Tutoring someone who hates math

[yossell]

There is no definitive way to make maths interesting. Why? Because different people find beauty and excitement in different aspects. Some love the abstract general principle that unifies; others don't see the point unless there's a concrete application; others respond to the pure formalism; others love crazy and wild and mind-bending concepts. As a personal tutor, you should try and find out what he best responds to and tailor it to him. It's not easy, but as your experience grows, you'll get better at recognising what works for an individual.

 

[Agent M27]

I came from a simillar backround as the OP's tutoree aside frrom the home schooled bit. I hated math and didn't really have a support system at home that inspired me to strive for higher education. I hated math all the way up until I was 24 when I began a degree in physics. I will say that it is most likely not your ability to tutor the young man, but rather his lack of maturity. Sure the question "When will I ever need this?" is a valid one, but thinking of life in terms of why do I need to do this or when will I need to use this is just plain inmaturity. The truth about life is that we will all have to do things we don't particularly like or even hate, but we can't snub our nose at them because of such, you should drive this point home without sounding like a dictator. I remember what sparked my interest in math was when I realized the logic behind it, and how simplistic, relatively speaking, the laws of the world are written. Try stressing this, as this is probably what makes math interesting and fun for most people. Good luck and don't give up. I have taken on a simillar project with a friend of mine who is 28 going back to CC, and I will be damned if he won't know algebra by the end of the fall, even as discouraging as it may get, just keep pushing. I am actually having the same problem, "finding x" as you are with your tutoree.

Joe

 

[DrRocket]

Maybe I should have clarified. I am mostly interested in pure math applications, which is why I disputed the notion that complex analysis did not have much to do with other pure math courses. Specifically I wanted to know what you can do with the tools of abstract algebra in other areas of pure mathematics. For instance, I've only officially taken real analysis courses, but basic real-analytic tools have been useful for me in understanding topology, probability theory, and complex analysis (this last one is kind of cheap, analysis is useful for more analysis). Of course laplace transforms and differential equations are all mathematically interesting in their own right, so the basic analytic tools can go a long way in better understanding these topics.

Reasonably, I understand that to gain an appreciation for the relevant tools that algebra provides, I probably have to actually know some algebra. However, I feel that some algebraists tend to use their tools just to reach an intellectual endpoint in the subject itself, say in the classification of finite simple groups. On the other hand, I think very few people study measure theory for its own sake. This would seem like an esoteric endeavor since measure theory has various uses in pure mathematics. Hopefully this example doesn't make my position less clear.

Anyways, sorry for somewhat hijacking the thread. I think the OP left though.

Mathematics is interconnected. Algebra, topology, and analysis are note separate subjects.

Try learning some functional analysis -- you will find that the study of topological vector spaces and Banach algebras requires all of the above simultaneously. Fourier analysis on locally compact abelian groups is an excellent example of just such an application.

 

[Null_]

Wow, I come back after a few days and there's a whole argument/discussion going on. :P

Thanks for all of the replies. I'll be sorting through them and thinking of ideas within the next few days.

So far I've just been working with concepts. We've gone through a few review tests of basic arithmetic..trying to reinforce the properties of #s, basically. I do think this is helping me to understand math better (some of you were correct...I am a "good" math student, but now I'm having to think for myself numerous ways to explain a single concept..i.e. subtracting negatives. I'm trying to be patient and teach him the logic behind it, rather than simply telling him to memorize a formula. Another i.e. I show him that the distance formula (which he'd never heard of before) can be gotten from the Pythagorean theorem (which he'd also never heard of!).

It's really hard to get a grasp of what he already knows...I hate to say it, but his parents did a HORRIBLE job of getting the foundation set. He's catching on quickly, I suppose for his level. I would say he's average in intelligence, but being brought up in the whole church setting kind of made math and science seem less important to him, for some reason. Funny thing, I don't even go to church and had only met the mother a few times at soccer games when she asked me to tutor...I couldn't refuse the $$. :)I know I'm starting at a disadvantage. But hopefully I'll at least get him to a basic understanding of it...I think I'll have to spend more time on pre-alegbra than alg...can't play Moonlight Sonata before you can play Hot Cross Buns.
On the plus side, I found out that he's somewhat interested in computers. I plan to take "advantage" of this and teach him binary. Shouldn't take but a few minutes and it'll help him understand the basis of our # system. I've tried throwing little pieces of history in when introducting a new concept too...like the discovery of 0. He doesn't seem to care about that though, so I'm going to stop.

All in all, I know I can't be a teacher. I don't have the patience. However, this review of Algebra has been great for me so far, and it's helped me see from the eyes of a teacher. I think tutoring could be a good part time job for me during college. Hopefully this will help me in my math classes next year...surely beats flipping burgers at McDonalds for a summer job. :)

 

[saim_]

Every averagely intelligent student should be able to "appreciate" math, at least, given the right guidance. I'm not doubting your sincerity towards teaching this kid, but, as a student looking forward to college, you cannot devote yourself to the kid as a good teacher should and this is main problem. For a good educator (not you!) if student is not learning or doesn't like the subject, its the teacher who is at fault and who is not understanding how to convey the concepts. At this age you cannot hold the kid responsible for not seeing the concepts. At this point factorizing is just as complex for him as abstract algebra is for you, and maybe just as abstract if not more so! Don't be frustrated with him, he is doing what he is supposed to do, being a normal kid, hating math :D Its your JOB to change that... It might not be practically correct to put all the blame on teacher but in principle this is correct... all blame IS supposed to be on the teacher and parents.

 

[DrRocket]

It might not be practically correct to put all the blame on teacher but in principle this is correct... all blame IS supposed to be on the teacher and parents.

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 responsibiliy 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.

 

[Null_]

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 responsibiliy 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.

My feelings exactly. I had a HORRIBLE geometry teacher, and I blamed her for ~2 years for me hating the subject. It wasn't until I got to calculus that I started taking responsibility for my own learning...and it just so happened that that's when I really started liking and understanding math. [When I say horrible, I mean she was pregnant for the first week of class then went on maternity leave for the rest of the semester and we were left with some crazy lady sub.]

 

[khemist]

I would just like to reinforce the statements made in the last two posts. Until the desire to know the material comes from the student, he will never be able to fully understand the subject matter. However, like DrRocket said, it is important for the teacher to help "plant seeds of education" into the student's mind, hopefully giving him the desire to actually learn the material. Most of the time that "seed" is the grade, though the most successful students care not about the grade, for they realize understanding the material and knowing it through and through will earn one their grade.

It is a common misconception that grades are given. While It may appear obvious, the two posters above me both reiterate the difficulty in actually knowing that that means; the teacher is not at fault for any laziness done by the student (it took me quite a while to understand that as well... Longer than I would have liked )

 

[Bohrok]

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 responsibiliy 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.

That's true, to an extent. There are some students who are so good that, no matter how horrible the teacher is, they'll still get an A. But for the rest of the students, many need more work. Some spend many extra hours studying on their own and truly want to understand it (so they can get passing grades, but that's good motivation right there), but they still can't hack it without some help from someone with patience and who's willing to go through each step when the teacher and textbook just aren't any help.

I've been tutoring introductory chemistry for over 2 years at a community college, and the teacher is horrible. He has a reputation there and even at some other local colleges and universities! (If they know you passed his class with a C, some of them will be fine with it because they know he's so hard.) Some students come in very positive and don't say anything bad about him, but eventually they break down and really dislike him.

I hear a lot of things like "When will I need this in the emergency room or anywhere else in nursing?" Fortunately they realize it's just part of the system to get a degree in nursing and they just persevere through it, knowing that if they don't pass it now, they'll just have to take it again. I do know that when it comes to math, some people I've helped just can't or won't change their opinions on it. If they say "I hate this," I'll tell them that I've had to do stuff that I hate too (read English, social sciences,...).

One thing I've heard another experienced tutor tell his students is that even though there are a lot of rules in math, they never change. That's one of the things that's best about math.
I'd say more but my time is short right now...

 

[dulrich]

That's true, to an extent. There are some students who are so good that, no matter how horrible the teacher is, they'll still get an A. But for the rest of the students, many need more work. Some spend many extra hours studying on their own and truly want to understand it (so they can get passing grades, but that's good motivation right there), but they still can't hack it without some help from someone with patience and who's willing to go through each step when the teacher and textbook just aren't any help.

I was thinking the same thing. It's both, right? Both the student and the teacher bring something to the table -- 80% student, 20% teacher. Certainly there are good teachers and bad teachers. Just do your best. You've got some advantages: closer in age, one-on-one interaction. Your thoughts about customizing the material are great. You will find it is 100 times more difficult than you thought. But you will get a lot out of the experience too. You may get more out of it than your student! You seem to have the right attitude about it. I would definitely encourage you to continue tutoring in college. A little bit of cash on side doesn't hurt either!

 

[DrRocket]

I was thinking the same thing. It's both, right? Both the student and the teacher bring something to the table -- 80% student, 20% teacher. Certainly there are good teachers and bad teachers. Just do your best. You've got some advantages: closer in age, one-on-one interaction. Your thoughts about customizing the material are great. You will find it is 100 times more difficult than you thought. But you will get a lot out of the experience too. You may get more out of it than your student! You seem to have the right attitude about it. I would definitely encourage you to continue tutoring in college. A little bit of cash on side doesn't hurt either!

Nope.

As soon as you assign 20% of the responsibiilty to someone other than the student, you have relieved the student of the responsibility for learning. A teacher can help and facilitate, but a teacher is not necessary to the process. A student is necessary.

100%, not 80% or even 99.95%, of the responsibility lies with the student, and the sooner a student accepts this the more likely is the student to succeed at learninng.

There may come a point at which it is necessary for one to learn without benefit of any teacher at all, or with minimal input. That is quite common when one is doing the research for a PhD -- the advisor is usually just a sounding board, and other graduate students often also serve as a sounding board, just as do colleagues after one has obtained a final degree. The situation is not much different at an undergraduate or high school level -- just think about study groups, which can be very effective. One good way to learn a subject is to teach it to someone else. It is not uncommon for professors to teach classes that cover material that they did not encountere themselves in any formal class.

The number one lesson to be learned is that learning is your responsibility, 100%, and not the responsibility of anyone else. The second lesson to be learned is that you are capable of fulfilling that responsibility.

None of this meant to imply that there are not some instructors who are not better received than others, especially by individual students. But there is not a very good correlation between well-liked professors and effective professors. In fact some the more popular and "easier" professors tend to be well-liked by the poorer students and not so much by the better students.

 

[dulrich]

Why have teachers at all? Of course everything learned by the student is a product of his/her effort. But the teacher acts as a catalyst ... speeds up the process. Helps you avoid pitfalls. Puts together connection you might miss. I don't like the idea of absolving the teacher from any responsibility to teach!

BTW, I completely agree that student "popularity" is a horrible way to judge good vs. bad instructors. Students are often in the worst place to make such a judgement (for a variety of reasons).

 

[DrRocket]

Why have teachers at all? Of course everything learned by the student is a product of his/her effort. But the teacher acts as a catalyst ... speeds up the process. Helps you avoid pitfalls. Puts together connection you might miss. I don't like the idea of absolving the teacher from any responsibility to teach!

BTW, I completely agree that student "popularity" is a horrible way to judge good vs. bad instructors. Students are often in the worst place to make such a judgement (for a variety of reasons).

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.

Teaching is not really measurable. Learning is.

I can agree that the teacher can act as a catalyst -- though I prefer the character the role as a "facilitator".

I doubt that teacher can help a student avoid pitfalls. But perhaps a teacher can help the student extricate himself from the pit a bit quicker -- falling into pitfalls is part of the learning process and should not be avoided.

But the point remains that the responsibility lies squarely on the student. 100%. This is important.

The very most enjoyable classes that I ever took involved nearly 0 active participation by the professor. The professor organized the material to be covered, and we did the rest of the work -- including all the presentations.

 

[Null_]

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/

 

[dulrich]

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.

Teaching is not really measurable. Learning is.

I can agree that the teacher can act as a catalyst -- though I prefer the character the role as a "facilitator".

I doubt that teacher can help a student avoid pitfalls. But perhaps a teacher can help the student extricate himself from the pit a bit quicker -- falling into pitfalls is part of the learning process and should not be avoided.

But the point remains that the responsibility lies squarely on the student. 100%. This is important.

I agree with all of this, DrRocket -- which makes me think we are stuck on semantics. I would argue that the statement in bold is the definition of teaching.

My high school experience was similar to yours, Null_. And I think you nailed it on the head when you say

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.

Do that for your student and you'll do great.

The very most enjoyable classes that I ever took involved nearly 0 active participation by the professor. The professor organized the material to be covered, and we did the rest of the work -- including all the presentations.

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.

 

[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.