Frequently Asked Questions

About Math, a Math Tutor and Math Tutoring in Toronto

Here are some very natural questions we often receive from students about mathematics, learning math in general, a math tutor and math tutoring. We hope that the answers provided prove helpful.


Learning Mathematics

Q:  What is math?

A:  Mathematics is the study of number, structure, and reason.  It is a language, and the formal and precise foundation for all quantitative studies.

Q:  Why is math important?

A:  Mathematics is a cornerstone of human understanding.  Along with literacy, numeracy is one of the most fundamental and important tools of the mind.  Pythagoras, one of the greatest philosophers of all time, taught that all observable phenomena have number at the root of their essence and structure.

Q:  Why should I study math?

A:  Mathematics is a powerful tool.  Training in mathematics sharpens the mind and enhances its powers of observation and pattern recognition.  It also promotes logical and coherent thinking for success in all aspects of life.  Facility with numbers is also indispensable in the modern world, in both personal and professional life.  Specific disciplines of mathematics are highly instrumental in a broad range of disciplines and professions.

Q:  For what careers is math useful?

A:  Tell me what you want to be, and I will tell you how math will help you.  Math is not just for mathematicians. Mathematics has applications to medicine, law, engineering, science, accounting, business management, finance, statistics, computers & technology,manufacturing, skilled trades, agriculture, economics, politics, psychology, and the social sciences.

Q:  What can I do that doesn't require math?

A:  There are some areas of work which may not require a high degree of proficiency in mathematics, such as the arts and manual labour.  However, with all the technological advancements of a developing economy, traditional labourers are being replaced by machines, and these labour jobs are being replaced by robotics engineering and programming, which are highly mathematics-intensive.  The arts is a challenging sector in which to thrive, but even in this area, there is likely to be a surprising benefit from some degree of mathematical literacy, as there is often a fruitful interplay between disciplines of all kinds.  Careers in the complex modern world are becoming more dynamic and multi-staged, and mathematics is becoming increasingly useful in new areas.

Q:  Will math make me money?

A:  Yes.  A high degree of achievement in mathematicsis required for entrance into a majority of high-paying professions. Success in mathematics is highly correlated with financial success.

Q:  Math is hard.  Is it really worth the trouble?

A:  Math is definitely hard.  No matter what one's level of knowledge or study, advancing in mathematical understanding and solving new types of problems can be a tremendous challenge.  Albert Einstein once said, "whatever your troubles in mathematics, I assure you mine are far greater."  Believe it or not, there are unsolved problems in mathematics; that is, questions even the brightest and most dedicated minds, today or ever, have not yet been able to answer.  But challenges are what make life worthwhile.  Given the potential rewards, learning math it is too great an opportunity to miss.

Q:  I hate math!

A:  You may be frustrated by your studies in mathematics for a number of reasons.  One is that it is difficult.  Mathematics is the most difficult academic subject.  It is highly conceptual.  The density of ideas is such that one must absorb them gradually, with exposure to a number of examples to solidify understanding.  Math is also a complex language, with many intricate techniques and formulas to be remembered.  These can be learned through disciplined practice and problem solving.  With patient and thorough instruction, a deep understanding can be attained, and then the subject is no longer frightening, but can be familiar and fun.  Another is that it is abstract; it doesn't seem to relate to the real world.  One aspect of mathematical education which is often underemphasised is its applications.  With a thorough appreciation for the usefulness of math, it would be hard to turn away from it.

Q:  What is a mathematician?

A:  There are two types of mathematician.  A pure mathematician is someone who studies the universal truths of mathematical theories.  These are called theorems. He must prove them; that is, he must demonstrate that they are true from the basic truths we all accept, called axioms, using only the strict rules of logic.  An applied mathematician is someone who applies the theories of mathematics in order to assist industrial application.  This could be in a variety of areas such as physics,biochemistry, industrial production, statistical analysis, or finance.  She may also, in her work, encounter practical problems which in turn inspire the pure mathematician to formulate new theories to study abstractly.

Q:  How can I learn math?

A:  The first step is to be interested.  It is best to approach the subject with respect and patience, not as an enemy, but rather, an enigmatic friend.  It is helpful to have a good teacher, good books, and, above all, a hard-working persistent attitude.  More than anything, the faculty of curiosity drives all progress in learning.

Q:  Do I need to take math courses?

A:  The challenges, both conceptual and technical, in learning mathematics, as well as its abstract nature, are sufficient that it is helpful to have the structure of a course, and a teacher to assign regular homework and offer guidance in navigating this difficult field.  Math is only learned by problem solving.  The more problems, the better!

Q:  Do I need a math tutor?

A:  Math tutoring is helpful both to students who are falling behind, and to students who would like enrichment in their studies.  In either case, the level of achievement of a student is often not a reflexion of his or her innate ability, but rather, his or her experience to date.  For the lagging and the advanced student, a math tutor can provide the one-on-one attention that can be a catalyst to great academic progress.

Q:  Is math only useful for getting a job?

A:  Specialised studies in mathematics are undoubtedly critical for many programmes of study, and many careers.  Aside from professional applications, math is also useful for everyday life, like budgeting and planning, and for understanding statistics, which is useful for decision-making.  But math is also a way of thinking.  Facility with math cultivates the intellect, and trains the mind to give order to observations.  It has a subtle power which is often overlooked.  It strengthens the mind and helps us think clearly.  Lastly, mathematics is beautiful.  It is a language and aesthetic all its own, and can exist independent of the material world, like a painting, sculpture, or piece of music. But it is the interplay between mathematics and material reality which makes it truly beautiful.  It strips phenomena to their very essence, communicating only the purest nature of things.


Cardinal Math Tutoring


Q:  Do you do in-home math tutoring?

A:  Yes.  We often tutor in students' homes, because this ismost convenient to them.  However, we can also tutor at a public library or another quiet public place, according to the preference of the student.  This is negotiable, depending on your location in the Toronto area.

Q:  What levels of math do you teach?  Do you only teach math?

A:  We teach math at all levels of high school, college,university, graduate and professional studies, across a broad spectrum of courses in pure and applied math fields.  We not only teach math and applied math, but also many sciences and business-related fields, and just about any subject which is math-related.  There are too many to count!  Please see our subjects page for a more comprehensive list.

Q:  How long are math tutoring sessions?

A:  If students want to make progress in their understanding of math, and dramatically improve their grades, it is generally preferable to meet for longer sessions.  It takes some time to get into the material, and once you get focused, learning can accelerate.  A two hour period is usually an ideal time frame in which to make dramatic progress, and to cover a lot of material.  At most levels of math, the curricula of courses are dense, and there is a lot to cover.  In order to ensure success, it is important to allow enough time to address all topics in sufficient detail to allow you to master all mathematical techniques.

Q:  How many tutoring sessions do I need?  How frequently should I have math tutoring?

A:  It depends on the situation, including the level of study, the level of difficulty of the course, your academic background, your ability to work independently, and your goals.  In most cases,weekly sessions are ideal for keeping pace with a course, and consistently covering all material in the curriculum.  Frequent meetings also help you keep motivated, and avoid getting stuck on tough problems, which can be an obstacle both conceptually and psychologically.  In some cases students need more frequent sessions, or extra sessions before tests or exams, or for particular assignments.  In other cases, students benefit from meeting frequently at the beginning of their course in order to fill in major gaps in the prerequisite material from previous years' courses.  However, in all cases, we are flexible, and will only suggest a course of study, so that students may customise their tutoring schedule to meet their own needs and preferences.

Q:  What will we do in a tutoring session?  Is math tutoring just homework help?

A:  Good tutoring is not merely tutoring per se.  It is teaching.  The ideal components of a lesson are instruction and problem solving.  We begin by teaching the relevant topics from scratch, so if you absorbed nothing from your classroom or textbook, you can start from the basics.  You will learn not only the rules of mathematics, but why they are the way they are, why they are so important and how they help us to solve real world problems.  This way, you will understand the subject deeply, feel more comfortable with it, and maybe even like it!  Next, you will see examples which help to illustrate applications of the theory, and which illustrate various techniques which will be useful in your problem solving. These will go into your tool kit.  Next, you will apply these techniques on your own, with help, in order to get practice with these new tools.  Then, you will take away notes made during the lesson, with theory, formulas, and examples, which will help you in doing homework and assignments, and in preparing for tests and exams.  Lastly, you will be assigned suggested problems, which may or may not correspond with those assigned in your course, in order to solidify your knowledge and truly master the material.

Q:  Will I have even more work to do?  I want math to be easier, not harder!

A:  The benefit of tutoring is that you will have everything you need to succeed.  If there is anything you don't understand, you may ask.  If you are struggling with a topic, you will learn it from easy first steps, gradually building to the level of complexity of the theory you need to master.  You needn't ever get stuck or frustrated, and will make the best possible use of the time you choose to devote to your studies.  How much help you choose to seek and how much time and effort you allocate to homework is up to you, but the amount necessary for success will be clearly suggested, and you will know what you have to do to succeed.  Then the choice is yours.

Q:  I have to do homework too?

A:  To learn math, you must solve problems!  No matter how productive tutoring sessions are, in order to learn mathematics, it is vitally important to practise what you have learned.  You must prove to yourself that you can work independently, in order to be prepared for tests and exams.  You must also do many more examples than we can do in a lesson, in order to be able to solve problems properly, thoroughly, quickly, and without mistakes.  Working on your own also helps you to figure out what you know and don't know, and what questions you want to ask when you get help with math.  We are here to help, but learning requires independent thinking.

Q:  I am bad at math, and my marks are terrible.  How much improvement will I see?

A:  It depends on how hard you work.  If you want to make dramatic improvement, and you are devoted to the task, nothing will stop you.  Lessons will teach you everything you need to know. All you need to do is think and practise.  One thing which will help a lot is if you not only want to work hard to improve your marks, but also really want to understand the subject deeply.  This is not as hard as it sounds.  With good math tutoring,you can understand everything: the how, the when, and the why!

Q:  I still hate math!

A:  Mathematics is a beautiful subject.  But math is often taught badly.  Whether due to time constraints, poor textbooks, teachers who lack knowledge, teaching ability, enthusiasm or concern for students, or the limitations of the classroom environment, students often find math their least favourite subject.  But why is it that the few students who succeed at it do enjoy it?  It is probable that if you did well at it, you would like it, and if you truly liked it, with a little help, you would do very well at it.  Math is usually not taught on a very deep level, with proper motivation and justification.  If this is offered, you can see why we do math, how logical and sensible math is, and also how very powerful it is, by virtue of being applicable to so very many fields.  When a teacher approaches the subject with respect for a student's intellect and curiosity, math can be much more satisfying.  With a little patience, you can see that everything in math has a reason, and everything in math is useful.  And in math a right answer is a right answer.  100% correct!  What is more satisfying than perfection?  If you want to learn, the sky is the limit!