Linlithgow Maths Tutors and Linlithgow Maths Tuition

Personal Description:
I am committed to providing the best possible service for all my students . I can guarantee helping clients achieve success at whatever level.

Teaching Experience:
35 years in secondary schools. I teach maths and all science subjects up to GCSE level and KS3 . I also work for two examination boards as an examiner marking and setting examination questions.

Tutoring Approach:
I have a flexible approach tailored to the needs of the student. Having taught children of all abilities and different ages I can fulfil the requirements of any student from the most able to any with special needs.

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Personal Description:
I am an independent tutor with a strong scientific background and have lived in England since Aug 1965. Most of my school and college education took place in Dudley (West Midlands) and I studied Biochemistry, at Leeds University (1975-8). I am married and have lived in Cheshire since Dec 1978. We have a son and a daughter; both graduated from Universities in Manchester. Following my voluntary redundancy from AstraZeneca, (Jun 2008), I am now a self-employed Tutor / Consultant. In addition, I am able to speak additional languages (Punjabi; studied up to GCE A-level and Hindi) and prepared to travel up to 5 miles. I have been tutoring Yr 7 - 13 students, in Maths and all Science subjects, since Oct 2008. In addition, I have prepared students from Yr 6, for the 11+ exams; frequently used by private schools, as entrance exams. Testimonials / References (from Students and Parents) are available, on request.

Teaching Experience:
During my long service in the Pharma industry (~30 years), I have run many short courses and workshops. During 2005/6, I mentored a pupil (Year 10/11) at St. Peter's High School, Longsight, organised by the University of Manchester. In the past, I have also been responsible for organising and running the weekly classes at the Sikh Temple (Gurdwara), for teaching youngsters the Sikh way of life & Punjabi culture, in helping to improve their knowledge and integration into the Western Society over a period of ten years.

Tutoring Approach:
I can provide tuition to individual students (or small groups) in the form of friendly, relaxed lessons. Teaching sessions are always customised to meet the specific requirement of the students. Generally, I enjoy teaching and considered to have a caring approach. I use a combination of computer and 'white board' based approach, for creating informal interactive / discussion type sessions, with some form of regular tests and re-cap sessions. Closer to the exams, the lessons are much more focused on using past papers covering a wide range of questions, to enable the students increase their confidence in preparation for the examinations.

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Personal Description:
I am a retired professor looking to contribute to the success of young children. I have achieved everything in my life in terms of status and professional achievements. I have a strong passion for Maths and would like to make the learning of Maths a great success and a pleasurable experience for young children.

Teaching Experience:
I have 45 years of full-time teaching experience of Maths and physics in schools, colleges and universities. However for the past 13 years, I have been preparing students exclusively for the linear and modular GCSE Maths for the Edexcel, AQA and O&C examination boards with resounding success. I have the pleasure of tutoring those children who are borderline cases struggling to achieve grade 5 (old grade C) in the GCSE Maths. I have also the pleasure of tutoring high achievers doing higher GCSE Maths looking for top grades 8-9 (old grade A*) for easy admission to top universities in the UK.

Tutoring Approach:
1. My prime objective is to make Maths interesting, easy and simple to understand by all my tutees in a relaxed learning environment.

2. I make use of simple practical techniques to illustrate mathematical concepts which may otherwise be difficult to comprehend.

3. I try my best to motivate and inspire my tutees to do good quality Maths at the GCSE standard which unfailingly translates into improved exam grades.

4. I apply common sense strategies which enhance the learning process and help children achieve their full potential. Needless to say, tutoring of Maths is my absolute passion and I will continue to make a lasting impact on the way Maths is taught and perceived by young children in schools and colleges.

5. I have multiple modern approaches to solve the same mathematical problem in many different ways using conventional and non- conventional methods of learning and my pupil are at liberty to chose the one that they appreciate the most.. If you are looking for a targeted- performance Super Maths Tutor for the GCSE, search no further.

6. Any assignment will be accepted on the PAY AS YOU GO direct debit basis.

7. I charge £120 for a single 2-hours session and £70 for a single 1-hour session.

8. For a pupil doing Foundation Maths, I recommend one 2-hour sessions per week per Term to get grade 5 ( old grade C) and for a high performing pupil doing Higher Maths, I recommend one 2-hour sessions per week per Term to ensure a grade 8-9 ( old grade A*).

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Personal Description:
Worried you or your kid might be lacking at studies????? No worries!!!! I am here to help.
Maths has always been my favorite subject (scored 100 % in 2/4 modules in a level) so I am ready to help in Maths and all the Sciences.
Fully DBS (updated version of CRB) checked as I am a community first responder volunteer ambulance services and I am also a 5th year MEDICAL STUDENT.

Teaching Experience:
I have been a private tutor for many years now (since 2006) and have a record of 93% of my tutees so far having obtained grade A or above in the respective subjects with none of my tutees so far ever obtaining lower than B.
It all started when I was a prefect at my school and college where I used to help students of different levels (including my friends from my own year) in learning difficult topics (in maths and science) and in preparing for exams. I have also helped a few teachers several times during an actual school lesson as teacher's assistant. But most importantly, in these many years as a private tutor, I have helped a lot of pupils only do well in their GCSEs and A-level. So far they have all achieved much higher standard than they were predicted by their teachers and this success of all these past tutees of mine makes me work even harder with all the new ones every year.

Just to assure you that I am not shy of putting in hard work I would like to bring to your attention that I did all my GCSEs in a single year instead of 2 and also ended up doing 2 of the subjects early. Even though maths was one of the early subjects, I still got A* and went on to do AS maths in the same year in which I also got A. So, maybe I can help with not only Maths and sciences but also with the management of time and workloads along with building their confidence and bringing out their desire to learn.

Tutoring Approach:
Will depend on the needs of the tutee as everyone is different but one thing that remains the same for all is the commitment and the level of sincerity from me.

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Personal Description:
I am a native Chinese speaker from mainland China, and I have been living in the UK for more than 10 years, working as a Modern Foreign Languages (MFL) and Chinese teacher at a private school. I earned a PhD in Educational Studies from the University of Manchester in 2015. I have excellent teaching experience in Chinese at all levels, as well as in Maths (from KS1 up to GCSE). I have received positive feedback from my previous students, who have praised my patience, clear communication, and sense of responsibility. Additionally, I have worked as a Teaching Assistant (TA) in a secondary school, where I gained valuable experience supporting young people's learning.

In terms of personality, I am very easygoing, kind, and highly responsible. Since moving to the UK in 2010, I have lived in diverse environments, working with students from various creeds and ethnic backgrounds. This experience has enriched my understanding and appreciation of international cultures and individual differences.

I enjoy travelling and experiencing new things. I have visited several places, including European countries (England, Scotland, Wales, the Netherlands, Switzerland, France, Italy, Spain, Iceland, and Greenland), Africa (Cameroon), South Korea, Hong Kong, and Macau. I love sports, particularly swimming, yoga, cycling, hiking, and horse riding.

Teaching Experience:
I am an experienced and dedicated Modern Foreign Languages (MFL) and Chinese teacher, currently teaching students aged 3-18, including GCSE, GCE/A Level,HSK and YCT(Youth Chinese Test) Chinese, at an independent school in the UK. With about 15 years of experience teaching Mandarin both online and face-to-face to non-native English speakers of various ages and levels in both China and the UK, I have developed a deep understanding of effective teaching methods and the ability to meet individual student needs.

As a private Mandarin tutor, I bring the same level of commitment and personalized attention to each of my students. My extensive experience has equipped me with valuable insights into creating engaging and effective lessons tailored to each student's learning style and goals.

In addition to my current teaching role, I have been a freelance Mandarin teacher since 2012, collaborating with several language organizations. I am also an experienced interpreter and translator, with over ten years of expertise in both written and spoken translation. My background includes working in various sectors, such as business (e.g., 2010 EXPO Shanghai) and education (e.g., translating articles and interpreting at international conferences).

Testimonials:
"I decided to begin learning Mandarin with Yifen over the summer for business and travel purposes.
Given that I was a complete beginner, I was heartened by the friendliness and professional nature of the lessons and was delighted by the flexibility of the lessons.
The way Yifen catered the lessons to my specific areas of interest was very encouraging. It meant I was able to cover a lot more relevant content in the short time I had with her.
Had I not had to move back to University, I would've liked to continue my lessons." Matthew, a former Student

''I had the pleasure of taking my first steps in Mandarin with Yifen. I found her very knowledgeable, understanding, adaptable and extremely flexible to my needs. Only when I travelled to China, I could really appreciate how valuable her teachings were. Before Yifen, I could not understand anything at all. After only a few lessons with Yifen, my ability to understand had greatly improved and I could even venture into dialogues with Chinese people and, lo and behold, be understood!

Yifen's approach is systematic and practical at the same time. She frequently tested my comprehension ability, and engaged me in dialogues, but also illustrated the building blocks of the language, touching on grammar rules and special usage, as needed.
She was always keen on answering any additional questions that might have crossed my mind. She was motivating and an inspiration and greatly boosted my desire to learn more about the Chinese language and culture.
Yifen is a joy to work with and I would heartily recommend her to anyone who wants to approach the study of the Chinese language with a solid, competent and inspirational teacher.

老师，谢谢'' -Fernando, A former adult learner

"Yifen has been my teacher for the past four years throughout my GCSEs and A-levels! She helped me achieve an A* at GCSE and helped me achieve my required grade to get into university! With a lesson every week I was undoubtedly able to rely on Yifen for the support I needed for my work and to achieve the result that I not only wanted, but needed. She would always write lesson reviews and summaries for me to look upon to further improve my learning of Mandarin, and even set me work to challenge me and to push my ability further. I'm so grateful for all the time Yifen gave up for me and definitely wouldn't have been able to adapt and progress my Chinese without her help! Yifen is so helpful, reliable and able to focus on anything you ask her to help you with and I would highly recommend her to anyone who would want to learn or better their Mandarin!"-Bethan, a former GCSE and A-level learner.

Tutoring Approach:
I make every effort to prepare lessons that meet each student's individual needs. I strive to create a comfortable learning environment because I believe a good atmosphere is crucial for learning a language and encouraging learners to speak. Lessons are carefully prepared, incorporating engaging stories and other materials, so you can learn Mandarin and have fun at the same time!

I believe that a good teacher is responsible for meeting students' needs. My work experience has reinforced my belief that it is essential to teach the students in front of you rather than just following a textbook. I endeavour to be an attentive listener, observe, and identify any problems that arise during lessons. This approach helps me find solutions and maximise my potential.

I am passionate about helping my students succeed and am committed to providing high-quality, individualised instruction. If you are looking for a skilled and reliable private Mandarin tutor who can help you achieve your language goals, I would be delighted to work with you.

There are some textbooks I have been using for the learners, such as:
Confidence Chinese Vol. Getting Started
Confidence Chinese Vol2. Living in China
Chinese Made Easy Book1, 2 and 3.
Standard Course HSK
Edexcel Chinese for AS
Edexcel Chinese for A2
Chinese Made Easy for Kids.

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Personal Description:
I am a higher level TA with ten years of teaching experience. I am 98 years old and I am currently working with young people up to the age of 18 with RMBC and I also work with young people with disabilities.

Teaching Experience:
I have worked in primary education for ten years. I have worked as a one to one with children with Special Educational Needs and developed my skills training to be a Higher level Teaching Assistant.
Throughout my time in Primary education, I have worked effectively with teams in Key Stage one and two. Due to my extensive experience and educational background I often cover for teachers. I am able to confidently teach from a given plan, adapting the teaching where required and utilising support staff effectively. I have a solid understanding of the essential skills and learning outcomes and have used this knowledge to support children where necessary.

Tutoring Approach:
I believe in a personalised learning approach. The activities I use are dependent on the child and the way they learn. I understand that children can learn visually, kineasthetically or can be auditory learners. Therefore I adapt my teaching and my activities to suit the learner.

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Personal Description:
I have been teaching secondary school science since 2002. I have a wide experience across the age and ability range and prepare all lessons with learning style and individual differentiation in mind. I have been a private tutor since 2006 and worked with ages 7-16 across a wide range of subjects to equally great success. I prefer to tutor in the tutee's home as this is where they are most comfortable and therefore in a mindset ready to learn. I also work and mark GCSE exams and moderate controlled assessment.

I have been a highly successful 11+ expert tutor for 16years with a wealth of experience with a variety of exam boards, grammar and independent schools exam settings.

Teaching Experience:
Secondary Science and Maths teacher 2002-present day
Private tutor with various clients 2006 - present day
GCSE Sciences controlled assessment moderator for 2009-present day
GCSE Sciences examiner 2006-present day
Highly qualified and experienced Head of Faculty

Tutoring Approach:
I like to make activities fun and active to engage the student and also include an aspect of repetition to check learning and embed learning into long term memory to help prepare for future exams.

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Personal Description:
I am 28, currently working as a personal tutor.
My degrees in engineering have given me good problem solving skills and a good mathematical background. I enjoy tutoring, I have been teaching on one to one and group basis for a long time.

Teaching Experience:
Experienced in assisting students in improvement in maths, Physics, and also in civil and structure engineering.
I have had 21 student so far.
I have been teaching students from A-levels to university and with different backgrounds. I enjoy teaching and I am extremely patient.

Tutoring Approach:
A comprehensive approach to study ensures students are motivated and organised to benefit from all learning opportunities.

A range of materials is employed to stimulate interest and facilitate input.

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Personal Description:
Prior to becoming a maths teacher I trained as as a Chartered Accountant and worked in Business and Finance. After having my family I moved into education and qualified as a secondary maths teacher and have taught KS3 and KS4 maths in a high achieving, outstanding ofsted rated, 11- 18 local school for 9 years as well a providing one to one tuition both at school and privately.

Teaching Experience:
Secondary Maths teacher, KS3 and KS4 since 2009,
Sixth Form tutor in Business and accounting
Private Maths tutor, KS2,KS3 and KS4 for 10 years

Tutoring Approach:
I love maths and believe everyone is capable of succeeding and also learning to love maths if they are given the confidence to do so. Many students struggle because they may have been put off maths at a early age or missed out on some essential building blocks which have limited their progress.
I believe in going to back to basics and establishing a thorough understanding of crucial concepts, using different teaching styles to suit the individual needs of the student. I enjoy getting to know my students and being able to tailor my teaching to their personalities and needs.
My mission is to make maths fun and accessible to all.

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Personal Description:
Hi! My name is Brandon and I'm a Chartered Structural Engineer working in London part time and from home part time, in Hartford. I have been working professionally for 10 years now and have been involved in the design of some of London's most iconic skyscrapers. My job enables me to carry out mathematical problem solving on a daily basis, meaning I can easily transfer these skills into a tutoring environment and find pleasure in doing so.

I graduated from the University of Manchester in 2014 with a first class (hons) Masters degree in Civil and Structural Engineering.

Teaching Experience:
I have experience in tutoring GCSE & A-Level Maths and Physics in London, as well as assisting several students through their university applications. I have had great success in improving my tutees grades and helping them prepare more effectively for their exams and university applications.

I have also assisted the learning of many younger engineers in my day job, through weekly mentoring and coaching.

Tutoring Approach:
I like to start by spending some time to understand any problems or questions that the student might have, that may have recently arisen at school.

With subjects like Maths and Physics, an important way for students to understand problems is to visualise them before they can be solved. I usually employ analogies to help my students understand concepts and then test their understanding using exam type questions.

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Personal Description:
I'm an environmental scientist by training and I spent 16 years in the environmental chemistry sector before deciding that I wanted to teach.
I live in Little Sutton with my partner (also a teacher) and I have three children: Eleanor (19), Sarah (16) and Francis (13).
I have wide interests that include being out in the countryside a lot, cooking, fishkeeping and reading.

Teaching Experience:
During my time in industry I was heavily involved in the training and development of staff and this led neatly to my teaching career. I trained at the outstanding University Of Chester and worked across Wirral and Liverpool in a wide variety of primary school settings before teaching my own classes permanently and full time at schools in Birkenhead.
I relocated to North Wales in 2016, where I started to learn Welsh and to teach right across North Wales, from Wrexham to Llandudno and in primary and secondary schools. I have recently moved back to Wirral and so I teach in both countries now and I have built a reputation as a teacher with an outstanding rapport with children and the ability to teach children most subjects from age 4 to 16.

Tutoring Approach:
I will assess your child first, in order to gauge their strengths and areas for improvement and to benchmark their attainment, against which improvement can be measured.

I will spend time working with your child to understand their learning style 'mix' - this will allow me to tailor my approach to my teaching and to their learning.

It is important that children enjoy sessions, so wherever possible there will be fun!

My curricular strengths are English and maths, but I can also help out with 11 Plus and entrance exam preparation - verbal and non- verbal reasoning and mental maths. I am available in holidays also, if you want your child to catch up, or 'hit the ground running'on their return to school.

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Personal Description:
I hold a BSc (Hons) in Mathematics from Kings College London University. I am also a Postgraduate student studying for a Masters in Data Science.
My personal and interactive approach to tutoring is what has led to multiple success stories and has enhanced my desire to continue helping, developing and lending quality time to many more incredible students.

Teaching Experience:
I have been teaching for just under 3 years with 555+ hours of tutoring experience and therefore have the necessary experience to take my students education to the next level.

Tutoring Approach:
I will be giving one to one tuition to students who study A level Maths/Further Maths. Improving their understanding of the topics and supporting them in the areas which they find most difficult. I am determined to improve their problem solving abilities by providing them with challenging questions as well as answering any questions the student may have. I will be taking notes of the questions that my students struggle to understand or answer correctly, and from those questions i will form sets of questions that will aid the student in those areas and strengthen their weaknesses. I will be providing quality support during and after lessons. All students are unique so i will tailor my lessons according to the ability and needs of the student, with the overall goal of achieving the A* in the final exams.

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Personal Description:
Well, my teaching approaches vary based on the needs of the pupils and therefore the number of the pupils that consist in the classroom. I shall highly recommend that constructive and indirect teaching approaches are used.

Teaching Experience:
Not much actually.

Tutoring Approach:
Constructive and indirect approaches are the two best approaches for my pupils to learn.

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Personal Description:
Hey I'm Tau
Thought this would be a good way to make money on the side as my friends and family have always informed me I would be a good tutor, I focus around maths and English mostly for primary to secondary level, my rates are somewhat negotiable so contact me further for more information.

Teaching Experience:
As said prior I have helped a lot of my friends with tutoring and desire to help more people develop and improve with their subject

Tutoring Approach:
My main method is to figure out what type of learning your child is most accustomed to and what type they learn the most with and teach them how to understand their subject in that way.

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Personal Description:
After 37 years full time teaching maths, being an examiner with published materials, and for the last 25 years serving as head of department at a top, selective state school in the north, along with over 30 years of one-to one tuition experience, I have huge knowledge and understanding of how to help a student achieve their maximum potential

Hopefully my profile gives an insight to what I have gained from my professional career and how I can provide the support and help which you seek.

I am highly professional, totally non-judgmental and offer a relaxed, professional working environment in which students will feel relaxed, reassured and able to ask any question in full knowledge that any problems will be fully addressed at a pace and level of understanding which suits them and individually tailored to their needs.

All of this experience allows great attunement with the student, a deep understanding of their needs and difficulties and an excellent ability to address the problems with empathy and a great degree of patience.

Teaching Experience:
With 37 years as a full-time teacher of Mathematics and the last 25 years as Head of Department in one of the top selective state schools in the north, it would be a pleasure to be able to offer my experience to support, guide and help you in this subject.

During this time I have acquired a vast range of experience, navigating through numerous changes to GCSE, A-level as well as having to deal with the impact of Covid.

I have taught the full spectrum across GCSE and A-level, where my abilities to understand a pupil's difficulties and quest to achieve their potential in the subject is at the forefront of my work.

I have had many years as an A-level examiner, author of specimen examination papers for a major education publisher as well as having participated in projects on mathematical education from a European Research Institute.

Along with all of my classroom experience and expertise, I also have over thirty years experience of one-to-one private tuition with a wide variety of students whether they be local, resident in the UK or students from the USA or the Far East

Tutoring Approach:
Behind every target and expected grade, it must be remembered that each student is a unique individual. This has been at the heart of my teaching and tutoring over all these years. After an initial discussion, in which I get to know about your difficulties and goals, there would be a plan designed to address these and tailored made just for yourself.

In our tutor sessions I would offer you a highly professional, yet friendly, working bridge where you feel comfortable and relaxed. You know that you would be free to ask any question, confident that your understanding and ability is progressing forward and that I will always be non-judgmental.

Whilst every session would have a clear target and goal, combined with a sense of achievement, they have to be highly flexible. It may be that we need to take a sidestep to strengthen previous knowledge or alternatively, using my experience, prepare for something which lies ahead. You will feel reassured that my insight and knowledge is ensuring progress is as smooth as possible.

We will always work at a rate comfortable for you and build up and strengthen your knowledge and ability to apply it, as we progress. A solid understanding of especially 'why am I doing this', is very important.

Essential to your progress is the need to use your knowledge and understanding in not only 'standard textbook/worksheet questions' but those set in unfamiliar context as your final exam (or test/end of year) paper will be a mixture. Hence undertaking extra 'homework', will be an essential component to your progress in the subject. I will always ensure you feel prepared to undertake this work which will serve to practice basic understanding as well as pushing you into thinking carefully about how to apply your working knowledge. We would always agree a manageable amount to be completed by an agreed deadline. However, I may also need to be flexible with this as, of course, workloads and pressures can vary during a school year. The fact that you are comfortable raising this issue, means that we can easily work around the matter and reach a solution which eases the situation for you.

I would also offer all my support and experience in helping you prepare for any tests or final exams. There is a lot which can be done to help you mathematically, mentally and psychologically prepare for these stressful events.

Also provided as the result of every lesson, will be a pdf of the notes and work we undertook in a session. This maximises the learning potential in a session as the student is focused on the work being done and undertaking worked questions, and removing the need to 'take notes' and 'keep up'.

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Personal Description:
Hello! I would consider myself a patient tutor with experience. My preference is to hold in person lessons with my students and teach them to understand the topics, rather than to just pass the exam.

Teaching Experience:
I am a female maths tutor with 5 years experience teaching the subject to all abilities for GCSE and KS3. I am also familiar with Edexcel, OCR and AQA exam boards. If you have an alternative exam board, I would be happy to look into this as well. My preference is to hold in person lessons.

My own qualifications include studying maths within my Economics degree as well as at A-Level. I also have a DBS check which is available on request, as well as references.

Tutoring Approach:
I help students prepare for exams, work on class work with them where they need guidance with and help them improve in a particular subject that they're struggling in. I am also familiar with Edexcel, OCR and AQA exam boards. If you have an alternative exam board, I would be happy to look into this as well. My preference is to hold in person lessons with my students and teach them to understand the topics, rather than to just pass the exam.

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Personal Description:
I have done masters in physics and bachelor in double math and physics. Moreover, I am doing Post-Graduation from Univeristy of Hertfordshire UK,Hatfield. Student oriented and student care is my priority. I believe in student satisfaction and win-win situation only.

Teaching Experience:
I have a teaching experience of more than ten years. MBBS and Engineering students , GCSE Physics & Mathematics ,A level Physics & Mathematics.

Tutoring Approach:
Student oriented and student care is my priority. I believe in student satisfaction and win-win situation only. In short i am flexible and i believe to give extra help and online help on demand .

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Personal Description:
I have grown up studying the art of teaching and how students learn well. I have a broad education and can talk about ancient history, the elements of classical music, Latin texts, Jane Austen and Charles Dickens, Italian literature, and of course anything to do with maths and numbers.

I achieved an A1 in maths and was in the top 2.5 percentile for my year for Leaving Certificate (a broader A Level equivalent) reflecting my abilities in both maths and exam preparation.

Teaching Experience:
I have regularly taught in different ways while reading maths and Italian at Trinity College Dublin and have since started a PGCE teacher training course in maths. During my training I have gained extensive experience delivering lessons via OneNote and Microsoft Whiteboard via tablet and smart board, equipping me for effective online teaching of maths.

I already have experience teaching a weekly class of 10 young teenagers Latin as well as tutored maths, Music, and Latin to different ages and types of students. I'm a patient and considerate teacher and hope to bridge the gap that often plagues students in mathematics. I promise to be a good tutor and guide during some of the most formative and decisive years of your life.

Tutoring Approach:
My focus is on building the skills and concepts learnt at school through one-to-one 45-minute tutoring/grinds or small group lessons.

I aim to give an individual-focused approach. The lessons will focus on student's previous work and aim to improve skills and concepts already established. Great effort will be given to finding real world examples to motivate the exercises and to grasp or master a topic. The student will be encouraged to work out exercise in the tutor's presence and correct flaws or improve methods themselves.

I am willing to meet in Canterbury or give online lessons via Microsoft Apps such as OneNote, Whiteboard, and Teams.

I cover the GCSE curriculum as well as the pure Maths and Statistics aspects of A Level.

I am also available for university maths for 1st year and general maths tutoring for STEM subjects.

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