For me personally this is fascinating topic, so I would like to contribute.
I have spent many years thinking about teaching and learning - what makes a great teacher and what makes a great student? What is the difference between attending a lecture in a hall with 200 other people and watching this presentation at home in 3D-glasses? If everything the teacher says is already in the books, why do we need teachers?
Here are some ideas to reflect on.1. You never really know whether a tutor helped you or did not help you.
Have you heard the story about a hungry man who ate five bagels and was still hungry? Then he ate a donut and finally felt full and satisfied. Can we say that all the bagels were wasted for nothing? In much the same way, you can study with some tutor A and understand nothing. Then you study with another tutor B, and suddenly everything makes sense! It does not necessarily mean that the tutor B is any better. Perhaps tutor A was slowly building up your skills, but it took some time for your to notice the results. If a field is new for you, it can be really difficult to tell, how much you are actually learning. 2. The main obstacle in any learning is identifying and changing your own habits -- habitual ways of thinking, rigid ideas, preconceived notions.
This task can be excruciatingly difficult, as we are all limited by our own experience and perception. Good books can lead you a long way, but at some point in life everyone can benefit from guidance. This is the way we are created: we often do not see our own limitations.
A textbook or a test-prep guide can make sense to you and seem to be well-written and accessible. Yet it may be reinforcing the same old patterns of thought, feeling, or perception, that limit your progress.
For example, this article offers terrible advice: https://benchprep.com/blog/gmat-math-pr ... solutions/
(It took me quite a while to find such a remarkably bad example.)
The question this article is trying to solve is fairly simple:
X is the ratio between the perimeters of two similar triangles, and X = 5 : 7.
Y is the ratio between the areas of the same two similar triangles. If, when expressed as a fraction, Y is less than 1, what is the ratio of X to Y?
A. 5 : 7
B. 7 : 5
C. 25 : 49
D. 49 : 25
E. 5 : 12
First the article presents a "shortcut": when a number is divided by something less than 1.0, this number increases. Thus they manage to eliminate A, C, and E, because 5/7 is not greater than 5/7, 25/49 is not greater than 5/7, and 5/12 is not greater then 5/7. To make things worse, the article then takes two particular triangles with sides 15,20,25 and 21,28,35, and actually computes the ratios, until it gets (5/7):(25/49), and eventually arrives at the answer.
This is not a good way to solve such problems. This is not a good way to understand such problems, even while you are simply preparing to take the test. Mathematics is not about dealing with a lot of numbers; it is about recognizing patterns. A much better way to explain the same problem would be: Y=X^2. Hence, X/Y=1/X=7/5, the answer is B.
Here you need a tutor you trust to tell you with full conviction that it is better to do this problem in one line than to engage in all this number manipulation and answer elimination. You may want to keep solving the problem the way that you like, the old way, the usual way, because you know how to plug the numbers to get to the right answer. However, if you want to make progress, you will have to change your habits, and stop trying so hard to get to the right answer. A tutor can guide you towards such a change. Otherwise many people are likely to stay with their old way of doing things, well, because nobody is perfect.3. In any learning, things get worse before they get better.
This is related to my previous point. If you believe that you are an expert and than you know some topic or field, you are not going to get better in this area. Ever. It is only by rejecting what we have already mastered or acquired that we can move forward. As related to GMAT, there is no reason why your scores should always increase. If you change your strategy or your way of thinking about certain kinds of problems, your score can go down before it goes up. This is perfectly natural, and does not indicate that you are going in the wrong direction. You need to trust the process.
When you are working with an experienced teacher or tutor, trust is very important. If your trust your teacher and follow his or her directions, you will probably make progress. In fact, even if you think your teacher is not very good, with faith you will probably learn a lot. Not all teachers know how to reach their students. However, most teachers have a lot to offer. People become teachers for a reason. The less you are focused on evaluating or criticizing your teacher, the more likely you are to learn. Do not waste your energy figuring out whether your teacher is good or bad, whether you are good or bad. These are just labels.
As an exercise, next time with your teacher or tutor, imagine that he or she is the best teacher on Earth, possessing expert knowledge, great people skills, wise and compassionate. 4. Our time is limited.
A great tutor knows things you probably haven't thought about. This was huge value for me. I was merrily going along my way for months and then a tutor opened my eyes completely to new perspectives. A tutor can pinpoint things and be a shortcut in correcting your problem area
This is exactly right. We can learn a lot of things on our own. However, our days are limited. You are here in your current situation, and you only have that much free time every day until the end of the year. Sometimes you will be distracted; sometimes you will be sick or tired. We don't really have that much time in this life.
There are things that are impossible to learn without other people, such as compassion. GMAT is not one of them. I believe that given enough time, pretty much everyone can master the GMAT and most other academic subjects. It may take decades.
At this point, pretty much every practice question and test-taking tactic is published somewhere online (often for free)...
This is exactly my point. An average teacher can tell you everything that is wrong with you. A great teacher can tell you what you need to hear right now
In other words, a teacher allows you to focus your efforts in the direction that would be the most productive at the given moment. This saves your time: hours, days, years, decades. This is perhaps the main reason for paying for GMAT tutoring: increased efficiency. In much the same way you are paying for a taxi to get from one place to another faster, even though you could take your time and merely walk. 5. Private instruction is overused.
This point is specifically about tutoring, not teaching in general. In many cases you may get the same benefits from a class with several people. Do you really need to work with an experienced teacher one-on-one? Less often than you think; definitely not when you are reviewing the fundamentals. Find a friend or two, then ask a tutor to organize a small group class.
Also, if you are asking a tutor to come to your place at the time of your choice, understand that you are largely paying for convenience, not just for instruction. Offer your tutor to meet at the place of his/her choice and offer to accomodate his/her schedule. Then ask for a discount. Just think about the tutor's situation: imagine teaching someone 1-2pm at one part of the city, then someone else 4-5pm at another part of the city. The tutor leaves his home at noon and comes back at 6pm. The whole enterprise takes six hours, and he may have to eat out at some crowded fast food place between 2 and 4. If each tutoring session is $50, this effectively translates into $100/6=$16.66/hour. Now imagine instead that both students come to the tutor's place, and the sessions are 12-1 and 1-2pm. The tutor can actually teach five students between 12-6pm (including lunch that can be eaten at home) and, while charging only $35/session, almost double his/her income, and feel more productive instead of commuting all day long.
Now, let's look at the mentioned rate of $200/hour. Of course, it is pointless to discuss the rate without specifying the location, so I will assume New York City. This rate may just be for the first hour. Two-hour sessions may be $300, which lowers the effective rate to $150/hour, since teaching one two-hour class is more convenient than teaching two one-hour classes. (Although, two one-hour sessions may be objectively more valuable for the student than one two-hour session.) Now, there may packages offered with further discounts - say, $2400 for ten 2-hour sessions. This lowers the rate to $120/hour, and this is the rate that you should be comparing. When you are paying the original rate of $200/hour for the first few sessions, you are also paying for the effort the teacher/tutor has to invest to get to know you, a new student, and your situation. You are compensating the tutor for the uncertainty - you, the new student, can disappear, and then he/she will need to rearrange his/her shedule, look for other students, spend time and energy to get to know them. You can ask for a lower rate if you can eliminate those issues and make the life of your tutor easier. Also, a high tutoring rate includes some insurance against you not showing up or canceling a class with a short notice. If you can somehow cover this risk for the tutor, you can also ask for a lower rate.
Sergey Orshanskiy, Ph.D.