My Approach to Tutoring
Avoiding the pitfalls in the pathway of math success.
I do not like to treat the tutoring hour simply as an expensive study hall. If the student does not understand how to do the homework, working on the homework is the obvious place to start. Once the kid is up to speed on the homework though, I generally suggest that they put it aside, and do it by themselves at home. There are a number of more important things that I try to accomplish in the time that I have with the student, and I will try to describe those here.
A big problem that students run into, especially in the more difficult classes, is test questions that go beyond the homework and require quick, creative thinking under pressure. Over the years I've gotten better at anticipating what the test questions might be for a given course, and a given teacher. Once I've made certain that a student is up to speed with the homework, we start working on likely test questions. Many students have reported to me that this makes a real difference. In many classes, key concepts are presented too quickly, too abstractly or without enough explanation (with the teacher sometimes just repeating what's in the book). Sometimes the book isn't much help either, since it will provide examples of how to solve the easier problems, but give no examples of how to approach the harder ones.
Another tool I use in honor of preparing people for upcoming tests is to make up practice tests for them. I prepare a test that is designed to target that particular student’s weaknesses, and they take the test at home, simulating test conditions as closely as possible, i.e., no book, no notes, and a clock. In doing this exercise, you find out real quickly what you can and can’t do. It is a sort of dress rehearsal, and allows one to fix problem areas so that they don’t come crawling out of the woodwork to bite you on the real test. Adding this feature to the tutoring tool box usually results in better test scores.
Another role that I can play as a tutor is to go over the concepts before they come up in the classroom, it allows the student to better absorb the material as it is presented I the classroom during the days that follow. Since the kid already got a sneak preview of the overall concept, it is then possible to absorb some of the important details as they are presented by the teacher. This can also relieve a common source of anxiety, since the student knows that while the material may seem overwhelming as it is presented by the teacher, it really isn’t.
Many students have reported to me over the years that their teachers just don't seem to "get it" that the basic common-sense logic behind some of the complicated-sounding ideas or theorems in math can seem extremely non-obvious to somebody seeing them for the first time. As one kid described her math teacher's attitude: "Maybe it was never hard for her, or maybe she just learned this stuff so long ago that she doesn't remember what it was like to not get it." One advantage I have as a tutor is that while I get a big kick out of math, it has not always been easy for me. I am not a quick study, and have to spend time playing around with the concepts before they begin to take shape for me. I definitely do remember what it was like to not understand things that seem beyond obvious today.
One of the complaints I hear most often from kids goes something like this: "I understand the material. I know I do, because I can do the homework. The thing is, I do really badly on the tests." The kid, and often the parents as well, conclude from this experience that the problem must have something to do with test taking skills. In my experience, this syndrome is hardly ever due to a lack of test taking skills. In most cases, it really does have to do with not understanding the material very well. Let me explain.
If a student does not understand the underlying ideas in math, that student often resorts to rote memorization as an alternative strategy for getting through math classes. This memorization approach can more or less work all the way from the first grade up through pre-algebra. As far as math goes, there simply aren't that many things to either learn or memorize during those years. So if the student finds the concepts hard to grasp, they figure out early on that good grades can still be obtained by resorting to rote memorization. In fact, when such a student says that they "understand" the math homework, what they often mean is that they have sufficiently memorized the necessary formulas and procedures.
In this kind of situation, I have found that the aforementioned practice tests can be very illuminating. A kid who has taken the rote memorization approach as they try to prepare for an upcoming test in the classroom, will often think that they “get it,” and are well prepared for that test. However, when they do poorly on a practice test, it is clear that they are not, that our work is cut out for us, and that we know exactly where the weak spots are.
The basic bankruptcy of what I am calling the” rote approach” usually becomes apparent around the time the student gets to algebra, because at that point, the number of things that one must memorize in order to survive the class, begins to increase dramatically. If the student, ever since the first grade, has been mostly relying on their basic understanding of the concepts, the switch to the more rapid pace and the more sophisticated ideas encountered in high school, is a graceful one. However, if the student has long since abandoned the attempt to understand concepts, and has been using rote learning as their basic math tool, they will find that that tool is no longer equal to the task. There are a number of reasons for this, one of them being that there are simply too many things to memorize. This basic problem first begins to show up on the tests, not on the homework. Why? Because as the student does his or her homework, they have access to the book, so if they don't remember the correct procedure or formula for solving a certain kind of problem, they can just follow the steps as outlined in the book (or in their own class notes). This doesn't require much understanding; all you have to be able to do is follow steps. However, on the tests, without the book to prompt them, some students have only a very fuzzy idea as to which procedure or formula should be used when. They also might not perfectly remember the procedures themselves, to say nothing of having no understanding of why they work at all.
For such a student, all the teacher has to do is slightly reword a phrase, or present the idea from a slightly different point of view, and that student will be quite befuddled. The response I often hear from kids under these circumstances is “but he never taught us that.” Well…from the teacher’s point of view, it is often the case that he or she did teach that concept (although…sometimes not very well, I admit), but on the test, presented the concept in a slightly new context. This happens quite often in the more advanced classes and the honors classes especially. Generally speaking, the teachers are not simply engaging in cynical game-playing as they do this. They are trying to separate sheep from goats. Once again, this “different context” challenge is one that I try to address on my practice tests.
The real problem with taking the approach of rote memorization of formulas procedures, and phrases, is that in so doing, you are not really learning math at all. You may be honing your memorization skills, which is not a bad skill to have, but math isn’t about memorization. Math is about ideas, concepts, many of them quite profound, and the creative application of those concepts. I am not saying that memorization plays no role in learning math, because it does. It is just that rote memorization shouldn't be your main tool as you approach the material. The main tool needs to be understanding the ideas, seeing how they fit together. It is somewhat like the difference between memorizing a poem and actually understanding it. It might be useful to memorize a poem, but that is only the beginning. Imagine a student taking a literature class who simply memorizes a couple of poems, and thinks that this is going to be an adequate preparation for the upcoming test. Our poor student might be in for a rude shock when the test questions all turn out to be something along the lines of "compare and contrast these two poems in terms of what they are saying about the role of the family in modern society." If the student had only memorized the poems, but given no thought to their meaning, he or she would probably have no idea how to answer such a question. A somewhat similar dynamic can exist for students taking a math test. I sometimes find that students do not understand what the test questions are even asking for.
The problem I have described above does not have a quick or easy solution. Or maybe I should say that if it does, I don't have it. When I work with a student who comes to me believing that he or she simply needs to be taught some "test taking skills," I know that I am faced with a rather daunting task: I have to convince the student to try to reorient their entire approach to math. Basically, I have to convince them to think more, and memorize less. Almost always, this takes time and considerable effort, but I can honestly say that I usually get fair to excellent results, provided the student is at least somewhat willing to make this kind of change.
One of the main reasons, of course, that parents hire a math tutor for their child is that the child isn't getting what they need in the classroom. I often hear this expressed as "My teacher does not know how to explain what we are doing right now." I try to make my own explanations less lecture-like, and more conversation-like. I think that people learn most efficiently and deeply in the context of a two-way discussion, not a monologue. In other words, I try to take the Socratic approach. In order to make that discussion useful to the student, he or she has to feel comfortable asking questions, playing around with ideas, and making mistakes. My ability to be not just patient, but respectful (not patronizing) and engaged, is therefore crucial. The student needs to know that the teacher (or tutor, in this case) cares a lot about the interaction, and is not blasé about the whole thing.
I have found this approach to be effective whether the student attends Miramonte, Campolindo, Acalanes, Monte Vista and San Ramon High, as well as private schools in the area, Bentley, Head Royce, Athenian and College Preparatory School.
Finally, let me address the question of one-on-one tutoring vs. having two, or even three kids come for the same tutoring hour. Generally, I find that one-on-one is more effective, as I can then address, in a more focused way, that particular kid’s learning style and needs. The exception to this is in situations where the kids in question are well matched. By “well matched” I mean that they feel comfortable working together, are at about the same level of ability, ideally are in exactly the same class with exactly the same teacher, and both have a fairly strong work ethic. I have zero talent as a disciplinarian or a babysitter. Sometimes, in a group situation there is a tendency to want turn the tutoring hour into a social hour, I am no good at reining that in and getting everybody to focus back on the tasks at hand.
Please feel free contact me with any questions [email protected] or call me at (925) 247-8445 (office).
I do not like to treat the tutoring hour simply as an expensive study hall. If the student does not understand how to do the homework, working on the homework is the obvious place to start. Once the kid is up to speed on the homework though, I generally suggest that they put it aside, and do it by themselves at home. There are a number of more important things that I try to accomplish in the time that I have with the student, and I will try to describe those here.
A big problem that students run into, especially in the more difficult classes, is test questions that go beyond the homework and require quick, creative thinking under pressure. Over the years I've gotten better at anticipating what the test questions might be for a given course, and a given teacher. Once I've made certain that a student is up to speed with the homework, we start working on likely test questions. Many students have reported to me that this makes a real difference. In many classes, key concepts are presented too quickly, too abstractly or without enough explanation (with the teacher sometimes just repeating what's in the book). Sometimes the book isn't much help either, since it will provide examples of how to solve the easier problems, but give no examples of how to approach the harder ones.
Another tool I use in honor of preparing people for upcoming tests is to make up practice tests for them. I prepare a test that is designed to target that particular student’s weaknesses, and they take the test at home, simulating test conditions as closely as possible, i.e., no book, no notes, and a clock. In doing this exercise, you find out real quickly what you can and can’t do. It is a sort of dress rehearsal, and allows one to fix problem areas so that they don’t come crawling out of the woodwork to bite you on the real test. Adding this feature to the tutoring tool box usually results in better test scores.
Another role that I can play as a tutor is to go over the concepts before they come up in the classroom, it allows the student to better absorb the material as it is presented I the classroom during the days that follow. Since the kid already got a sneak preview of the overall concept, it is then possible to absorb some of the important details as they are presented by the teacher. This can also relieve a common source of anxiety, since the student knows that while the material may seem overwhelming as it is presented by the teacher, it really isn’t.
Many students have reported to me over the years that their teachers just don't seem to "get it" that the basic common-sense logic behind some of the complicated-sounding ideas or theorems in math can seem extremely non-obvious to somebody seeing them for the first time. As one kid described her math teacher's attitude: "Maybe it was never hard for her, or maybe she just learned this stuff so long ago that she doesn't remember what it was like to not get it." One advantage I have as a tutor is that while I get a big kick out of math, it has not always been easy for me. I am not a quick study, and have to spend time playing around with the concepts before they begin to take shape for me. I definitely do remember what it was like to not understand things that seem beyond obvious today.
One of the complaints I hear most often from kids goes something like this: "I understand the material. I know I do, because I can do the homework. The thing is, I do really badly on the tests." The kid, and often the parents as well, conclude from this experience that the problem must have something to do with test taking skills. In my experience, this syndrome is hardly ever due to a lack of test taking skills. In most cases, it really does have to do with not understanding the material very well. Let me explain.
If a student does not understand the underlying ideas in math, that student often resorts to rote memorization as an alternative strategy for getting through math classes. This memorization approach can more or less work all the way from the first grade up through pre-algebra. As far as math goes, there simply aren't that many things to either learn or memorize during those years. So if the student finds the concepts hard to grasp, they figure out early on that good grades can still be obtained by resorting to rote memorization. In fact, when such a student says that they "understand" the math homework, what they often mean is that they have sufficiently memorized the necessary formulas and procedures.
In this kind of situation, I have found that the aforementioned practice tests can be very illuminating. A kid who has taken the rote memorization approach as they try to prepare for an upcoming test in the classroom, will often think that they “get it,” and are well prepared for that test. However, when they do poorly on a practice test, it is clear that they are not, that our work is cut out for us, and that we know exactly where the weak spots are.
The basic bankruptcy of what I am calling the” rote approach” usually becomes apparent around the time the student gets to algebra, because at that point, the number of things that one must memorize in order to survive the class, begins to increase dramatically. If the student, ever since the first grade, has been mostly relying on their basic understanding of the concepts, the switch to the more rapid pace and the more sophisticated ideas encountered in high school, is a graceful one. However, if the student has long since abandoned the attempt to understand concepts, and has been using rote learning as their basic math tool, they will find that that tool is no longer equal to the task. There are a number of reasons for this, one of them being that there are simply too many things to memorize. This basic problem first begins to show up on the tests, not on the homework. Why? Because as the student does his or her homework, they have access to the book, so if they don't remember the correct procedure or formula for solving a certain kind of problem, they can just follow the steps as outlined in the book (or in their own class notes). This doesn't require much understanding; all you have to be able to do is follow steps. However, on the tests, without the book to prompt them, some students have only a very fuzzy idea as to which procedure or formula should be used when. They also might not perfectly remember the procedures themselves, to say nothing of having no understanding of why they work at all.
For such a student, all the teacher has to do is slightly reword a phrase, or present the idea from a slightly different point of view, and that student will be quite befuddled. The response I often hear from kids under these circumstances is “but he never taught us that.” Well…from the teacher’s point of view, it is often the case that he or she did teach that concept (although…sometimes not very well, I admit), but on the test, presented the concept in a slightly new context. This happens quite often in the more advanced classes and the honors classes especially. Generally speaking, the teachers are not simply engaging in cynical game-playing as they do this. They are trying to separate sheep from goats. Once again, this “different context” challenge is one that I try to address on my practice tests.
The real problem with taking the approach of rote memorization of formulas procedures, and phrases, is that in so doing, you are not really learning math at all. You may be honing your memorization skills, which is not a bad skill to have, but math isn’t about memorization. Math is about ideas, concepts, many of them quite profound, and the creative application of those concepts. I am not saying that memorization plays no role in learning math, because it does. It is just that rote memorization shouldn't be your main tool as you approach the material. The main tool needs to be understanding the ideas, seeing how they fit together. It is somewhat like the difference between memorizing a poem and actually understanding it. It might be useful to memorize a poem, but that is only the beginning. Imagine a student taking a literature class who simply memorizes a couple of poems, and thinks that this is going to be an adequate preparation for the upcoming test. Our poor student might be in for a rude shock when the test questions all turn out to be something along the lines of "compare and contrast these two poems in terms of what they are saying about the role of the family in modern society." If the student had only memorized the poems, but given no thought to their meaning, he or she would probably have no idea how to answer such a question. A somewhat similar dynamic can exist for students taking a math test. I sometimes find that students do not understand what the test questions are even asking for.
The problem I have described above does not have a quick or easy solution. Or maybe I should say that if it does, I don't have it. When I work with a student who comes to me believing that he or she simply needs to be taught some "test taking skills," I know that I am faced with a rather daunting task: I have to convince the student to try to reorient their entire approach to math. Basically, I have to convince them to think more, and memorize less. Almost always, this takes time and considerable effort, but I can honestly say that I usually get fair to excellent results, provided the student is at least somewhat willing to make this kind of change.
One of the main reasons, of course, that parents hire a math tutor for their child is that the child isn't getting what they need in the classroom. I often hear this expressed as "My teacher does not know how to explain what we are doing right now." I try to make my own explanations less lecture-like, and more conversation-like. I think that people learn most efficiently and deeply in the context of a two-way discussion, not a monologue. In other words, I try to take the Socratic approach. In order to make that discussion useful to the student, he or she has to feel comfortable asking questions, playing around with ideas, and making mistakes. My ability to be not just patient, but respectful (not patronizing) and engaged, is therefore crucial. The student needs to know that the teacher (or tutor, in this case) cares a lot about the interaction, and is not blasé about the whole thing.
I have found this approach to be effective whether the student attends Miramonte, Campolindo, Acalanes, Monte Vista and San Ramon High, as well as private schools in the area, Bentley, Head Royce, Athenian and College Preparatory School.
Finally, let me address the question of one-on-one tutoring vs. having two, or even three kids come for the same tutoring hour. Generally, I find that one-on-one is more effective, as I can then address, in a more focused way, that particular kid’s learning style and needs. The exception to this is in situations where the kids in question are well matched. By “well matched” I mean that they feel comfortable working together, are at about the same level of ability, ideally are in exactly the same class with exactly the same teacher, and both have a fairly strong work ethic. I have zero talent as a disciplinarian or a babysitter. Sometimes, in a group situation there is a tendency to want turn the tutoring hour into a social hour, I am no good at reining that in and getting everybody to focus back on the tasks at hand.
Please feel free contact me with any questions [email protected] or call me at (925) 247-8445 (office).