Carluke Maths Tutors and Carluke Maths Tuition

Personal Description:
I am a fully qualified and GTCS registered primary teacher of over fifteen years. I have considerable experience across all ages and stages and have extensive experience working with children with additional support needs, both in a classroom setting and 1-1 tutoring. I have a proven track record in delivering excellence and in supporting learners with a range of needs.

Teaching Experience:
I have been teaching for 10 years across all stages of the primary curriculum. I have experience of working with children with a range of additional support needs in the classroom and 1-1.

Tutoring Approach:
I try to make my tutoring sessions fun and interactive, using a mixture of ICT, games while maintaining a focus on formal written methods. I have experience of tutoring both maths and language and working to support learners needs such as hearing impairments, ASD and dyslexia.

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Personal Description:
My name is Ed. I am the Director of a private tuition company which has been providing impactful private teaching and tutoring services in a multitude of subjects across Common Entrance, GCSE, A-Level, IB and University.

We take pride in helping students to expand their minds, talents and skills, allowing them to reach their full potential. Our one-on-one tutoring brings a wealth of professional experience and expertise to those who strive to excel.

We offer personalised academic support, available in-person and online, to help students improve areas of difficulty and focus on exam techniques and preparation, helping them to succeed in attaining qualifications to their highest ability.

Please reach out and contact for further enquiries, look forward to hearing from you.

Teaching Experience:
Director, leading a team of tutors to support across a wide range of students including Common Entrance, GCSE, A-level, IB and University level - Present

Tutored a variety of subjects at different levels from primary schools, Common Entrance, GCSE, A-level, IB and University.

Offered service on giving academic advice as well as interview techniques for Oxford, Cambridge and other top schools and universities in the UK, US, Europe and Asia.

Tutoring Approach:
The approach is simple and effective. The general framework is to go through general concepts that are fundamental to student's understanding on the subject through the use of simple examples. I will then reinforce the message and encourage students to work on more specific and challenging problems.

Confidence is key and it is vital that my tutees are constantly motivated and encouraged in order to self-develop both at an academic and personal level.

We strive to make lessons as interactive as possible. We understand the different learning needs of different students. We will always be flexible with our teaching style and method and we are here to help you succeed.

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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:
I am 69 years old and retired from full time teaching in August 2014 after a teaching career of some 23 years. Since retiring I have done some part time teaching and private tuition. During the course of the last three years I have tutored some 30 students and have many written testimonials from parents regarding my tuition, you are welcome to contact current students to check the progress their child has made with my help. I am married with 3 children and live in the Chorley area. I graduated from Leeds Metropolitan University in 1979 with a degree in Construction Management and spent the first 12 years of my working life in the construction industry. I began teaching at Stockport College in 1991 and gained a P.G.C.E. in Secondary Maths shortly afterwards, I started at Oldham Sixth Form College in May 2003.
I have tutored a number of Primary School children during school closures and lockdowns and have access to a wealth of Secondary and Primary resources.
I have recently started tutoring as part of the National Tutoring Programme (NTP) giving on line lessons as part of the Government initiative to enable pupils to catch up on lost learning.
I am now offering online lessons at a rate of £25 per hour for Primary and G.C.S.E.
Levels. My Enhanced DBS is up to date and I subscribe to the updating service.

Teaching Experience:
I taught at Stockport College for 11 years retired from Oldham Sixth Form College in 2014 after almost 13 years there. I have taught a broad range of maths courses during that time and was course leader for level 2 maths at O.S.F.C. for 8 years before retirement. I have taught G.C.S.E maths for many years and have considerable experience teaching C1, C2 C3, C4 S1, S2 and D1 as part of A' level mathematics. I am familiar with both the Edexcel and AQA GCSE and A level specifications.
I have been an examiner for AQA at G.C.S.E. and am currently an examiner for The Cambridge Board marking the IGCSE and also for Edexcel marking C1 and C3, I have therefore lots of exam board experience and have many tips for maximising marks to pass on.
For students starting A level maths I have lots of bridging resources to enable students to make a seamless transition to advanced level study.
I am familiar with the requirements of the new G.C.S.E. maths 1-9 course and have access to resource bank created by AQA
I am familiar with the requirements of KS2 having marked the SATS tests for the last four years

Tutoring Approach:
I pride myself on my friendly and personable approach to tutoring endeavouring to remove the impression that maths is too hard that has grown up in the media in recent times. References are available from my past and current students.

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Personal Description:
I am a Depute Head Teacher based in the Motherwell area. I have fourteen years teaching experience with ten of those based in the classroom. I have taught in a variety of primary and SEBN schools in North Lanarkshire. I use a wide of range of innovative, inspiring techniques and strategies to engage the young people in my care.

Teaching Experience:
I am a Depute Head Teacher in North Lanarkshire with seventeen years teaching experience. I was classroom based for ten years and have had the pleasure of teaching a variety of young people ranging in age from 7-16 years old.

I look to build positive and lasting relationships with all young people in my care and use relationships to develop an in-depth understanding of what the needs of each individual child is. I use this information to derive a detailed individualised plan to meet the needs of your child. In addition to this I strive to use an assortment of teaching tools and approaches to ensure all learners are confident in understanding what is being taught.

Tutoring Approach:
As a private tutor I strive to give your child a positive and enjoyable learning experience, in turn enhancing their self-belief and self-confidence in a classroom environment. I use both practical and interactive teaching tools to help make all areas of the curriculum clearer and easier for a child to understand.

I use current and up to date materials to help give your child a better understanding and grasp of the curriculum as taught in his/her own classroom.

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Personal Description:
I am a 21 year old Accounting graduate from the University of Worcesfer. I achieved a very high A* at GCSE Maths and C at A-Level Maths. I am friendly and approachable and have a passion from problem solving at any level of Maths.

Teaching Experience:
I have had plenty of experience teaching children in many times of my life. From coaching cricket to teaching English and Maths in Madagascar! Last year I also tutored Maths to my 10 year old step sister when she moved schools as she was finding it very difficult to adjust to teachings at her new school.

Tutoring Approach:
As Maths comes very naturally to me, my approach to tutoring has always been calm and friendly, as I am always very patient with each tutee. One of my best skills is being able to find different solutions to problems, and finding the best way for each individual person to learn a new skill that he/she might be struggling with. I can also adapt to any role, whether it is helping a person to keep up with class or homework studies, or to help them advance to the next level.

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Personal Description:
My name is Samantha. I am a qualified and very experienced maths teacher. I have 28 years of teaching experience at all levels of secondary education as well as being a local authority maths advisor. I'm passionate about maths, easy going and relaxed, but get the best out of my students by making the subject easily accessible and interesting. My hobbies include music (playing various instruments and also watching a wide range of bands) and supporting my football team at live games.

Teaching Experience:
I have taught in 4 different secondary schools and held a variety of roles including head of department and lead practitioner. I started my teaching career in South Yorkshire in 1992, then moved to Staffordshire in 1994. My experience of teaching maths includes KS3, GCSE ( maths and further maths) and A level. I have taught pure mathematics, statistics and mechanics at A level and also Further maths

Tutoring Approach:
I am patient and understanding. I appreciate that maths is a challenge for some students but I understand how to clarify the subject. Students learn through getting answers wrong and shouldnt worry about making mistakes. I aim to build confidence through increased understanding and enjoyment.
The sessions I run are specifically designed for each individual student. This takes into account the level they are currently working at, target grade, their areas for development and preferred learning style.
At GCSE and A level I build into each session past exam questions, including problem solving questions using the techniques learnt in the lesson.
I am happy to set homework questions to build upon the skills covered and will mark and give feedback on any work completed. In addition, I provide a plan of work to be covered for the term/ year after consulting with students and parents.

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Personal Description:
I am a Qualified Engineer (D.Phil, Oxon, MSc, BSc Imperial College), Qualified University Educator (PG Dip) and Fellow of the Higher Education Academy (FHEA) with over 20 years' experience teaching university engineering, including 13 years as an Oxbridge lecturer, 7 years as a Senior Lecturer at an elite Russel Group university and a year as a Professor at a highly-ranked US university. I also have over 10 years' experience in aerospace and defence research with Rolls-Royce PLC, Qinetiq, Volvo Aeropsace in Sweden, and Mitsubishi Heavy Industries in Japan.

My work has given me the privilege of working with many hundreds of student-engineers across all branches of engineering. I know how difficult and challenging university engineering can be. My approach is warm, open and professional.

Teaching Experience:
In my 20 years of professional and private practice I have taught all branches of university engineering and engineering science including Aerospace, Mechanical, Civil, Electrical and Electronic, Chemical, Bioengineering, Materials, Design, Motorsport, etc. and even related subjects such as Physics, Architecture etc. Whilst most of my work is with undergraduates I regularly teach Masters/MSc students and doctoral/PhD students, as well as professional engineers.

I hold a PhD in Engineering Science from Oxford University (where they call it a D.Phil), an MSc in Mechanical Engineering and a BSc in Physics, both from Imperial College London, as well as a PGdip in University Learning and Teaching.

I also have over a decade of experience in experimental aerospace and defence research, as part of which I conducted ground-shaking jet engine tests at military and civilian test sites in the UK and Europe, working with companies including Rolls-Royce aero engines, Qinetiq, Volvo Aeropspace, and Mitsubishi Heavy Industries in Japan.

As well as having designed numerous large-scale experiments, my practical hobbies include classic car restoration and designing and building the places where I live. This hands on engineering experience means that I don't just teach the theory, I teach the reality and how the theoretical concepts you are learning in class relate to the real world around you. This is the beauty of Engineering.

Outside engineering, I enjoy freeride skiing, ice and inline hockey, and downhill mountain biking. I travel extensively with sport and have played hockey in almost every country in continental Europe and skied in virtually every country in the alps.

I am comfortable teaching in French as well as English.

Tutoring Approach:
Engineering is one of the hardest subjects you can study, and it doesn't help when module content is disorganised, learning materials are messy and hard to follow, and when lecturers are too busy to respond to your questions. If you are not getting the support you need, I know how this feels and I can help.

My overall aim is to teach you to become an independent learner, to teach you how to learn, so that you can learn regardless of the support from your university, and so you can continue learning when you leave university into whatever career path you take.

If you have a set budget for lessons then we won't go over this, even if we overrun the hour.

I offer an initial meeting free of charge to discuss your learning requirements, so you can show me what you need help with, what your learning aims and objectives are, and to plan our sessions together.

I am flexible in terms of scheduling, I'm happy to reschedule with sensible notice etc.

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Personal Description:
I am a qualified teacher with over 30 years teaching experience, mainly in KS2. I have QTS to teach English and maths / any National Curriculum subject, to any age group. Also I teach adult literacy and numeracy.

Teaching Experience:
KS2 / KS3 supply teacher and private tutor in London, Sheffield, Rotherham and Doncaster (1980 to present)

Tutoring Approach:
I have a friendly and patient approach. I build my student's confidence by differentiating work to match their individual abilities and interests.

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Personal Description:
Hello my name is Anne-Marie, I am from Ireland but have been living in the UK since 2004. This is now a place I call home. I realised I had a flare for imparting knowledge when I became a basketball trainer at 15, working with Primary and Secondary pupils. I thoroughly enjoyed the experience, saw the progress the pupils I trained had made and knew from that moment that teaching was my vocation as it was and is so rewarding. I now have a 5 year old son who loves reading and writing. He can articulate himself well and it's truly a joy to see. It's amazing the wonder a child sees in learning.

Teaching Experience:
From September this year I have been teaching English, Geography and RE at Beckfoot School in Bingley. I am a tutor as well (GCSE English, KS3 English, Maths and Science). As well as that, I am an EAL teacher to Chinese children online. In the past I have taught English up to GCSE at Laisterdyke Leadership Academy and English and French at Pudsey Grangefield School. In addition to this, l have taught Spanish and French at Carr Manor Community School. I taught the same subjects at St. Bede's and St. Joseph's Catholic College in Bradford from September 2017 to May 2018. Prior to that I was teaching French and Spanish at Cardinal Heenan Catholic High School (formerly a Language College). In addition, I assisted students to prepare for the GCSE German exam. As well as my teaching responsibilities, my pastoral duties included being a Year 10 form tutor. From February to December 2016, I was a teacher of French at Key Stage 3, Spanish at Key Stages 3 and 4 and was responsible for a Year 9 form at Queensbury School. From September 2015 to January 2016, I taught German at Key Stages 3 and 4 and French at Key Stage 3 at Oakbank School in Keighley. I previously worked at Rastrick High School and Sixth Form College where I was a teacher of French at Key Stage 3 and Spanish at Key Stages 3, 4 and 5. I also taught German and PSHCE to Year 9 students, and Accelerated Reading to Year 7 pupils. Four years ago, I was a Year 11 form tutor. This role entailed planner signing, reading and guiding pupils on college and career choices as well as helping them with exam revision skills. During registration, I covered some PSHCE topics and encouraged my tutees to write reviews on the books they were reading in order to find out more about their interests and consequently get to know them better. My form was involved in fundraising activities and have participated in assemblies. As well as that, I have mentored a PGCE student on how to become a form tutor and in addition I had a GTP student in my Key Stage 3 and 4 Spanish classes. In 2015 whilst on maternity leave, I taught Spanish to Years 2 and 6 and French to Years 3 and 4 at a local Primary School on a voluntary basis.

Tutoring Approach:
I like to use an approach that suits the students I teach. I discuss what needs they have and what their interests are and work from there. I like to be well-prepared yet flexible when necessary. I like to do kineasthetic activities to keep the students engaged in their learning and use a variety of resources to enable my students to gain as much confidence when speaking, reading writing etc.

I also create an environment where my students feel safe and at ease when learning meaning they are not afraid to make mistakes and are keen to build on this and see that mistakes are evidence of effort.

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Personal Description:
I am a Maths and Physics teacher and have been for nearly 40 years in both secondary and further education. I am very enthusiastic about the subjects I teach and enjoy helping my tutees to understand and progress. Both Maths and Physics are difficult for most people and it is a privilege to be able to explain ideas in these subjects in such a way that students can understand at whatever level they are working at.

I have been a keen amateur astronomer for all of my life and I am still in awe at the mysteries of the universe when I am looking through a telescope.

Teaching Experience:
10 years teaching Maths GCSE/A level in secondary education
30 years teaching Maths/Physics/Computing in further education

I have taught Maths and Physics for a wide range of examination boards and have taught one to one tuition to pupils from the age of 10 to A level and some undergraduate work in Maths, Physics and Engineering. I have prepared mature students for numeracy exams in order to gain entry into a teaching course or the armed services.

Tutoring Approach:
I am patient, friendly, enthusiastic and methodical in my approach to tutoring and try to instil confidence in my tutees as quickly as possible. I am flexible in my teaching methods and adapt my pace of delivery to the needs and ability of my tutees.

I am happy to work with the tutee to explain and reinforce the ideas behind the current topics that they are studying in school or college so they are able to keep up with their classwork. One of the worst fears amongst students especially in Maths is falling behind the rest of their peer group and not understanding the work as well as everyone else. When I am satisfied that my tutee is able to cope with their current work, I will revise topics to prepare them for tests and exams.

Both Maths and Physics require development of skills that constantly need practice. When it is close to tests or exams I will focus on exam questions so that tutees are aware of the standard required for the grade they are aiming to achieve.

For my online lessons, I am happy to arrange an initial free meeting with you to introduce the Groupworld whiteboard environment which I use for my teaching and to discuss what strategies I will employ to help you achieve your goals. There is absolutely no commitment after this initial session but hopefully it will match your expectations and we can arrange further lessons to give you the support that you need.

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Personal Description:
I am a 19 year old apprentice in Oxford who has always had a strong interest and competency in mathematics.

I am friendly, approachable and have a passion for helping others improve.

My other passions include sport, particularly weightlifting.

I believe that with hard work and the correct positive mindset, people have the ability to achieve great accomplishments and meet their goals.

Teaching Experience:
I have previously tutored a GCSE level student, as well as running training sessions at work for clients/new colleagues.

Tutoring Approach:
I believe in order for a student to achieve their potential, they must enjoy they way in which they are being taught maths. I therefore think it is important to tailor the way in which maths is taught to each student to make learning more entertaining and engaging.

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Personal Description:
I am PhD student at Harper Adams University, working on my final stages on my thesis. While I always enjoyed sharing my knowledge, I found lot of satisfaction from my students and there successes. It is really refreshing to work with young students, and that's why I am engaged in private tuition.

Also, I am Greek, but I am living and working 5 years in UK. I try to learn German, and I love DYI projects and crafts.

My professional life is mainly in the Vertical Farming sector, where my day job involves a combination of business and science tasks. Feel free to check my LinkedIn profile (Katia Zacharaki) for my background.

I have also a young daughter (9 years old), who has to have me as her tutor :).

Teaching Experience:
I have teaching experience in further and higher education, see below:
º Delivery of HE courses in Agriculture and Countryside Management
º Module leader for Strategic and Farm Business Management, Marketing, Environmental Sustainability, Global Food Security, Precision Agriculture and Dissertation for Level 4-6.
º Supervisor for Industrial Projects (Level 5) and Dissertations (Level 6)
º Engage with teaching, research and subject specific training
º Delivery of FE courses in Agriculture (Level 3) and modules as: Plant and Soil Science, Grassland Management, Business Planning and Investigative Projects (2017)
º Adult training on Agriculture, Countryside Management and Business subjects

Tutoring Approach:
My goal is to cover the necessary content with the most effective, efficient and quickest possible way. I never forget to add some fun :) .
I have already created lesson plants, which help me with the distribution of the content throughout the year/term.
I regularly assess student's progress with questions during the lesson, but also incorporating in the tests Mock tests. Mock tests help the student to familiarise with the process and reduce stress levels for all (student, parents and tutor). Mock tests include past papers (example GCSE/ A levels).
When relevant, we might use demonstrative lectures for science subjects.

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Personal Description:
I am currently an Academic Foundation Doctor at University Hospital Southampton. I studied at Westminster School as a Queen's Scholar and secured 14 A* at GCSE and 4 A* at A-level. In 2020 I received first class honours in Natural Sciences and was awarded a scholarship by Jesus College in 2020. I graduated Cambridge University in 2023 (MBBChir)

I am also a keen musician and played the clarinet with the National Youth Orchestra of Great Britain between 2014-2017. On holidays you might see me climbing and camping around Scotland or catching up with close friends in London.

What do I offer?:
• 13+ entry scholarship examination to Westminster School; 'The Challenge'
• Oxbridge interview preparation for medical applications
• BMAT (BioMedical Admissions Test)
• UCAS personal statement
• Other; please reach out to discuss

Teaching Experience:
Between 2020-2022 I have taught the neuroscience course (NHB) for 2nd year undergraduates at Jesus College Cambridge. Supervisions comprise of weekly small group teaching. I have also taught the NHB course privately 1:1. I regularly teach younger students (10-14).

Tutoring Approach:
I am a kind and supportive tutor looking to work with my tutees to identify and consolidate areas of weakness. In addition, I hope to provide insight into the skills required to tackle competitive application processes, including scholarship exams and medical interviews.

I prioritise improving exam performance and I encourage the development of critical thinking skills at all levels of learning. In undergraduate supervisions, I aim to tackle difficult concepts from first principles and question underlying assumptions, as well as help undergraduates develop their written communication. I believe these skills are highly valuable for writing personal statements and for success at interview.

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Personal Description:
I currently work as a Senior Global Project Manager for a clinical research company. Since graduating in 2015, I have worked in clinical research, progressing my career in Project Management.

Teaching Experience:
I have been tutoring for the last 5 years from ages 6-16

Tutoring Approach:
My approach is flexible depending on the students needs. I would initially want to understand what areas the focus would be, where I would then plan lessons and ensure there is mutual understanding. I believe it is important to encourage the student with the belief that they can overcome what they feel like they dont understand and be successful

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Personal Description:
My name is Elliot and I am an English tutor based in Central London. I have been tutoring since 2018 but my background is in Law. I have a Bachelor of Laws (2.1) from the University of Birmingham and a Master of Laws (LLM Human Rights Law) from the University of Nottingham (Distinction). For three years, I worked as an immigration lawyer in the UK before deciding to tutor full-time. I have lived in several different countries and am a keen language learner myself. In my spare time, I enjoy reading, running and writing. I have written for publications such as Reader`s Digest UK and am currently working on a collection of fictional short stories to be published late 2023. I enjoy entering my stories into short story competitions.

Teaching Experience:
I have been working as an English tutor since 2018. During this time I have taught hundreds of students and acquired thousands of teaching hours. I have taught students from three years old all the way up to adults. I have a significant amount of experience in teaching a range of abilities from complete beginners to proficient students. I have successfully prepared students for a range of exams including (but not limited to): IELTS, Cambridge Advanced, Cambridge Young Learners, UKiset (for entrance to UK independent schools) and much more. I have particular experience in teaching essay writing skills.

Tutoring Approach:
My approach to tutoring is flexible, patient and rigorous. From the very outset, I will ensure that we determine your specific academic goals and move towards them a little bit each lesson. Most importantly, I want you to enjoy our lessons and have a fun yet productive experience.

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Personal Description:
I'm a current second year student at the University of Bath, studying mathematics. I have a passion for my subject and that comes through in my lessons, this helps to enhance my teaching. My aspiration one day is to become a lecture in my chosen subject, and this is a great way for me to learn and become experienced early on in my potential career.

Teaching Experience:
I currently tutor one student in maths, However my experience stems further than this as I have always tutored and taught friends through GCSE and A-levels. A key highlight of my background is that I self taught A-level further maths as it wasn't a subject they offered at my school. This choice further shows my passion and drive for learning, but gave me a deeper understanding of studying and learning.

Tutoring Approach:
my tutoring style is highly adaptable, as I tailor make/ plan my lessons based on the student. No two lessons on the same topic are alike, ensuring a fresh and engaging approach each time! I have good ability at explaining complex concepts clearly and effectively, making my lessons more accessible and enjoyable as nothing is better than understanding a hard concept! my focus on getting students to challenge themselves with the harder problems builds confidence and results in excellent progress.
I always begin my tutoring with an introductory lesson ( a quick chat ) just to get to know the needs of the student, and so you can check to see if you match with my styles.

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Personal Description:
I recently graduated from LSE with a BSc in Financial Mathematics and Statistics, and I'm set to begin an MSc in Applied AI at Warwick.

Maths primary school, 11-14 years, GCSE and A-Level tutoring.
Further Maths A-Level tutoring.
Chemistry GCSE A-Level tutoring.

I achieved 9s in GCSE Maths and Chemistry, and A*s in A-Level Maths, Further Maths, and Chemistry.

Based in Elstree. Willing to travel to Borehamwood, Radlett, Bushey, Stanmore.

+£5 for Edgware, Mill Hill, Harrow, Watford and Barnet

Teaching Experience:
I have several years of tutoring and teaching experience across a range of age groups. I began by supporting younger students in Years 3-4 with Maths and English at school, and helped organise assemblies to build their confidence and communication.

In sixth form, I tutored GCSE Maths students (Years 10-11), helping them prepare for exams with structured revision and personalised support.

I also currently teach Religious Education at Sunday School, where I lead weekly sessions focused on values, reflection, and critical thinking in a faith-based context.

These experiences have helped me develop a calm, clear teaching style that's adaptable to different students' needs and learning styles.

Tutoring Approach:
My teaching style is calm, structured, and tailored to each student. I begin by identifying their strengths, gaps, and preferred learning style, and then adapt my sessions accordingly.

I guide students through concepts using worked examples and intuitive explanations, and encourage active problem-solving so they build confidence step by step. I never just give the answer-instead, I offer prompts and hints to help students arrive at solutions themselves.

I place a strong emphasis on exam technique and confidence-building. Once a topic is understood, I support students with targeted exam-style questions and past paper strategies.

Lessons are typically 60 minutes, but I'm flexible depending on what a student needs that day.

My goal is to make maths and chemistry feel manageable - even enjoyable - by helping students feel genuinely prepared and capable, not just memorising steps before an exam.

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