My Approach to Tutoring
Why Hire a Tutor?
One of the main reasons that parents hire a math tutor for their child is that their child isn't getting the understanding they need in the classroom. Often, the alarm bell goes off when the student’s grade is steadily slipping, with no sign of turning around. Another reason is that the student is doing fine in the class, but wants to take a more challenging course during the following year.
Classroom Instruction Not Meeting Student’s Needs
I often hear this expressed as, "My teacher does not know how to explain what we are doing right now." I believe people learn most efficiently and deeply in the context of a two-way discussion, not a monologue; therefore, I try to make my explanations less lecture-like and more conversation-like. Good teaching isn’t just a matter of unzipping the student’s head, pouring knowledge in, and zipping it back up again; it’s much more interactive than that. 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 cares about the interaction.
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. Here is how one student 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." I can relate: while I enjoy math, it was not always easy for me. I was not a quick study and had to spend time playing around with the concepts before they began to take shape for me. I do remember what it was like to not understand things that seem obvious to me today.
One way I try to help make the classroom instruction more useful and “sink in” is to devote time in our sessions to going over the concepts before they come up in the classroom. This allows the student to better absorb the material as it is presented in the classroom during the following week. Since they already got a sneak preview of the overall concept, it is then possible for them to absorb some of the important details as they are presented in the classroom. 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 that this makes a real difference. In many classes, key concepts are presented too quickly, too abstractly, or without enough explanation (with the teacher simply repeating what is in the book). Sometimes the book, the online platform and/or the teachers’ worksheets aren’t much help either, since they will provide examples of how to solve the easier problems but give no examples of how to approach the harder ones.
Poor Test Grades
One of the complaints I hear most often from students 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 student, and often the parents as well, conclude from this experience that the problem must have something to do with test taking skills, or potentially lack of confidence. In my experience, this syndrome is hardly ever due to either of those reasons. In most cases, it really does have to do with not understanding the material very well.
If a student does not understand the underlying ideas in math, they often resort 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. The basic bankruptcy of what I am calling the “rote memorization approach” usually becomes apparent around the time the student gets to Algebra 1, 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 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 students 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.
A student 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, only to be disappointed when a poor test grade comes back. One way I try to address this, is to make up practice tests for them designed to target that 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 quick 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.
A big problem that students run into, especially in 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. I often use the aforementioned practice tests to address this problem. I have found this approach to be effective.
Student Wants to Prepare for a More Challenging Course
In any given year, I have a number of students that fall into this category. For example, this might be a student in a pre-algebra course, who wants to jump to the higher level Algebra 1 course during the following year. With this student, I do an initial session to find out where their skills stand at the moment and start a study program from there. The tutoring is most effective if the student is willing to do homework between sessions. To facilitate this, I suggest that the parents buy an actual textbook (I have recommendations). Then, the student and I usually meet on a weekly basis and get to work.
Another situation might be when a student wants to do some preparation over the summer, for a difficult course coming up in the Fall. Examples might include a student who has just finished a geometry course and wants to go directly into a pre-calculus course. In those cases, I suggest that the parents buy the book that the teacher will be using (although many teachers now rely mostly on worksheets) and simply launch into learning the material, starting with Chapter 1. Once again, the tutoring sessions are almost always augmented with homework.
Why Understanding the Concepts is Crucial (even if what you mostly want is just a better grade)
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. A high school math course can and should be an opportunity for a student to develop deductive reasoning skills. Especially considering the world that these kids are going to be entering into as young adults, I don’t think that memorization skills are the thing to be emphasizing. Going forward, if someone, for example, needs the formula for the volume of a sphere, they can simply google it. I am not saying that memorization plays no role whatsoever 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 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 good results, provided the student is at least somewhat willing to make this kind of change.
What Kind of Improvement Do My Students Usually Experience?
When I get a call from a parent looking to hire a tutor, a typical scenario is the one where their student’s grade has been steadily slipping for awhile, with no end to that slippage in sight. My success rate in this kind of situation depends upon what the underlying problem is.
If it is the case that the student is doing poorly because their learning style is not a good match with the way the teacher presents the material in the classroom, all that student needs is an explanation they can understand. For example, if the student is a visual learner and the teacher hardly ever draws pictures or graphs, I demonstrate to them that drawing and graphing can be a first step in tackling the problem. With this kind of student, about 80% of the time they go from that slipping “C” to a “B” or an “A” within a month or so of weekly tutoring sessions, and stays there until the end of the semester. About 10% of the time, the tutoring is ineffective, and about 10% of the time we have outstanding success and the student goes from a "D" to an "A" within a month or so..
If it is the case that the student is doing poorly because they have been trying to get through the class via rote memorization, I try to convince them that a conceptual, (“understand the idea behind the formula”) approach will yield a better grade. If I am successful, the student’s grade goes from that low “C” to a mid to high “B”, or maybe even an “A”; however, it may be a longer process. My best success with this kind of student happens when I start working with them in middle school, and then we go through high school together.
If it is the case that the student is doing poorly because they have a weak grasp of the prerequisite material required for the class they are taking, I try to strengthen the grasp of the prerequisite material. A typical example of this would be a student trying to get through calculus without a good grasp of trigonometry or logarithms. During our first session, that will become obvious to me, at which point I will offer to help the student by designing a course of study that will get those prerequisite tools under his or her belt. This course of study inevitably implies a substantial amount of extra work. My success rate hovers in the 80% range when the student is accepting of this change in workload. The results are not overnight, and I cannot help students who are not willing to put in the work.
When I get a call from parent because they want their student to get ahead and take the more difficult courses (AP and honors) in the coming years, that call usually comes from the parent of a student in middle school. If we do wind up working together, it often turns into a long term tutoring relationship that results in good success.
Another situation in which a parent would call to a tutor such as myself, is one where the student is not getting the homework done and doesn’t study for the tests because they are unmotivated. I am not the right tutor to hire in this case. If the student is motivated and does want to do well in the class, but is having a hard time with the homework, then I am more than willing to work with them, and the homework is obviously the place to start. However, once it is clear that they can do the homework by themselves (or at least the easier problems), it is best to let them do that by themselves at home and spend our tutoring hour working on the harder problems, as well as likely test questions.
Online, “Remote” Tutoring Versus In-Person Office Tutoring
The system I use involves an interactive online whiteboard, and a phone (not Zoom). The student and I both sit in front of a computer (or iPad or iPhone) screen where the whiteboard is displayed, while we are simultaneously on the phone to each other. I can write on the whiteboard as we verbally discuss the material, and the student can write back to me. This platform does have a video option, but I don’t use that much, unless I must demonstrate something physically (usually with a geometry problem). Most of the students I work with prefer in-person tutoring at my office, saying that it is easier to focus while in-person; however, I do have a students who choose the online option. I would say that if the student does not have focusing issues, the online tutoring is quite effective, as well as being more convenient.
Group Tutoring
Generally, one-on-one tutoring is more effective as I can address, in a more focused way, that particular student’s learning style and needs. The exception is when students are well matched with not just the same material they are studying, but, more importantly, similar learning styles and ability.
I expect all of my students to be self disciplined and prepared for the sessions, not just in one-on-one tutoring, but in group tutoring as well. This is particularly important in group sessions in which socialization is a temptation. I am not a disciplinarian or babysitter, and a group’s session will cease once focus is lost.
Please feel free contact me with any questions:
Email [email protected]
Text (925) 247-8445
Classroom Instruction Not Meeting Student’s Needs
I often hear this expressed as, "My teacher does not know how to explain what we are doing right now." I believe people learn most efficiently and deeply in the context of a two-way discussion, not a monologue; therefore, I try to make my explanations less lecture-like and more conversation-like. Good teaching isn’t just a matter of unzipping the student’s head, pouring knowledge in, and zipping it back up again; it’s much more interactive than that. 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 cares about the interaction.
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. Here is how one student 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." I can relate: while I enjoy math, it was not always easy for me. I was not a quick study and had to spend time playing around with the concepts before they began to take shape for me. I do remember what it was like to not understand things that seem obvious to me today.
One way I try to help make the classroom instruction more useful and “sink in” is to devote time in our sessions to going over the concepts before they come up in the classroom. This allows the student to better absorb the material as it is presented in the classroom during the following week. Since they already got a sneak preview of the overall concept, it is then possible for them to absorb some of the important details as they are presented in the classroom. 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 that this makes a real difference. In many classes, key concepts are presented too quickly, too abstractly, or without enough explanation (with the teacher simply repeating what is in the book). Sometimes the book, the online platform and/or the teachers’ worksheets aren’t much help either, since they will provide examples of how to solve the easier problems but give no examples of how to approach the harder ones.
Poor Test Grades
One of the complaints I hear most often from students 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 student, and often the parents as well, conclude from this experience that the problem must have something to do with test taking skills, or potentially lack of confidence. In my experience, this syndrome is hardly ever due to either of those reasons. In most cases, it really does have to do with not understanding the material very well.
If a student does not understand the underlying ideas in math, they often resort 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. The basic bankruptcy of what I am calling the “rote memorization approach” usually becomes apparent around the time the student gets to Algebra 1, 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 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 students 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.
A student 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, only to be disappointed when a poor test grade comes back. One way I try to address this, is to make up practice tests for them designed to target that 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 quick 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.
A big problem that students run into, especially in 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. I often use the aforementioned practice tests to address this problem. I have found this approach to be effective.
Student Wants to Prepare for a More Challenging Course
In any given year, I have a number of students that fall into this category. For example, this might be a student in a pre-algebra course, who wants to jump to the higher level Algebra 1 course during the following year. With this student, I do an initial session to find out where their skills stand at the moment and start a study program from there. The tutoring is most effective if the student is willing to do homework between sessions. To facilitate this, I suggest that the parents buy an actual textbook (I have recommendations). Then, the student and I usually meet on a weekly basis and get to work.
Another situation might be when a student wants to do some preparation over the summer, for a difficult course coming up in the Fall. Examples might include a student who has just finished a geometry course and wants to go directly into a pre-calculus course. In those cases, I suggest that the parents buy the book that the teacher will be using (although many teachers now rely mostly on worksheets) and simply launch into learning the material, starting with Chapter 1. Once again, the tutoring sessions are almost always augmented with homework.
Why Understanding the Concepts is Crucial (even if what you mostly want is just a better grade)
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. A high school math course can and should be an opportunity for a student to develop deductive reasoning skills. Especially considering the world that these kids are going to be entering into as young adults, I don’t think that memorization skills are the thing to be emphasizing. Going forward, if someone, for example, needs the formula for the volume of a sphere, they can simply google it. I am not saying that memorization plays no role whatsoever 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 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 good results, provided the student is at least somewhat willing to make this kind of change.
What Kind of Improvement Do My Students Usually Experience?
When I get a call from a parent looking to hire a tutor, a typical scenario is the one where their student’s grade has been steadily slipping for awhile, with no end to that slippage in sight. My success rate in this kind of situation depends upon what the underlying problem is.
If it is the case that the student is doing poorly because their learning style is not a good match with the way the teacher presents the material in the classroom, all that student needs is an explanation they can understand. For example, if the student is a visual learner and the teacher hardly ever draws pictures or graphs, I demonstrate to them that drawing and graphing can be a first step in tackling the problem. With this kind of student, about 80% of the time they go from that slipping “C” to a “B” or an “A” within a month or so of weekly tutoring sessions, and stays there until the end of the semester. About 10% of the time, the tutoring is ineffective, and about 10% of the time we have outstanding success and the student goes from a "D" to an "A" within a month or so..
If it is the case that the student is doing poorly because they have been trying to get through the class via rote memorization, I try to convince them that a conceptual, (“understand the idea behind the formula”) approach will yield a better grade. If I am successful, the student’s grade goes from that low “C” to a mid to high “B”, or maybe even an “A”; however, it may be a longer process. My best success with this kind of student happens when I start working with them in middle school, and then we go through high school together.
If it is the case that the student is doing poorly because they have a weak grasp of the prerequisite material required for the class they are taking, I try to strengthen the grasp of the prerequisite material. A typical example of this would be a student trying to get through calculus without a good grasp of trigonometry or logarithms. During our first session, that will become obvious to me, at which point I will offer to help the student by designing a course of study that will get those prerequisite tools under his or her belt. This course of study inevitably implies a substantial amount of extra work. My success rate hovers in the 80% range when the student is accepting of this change in workload. The results are not overnight, and I cannot help students who are not willing to put in the work.
When I get a call from parent because they want their student to get ahead and take the more difficult courses (AP and honors) in the coming years, that call usually comes from the parent of a student in middle school. If we do wind up working together, it often turns into a long term tutoring relationship that results in good success.
Another situation in which a parent would call to a tutor such as myself, is one where the student is not getting the homework done and doesn’t study for the tests because they are unmotivated. I am not the right tutor to hire in this case. If the student is motivated and does want to do well in the class, but is having a hard time with the homework, then I am more than willing to work with them, and the homework is obviously the place to start. However, once it is clear that they can do the homework by themselves (or at least the easier problems), it is best to let them do that by themselves at home and spend our tutoring hour working on the harder problems, as well as likely test questions.
Online, “Remote” Tutoring Versus In-Person Office Tutoring
The system I use involves an interactive online whiteboard, and a phone (not Zoom). The student and I both sit in front of a computer (or iPad or iPhone) screen where the whiteboard is displayed, while we are simultaneously on the phone to each other. I can write on the whiteboard as we verbally discuss the material, and the student can write back to me. This platform does have a video option, but I don’t use that much, unless I must demonstrate something physically (usually with a geometry problem). Most of the students I work with prefer in-person tutoring at my office, saying that it is easier to focus while in-person; however, I do have a students who choose the online option. I would say that if the student does not have focusing issues, the online tutoring is quite effective, as well as being more convenient.
Group Tutoring
Generally, one-on-one tutoring is more effective as I can address, in a more focused way, that particular student’s learning style and needs. The exception is when students are well matched with not just the same material they are studying, but, more importantly, similar learning styles and ability.
I expect all of my students to be self disciplined and prepared for the sessions, not just in one-on-one tutoring, but in group tutoring as well. This is particularly important in group sessions in which socialization is a temptation. I am not a disciplinarian or babysitter, and a group’s session will cease once focus is lost.
Please feel free contact me with any questions:
Email [email protected]
Text (925) 247-8445