Tutoring someone who hates math

[DrRocket]

I would be very interested in hearing about this experience. Seriously. I imagine the professor worked very hard in building those sessions -- and deserves credit for being a great teacher.

There were more than one professor involved. The teaching method is known as the "Moore method" or "Texas method", after R.L. Moore. Moore developed the method for teaching topology and produced some outstanding students along the way -- Mary Ellen Rudin, Dick Anderson, R.L. Bing among others.

It is not limited to topology and works quite well for algebra and analysis as well.

There are variations on the theme depending on whether there is an actual textbook for the class. But the amount of work required of the professor is less than you think, particularly after a set of notes is available.

In a true Moore method class there is a lset of notes handed out on day 1. Those notes contain the theorems and examples for the class, but none of the theorems are proved and none of the examples are worked out. It is the job of the students to prove all of the theorem and work out all of the examples, for presentation in class. Students are not allowed to consult or to use any references. The role of the professor is basically to nod yes or no, and drink coffee.

In a class that uses a textbook, it is typically the job of the students to be prepared to present the lectures, and present worked out problems as assigned from the book.

In at least one class that preceded mine, an entire chapter in a well-known book disappeared when a student presented a counter-example that showed that everything in the chapter was wrong (this was the Tomita decomposition theory for operators on a Hilbert space and the book was the first edition of Naimark's "Normed Rings").

These classes are to be contrasted with lecture classes, which I never did like.

 

[hadsed]

I think it's 100% the teacher's responsibility to teach, as much as it is 100% the student's responsibility to learn. If the teacher knew that a student could learn just as effectively without him/her teaching it to the student, then there would be no need for our modern system of schooling. I've only just graduated from high school, but I do think that the best teachers I've had have made me dig into the material myself. That's how I got really interested in physics (having never taken a physics class)...my chemistry teacher encouraged me. Therefore, I'm not sure that it's the teacher's job to teach, per-se, as it is more to encourage the intellectual growth of the student. I honestly never put forth any effort in school until my senior year, and I graduated with a pretty high gpa in all ap classes. I didn't even need to put forth effort this year, but I finally realized what education was all about...not the grades, not the teachers, not the work, but the information grasped and understood. That said, my high school teachers did a bad job [overall] of pushing me to want to do that...it was only through my own personal search that I found this out. I have to say, Carl Sagan helped a lot. :)

/rant about hating high school/

Ditto about everything you said. Only difference was that instead of Carl Sagan, it was Richard Feynman for me.

And I must comment on what DrRocket mentioned.. that sounds like a brilliant way to teach. I think that most intelligent students do this anyway, if they're sufficiently motivated. Personally, I hate teachers that just tell you to 'know' this thing over that thing (so that you pass the tests).. as if some things really just aren't even worth learning! Of course there are some cases where it may not be as useful, but I find it shocking especially since this happens most in my math classes..

 

[dulrich]

The teaching method is known as the "Moore method" or "Texas method", after R.L. Moore...

Thanks for sharing that experience. I'll see what else I can dig up on the method.

 

[saim_]

That is completely backwards and is the sort of thing one hears as an excuse from poor students all the time.

Learning is the responsibility of the student. The teacher can facilitate learning, but no one can make anyone else learn. If the student does not learn, the blame lies 100% with the student. Period.

Unless and until the student takes responsibility for his education, there is likey to be little education at all. Learning is a lifelong pursuit, whether with or without a teacher. Learning just that lesson is major step towards becoming educated.

I think there is too much of a difference of opinion to be resolved but I'll try to explain my side. You have to give the kids a foundation upon which they can build. As a kid one doesn't know what's important in life and its your responsibility to make them see it correctly. You think kids are born good or bad students? I don't and I think its the teaching effort of their parents and teachers that make them good or bad students. If a kid is turning out to be a bad student or is not interested in his studies its not because he is stupid or a born dummy, its the failure of his teachers to teach him right and to cater to his needs. Instilling interest and "making" students understand are essential parts of good teaching, not optional duites that a teacher may or may not perform. I think its the teachers who makes excuses of stupidity and dumbness (sugar-coated in politically correct words) and destroy the kid's education. As for the kids at this stage, most don't even have developed a strong ability to lie and make excuses :D (high school kids have ruined it for the children :p).

I think you are confusing your point of view for advanced high school and university students with children. In my opinion it will be generally agreed upon that the role of teacher starts diminishing at high school level and at university level the concept of a "teacher", as one experiences in school, almost dies off and you just have instructors and tutors but you can't extrapolate that back to a child's education.

Bottom line: No kid is good or bad. Its his teachers, which includes everyone who is supposed to be closely associated to his development, that make him one or the other.

 

[Null_]

I think there is too much of a difference of opinion to be resolved but I'll try to explain my side. You have to give the kids a foundation upon which they can build. As a kid one doesn't know what's important in life and its your responsibility to make them see it correctly. You think kids are born good or bad students? I don't and I think its the teaching effort of their parents and teachers that make them good or bad students. If a kid is turning out to be a bad student or is not interested in his studies its not because he is stupid or a born dummy, its the failure of his teachers to teach him right and to cater to his needs. Instilling interest and "making" students understand are essential parts of good teaching, not optional duites that a teacher may or may not perform. I think its the teachers who makes excuses of stupidity and dumbness (sugar-coated in politically correct words) and destroy the kid's education. As for the kids at this stage, most don't even have developed a strong ability to lie and make excuses :D (high school kids have ruined it for the children :p).

I think you are confusing your point of view for advanced high school and university students with children. In my opinion it will be generally agreed upon that the role of teacher starts diminishing at high school level and at university level the concept of a "teacher", as one experiences in school, almost dies off and you just have instructors and tutors but you can't extrapolate that back to a child's education.

Bottom line: No kid is good or bad. Its his teachers, which includes everyone who is supposed to be closely associated to his development, that make him one or the other.

I agree that the maturity level of most isn't high enough until high school, but looking back on it, I really think I could have started caring and understanding in middle school at the latest. I was in a group of about 10 kids who was pulled from class since elementary school for working on harder stuff, i.e. learning multiplication and division in first grade, reading books like The Hobbit in third grade, etc. However, even this teacher never made me want to learn...she just taught us as if we already knew how to do it. I'm not really sure how self-motivated I could have been if she fostered our personal growth, but all I know is she didn't...out of those 10 kids I studied with until middle school, I honestly think that only two of us actually care about conceptual knowledge. The rest are just memorizing machines.

So while it is more the teacher's job to teach the younger grade levels, they should still encourage intellectual growth by the student at a personal level just as much as a high school teacher or college professor. Sure, all kids might not be ready for it, but some are. It's not like it would hurt those who aren't quite ready.

 

[abelgalois]

Math hater here. Keep this thread moving. I JUST started studying math again and I'm bored as Hell already. I'm preparing to go back to school in two years for engineering so I have a lot of time but I'm just not captivated by what I've studied so far. Granted I'm still on algebra 1 stuff. Things I find exciting: Judo, Going out at night, great games, thought provoking movies, a good sci fi book, starcraft 2. Things I don't: Math. I think maybe I'm just a visual person.

The odd thing is that I'm also studying philosophy and I'm enjoying it quite a lot. I haven't even gotten to the "philosophy" stuff either. I'm studying logic and I enjoy tinkering around with validity, invalidity, deduction, truth tables and what not. I'm sure this is some pretty dry stuff that would bore the pants off most people. But it's quite relatable stuff anyhow because with logic you can draw some pretty practical and relatable examples i.e. "All Canadians like hockey, Drake is a Canadian therefore Drake likes Hockey." Or you can translate an argument about abortion into a set of propositions and analyze whether the conclusion follows from the premises. With math it's just completely abstract.

But hopefully once I get to the more meaty topics in math I'll start to see what all the big fuss is about. I really want to find the beauty in math. I really want to like it. And I want to do it for the sake of doing it. The first book I'm on right now is called, "Algebra Survival Guide: A Conversational Handbook for the Thoroughly befuddled." It got rave reviews from other mathaphobes on Amazon so naturally I bought it. The next two books in the lineup are "Geometry" by Harold Jacobs and "Elements" by Euclid. I know this is when I'll first start dealing with precise definitions, axioms, and proofs so things should start to get a little more exciting. Maybe I'll enjoy the logic of it.

But if anyone in this thread has any suggestions on how to make studying math enjoyable then I'll be more than happy to try them out.

One thing's for certain. I really hate doing repetitive, trivial exercises following an explanation of something. For example, defining what the transitive property is and giving me 15 exercises to do that are practically the same and ridiculously easy. I think what I'll enjoy is dealing with an actual problem and using ingenuity to come up with a solution.

 

[hadsed]

What helps me when I'm bored is trying to figure out how to do the math myself. I try to just look at the rule or law or whatever and try to do problems without looking at any examples at all. If I get stuck on something then I'll go back and check it out, but I'll try to look at only the part I need in order to finish the problem. I think that way I learn more effectively and it keeps me thinking hard. So it's a good exercise for me. Of course it can get very frustrating sometimes so it's good not to do it under pressure (ie study for an exam that way).

 

[Jokerhelper]

A lot of art majors don't share your enthusiasm for math and could care less about solving linear equations, but they probably need to know a thing or two about art (ok so I don't know what an art major actually does).

It is NOT the responsibility of the teacher to teach. It is the responsibility of the student to learn. It is possible to help someone to learn. It is not possible to simply teach someone --the act of acquiring understanding is not passive.

You probably were trying to be "paradoxical" with that that statement, but do you actually believe that? Also, for example how can a 5 or 6 year old be 100% responsible for learning something like alphabet?

 

[DrRocket]

You probably were trying to be "paradoxical" with that that statement, but do you actually believe that? Also, for example how can a 5 or 6 year old be 100% responsible for learning something like alphabet?

There is no paradox and I fail to understand where you could possibly see one.

A 5 or 6 year old learns the alphabet because student wants to learn it. The student is responsible for the learning, the teacher only facilitates.

No one force fed me the alphabet, nor did they do likewise to anyone of my acquaintance. I do know people who taught themselves to read long before kindergarten.

 

[Jokerhelper]

There is no paradox and I fail to understand where you could possibly see one.

So you just said with a straight face that a professional teacher, someone who is hired to teach, had no responsibility to actually teach, hence to fulfil the job he gets paid for. OK...

A 5 or 6 year old learns the alphabet because student wants to learn it. No one force fed me the alphabet, nor did they do likewise to anyone of my acquaintance.

Seriously? How many 5 year olds have you actually ever met recently?

But I must say you are right. These definitely want to learn the alphabet immediately and can't wait to do so as soon as possible. You can already imagine their conversations with their parents: "Mommy, I want to learn the alphabet right now so I can't start associating sounds that come from my mouth with those weird shapes called "letters" that always flash during commercials when I watch Dora the Explorer. Please make me sing those great ABC songs, especially the one with the Mozart tune that all my friends love so much. Also, get for me those big books so I can learn how to draw those weird shapes by scribbling them over and over again? Maybe next week I can learn cursive too, yay! By the way, why do we have both capital and lower case letters? Please tell me about the great history of the latin alphabet that I am really interested in."

Ok, now back from La La Land to Real World.

I do know people who taught themselves to read long before kindergarten.

[URL]http://i772.photobucket.com/albums/yy8/photodonknome/seriously.gif[/URL]
What do you actually mean by "taught themselves"?

 

[DrRocket]

So you just said with a straight face that a professional teacher, someone who is hired to teach, had no responsibility to actually teach, hence to fulfil the job he gets paid for. OK...




Seriously? How many 5 year olds have you actually ever met recently?

But I must say you are right. These definitely want to learn the alphabet immediately and can't wait to do so as soon as possible. You can already imagine their conversations with their parents: "Mommy, I want to learn the alphabet right now so I can't start associating sounds that come from my mouth with those weird shapes called "letters" that always flash during commercials when I watch Dora the Explorer. Please make me sing those great ABC songs, especially the one with the Mozart tune that all my friends love so much. Also, get for me those big books so I can learn how to draw those weird shapes by scribbling them over and over again? Maybe next week I can learn cursive too, yay! By the way, why do we have both capital and lower case letters? Please tell me about the great history of the latin alphabet that I am really interested in."

Ok, now back from La La Land to Real World.



[URL]http://i772.photobucket.com/albums/yy8/photodonknome/seriously.gif[/URL]
What do you actually mean by "taught themselves"?

Sorry this is the real world.

I mean took elementary books with pictures and taught themselves to read. Did a rather good job of it too.

Some kids are a lot smarter than their teachers. That is fortunate.

 

[Bourbaki1123]

So, have you tried any tricks? For balancing a linear equation he should just be able to memorize the formula. It's always ax + b = cx + d if anything is zero, just use a place keeper.
For instance 3x -5 = 10, restate this with a = 3 b = -5 c =0 and d = 10, ax -cx = d - b => (a-c)x = d - b => (d-b)/(a-c) = x so 15/ 3 = x or x = 5. Is he unable to memorize a simple procedure like that? Or is he just unwilling? If he is just not willing to practice, that is a problem that needs to be reported to the parents.

It's pretty easy to break down all of high school math into formulas. As a tutor you should be able to figure out a way to do this on the fly, and if you can't you need to think about it outside of your tutoring sessions and become skilled at it.

 

[DrRocket]

It's pretty easy to break down all of high school math into formulas. As a tutor you should be able to figure out a way to do this on the fly, and if you can't you need to think about it outside of your tutoring sessions and become skilled at it.

If you handle mathematics by breaking it down into formulas that you then memorize you are wasting your time and learning nothing. The point of mathematics is to understand it so that the formulas are obvious, i.e. so that you understand the subject and are not just manipulating symbols. If all you do is manipulate symbols then your effort would be better spent on something else.

Reliance on rote memorization is the source of good deal of the lack of interest in mathematics, and on the ability to understand and use it for the long term.

 

[Null_]

If you handle mathematics by breaking it down into formulas that you then memorize you are wasting your time and learning nothing. The point of mathematics is to understand it so that the formulas are obvious, i.e. so that you understand the subject and are not just manipulating symbols. If all you do is manipulate symbols then your effort would be better spent on something else.

Reliance on rote memorization is the source of good deal of the lack of interest in mathematics, and on the ability to understand and use it for the long term.

Exactly. I was taught math by being spoon fed formulas. Truth of the matter is, I never learned WHY the quadratic equation or the Pythagorean theorem works. I was taught the Pythagorean theorem as a^2=b^2+c^2, and after I googled it and told my teacher, she told me that I was wrong and that the Greeks came up with the formula. That teacher was probably the best teacher I'd had, since she taught me to never trust anything that a math teacher says. If I ever had a question on anything in the book, I'd go straight to google. ^_^

I taught him the distance formula the other day, but instead of the formula, we first talked about the area of a triangle using the Pythagorean theorem. I tried giving a little talk and a picture of the simplest proof, but he wasn't too interested. He did learn the formula for it :/. But he now knows the reasoning behind the distance formula.

 

[Bourbaki1123]

If you handle mathematics by breaking it down into formulas that you then memorize you are wasting your time and learning nothing. The point of mathematics is to understand it so that the formulas are obvious, i.e. so that you understand the subject and are not just manipulating symbols. If all you do is manipulate symbols then your effort would be better spent on something else.

Reliance on rote memorization is the source of good deal of the lack of interest in mathematics, and on the ability to understand and use it for the long term.

Why would I teach mathematics in the same way that I learn mathematics when the student is clearly not interested in fully understanding it? You have to go one step at a time. If he asks you for the formula, you give him one. If he asks why it works, then you show him. If he doesn't want to know why it works, then you can only use rote. Prodding him will only make him close up, but answering his questions will pique his curiosity. If you remind him from time to time that a full understanding of the ideas will make things easier, he might eventually give it a solid shot.

Also, who's to say that this kid's time wouldn't be better spent on something else? High school mathematics curricula tend to be pretty arbitrary, and most people forget nearly everything besides what is needed to make sure they don't get ripped off at the grocery store. Maybe this kid's talents lie elsewhere. I have a friend who is a very talented and creative musician and visual artist, but he couldn't do mathematics for the life of him. He finally started to get it towards the latter half of senior year, but he had no interest in it. Perhaps this student is like him.

Either way, he needs to learn the material to get through his testing. You shouldn't totally drop trying to get him to fully understand the material, but if he's resisting there is nothing you can really do. Also, to the OP, are you certain that he understands your explanations? Can he reproduce them later?

 

[abelgalois]

Exactly. I was taught math by being spoon fed formulas. Truth of the matter is, I never learned WHY the quadratic equation or the Pythagorean theorem works. I was taught the Pythagorean theorem as a^2=b^2+c^2, and after I googled it and told my teacher, she told me that I was wrong and that the Greeks came up with the formula. That teacher was probably the best teacher I'd had, since she taught me to never trust anything that a math teacher says. If I ever had a question on anything in the book, I'd go straight to google. ^_^

I taught him the distance formula the other day, but instead of the formula, we first talked about the area of a triangle using the Pythagorean theorem. I tried giving a little talk and a picture of the simplest proof, but he wasn't too interested. He did learn the formula for it :/. But he now knows the reasoning behind the distance formula.

This is such a good point. There's a reason why it's called spoon feeding. You're stuffing crap down my throat. My arms are flailing, I'm hyperventilating, I clearly don't want it! I absolutely hhhaatedd memorizing theorems and plugging them into solve mind numbingly repetitive, trivial exercises. In fact, I can pinpoint the SINGLE pleasurable moment I had learning math in school. It was learning not THAT zero divided a number equals zero but a number divided by zero equals "unidentified", but learning WHY it was so. The simple, elegant proof behind it. I was so excited when I pulled out my calculator to check what sort of answer it would yield if I had entered 8 / 0. And sure enough an error sign popped up and I was ecstatic.

I reaaaallly wish I had picked up "Geometry" by Harold Jacobs that day.

And if the OP is still looking inspiration, someone had suggested this book in another thread:

"Introducing Mathematics"

https://www.amazon.com/dp/1840466375/?tag=pfamazon01-20

The purpose behind this book is not to teach math but to inspire some sort of purpose for learning math. Which is probably the single most important (And neglected) lesson a teacher can teach his student.

This book doesn't tutor you in mathematics so if that is what you want then go elsewhere now.

If you are looking to learn mathematics without a good cause then I would say that you better have the attention span to learn something absolutely mundane if you don't have a reason for it. A reason to learn mathematics is as vital to grasping mathematics as our brain needing a spinal cord to work.