ACT Math,
ACT Math
My system of preparation for the math portion of the ACT (and, more generally, for the standardized tests in mathematics) is somewhat unique and unconventional. In fact, it goes against the grain of *most* of what you have been taught in school... and likely even in a test-prep class, if you have taken one. Sound a bit unnerving? Perhaps. But consider this: those same math teachers who tell you what to do, had most certainly not scored well themselves when they were your age. What's more, chances are good that they cannot score that well now, either. That's because their ways are... well, unduly complicated.
What is a better approach? First of all, I will teach you how to solve 95% of all questions *mentally*, without writing a thing. Why bother, you may ask. Several reasons.
One, it will teach you---anew---what you once knew but have since forgotten: the mathematical imagination. Its importance is hard to overemphasize. If you can imagine what is going to happen when you do this or that, say to a math expression at hand, you are going to solve the problem that much faster!
Two, doing math mentally teaches you to *look*---typically for a shorter way to solve the problem---and eventually to *see* such a short solution. A typical ACT problem can be solved in under 10 seconds---once you've slowly read it---mentally.
There are other [inter-related] benefits in mental math: improved short-term memory, reduction in the number of 'silly mistakes,' increased accuracy and speed, etc.
Next, since you are not writing, you cannot 'show your work.' But to take it further, I will not let you 'show your work' even in articulating your solution orally, either to me or to yourself. Why not? Because 'showing your work' prevents you from short-circuiting the steps that at some point in the past should have become trivial. For example, years ago, when you were learning how to read, you had to first learn how to recognize the shapes of individual letters, and the sounds that each of them made. But since then, these---formally formidable---tasks have long become superfluous. Thus, when reading today, it would be preposterous if you were required to 'show your work' by calling out the sound that each and every letter makes. You would never accept such an 'educational' approach to reading. Why should one accept it in mathematics?
As in reading, or sports, or any other human endeavor, the process of learning consists of combining formally separate steps into a single new step. 'Showing your work' prevents you exactly from doing this, and so from becoming better in mathematics. Hence, it must be rejected.
Next, I will ask that you 'throw out the clock,' i.e. have no concept of time when you are preparing. "But I have a very limited amount of time on the test!" you may object. That's true. Perhaps somewhat counter-intuitively though, the more time you spend 'dwelling' on a problem during preparation, to painstakingly slowly build a quality mental model, the faster your thoughts in the future will be able to access it.
There are other tidbits to my approach, dovetailing to what is described above. For example, for the vast majority of questions, even of the form "which of the following...", I will ask you not to be looking at the answer choices. The reason for that is simple: by covering the answer choices, you are forced to think about the problem deeper, sometimes even putting yourself in the shoes of a problem *maker*: a higher level of mastery. Of course, this contradicts what you may have heard elsewhere about the process of elimination. Alas, I'd much rather teach you how to *dominate* problems, than to be defending yourself against their onslaught.
I should add that the proof is in the pudding. I had taught a number of my young students to achieve the perfect score on the math portion of the SAT long before they would reach high school. I had also tutored a number of high-school students to score either perfectly or near-perfectly on the math portions of the ACT and SAT. If you buy into my method, I can teach you how to do it, too.
ISEE,
ISEE
Over the years, I have successfully prepared for the Math portions of the ISEE (and the SSAT) a number of students applying to (and getting into) highly selective private schools (at any grade level).
My system of preparation for these standardized tests in mathematics is somewhat unique and unconventional. In fact, it goes against the grain of *most* of what you have been taught in school... and likely even in a test-prep class, if you have taken one. Sound a bit unnerving? Perhaps. But consider this: those same math teachers who tell you what to do, had most likely not scored well themselves when they were your age. What's more, chances are good that they cannot score that well now, either. That's because their ways are... well, unduly complicated.
What is a better approach? First of all, I will teach you how to solve 95% of all questions *mentally*, without writing a thing. Why bother, you may ask. Several reasons.
One, it will teach you---anew---what you once knew but have since forgotten: the mathematical imagination. Its importance is hard to overemphasize. If you can imagine what is going to happen when you do this or that, say to a math expression at hand, you are going to solve the problem that much faster!
Two, doing math mentally teaches you to *look*---typically for a shorter way to solve the problem---and eventually to *see* such a short solution. A typical SSAT problem can be solved---mentally---in under 10 seconds (that is, once you've slowly read it).
There are other [inter-related] benefits in mental math: improved short-term memory, reduction in the number of 'silly mistakes,' increased accuracy and speed, etc.
Next, since you are not writing, you cannot 'show your work.' But to take it further, I will not let you 'show your work' even in articulating your solution orally, either to me or to yourself. Why not? Because 'showing your work' prevents you from short-circuiting the steps that at some point in the past should have become trivial. For example, years ago, when you were learning how to read, you had to first learn how to recognize the shapes of individual letters, and the sounds that each of them made. But since then, these---formally formidable---tasks have long become superfluous. Thus, when reading today, it would be preposterous if you were required to 'show your work' by calling out the sound that each and every letter makes. You would never accept such an 'educational' approach to reading. Why should one accept it in mathematics?
As in reading, or sports, or any other human endeavor, the process of learning consists of combining formally separate steps into a single new step. 'Showing your work' prevents you exactly from doing this, and so from becoming better in mathematics. Hence, it must be rejected.
Next, I will ask that you 'throw out the clock,' i.e. have no concept of time when you are preparing. "But I have a very limited amount of time on the test!" you may object. That's true. Perhaps somewhat counter-intuitively though, the more time you spend 'dwelling' on a problem during preparation, to painstakingly slowly build a quality mental model, the faster your thoughts in the future will be able to access it.
There are other tidbits to my approach, dovetailing to what is described above. For example, for the vast majority of questions, even of the form "which of the following...", I will ask you not to be looking at the answer choices. The reason for that is simple: by covering the answer choices, you are forced to think about the problem deeper, sometimes even putting yourself in the shoes of a problem *maker*: a higher level of mastery. Of course, this contradicts what you may have heard elsewhere about the process of elimination. Alas, I'd much rather teach you how to *dominate* problems, than to be defending yourself against their onslaught.
I should add that the proof is in the pudding. I had taught a number of my middle-school students, for example, to achieve the perfect score on the math portion of the SAT long before they would reach high school. I had tutored a number of students to score in the 90th (and higher!) percentiles on the math portions of the ISEE (and SSAT) so that they could go into a highly selective private school of their choice.
If you buy into my method, I can teach you how to do it, too.
SSAT,
SSAT
My system of preparation for the math portion of the SSAT (and, more generally, for the standardized tests in mathematics) is somewhat unique and unconventional. In fact, it goes against the grain of *most* of what you have been taught in school... and likely even in a test-prep class, if you have taken one. Sound a bit unnerving? Perhaps. But consider this: those same math teachers who tell you what to do, had most likely not scored well themselves when they were your age. What's more, chances are good that they cannot score that well now, either. That's because their ways are... well, unduly complicated.
What is a better approach? First of all, I will teach you how to solve 95% of all questions *mentally*, without writing a thing. Why bother, you may ask. Several reasons.
One, it will teach you---anew---what you once knew but have since forgotten: the mathematical imagination. Its importance is hard to overemphasize. If you can imagine what is going to happen when you do this or that, say to a math expression at hand, you are going to solve the problem that much faster!
Two, doing math mentally teaches you to *look*---typically for a shorter way to solve the problem---and eventually to *see* such a short solution. A typical SSAT problem can be solved---mentally---in under 10 seconds (that is, once you've slowly read it).
There are other [inter-related] benefits in mental math: improved short-term memory, reduction in the number of 'silly mistakes,' increased accuracy and speed, etc.
Next, since you are not writing, you cannot 'show your work.' But to take it further, I will not let you 'show your work' even in articulating your solution orally, either to me or to yourself. Why not? Because 'showing your work' prevents you from short-circuiting the steps that at some point in the past should have become trivial. For example, years ago, when you were learning how to read, you had to first learn how to recognize the shapes of individual letters, and the sounds that each of them made. But since then, these---formally formidable---tasks have long become superfluous. Thus, when reading today, it would be preposterous if you were required to 'show your work' by calling out the sound that each and every letter makes. You would never accept such an 'educational' approach to reading. Why should one accept it in mathematics?
As in reading, or sports, or any other human endeavor, the process of learning consists of combining formally separate steps into a single new step. 'Showing your work' prevents you exactly from doing this, and so from becoming better in mathematics. Hence, it must be rejected.
Next, I will ask that you 'throw out the clock,' i.e. have no concept of time when you are preparing. "But I have a very limited amount of time on the test!" you may object. That's true. Perhaps somewhat counter-intuitively though, the more time you spend 'dwelling' on a problem during preparation, to painstakingly slowly build a quality mental model, the faster your thoughts in the future will be able to access it.
There are other tidbits to my approach, dovetailing to what is described above. For example, for the vast majority of questions, even of the form "which of the following...", I will ask you not to be looking at the answer choices. The reason for that is simple: by covering the answer choices, you are forced to think about the problem deeper, sometimes even putting yourself in the shoes of a problem *maker*: a higher level of mastery. Of course, this contradicts what you may have heard elsewhere about the process of elimination. Alas, I'd much rather teach you how to *dominate* problems, than to be defending yourself against their onslaught.
I should add that the proof is in the pudding. I had taught a number of my middle-school students, for example, to achieve the perfect score on the math portion of the SAT long before they would reach high school. I had tutored a number of students to score in the 90th (and higher!) percentiles on the math portions of the SSAT (and ISEE) so that they could go into a highly selective private school of their choice.
If you buy into my method, I can teach you how to do it, too.
ACT English,
ACT Reading,
SAT Reading,
SAT Writing