# Learning mathematics as if an absolute beginner?

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the epitome of evil. She would take any opportunity to yell and scream at me when I struggled to comprehend the problems given. She approached the kids in my class as if their struggling wasn't a result of a misunderstanding, but rather from a lack of discipline, one that she could solve by being some sort of mathematics drill sergeant. This was when I was a small child, which obviously left an impression on my mind that probably wouldn't have existed had I been older.

Now that I am older, however, I need mathematics. I also have a growing curiosity and interest for it. Right now, I am planning to move out of my parent's house and live elsewhere. However, I have a fear in the back of my mind that my understanding of mathematics is not sufficient enough to do all of this; to handle a job; to handle expenses; to handle day-to-day life. Even the idea of becoming a cashier and having to handle money frightens me into avoiding those jobs; which leaves me (having no formal education) with virtually no options for employment. It's pretty intimidating. I seem to have some problem grasping even the simplest mathematic questions. Come up to me and ask me "What's 8 + 6?" and my mind wanders for the answer as if blindfolded. I would probably resort to sticking my hands behind my back and counting it off on my fingers or counting one at a time in my head. This just doesn't seem normal.

I want to conquer my fear of mathematics and educate myself. I want to approach the field as an absolute beginner, and by that, I mean go back to the very basics and work my way up, no matter how reassured I am of my abilities at times. I know it's impossible to conquer the entire mathematic field, but I want to conquer what is necessary and then some. I need the bare minimum, though I want a sufficient understanding. Are there any approaches or, what I am specifically requesting, books or courses, that would allow me to to teach myself in such a manner?

Sorry for the history lesson and/or if this is not a legitimate question.

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@Kirva: I find your question difficult to answer. The part of mathematics that you learn at primary school, like e.g. what is $9*8$, is quite different from actual mathematics. Unfortunately, one can say that in general mathematics as taught at schools has not much to do with mathematics. "Proper mathematics" is like art, in that it requires creativity and thinking out of the box whereas maths at school is treated like learning recipes by heart and then applying them to boring "problems". I'm sorry if this doesn't anser your question. –  Rudy the Reindeer Feb 17 '11 at 15:28
@Kirva: one of my favourite essays related to this is Lockhart's lament: maa.org/devlin/LockhartsLament.pdf –  Rudy the Reindeer Feb 17 '11 at 15:30
It sounds like your problems are more serious than just not knowing mathematics. You may have what is known as in some circles as math anxiety, and this may not be a problem you can fix on your own. –  Qiaochu Yuan Feb 17 '11 at 15:34
+1 This is one of the best questions I've read on the Stack Exchange sites. It's brutally honest, well thought out, and portrays what I believe is probably a common issue with many people. Would vote up more than once if I could. –  JYelton Feb 17 '11 at 17:39
@Kirva: I think you should sue this teacher for wrecking your life. Psychological trauma inflicted by a teacher (!?) is something one should sue for. –  Rudy the Reindeer Feb 17 '11 at 22:08

This is a difficult question to answer, mainly because any advice must be very personal to be useful for you. I'll try anyway.

Before learning mathematics, one has to learn how to learn mathematics.

Concerning the contemporary school system, it simply does not do a good job at what it is supposed to do. The range of children who learn successfully from it, or rather in spite of it, is quite narrow. You simply fell through the cracks, as many others, but that does need to have any relation to your general ability to learn mathematics. (I once instructed someone who taught himself programming after dropping out of college. He was very capabable, though he lacked methods to learn efficiently.) You are simply outside the way too narrow scope of the school system.

Still, the best advice for learning mathematics is to find a good teacher, but these are very hard to come by, so that this advice may be useless. (That's basically the same advice as for learning to play the piano.)

Then, there is the issue that school does not even teach proper mathematics, only some nonsense that they label "mathematics" but which is better described as "rote arithmetics".

Two of the sins of the rote arithmetics as taught in school are the notions that 1) every problem has a definite answer and 2) that you should be able to come up with that answer instantly or you're stupid. Both are wrong. The book Thinking Mathematically dispels these myths and presents a proper way to learn mathematics. However, note that learning how to learn mathematics from a book is quite difficult. It is easy to miss the point, for instance by not doing the exercises. A good teacher would be preferable.

That said, "simple" questions like "what is 8+6" are also a matter of rote learning. This is something that can be learned in the school system at least, but again, it's equally easy to pass the school system and never learn how to do rote learning properly. Learning a foreign language, in particular vocabulary, is usually a good way to exercise rote learning.

Another sin of school teaching is 3) the notion that learning is no fun. It baffles me how the key ingredient to learning, fun, is entirely absent from the school system. (I don't know any mathematician who is doing mathematics for reasons other than that he/she loves it and that it's a lot of fun.) Fortunately, since you are motivated to learn mathematics by yourself, this should be no problem for you. Every moment of understanding is a tremendous amount of fun, and if you have enough of these moments in the beginning, you'll be hooked for life.

Concerning the process of learning, there is another problem that might or might not apply to you, namely the issue of genuine medical conditions that can inhibit learning. ("Inability to concentrate", undiagnosed food allergies, ...) However, given all the things above that can go wrong before that, I'm hesitant to put blame on medical conditions. Still, it may be worth keeping in mind, though personally, I'm not convinced that current treatment options actually help (and don't just accidentally fix some of the 3 problems mentioned above). In case you have a medical condition that can be fixed, fix it, otherwise you're kinda screwed anyway, though not necessarily when it comes to learning mathematics.

After these general but very important considerations of the process of learning itself, there is the problem of finding good materials for the actual mathematics. Fortunately, this is a much easier problem, largely solved by the videos from the KhanAcademy.

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A very helpful answer this is. By the way, the education system failure you're refering to is based on your experience in what country? –  Myself Feb 17 '11 at 17:28
I'm afraid it's a characteristic of many a country's eductional system. –  Raskolnikov Feb 17 '11 at 17:35
@Greg: +1 for a nice answer. To touch upon the point made about learning (and mathematics) being fun: I think my own experience (and possibly of many others) is that in school, I saw no purpose for some of the concepts in math, but later in life developed an appreciation that somehow evaded me in school. Now, I desire to learn more and find it fascinating. However, my lack of effort/interest in school has left me with somewhat of a knowledge gap which I will need to repair. –  JYelton Feb 17 '11 at 17:44
Another problem: In Canada, I've been retaught the same thing I learned in school the previous year, over and over. It's supposed to help those who forget remember. Only a small percentage of time is actually spent in learning new stuff. Of course, I'm talking about Elementary/Middle school, but I don't know how the non-AP/Honours Secondary school stuff is like. Since there is no definite record that a student has been taught something before, they reteach it for the few students who hadn't learned it before, setting back the rest of the class... (continued) –  Mateen Ulhaq Feb 17 '11 at 20:03
@Rasmus, Myself: I have personal experience with the school system in Germany, but it's pretty similar in most developed countries and nonexistent in most undeveloped countries. As for the evidence, take the OP, JYelton's comment, any school in a "bad" neighborhood. I have taught extracurricular math circles and it was depressing how much school has sucked out the students' desire to learn. It should be clear that points 1-3) are true, too. If anything, I'd like to see evidence that the school system does work as intended. –  Greg Graviton Feb 18 '11 at 8:31

A point to keep in mind throughout any studies, and ... if only it were truly possible... in hindsight, is that there is an extremely unfortunate tendency of schools to have "math teachers" who have more interest in "obedience" or "conformity" or "rule"... than in explaining to kids how mathematics can express useful things about the world.

We can understand this as yet-another weakness in the human species' psychology, but that doesn't make it any pleasanter for any individual subjected to a neurotic "teacher".

I think the first point, necessary for any thinking being, is to _TRUST_YOURSELF_. Any other principle leads to madness. Now, of course, even while trusting oneself, one does recognize that one might make mistakes. Ok. Not the end of the world!

Bang.

:)

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Tools: There are a few online resources for "teaching yourself" such as Khan Academy, which has a very helpful 'practice' feature.

Real Life: A best first step to overcoming the math anxiety may be to expose yourself to the problems (basic math problems in this case) and then start asking yourself, and others, more specific questions.

For example, if you fear addition then every time you go grocery shopping, have a budget for yourself and estimate the total of your purchases by adding them together before checking out. Try to be exact. Use a pencil and paper or do it all in your head.

Sources: Personal Experience

Philosophy: Furthermore, considering fear of anything... remember that those who laugh or make fun can quickly become subject to those they laugh at. Next time someone laughs at you (or if you can think of someone who already has) try asking them for help. (Probably not your evil teacher.) You may sooner or later exceed them... Don't laugh.

:D

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I think your question is very valuable and of interest to many people.

There is one book that perfectly fits your needs:

The Number Devil: A Mathematical Adventure
by Hans Magnus Enzensberger

You can find some information on Wikipedia.

I would highly recommend it!

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If you really have to start from the very basics, then maybe following an educational program for adults is the solution. It's still the rote learning, but for the very basic stuff, provided you are motivated, this is not such a bad approach. It gets bad if you want to go into real mathematics. On the other hand, since you are already an adult, the teachers will approach the subject matter differently than they would with kids. Try to find out what the possibilities are for adult school education near your living place.

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+1 for not just dissing the current school system and talking vaguely about possible approaches, but for actually providing a concrete solution. –  Sam Jun 28 '11 at 11:12

I am sorry to hear that mathematics has been an unfortunate problem in your life because of your teachers and their way of presenting the subject. Before I give you a suggestion of what to do I want to tell you that you are not alone in this. I cannot speak from my experience, since math was my passion from my early years, but I can give you a few examples of bad teaching in my country, Romania.

• My wife, which is very scared of mathematics, had a teacher in highschool which gave her a small grade for not understanding the words of the question she asked and another time for answering a different problem than she asked. This marked mathematics as an impossible subject and my wife was unable to process and learn mathematics from there on because of the fear she felt in every class after those incidents, that the teacher may ask her again something she doesn't understand.

• One of my parallel classes in highschool had a teacher which would give small grades to half of its class if they didn't knew by heart the previous lesson.

• Even in the university level, at least in my country, math exams are still based on memorizing proofs and difficult counterexamples, and some of the teachers are eager to find out what you don't know instead of what you know.

I am very sad to hear your story, and I hope you will be able to do something about it. Mathematics is beautiful even in the simplest things, learned in primary grades. My suggestion for you is to find (and buy if you afford it) some mathematics textbooks for the first years of school (1,2,3,4th grades). Maybe you could find some at your local libraries, or you could borrow some from someone you know. Since you say that you have trouble grasping elementary math, those textbooks may be helpful since there are lots of images in them, and in my opinion, visualizing mathematics makes it much more easier to understand. You should work as many exercises you can from those textbooks, and solve them over and over, until you fell that you can handle the basic operation with ease. Do not give up if it's hard. Think of it like this: to reach a level of understanding math, a 18 year old has at least 10 years of mathematics subjects in school. It is not easy, and surely not fast or instant. You should be perseverent and do not give up.

I wish you all the best, and good luck in your quest of understanding mathematics.

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I think that as one takes something up from the start, there should be one or more objectives at all times. Otherwise, it's really very hard to keep up. By objectives I mean something simple that one tries to understand, but which is nonetheless motivating. Questions like:

1) you're throwing a ball into the air (assuming some easy initial conditions and parabolic trajectory). How high would it go into the air before starting to fall down? How much time would it take for the ball to reach the ground?

2) how high are your chances to win in a lottery?

...

As you will be trying to find an answer to these kind of questions (which would stem from your personal interests), you'll cover a substantial part of material which will encourage you to push further.

As others have noted, online resources such as Khan Academy or more advanced MIT OpenCourseWare are pretty amazing tools.

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In India , there is the story of Panini , who wrote the first grammar book of Sanskrit around 1500BC.He lived with his teacher for fifteen years but could not master the Vedas (Religious scriptures --like the Bible or Koran) . So he thought of classifying the words and sentences , the way sounds are classified to form the alphabet. For this exercise , he had to go back to his childhood days and recollect the events of learning , by distinguishing between various sounds , classifing them mentally , and create different words and sentences by permutation and combination.He created a new set of letters for the Sanskrit alphabet--each letter representing an unique sound .From there he created the words and sentences --by various permutation and combination.The methodology he used , is now-a-days is referred to as the Scientific method. You can take the example of Mendeleyev , who created the periodic table for Chemistry. Abraham lincoln is an example of a self educated man .His writings and speeches are in non-conventional--but easy to understand English. There may be many such examples. If you fail to understand something --does not mean that you are not-intelligent. It means usually , that the methodology which you use to learn ,is different from the convention. You can re-learn the subject ,in your own way . But for that , you have to re-learn the subject from the very beginning . Assume that you are a child , learning A,B, C,D..and 1,2,3,4 .etc.Statr re-learning the subject in your own way . Keep records of important formulas which you have to remember -starting from the very beginning . After some time you will find that you have discovered a new way of learning the subject. Oriya, is one of the written languages in Orissa, India--but it did not have a Grammar.in the 19th century AD , the first Grammar book in Oriya was written by Madhusudan . He was a master of many languages--English , Sanskrit, Bengali , Hindi and Telugu. He used his knowledge of these languages and their grammars , to create a Grammar for Oriya --which is used even now . I had faced problem in understanding Taylors Series --which is used to predict the value of a function in future using an infinite set of differentials in the presnt.As an Engineering I looked at the prctical realisabilty of the function .I asked my teachers --they told me to get the formula and solved examples by heart , pass the exams and think about it after getting a job. Forty years later , i am still trying to understand this formula and trying to put it in a realsable form. If you re-learn a subject ( Mathematics , in your case),you may create a new methodology of learning . This might help many students who are facing difficulty with learning the subject.

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