changes depending on every student I face. I would identify as having the facilitator style which is someone who encourages self-learning by asking the student questions rather than telling them the answer.

I also specialise in last minute GCSE revision where I am able to make the subject matter seem much simpler than how it is explained in many schools.

I have done a huge amount of work with ADHD and dyslexic students so I have had to deal with about every behavioural issue there is with the utmost patience and I experience a lot of joy in learning how the students get to the answer.

I have created many lesson plans myself for ages 4-16, which include animated PowerPoints, mainly in maths but I am happy to create them for any subject.

I always begin with a game or a riddle just to get thinking cap on and then we will tackle a subject with an explanation and worked examples.

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