Tutoring someone who hates math

[Null_]

Tutoring someone who "hates math"

I just graduated from high school and have landed a job tutoring a 15-year old boy in Algebra 1. Some things in Algebra I just understand, and it's difficult for me to find alternative ways to explain them when he doesn't get it. Ex: 3x+5=10, solve for x. He sometimes gets these and sometimes doesn't. Factoring is also difficult for him to grasp. I've gone through how it's really the same equation as the binomial (we're stuck on binomial factoring for now), but it doesn't always work.

I want him to see the joy I find in math. Honestly, when doing problems such as the ones we're going over now, I found myself bored (I was 12-13 however). His mom wants me to stick to the curriculum, so I can't just show him the fun stuff.

Any advice about how to make it more interesting? I want to introduce him to Asimov on Numbers, one of my first favorite math books; however, his father is a pastor and doesn't appreciate Asimov. It's an interesting situation, to say the least. He likes reading, so is something like Newton's Principia too dense for one struggling in basic Alg.?

I tutor for 1-1.5 hours 3 times a week. I've thought about doing 1 hour of the mandatory stuff, then the last 15 minutes introducing something by a famous mathematician or a physics type problem that uses Algebra. He keeps asking "when will I ever need to know this?"


I hope to make him appreciate, if not love, math before I leave for college in August.

 

[Klockan3]

The most important thing to know when you teach maths is that what's fun to you doesn't have to be fun to him. You can't make anyone love maths.

Now, even though you found this stuff really boring when you were his age it doesn't mean that you shouldn't teach it to him now, he mos likely have a problem learning it so focus on teaching that. People just like you have tried to get people to love their subject for as long as the subjects have existed, but you can't make people love everything.

The best thing you can do is to be a great inspiration, show that these problems aren't really hard but don't say it, also the worst thing you can do is to point out that it is boring since he already knows that and you just makes it harder for him. He really needs to learn this and the best you can do for him is to get him to like it more.

Elementary algebra is really interesting by the way, manipulating equations is an extremely powerful tool which is used literary everywhere and is one of the most important stepping stones towards really understanding maths. Many have problems with it, you might not understand why they have problems with it but they do.

For example, 3x+5=10, how do you solve this? Well, we know that both sides of a "=" are the same thing so if we do the same to both sides they must still be equal. For example if we subtract 5 from both sides we got 3x=5 then we just divide by 3 on both sides and we got x=5/3.

Things like this, explain why the maths is logical! Maths is not just a set of random rules made up to make life hard for students, many of them still thinks that. Making them see the logic is the first step towards making them appreciate maths. Also until they understand or appreciate elementary things like this neven show them more abstract and advanced things, it will only turn them off more.

 

[zhermes]

Really appreciate your passion and strive to help this kid, kudos.

I think the principia would be WAY too much for him. I've been tutoring kids in math/science for a good while now, and one of the things I'm (still) learning is the effectiveness of subtlety. Is easy to do the exact same problems, with a simple/interesting story behind it: how fast to fire a projectile to go ______ distance, how much to sell _____ for to break even after costs, how fast is a car going if it _______ etc etc.
Often when the student gets a better foundation about where the problems come from, and how they fit into the real world--they become much more manageable and appealing to solve. Also, never forget that once a type of problem starts getting easier for kids--it usually becomes more enjoyable, which is good encouragement for you to push the repetition (which is key).

Never give up.

 

[kramer733]

I hope to make him appreciate, if not love, math before I leave for college in August.[/B]

When people say "when will i ever need this" I feel like taking them down and punching in the face and then breaking their arms. WHEN WILL YOU EVER NEED TO KNOW HOW WAR STARTED?. WhEN WILL YOU EVER NEED TO KNOW ANYTHING?!@ You don't actually need anything in life but it's sure as hell fun to do math (atleast for me)Also how i really started understanding math was when my friend told me "math is all about equivalency" And for some reason, everything in the math world clicked. I suddenly understood algebra a lot better.

 

[twofish-quant]

I want him to see the joy I find in math.

Don't bother.

You're main goal in this situation is to set things up so that he doesn't hate math more than he already does. He is probably interested in doing the absolute minimum that he can to pass the tests, and your tutoring should be focused toward that.

I tutor for 1-1.5 hours 3 times a week. I've thought about doing 1 hour of the mandatory stuff, then the last 15 minutes introducing something by a famous mathematician or a physics type problem that uses Algebra. He keeps asking "when will I ever need to know this?"

To be honest, he probably won't other than to pass some minimum test. If you know him well enough find out what he is interested in, and if you can then show him how math would be useful for him. If he is interested in sports betting, then show him how to calculate point spreads.

Other than that, you might want to make math intentionally boring. What I find with people with low math skills and interest, is that drill and cookbook teaching works best for them.

I hope to make him appreciate, if not love, math before I leave for college in August.

You have to realize that you are not that important in his life. If he lives in a social environment that doesn't value math, then there is not that much that you can do. Ultimately, he is old enough to make some decisions in his life, and if he hates math, you have to respect that.

 

[snipez90]

When people say "when will i ever need this" I feel like taking them down and punching in the face and then breaking their arms. WHEN WILL YOU EVER NEED TO KNOW HOW WAR STARTED?. WhEN WILL YOU EVER NEED TO KNOW ANYTHING?!@ You don't actually need anything in life but it's sure as hell fun to do math (atleast for me)


Also how i really started understanding math was when my friend told me "math is all about equivalency" And for some reason, everything in the math world clicked. I suddenly understood algebra a lot better.

Dude that is kind of unnecessary. "When will i ever need this" is a perfectly legitimate question. 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). Even math majors ask the question, e.g., I asked myself when I will ever need a good deal of abstract algebra. It's not fun for me, which probably explains why I'm making a lot more progress studying complex analysis right now. Obviously abstract algebra is useful if I plan on studying certain disciplines in mathematics, but I'll still consider the question and hopefully someone will come along and give me a good answer (this is probably a terrible example). Also solving lots of linear equations is not fun as hell.

Also I think only an algebraist might say something along the lines of "math is all about equivalency". Personally, I do not particularly care for equivalency or equality or related junk. I like inequalities though.

 

[Dickfore]

I just graduated from high school and have landed a job tutoring a 15-year old boy in Algebra 1. Some things in Algebra I just understand, and it's difficult for me to find alternative ways to explain them when he doesn't get it. Ex: 3x+5=10, solve for x. He sometimes gets these and sometimes doesn't. Factoring is also difficult for him to grasp. I've gone through how it's really the same equation as the binomial (we're stuck on binomial factoring for now), but it doesn't always work.

I want him to see the joy I find in math. Honestly, when doing problems such as the ones we're going over now, I found myself bored (I was 12-13 however). His mom wants me to stick to the curriculum, so I can't just show him the fun stuff.

Any advice about how to make it more interesting? I want to introduce him to Asimov on Numbers, one of my first favorite math books; however, his father is a pastor and doesn't appreciate Asimov. It's an interesting situation, to say the least. He likes reading, so is something like Newton's Principia too dense for one struggling in basic Alg.?

I tutor for 1-1.5 hours 3 times a week. I've thought about doing 1 hour of the mandatory stuff, then the last 15 minutes introducing something by a famous mathematician or a physics type problem that uses Algebra. He keeps asking "when will I ever need to know this?"


I hope to make him appreciate, if not love, math before I leave for college in August.

Maybe you should consider giving up tutoring as a source of income, since you are probably not good at it.

 

[Angry Citizen]

Just wait it out. Teach him fundamentals. Drill the following mantra into his head, every single time you meet him, and every single time you leave: "What thou doest to one side, thou doest to another." That, fundamentally, is the biggest, most important concept anyone could ever know in algebra. Another is teaching 'find x' as nothing more than eliminating numbers. Take 3x+5=10, for instance. It's all about finding x. First you zap the 5 (again, from both sides), then you zap the 3. You do this through inverse operations. Knowing that everything has an inverse is extremely important in algebra, as you already know. Drill it into his head that addition's inverse is subtraction, and division's is multiplication, and logarithm's is exponential, and so on and so forth. Algebra, in my opinion, comes down to those two concepts. Rational functions, exponential functions, inverse functions, polynomial functions... much of it can be known with a thorough knowledge of those two pillars. It won't help you solve his factoring problems (that one just takes practice), but it'll solve his 3x+5 problems (and to be honest, I don't see why he's learning factorization if he can't solve 3x+5).

 

[Klockan3]

Also I think only an algebraist might say something along the lines of "math is all about equivalency". Personally, I do not particularly care for equivalency or equality or related junk. I like inequalities though.

Complex analysis is still quite soft maths and really that course don't got much to do with any of the pure maths courses. See how much you like it after real analysis, abstract algebra is one of the more applicable of the pure maths subjects and is also much cleaner than real analysis which is mostly a chore consisting of writing out a ton of definitions.

 

[Null_]

Thanks for the reality check everyone. I personally never really liked math until I got to Calculus because all we did were textbook examples, and I had hoped that he would "turn out" the same way. He's homeschooled and neither of his parents are good at math, which is why they sought help. He had trouble with some things, like adding and subtracting negative values, that we were able to fix the first day...he had just been told the rules but had never thought about them.

I'll focus more on making sure that he learns the material this summer, rather than trying to show him the beauty of it all. That's not to say I won't still try...I'm going to do one problem a week that is interesting and complex.



He's never used a graphing calculator before. When I showed him a graph on mine, he was stunned that it could graph. I remember learning how to use TI-83s in Algebra 1. He doesn't have one of his own, and I really don't want to ask his mom to get one, even if they're cheap off ebay. Should I spend some time going over basic calculator tips or teach it like Newton learned it?

 

[snipez90]

Complex analysis is still quite soft maths and really that course don't got much to do with any of the pure maths courses. See how much you like it after real analysis, abstract algebra is one of the more applicable of the pure maths subjects and is also much cleaner than real analysis which is mostly a chore consisting of writing out a ton of definitions.

Um, how is complex analysis soft maths, and I'm pretty sure it has a lot do with pure math courses. I have taken two yearlong sequences in real analysis, which included basic real analysis, measure and integration, and functional analysis. I'm pretty sure complex analysis has its own unique challenges and deep results, even though I am still learning the basics such as standard results in complex integration.

The fact that an injective polynomial map from C^n to C^n is also surjective is probably an example of a nontrivial result that has a complex-analytic approach. The easiest example of the applicability of complex analysis is the evaluation of definite integrals, which is of obvious interest to mathematicians as well as people working in applied disciplines. Complex analysis is also used extensively in analytic number theory, and has ties to Fourier analysis, algebraic geometry, topology, dynamics, to name just a few more.

I'm not sure what you mean by abstract algebra is "cleaner". That doesn't really motivate me to study abstract algebraic structures. I know that understanding the basic algebraic structure you're dealing with is important, but I've never needed to know an extensive list of properties about the structure to do the analysis.

 

[Mark44]

Really appreciate your passion and strive to help this kid, kudos.

I think the principia would be WAY too much for him. I've been tutoring kids in math/science for a good while now, and one of the things I'm (still) learning is the effectiveness of subtlety. Is easy to do the exact same problems, with a simple/interesting story behind it: how fast to fire a projectile to go ______ distance, how much to sell _____ for to break even after costs, how fast is a car going if it _______ etc etc.
Often when the student gets a better foundation about where the problems come from, and how they fit into the real world--they become much more manageable and appealing to solve. Also, never forget that once a type of problem starts getting easier for kids--it usually becomes more enjoyable, which is good encouragement for you to push the repetition (which is key).

Never give up.

Here's one in the same vein of distance, rate, and time. If I drive a car up a one-mile long hill at 30 mph, how fast to I need to drive back down the hill to average 60 mph for the entire trip? There's a very obvious (but incorrect) answer, and then there's the correct answer.

 

[Mathnomalous]

90mph. May I get my participation star?

 

[twofish-quant]

Maybe you should consider giving up tutoring as a source of income, since you are probably not good at it.

No one is good at something when they first start doing it. Math teaching is an extremely difficult skill, and the OP has just learned an important lesson about why math teaching is difficult. Sometimes people who are extremely gifted at math make lousy math teachers because they just have difficulty putting themselves in the shoes of the student.

Teaching is easy if you have good students. If you have a super-enthusiatic student that comes from an environment that is supportive, then teaching them is rather simple. If you just give them a reading list, they'll often do just fine. The difficulty is that people that are super-enthusiatic about math make up a very, very small fraction of the general population, and most of the time, you end up teaching someone that is indifferent toward math or at times hostile toward it.

 

[Klockan3]

I know that understanding the basic algebraic structure you're dealing with is important, but I've never needed to know an extensive list of properties about the structure to do the analysis.

You never need the long list of properties about the analytical structure to do any applied integration, transforms or differential equations either, just the basics taught in the standard courses. Abstract algebra is used a lot in higher level physics since a lot of non standard algebraic structures appears everywhere while the analytical things which are used are all pretty standard analysis stuff.

I am not saying that either thing is better, just that what you do in the more pure analysis courses is no more applicable than what you do in abstract algebra since almost the applicable parts of analysis are already taught in the basic courses while algebra goes mostly unexplored until the real courses.

 

[Dickfore]

No one is good at something when they first start doing it. Math teaching is an extremely difficult skill, and the OP has just learned an important lesson about why math teaching is difficult. Sometimes people who are extremely gifted at math make lousy math teachers because they just have difficulty putting themselves in the shoes of the student.

Teaching is easy if you have good students. If you have a super-enthusiatic student that comes from an environment that is supportive, then teaching them is rather simple. If you just give them a reading list, they'll often do just fine. The difficulty is that people that are super-enthusiatic about math make up a very, very small fraction of the general population, and most of the time, you end up teaching someone that is indifferent toward math or at times hostile toward it.

The reason why he isn't good at it has nothing to do with him being a novice in the didactic method, but more so because he himself does not grasp the material well enough. He is eager to speak to him about 'applications' of the learned math skills to 'real-life situations' to a person who finds it hard to factor binomials. Regular students (not home schooled) learn this when they are in seventh grade and this boy is 15 making him equivalent to finished ninth grade. The point is, in order to teach a person to run, you must make them learn to walk first :)

On a side note, people who ask where they will apply their knowledge in math are dumb at best and probably their knowledge is so limited that it will never find any real application beyond ephemeric arithmetics at the local grocery store. Math is a language with which the Laws of Nature are written. The problem is, as we discover new physical laws, we find an ever increasing need to refine and extend our language - math. Therefore, research in other sciences goes hand in hand with research in pure math. Mathematicians have found that the rules in mathematics are a topic of research on their own and have elevated it to the level of a science - Pure Mathematics. But, for the student, it is best if he or she adopts an attitude of learning a new language, at least at the level of High School math. You don't ask why French grammar is different from English and search for 'alternative' explanations of the rules. You just learn it as all the French people had done it. Surely you can't be that different from an average Frenchman. Similarly, the math that is learned in High School is known to all generations and everywhere throughout the world. If everyone can learn how to find the GCD of two monomials and take it out as a common factor, then surely you can also do it.

 

[hadsed]

Dickforce I don't think people who ask the applications of math are all dumb. I certainly didn't know the applications, atleast the scope of it, of math until I used math to figure things out in math class.. a la physics class. That was a very eye opening year for me, and I'm sure it is for many people.

 

[Dickfore]

Dickforce I don't think people who ask the applications of math are all dumb. I certainly didn't know the applications...

This doesn't mean anything.

 

[hadsed]

So you've known the applications of math completely the entire time you've ever been learning it?

You are a fool.

 

[twofish-quant]

The reason why he isn't good at it has nothing to do with him being a novice in the didactic method, but more so because he himself does not grasp the material well enough.

I don't see any sign of that. His algebra seems to be good enough to tutor algebra.

Also the question is not whether he is good or not at something. If he was a perfect math tutor, he wouldn't be asking for help on this forum. The education questions is how do you turn someone that is bad at something into someone that is good or at least less bad at it.

People that are excellent at math often turn out to be horrible math teachers, because they don't have the patience or empathy to deal with someone that is just not good at math or who is extremely unmotivated.

On a side note, people who ask where they will apply their knowledge in math are dumb at best and probably their knowledge is so limited that it will never find any real application beyond ephemeric arithmetics at the local grocery store.

That may will be true, but they still have to be taught math, for various reasons. Teaching good students is easy (which is why a large number of professors at MIT just suck at classroom instruction). It's getting good performance out of students who are less than ideal that requires a huge amount of effort and patience.

Teaching someone that is "smart" is relatively easy. The true test of a teacher is what they can do with people that are "dumb."

 

[Dickfore]

Both of the replies missed the point completely. You may be a smart person, but not know math. This is not the issue. The issue is that a person who doubts the applicability of math is likely a dumb person AND has a poor knowledge in it.

 

[hadsed]

Wasn't the kid homeschooled.. by parents who aren't good at math? It's not unreasonable to think that he just wasn't taught it well enough. This may also contribute to the poor knowledge aspect of this..

I can't see how it makes sense at all to find it necessary to correlate the ability of a student to learn math versus his knowledge of its applicability. They are two different things.

 

[Dickfore]

Wasn't the kid homeschooled.. by parents who aren't good at math? It's not unreasonable to think that he just wasn't taught it well enough. This may also contribute to the poor knowledge aspect of this..

I can't see how it makes sense at all to find it necessary to correlate the ability of a student to learn math versus his knowledge of its applicability. They are two different things.

Where did I mention the student's ability to learn math?

 

[hadsed]

That is implied by his being 'dumb', as you're describing him unless you mean something else. In that case, please clarify what exactly you're saying here.

 

[Dickfore]

So, according to your logic, a person who is able to learn math is smart.

 

[hadsed]

It doesn't quite work that way as well as it works in the reverse order (an intelligent person is likely able to learn math [well]).

What are you even trying to argue?

 

[Dickfore]

It doesn't quite work that way as well as it works in the reverse order (an intelligent person is likely able to learn math [well]).

What are you even trying to argue?

Then, your previous argument is a non-sequitur. Please do not change the subject of discussion.

 

[hadsed]

It is actually your argument; a person is dumb because he cannot understand math, perhaps for reasons that are beyond his control. That is a very big assumption to make. You ignore other possible reasons and simply assume that he's an idiot because he can't 'get' math. Not only that, but learning math very well isn't a requirement to being an intelligent individual.

My previous argument is also based on certain assumptions, just like yours. Why you feel the need to try and break it down logically, I'm not quite sure since we're dealing with situations that can't really be described universally. If he was in public school and everyone else in his class was doing well, then you'd have license to generalize a bit.

No one is changing the discussion. You are making baseless assumptions and you haven't made any attempts to explain yourself. You took a very immature potshot at my intelligence (something you know absolutely nothing about) when I was providing some anecdotal evidence to try to make my point clear. I wouldn't be surprised if you turned out to be just another arrogant high school student who thinks he's good at math. Regardless of whether you are or not, that's exactly how you sound like at the moment.

 

[Dickfore]

It is actually your argument; a person is dumb because he cannot understand math,

Here, let me show you. You used the term 'imply in a previous post. Your interpretation of my argument is:

If a person cannot learn math, then they are dumb.

By contraposition ([itex](p \Rightarrow q) \Leftrightarrow \neg q \Rightarrow \neg p), this statement is logically equivalent to:

If a person is not dumb, they can understand math.

If a person is smart, then they are not dumb (since being dumb is a disparate term to being smart).

By hypothetical sylogism:

If a person is smart, then they can understand math. (Understand = being able to learn).

This is what I asked you. But, you said it does not work that way. You said that:

If a person is smart then they are likely to be able to learn math.

This statement is in no logical connection with the statement that you used to interpret my words. This is why I said your interpretation of my claims is a non-sequitur. And, you have changed the thesis of your argument several times. Therefore, I find it impossible to debate with you.

 

[DrRocket]

I just graduated from high school and have landed a job tutoring a 15-year old boy in Algebra 1. Some things in Algebra I just understand, and it's difficult for me to find alternative ways to explain them when he doesn't get it. Ex: 3x+5=10, solve for x. He sometimes gets these and sometimes doesn't. Factoring is also difficult for him to grasp. I've gone through how it's really the same equation as the binomial (we're stuck on binomial factoring for now), but it doesn't always work.

I want him to see the joy I find in math. Honestly, when doing problems such as the ones we're going over now, I found myself bored (I was 12-13 however). His mom wants me to stick to the curriculum, so I can't just show him the fun stuff.

Any advice about how to make it more interesting? I want to introduce him to Asimov on Numbers, one of my first favorite math books; however, his father is a pastor and doesn't appreciate Asimov. It's an interesting situation, to say the least. He likes reading, so is something like Newton's Principia too dense for one struggling in basic Alg.?

I tutor for 1-1.5 hours 3 times a week. I've thought about doing 1 hour of the mandatory stuff, then the last 15 minutes introducing something by a famous mathematician or a physics type problem that uses Algebra. He keeps asking "when will I ever need to know this?"


I hope to make him appreciate, if not love, math before I leave for college in August.

You have a number of problems.

1. You are probably a good math student and have never seen the work of a mediocre student. It is worse than you imagine.

2. You are not and experienced instructor and you have the most difficult possible student -- one who is demonstrably having trouble.

3. A great deal of the problem with the learning of mathematics is a mind set that is simply not conducive to learning mathematics. Quite a bit of that comes from the home environment. In this case you have one in which the parents are clearly not themselves comfortable with mathematics, or else they would be doing this themselves. In addition you have the mother dictating to you how to do the job that she herself is unable to do.

4. If the kid does not care about mathematics it is unlikely that you will be able to get him to care. Not everyone does, or for that matter necessarily should, but without interest and curiosity about the subject it is just a bunch of rote -- and nothing could be more boring.

The cards are stacked against you, but that is not your fault.

This son of a preacher may make a great preacher but he is not likely to be a mathematician. (Dont' take this as a statement about sons of preachers. David Vogan is a son of a preacher and they don't make any better mathematicians.)

 

[Dickfore]

Bernhard Riemann was also a preacher's son. Apparently, he seemed to understand math.

 

[snipez90]

You never need the long list of properties about the analytical structure to do any applied integration, transforms or differential equations either, just the basics taught in the standard courses. Abstract algebra is used a lot in higher level physics since a lot of non standard algebraic structures appears everywhere while the analytical things which are used are all pretty standard analysis stuff.

I am not saying that either thing is better, just that what you do in the more pure analysis courses is no more applicable than what you do in abstract algebra since almost the applicable parts of analysis are already taught in the basic courses while algebra goes mostly unexplored until the real courses.

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.

 

[Klockan3]

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.

Ah, but the main math fields have many subfields and you are now mostly talking about the subfields to analysis.
Here is one for algebra:
http://en.wikipedia.org/wiki/Algebraic_geometry
The deal is that as soon as you got a function or other kind of object which looks like an element of some algebraic structure you can gather a ton of properties about it just by knowing how that structure behaves. Therefore abstract algebra has its uses almost everywhere in maths.

Also topology can be approached in different ways, historically it was approached using algebra while as it is now most approaches it using analysis.

If you haven't taken any abstract algebra course I'd recommend you to take at least the first course in it since it is one of the main fields of maths and most I know who likes maths likes it.

 

[Noxide]

Making it "fun" and looking for applications ruins math. There are some techniques that must be practiced. Make sure your student knows how to perform addition and multiplication of real numbers. Teach him algebra from the ground up. Define everything, no matter how small. If he still can't do it, then there is something wrong with him (i.e. learning disability). All he has to do is recall a definition and apply it. That's all math is. Definition/theorem, application of definition/theorem, result. It's that simple.

 

[Klockan3]

Making it "fun" and looking for applications ruins math. There are some techniques that must be practiced.

Looking as maths as just a bunch of axions, theorems and definitions might get you exam results and some publications but that is not what maths is founded upon nor what it is about in my opinion. Maths is both about finding implications given a logic set and finding/mapping new logic sets, the later is totally ignored with your way. You need to understand why the ones they show you are built like they are, that is the essence of maths.