How did you learn Mathematics?

[Flatfrog]

Hi all

I'm currently writing a book about the teaching and learning of mathematics and I'm interested in hearing any anecdotes you may have about your experiences. Did you have particularly good or bad teachers? At what age did you decide whether or not you enjoyed the subject? Any particular moment at which you suddenly discovered you didn't understand a word the teacher was saying?

Also, I'm interested in specific country-by-country information. In particular, one question interests me, which is that in Britain, young children tend to be taught by a single teacher each year, who is expected to teach all the required subjects, including Maths, Science and English. Is that the case where you are, or did you have subject specialists at your age?

Anything else you may have to say on the subject would be of interest too. For example, what does the word mathematics mean to you? What would you say a mathematician studies? What makes a good mathematician? What makes a good maths teacher?

Thanks for any thoughts you may have!

 

[Queen Michael]

My dad taught me to count when I was a kid, so I always was ahead of the stuff the school taught until I was around 11. By that point he wasn't teaching me anymore.

 

[Thaluikhain]

Had some good and bad teachers.

What I most remember, though, was posters up on the walls about different mathematicians and the different ways of doing maths. Always seemed strange that there were so many different ways to multiply and divide.

Mind you, never got the hang of long division. I'd always just skip all the difficult and tedious mucking about and just work out the answer to the question...had a lot of trouble with a lot of maths related stuff because of that.

 

[Wraith]

Had a teacher that got violently upset that we (a bunch of 8-year-olds) couldn't memorize most of our times tables after she taught them to us for about a week. I'm talking yelling as loud as she can, removing students from class and straight up cursing and practically calling us retarded for not remembering that 8x8=64 after she showed it to us once 5 days ago.

I was pretty good at math myself, but I personally began to hate it when I realized anything passed multiplying and dividing fractions was stuff I was never going to use personally. After that, everything I newly learned in math was kept in my mind just long enough to pass the tests then quickly forgotten.

So when I hear the word mathematics I think numbers, yelling, and boredom, but I understand that numbers and math have greatly helped us understand the world around us and it's pretty damn cool when you realize math is the only language humanity speaks in all areas of the world.

 

[theboombody]

My calculus teacher made me love it, at least until it got more complicated. It wasn't until my real analysis class that I realized that even mathematics is not immune to subjectivity, gray areas, and controversy. I believe the axiom of choice is the hot topic these days, although I've always been intrigued by zero factorial.

I would like to understand more how the Taylor series was derived, and perhaps by doing so I can figure out how Euler solved the Basel problem. Wikipedia is a start, but it's tough to work with. Still, I don't have the heart for mathematics that those guys did, so I'll probably never fully understand their techniques. There is no substitute for desire. Desire is much more powerful than mental capability, even though I'm lacking in that area as well.

 

[Esotera]

I basically didn't learn any mathematics at secondary school in the UK due to poor teaching and disinterest, which led to a mad rush towards the end of Year 11 learning all the relevant material. As for how I learnt it, I don't think I've quite stopped yet as it's a relatively large part of my university course. Also I'm now writing maths questions to help the freshers practice with an online quiz, so I suppose I could be considered competent now? I definitely don't feel secure in my skills though...

 

[Flatfrog]

It wasn't until my real analysis class that I realized that even mathematics is not immune to subjectivity, gray areas, and controversy.

I've been reading up on this aspect of the philosophy of maths myself recently and I was surprised how much it's debated. As far as I'm concerned, one of the main joys of Maths is that it's the one subject where everything you learn is true. But people seem to get very bothered by this notion and start worrying about questions like whether it's based on cultural conventions, or whether we can prove the principles we use to prove things, and suchlike philosophical nonsense.

Obviously it's perfectly possible to set up alternative mathematical realities where 2 + 2 =/= 4, just as we already deal with mathematical worlds where there are no parallel lines or where negative numbers have a square root. Maths isn't about whether these things are 'real', it's about examining them and working out how they behave.

 

[SckizoBoy]

Eh... my old man tutored me from the age of about three... or something...

To the extent that I didn't attend a single maths class at school (with the express intention of learning maths) until I was eleven. From then on, I got stuck with students six years older... that lasted for about two years, then I just did my own thing as far as maths was concerned.

Upper Fifth (year 11, I think... or eleventh grade... or something) was strange for me... I didn't do a single maths exam for the first time throughout the whole year in seven years. Did AS Level Further Maths for shits and giggles afterwards and it was rather fun.

Bizarrely... I somewhat suck at maths... ¬_¬

 

[Shadu]

I was horrible at math until around sixth or seventh grade (shortly after I joined band class). I actually then got into an accelerated class that did Pre-Algebra in one semester instead of the usual two so I could be in Algebra the next year, which was a year ahead of most others.

Algebra made sense. Geometry didn't. And then in Algebra 2, I had a teacher that hadn't taught any form of Algebra in something like 5-10 years and was suddenly expected to teach advanced math which she had never done nor understood. She told my parents at the first "Meet the teacher" parent-teacher conference thing that she and her students were "learning together." How can a teacher teach students if they do not understand the subject either? She was the worst teacher I have ever had in any subject and I basically understood nothing after I was done with that class.

As it was, my parents came home from that and told me "We're not expecting an A. Just do the best you can." This was unusual as they expected A's and B's at the very least.

In the end, however, she was apparently in the administrative offices of the school near the beginning of the second semester and was leaning back in her chair when it slipped and she whacked her head really hard on the tray on a whiteboard. She went to the hospital with a concussion, was in and out of school throughout the rest of the year, had weakness on one side of her head, and I heard from someone I knew who had her a few years later that she had developed a tumor where she got hit and had basically lost her ability to speak louder than a loud whisper.

I ended up doing decently well on the math portion of the ACT, and when I did college algebra, I learned a lot more and understood everything much better. But I still don't like math and it is definitely not my subject.

As for one teacher doing multiple subjects, at least in my part of the US, that only happens in the lower grades. I had one teacher for everything from kindergarten to fifth grade, and starting in sixth grade and going straight through until I graduated college, I had a different teacher for every subject.

 

[geK0]

I would heave teacher who would explain the topics very poorly using language that was very confusing to me; they would explain carrying the digits in addition as "a person lending sugar to his neighbour" I would have the slope variable in linear equations explained as "A heavy man on a teeter totter making it tilt upwards" these are just a few examples. I found that I would learn these topics better by just reading the text books because teachers always tried to teach us with bullshit metaphors instead of actually explaining what you were doing and why.

I was actually quite mathematically inclined as a child, I just had a really hard time interpreting what the teachers were trying to teach so I had to actually teach the stuff to myself on my own time. I would look in the book and think "oh this is what they were trying to say? that's so simple! why didn't they just fucking say it that way?!"

Not all of my teachers were like this, but way too many of them were. I didn't actually start doing well in math until third grade, when I realized it wasn't nearly as hard as the teachers made it seem to me.

I was also not able to tie my shoes for a while because it was explained to me as " the rabbit runs around the tree and crawls into the hole." instead of telling me how to tie my god damned shoes : |

 

[Someone Depressing]

Practise.

Still learning how the fuck one does SohCahToa today. Just... why...

Also, books and the internet.

 

[DSK-]

I'm still learning. Only last year I learned how to divide on paper, without using a calculator. It's a rather long, arduous methodology but it works time and time again for me.

Mathematics for me is yet another reason to laugh (at the multitude of mistakes and failures in my overall mechanics and understanding).

Good times!

 

[qeinar]

Never really needed much teacher help in math. I just pretty much did (some of) the homework assigned and then was able to do maths. A lot of the questions were pretty repetitive in elementary school so i remember me and a friend doing half of the problems each and then copying the other half from each other. I think i might have unconsciously learned some math from games as well. can't specifically say what games, but in a lot of games you can gain a advantage by counting things or remembering numbers.

I feel like if you find ways to use math in day to day life you'll learn it easier and faster. I also recall that when i went to the shops after learning to count i used to try and count how much it's going to cost when we got to the till. I still to this day always count roughly how much the items i'm buying is going to cost. For more advanced math it's kinda harder to use it to day to day life, but there's still situations where it can come in handy.

 

[EHKOS]

My dad taught me multiplication with a puppet named Snuggles. (yes he was from the commercials and laundry detergent brand)
For every answer I got right, he would do something funny, being young at the time, it was usually bathroom humor. He also taught me that 6x8=48 because it rhymes.

When I think of the word though, I think of boredom and impossible to attain knowledge. I hate using this analogy because people look at me weird, but the best way I can describe it is my clock speed and HDD space is really bad ever since I hit 18. So I don't retain a lot and math takes a lot of mental resources.

I can do simple fractions, decimals, and percentages though, anything above that and I'm fucked. If a fraction has a denominator higher than a numerator, I can't do it, and I can't multiply them either.

I was fifteen when I knew I hated it, that was when shit got real. As for teaching it, you really can't do much in getting someone interested in numbers. It's something you're born into. Either you love them or you hate them.

 

[Ancient Mariner]

In elementary school my performance was fairly poor in math. Back then it was mostly arithmetic. Once I got into algebra in middle school, things started to get better as I found the content intriguing. By the time I was in high school I was fortunate enough to be taught by some excellent teachers, the entire math department in my high school was stellar. My grade 11 math teacher was certainly a standout, she was demanding yet concise and made her expectations really clear. I am now in second year calculus in university and I am loving it. Calculus has this sublime quality to it that allows us to solve so many things. I think the key to excelling in any field is to have a passion for the content. For me it would probably be my grade 11 math teacher that really cultivated my interest in math, and since then it's been my fascination with the content that keeps me going.

 

[Drummodino]

My mother taught me my numbers as well as how to read when I was very young. I really appreciate that now, although I probably didn't at the time.

Maths was always one of my strongest subjects, although by the end of high school chemistry and physics were my top two with math behind them. I've had a mix of good teachers and bad, my year 11 and 12 calculus teacher was probably the best. She expected us to go above and beyond the course, really pushing us to learn.

I'm an engineering student now so I do a lot of math regularly. I did fail one pure math unit first year from a combination of laziness and terrible teaching. They reworked the course after that and we got much better tutoring and lecturers, so I did pretty well. These days I just apply math in my regular units.

Maths and I get along pretty well, calculus is fun. Statistics can get rather dry though, I prefer differentiation to t-tests any day.

 

[Mithcha]

The whole "one teacher a year", whilst true, doesn't exactly work like that really. Yes the class is overall observed, monitored and regularly taught by a single teacher, but often times a teacher will (and frankly any teacher worth any sort of time definitely would do) turn to a TA or teacher who knows the subject better. The school I worked at had a specialist PE teacher, (well ok he was a floating cover teacher who did a sports degree or some shit) the two same TA's would take art for all classes, the deputy would take French etc. Each teacher also had a field they were in charge of and monitored for all year groups so it's a bit more complex than one teacher does EVERYTHING in a single class. And we weren't a posh upper class twat school, it was a proper inner city London school so I'd imagine a school with cash to throw around is even more layered. Kinda irrelevant and a bit ranty but hey.

As for learning maths myself, never did. My times tables are kept in a book that I refer too whenever I need them and I still mostly count on my fingers. I blame a lack of giving a shit coupled with a teacher who insisted a metre was as high as a fucking 6 foot door.

 

[Lynx]

Hi all

I'm currently writing a book about the teaching and learning of mathematics and I'm interested in hearing any anecdotes you may have about your experiences. Did you have particularly good or bad teachers? At what age did you decide whether or not you enjoyed the subject? Any particular moment at which you suddenly discovered you didn't understand a word the teacher was saying?

Also, I'm interested in specific country-by-country information. In particular, one question interests me, which is that in Britain, young children tend to be taught by a single teacher each year, who is expected to teach all the required subjects, including Maths, Science and English. Is that the case where you are, or did you have subject specialists at your age?

Anything else you may have to say on the subject would be of interest too. For example, what does the word mathematics mean to you? What would you say a mathematician studies? What makes a good mathematician? What makes a good maths teacher?

Thanks for any thoughts you may have!

Sweden here. Our math education kind of sucks, by the way.

Year 1-5 (age 7-11) we're taught everything by one teacher, with the exception of practical subjects such as P.E., music, woodwork, etc. Year 6-9 + year 10-12 (the Gymnasium, our version of highschool) you have several teachers that are usually specialized in two subjects, e.g. math + physics, history + social science, Swedish + English, and so on.

I myself got headaches and crying fits from mathematics throughout most of my teens. The teachers have too much on their hands to help you, so unless you have someone else around who has the time, you're on your own with a crappy book. For kids (like me) who needed more help than what was given, it was hell.

But the older I got, the more structured my thinking got, the more focused I became. I was lucky that way. I realized somewhere at the age of nineteen that I was actually pretty good at math and had a talent, albeit an understimulated one, for logical reasoning. I wish I could have discovered that at thirteen instead, but hey, what's done is done.

I eventually ended up with a part time job as a math tutor for young teens that were in the same situation as I had been, and it was the most wonderful feeling to see those kids go from "Damn it, why am I so stupid?" to "Hey, wait, I can totally do this!" in a matter of months. I felt like I really made a difference.

Private tutoring services are getting increasingly popular in Sweden because the schools themselves can't teach it on their own anymore. The kids who can't learn the curriculum with just a badly written book and half a teacher, end up resenting themselves "for being stupid". Swedish teachers are grossly underpaid and their status as a profession has become ridiculously undermined, not entirely unlike the nursing profession. Because of this, truly talented mathematicians build careers in engineering or economics instead of teaching - and the idiots who can't get accepted to any other program decide to become teachers. Politicians blab all the time about raising the teachers' salaries so more talented people will be tempted to pick that route, but they never do.

Just my two cents. Let me know if there's anything else you'd like to know.

 

[FPLOON]

I learned through audio logs of myself on tape, playing Lemmings on a mid-90s Mac computer[footnote]I don't know what the particular model was... but, I know it wasn't a G3...[/footnote], and through a kindhearted kindergarten teacher who was in her 70s at the time[footnote]She turned 95, I think, in January of this year...[/footnote]...

Anyway, my best years learning anything math-related was when I had the same high school math teacher two years in a row, only under different math levels... He was the type of guy who would intimidate the other students by coming into class in a white dress shirt and black tie during the first several weeks of school before changing into colored polo shirts for the rest of the year. He loved teaching the math subjects to the point that he would make [mostly] obscure sci-fi references in his teachings just to see if anyone would catch them... He was also one of the few teachers in high school I could match both wits, humor, and obscure referencing with, even when he would tell me to settle down because he thought that it would cause me to not do well in the class...

Nevertheless, he was a pretty awesome guy, taught Algebra 2 and Pre-Calculus like a boss, and really appreciated me showing him <link=http://www.youtube.com/watch?v=zSgiXGELjbc>this video without the [hidden] ploy of wanting extra credit in the first place...