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Teaching Maths: a Comprehensive Overview

From Sophia, published on 02/06/2017 We Love Prof - UK > Academia > Maths > Maths Tuition: An In-depth Review

Practical mathematics has always been a facet of human activity, as indicated by the earliest written records. Ancient societies encouraged learning Arithmetic and Geometry as a way to train the mind into logical thinking.

Beyond that, maths was used by tradesmen and merchants in the course of their business.

In intellectual circles, Mathematicians and philosophers have for centuries been debating the exact scope and definition of mathematics. Aristotle defined maths as the science of quantities.

Centuries later, Benjamin Pierce declared mathematics to be the science that draws necessary conclusions.

In spite of the greatest minds of all time applying the principles of mathematics in all of the science disciplines, there is yet to be a generally accepted definition of what exactly maths is.

For our purposes, we don’t need to know whether maths is logicist or formalist. As for every tutor before us, of our sole aim is to help students get a fundamental grasp on the topic.

Math teachers are an elite group You can combine your love of math with your desire to help others by becoming a maths teacher. Source: Pixabay


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The Roadmap for Teaching Maths

Before embarking on a career as a maths tutor or teacher, you should determine:

  • Would you enjoy leading a classroom, or do you prefer the idea of one-on-one lessons? (Some teachers enjoy doing both: teaching during the day and providing private instruction outside of class).
  • Would you wish to lecture at university, or do you more appreciate younger learners openness to new concepts?
  • What are your math abilities? Could you confidently guide graduate students, or does KS3 level Maths suit you better?
  • Do you want to teach full time, part time or do you specialize in a certain aspect of maths teaching, such as exam preparation?

These questions can help you determine what level of Maths instruction you give, when and where you contribute to students’ maths education and how you would deliver lessons.

Whereas schools in England require an undergraduate degree AND a grade of at least C or more at GCSE in order to train for teaching in public schools, private tutoring does not require any particular license or certification.

A rule of thumb for tutoring: you should be at least one year more advanced than those receiving instruction from you.

With that in mind, you could begin helping learners understand the subjects such as algebra and factoring while you are still in college.

Anyone with maths ability and desire to help can tutor in maths, but there are certain qualities a teacher must possess to impart knowledge effectively.

The best maths teachers are patient. Students may present with a variety of conditions that could prevent them from absorbing your teachings.

Frustration and reprimanding do little to encourage learners with math anxiety. A calm and gentle demeanor when conducting lessons is vital.

Empathy is a must.

Preparation is essential.

Maths lessons are seldom spontaneous. Each learning session should build on previous teachings.

As a tutor of Maths, it is critical that you maintain a profile for each student you work with so that you can present a logical flow of instruction and ensure their understanding of each phase before progressing further.

Enthusiasm is contagious! If you enjoy giving instruction in maths, your students will be more likely to appreciate learning from you.

Abaci are still used in primary schools and schools for the blind. Calculation tools and teaching methods have not changed significantly over time. Source: Pixabay

How Maths Tuition has Changed over the Centuries

Since the time of Ancient Greeks, tutors have featured prominently in the teaching of maths.

During that period, elementary education started in the home. Students matriculated at schools around age 12, mainly to learn more about Grammar, Logic and Rhetoric.

Arithmetic and Geometry were seen primarily as a way to sharpen mental abilities. Plato recommended that Maths be taught only for ten years, as a way to train the brain develop Logic, for example.

Maths teaching was initially geared towards merchants and business applications. Teaching maths at that time involved inexplicable equations, note repetition, memorizing multiplication tables – all with little to no understanding of underlying concepts on the students’ parts.

The ability to cypher and write was enough to secure gainful employment through the Dark Ages to beyond the Renaissance period.

For centuries, the Roman Catholic Church controlled and determined what was taught, and how. The study of Maths gained prominence in that circle during the 5th century, after the Pope copied a found mathematics work by Boethius and declared it essential teaching.

However, numbers and Sciences did not truly gain a place in academia until the 19th century, when more focus was given to how and when Arithmetics should be taught:

Basic Arithmetic should be taught as soon as children start school, and their learning should be based on perception of physical objects. Arithmetic, Geometry and Astronomy, so crucial to the burgeoning science of navigation, demanded seagoing entrepreneurs be able to calculate position and travel speed accurately.

Augustus De Morgan, first chair at the University of London, revolutionized the way Maths was taught. Firm in the belief that students must grasp underlying concepts of lecture topics, he prepared questionnaires, to be given out at the end of each lecture.

Reviewing these student exam responses, he could determine what applications had been clearly understood and what aspects of the lesson he needed to spend more time on.

The next lecture would see him returning his students’ efforts with corrections, and reinforcement of the previous session’s missed constructs.

Even today, the best teachers embrace this form of Maths instruction.

Teaching in school requires certification Maths teachers are highly qualified. Source: Pixabay

What Qualifications are Needed to Become a Maths Tutor?

While teaching Maths in a school requires, at a minimum, an undergraduate’s degree, a score higher than a C or more on your GCSE and a significant amount of training, tutoring in maths only requires your commitment, knowledge and passion.

That being said, the very nature of maths demands some level of proficiency and expertise.

Should your student have difficulty grasping the concept you are currently expounding on, you will have to find innovative ways to approach the topic, so that you can render the material not only understandable but memorable.

You should, at all stages of teaching but especially before progressing to a further premise, test your student on his/her ability to exercise the material just taught. You can do so with a traditional paper exam or by verbally quizzing your pupil(s).

At the very least, you must be prepared to answer questions relating to:

  • Numbers, negative numbers, whole numbers, integers, decimals and fractions
  • Properties of arithmetic, multiplication, subtraction and division
  • Ratio and proportion
  • Exponents and factors
  • Angles, arcs and radii
  • Sine, cosine and tangent
  • Solving for unknown values
  • functions
  • square roots
  • subsets and secondary equations
  • Polynomials
  • Pythagorean Theory

You should be able to do so in a way that is understandable and easily digestible for every type of student, and every age of learner.

Rigidity has no place in Maths instruction!

While you should lead the instruction, permit your student to lead by need. Invest your time where your student needs help the most. If algebra is a cinch but trigonometry trips him/her up, that is where your focus should be.

Achieving positive results in Maths tutoring can only occur if the teacher is competent, well-versed in the subject matter, and flexible in teaching style.

There is no law or certification needed to tutor in the UK. However, you should obtain a DBS, and you will be required to register yourself as self-employed at HMRC.

Bottom line on the question of certification: the onus is on you. Nobody is going to demand official credentials from you, but you will have to prove your ability one student, one lesson at a time.

Teaching Maths Online

Online tutoring is most likely the easiest way to gain an excellent reputation as a tutor of maths.

Operating on this platform greatly expands your teaching arena. From the comfort of your home, you can reach out to students who need you, anywhere in the world.

Most likely though, you would focus on your immediate vicinity, or at least your own country, where you know the requirements for maths education imposed by the school systems.

Teaching online offers many tools to help your student progress. You could use video chat while instructing, and then adopt screen sharing to illustrate concepts. You can incorporate any of the available online resources to develop your curriculum.

You can exchange documents, prepare quizzes and assign extracurricular work.

Online maths instruction calls for an added skills set. You must:

  • Be personable and engaging.
  • Be able to project enthusiasm and competence remotely.
  • Be able to concisely explain difficult concepts, using only voice and tone.

Naturally, these qualities are vital whether you teach face-to-face or in a classroom, but you must amplify them online in order to give your student a sense of stability while navigating the perilous seas of maths comprehension.

To be effective in the online teaching arena, you should work from a quiet, orderly space, free of interruptions and distractions. You should radiate professionalism, even though nobody is in the room with you.

The Internet is rife with meeting and sharing applications. Some charge a monthly fee while others, such as Zoom permit basic use of their platform for free.

An added bonus to online instruction is that you or your student can record the lesson and play it back later, as needed.

You can advertise your tutoring skills online Finding students in need of tutoring can be done online. Source: Pixabay

How to Find Students for Maths Tuition

Finding students is not a difficult enterprise. A simple online search demonstrates the need for quality maths tutors; might you be able to meet that need?

In these days of instant communication and Internet commerce, using the Web to find students and advertise your services is easy and cost-effective.

Gumtree, Freeads and your local online ad outlet will permit you to elaborate: your particular maths specialty, from GCSE exam prep to homework help.

Note: some sites permit you to list your advert or profile for free; others demand payment for ads, or for premium placement. That latter choice gives your promo higher visibility and the possibility of greater traffic.

Sites such as Superprof permit you to build a profile, detailing your experience and capabilities.

The greatest aspect of recruiting students online is that they can leave feedback and rate you as a teacher, and their opinions are posted for everyone to see.

A bit of legwork can also help to find students.

Word of mouth advertising is one of the most effective means of attracting clients. Talk yourself up at your local grocers, petrol station and library. Do you visit a certain pub regularly? Maybe someone there know of a student or two in need of your skills.

What about your neighbors? Especially if you live in a community with a lot of school-aged children, you might invite those living closest to you to test your trigonometry talents by offering a free introductory session.

Posting on bulletin boards can also bring business your way. Food stores and shopping plazas, libraries and community centers all have a space dedicated to promoting signature services.

Your bulletin should include your maths area of specialty, your preferred method of teaching, how much you will charge per hour and, of course, your contact information.

As long as you are dealing with bulletins, why not print a few extra and hand them out in car parks, shopping centers and school campuses?

Visiting schools could potentially bring you clients. Some schools keep a list of tutors for recommendation, should parents ask for such help.

If the institutions closest to you do not have such a list, you could recommend they start one, and put your name first on the list!

Using this multi-pronged approach – online, in shops and in your neighborhood is sure to bring students seeking succour your way.

How to Set Prices for Tutoring Maths

What you charge for giving maths tuition depends on a variety of factors:

  • your level of expertise
  • the depth of your experience
    • not just with the subject matter but with teaching in general
  • what you teach
    • exam prep, homework help, general maths support
  • what level you teach
  • where in the country you are.

Maths tutors in London and immediate vicinity, and in Scotland command between £27 and £33 per session.

Elsewhere in England, Maths tutors report earning of between £25 and £28 per hour of instruction.

Tutors in Ireland bring in between £25 and £30 for each teaching hour, while Wales Maths tutors receive between £25 and £37 an hour.

Maths comprehension and ability is especially critical in Ireland as foundation certificates can only be obtained in 2 subjects: English and Math. Furthermore, Irish test takers can be awarded maths bonus points (25), making a merely passing score outstanding. This extra requirement makes tutoring in Ireland especially lucrative.

The range of fees listed above serves in part to illustrate how crucial what type of help and what level maths you offer is.

For example: a London tutor coaching fractions and rational numbers to a pre-KS3 learner would get paid less than a tutor in London who is assisting in GCSE test prep.

Equally true: a tutor with several years of teaching experience in applied mathematics, anywhere in the UK, will bring in more than a university student earning extra money by tutoring who, himself is studying applied mathematics.

That doesn’t mean that great earning opportunities will be denied to you if you are that university student. You can still derive a satisfying income tutoring maths during semester breaks and/or after class, especially by offering general maths support, test prep assistance and homework help.

The best way to set a price for your efforts would be to investigate what other tutors with similar experience levels and subject matter knowledge in your area of the country charge. You should then adjust your hourly rate according to how your experience and ability measures against theirs.

Caution: although it might be tempting to underbid your competition in an effort to attract clients, it is never a good idea to under-represent yourself. Assessing a reasonable fee for your time and skills gives you more credibility and authenticity.

However, offering an introductory session at no cost is a great way to present yourself to prospective students.

Salaries for maths teachers is commensurate with performance Teachers can earn more salary by taking on extra responsibility. Source: Pixabay

How Much do Maths Teachers Earn in the UK Educational System

Before discussing potential earnings of Maths teachers, let us examine a disconcerting fact of science, technology, engineering and maths (STEM) teachers in general:

People who are STEM-skilled generally earn more in the private sector than as teachers in the education system.

Of course, this is great news for you if you are in fact quite skilled at maths and hoping to engage as a Maths and Sciences tutor.

As far as schools all over the UK are concerned, in an attempt to attract and retain talented STEM teachers, many offer golden hello packages and other incentives.

One type of extra earning opportunity that teachers have is TLR. The Teaching and Learning Responsibility program offers supplemental income if you take on sustained extra responsibilities such as after school help, in a range from £2,640 to £12,898 per annum.

Admittedly, TLR opportunities are available to teachers of all subjects, not just maths teachers.

Similarly, base pay for maths teachers is close in range to teachers of other disciplines.

Base salaries for teachers in the UKs education system are classified into five ‘steps’ and are paid accordingly.

  • ‘Unqualified Teacher’ – a new teacher with little to no experience
    • in and around London: between £17.000,00 and £30.000,00 per annum
    • England and Wales: between £16.000,00 and £26.000,00 per annum
  • ‘Main Pay Ranges’
    • in and around London: between £23.500,00 and £38.000,00 per annum
    • England and Wales: between £22.000,00 and £33.000,00 per annum
  • ‘Upper Pay Ranges’
    • in and around London: between £36.600,00 and £46.800,00 per annum
    • England and Wales: between £35.500,00 and £38.000,00 per annum
  • ‘Leading Practitioners’
    • in and around London: between £40.000,00 and £66.600,00 per annum
    • England and Wales: between £38.900,00 and £59.000,00 per annum
  • ‘Head Teachers’
    • in and around London: between £45.000,00 and £115.500,00 per annum
    • England and Wales: between £44.000,00 and £108.000,00 per annum

In Scotland, new maths teachers at secondary school start at £24.000,00 per year, with the average annual salary being a little over £34.000,00.

Teachers in Scotland, on average, earn more than elsewhere in the UK.

It is worth mentioning that UK schools have reevaluated teachers’ pay. Under the new system, teachers are compensated for performance rather than years of service.

That means that if you are enthusiastic, dynamic and in tune with your students, you stand to come up through the ranks faster.

Good teachers allow students to practice math any way they feel comfortable Maths teachers bring success, one student at a time. Source: Pixabay

Giving Maths Tuition

Most maths teachers will tell you they are not in it for the money.

Teaching is an art, and teaching maths is one of the more sublime ways to express that art.

Through the centuries, maths teachers have fought for validation of their subject matter, often in the face of scorn and derision.

While the science of maths has expanded, the way maths is taught has remained essentially unchanged for the past two hundred years.

However, tutoring in maths has changed greatly due to technical innovations and the understanding of learning disabilities. Tutors can spend more time working with individual students to ease maths anxiety than teachers with a roomful of students can.

Computers aside, Calculation tools have also been slow to evolve. The abacus is still used as a calculating tool in primary schools. Schools for the blind use adapted abaci to teach everything from arithmetic to square and cube roots.

Although the law does not require anyone to be a maths professor in order to tutor maths, a level of competency is expected of anyone who would offer supplemental maths education.

How much you charge per hour of maths instruction depends on your level of expertise and experience in teaching, as well as what type of assistance you provide.

The bottom line is: renumeration can be handsome in the field of maths tutoring but it is the love of the discipline that drives teachers of maths.

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