Numbers and letters

[dolorosa_12]

So, I stayed away longer than I intended, but I have now submitted what I hope to be the penultimate draft of the first two chapters of my thesis to my supervisor! That's 40,000 words. I am very, very relieved. So I celebrated today by doing nothing but exercising. I went to a yoga class in the morning (which was filled with little old ladies who were much more flexible than I am), and then a long run in the sunshine. I really cannot express how good all this exercise is for my mental health. I'm not saying that you can cure depression and anxiety with a daily run, but it does help to keep the awfulness still and quiet for a little while.

We have our annual student conference in our department. I helped organise it in my MPhil year, and I presented at it in the first year of my PhD, but ever since I've just gone along for the fun of it. We've got our friends J, L and C staying with us for the weekend. J is going to be presenting there. We're going to spend tonight eating take-away and watching cheesy medieval films, and then head off to the conference in the morning. Our new house is very conveniently located - only fifteen minutes' walk to the department, and very close to the college where the dinner will be. And then on Sunday Matthias and I are going to see Paloma Faith.

One of my friends (one of my group of friends from uni, who mainly studied maths or other sciences) posted a link to an article about a study which found that the number of girls studying maths in the HSC (the equivalent of the A Levels for students in NSW; Australia doesn't have a national education system) has increased dramatically in the past decade. While I think there is a problem in encouraging girls and women to pursue study or careers in mathematical or scientific fields, and that mathematical literacy is pretty poor in the Australian adult population (I used to work as a newspaper subeditor, so I have some first-hand experience of this), I'm not sure exactly what the right way to go about fixing this is. Some of my friends were suggesting that maths be made compulsory up to Year 12 (the final year of high school - right now it's only compulsory up to Year 10, and the only compulsory subject is English), but I'm a little dubious about whether forcing people to study something would increase their enjoyment of it (or encourage them to pursue it after secondary school).*

I am going to tell you my own story, because this is the only way that I manage to work out what I think about such issues.

I did (mostly) okay in maths and science classes in secondary school up until the end of Year 10. I was in the top class for both (out of four levels in Maths and three in Science), and managed solid Bs, with the occasional A. As long as I did my homework and studied a little bit before tests, I could keep up. But when I started Year 11, and maths became much more abstract, I really, really struggled. I had to stay in the top class because I was doing the International Baccalaureate, and only the top class covered all the IB material.

I spent every evening doing maths homework. I failed every single test. The highest grade I got on a test was probably around 35% (because of the way my state's education system worked, that scaled up to about 75%, which meant it didn't affect my overall grade). Can you imagine what it feels like to spend all of your studying time working on one subject, and get results like that? It was the first (and only) time where there was no correlation between my effort and the outcome.

In contrast, in my literature class, everything just clicked. I'd always found it very easy to spot themes, stylistic devices and all that stuff in works of literature - I'd been doing it since I was a child, every time I opened a book, for fun. After a long struggle during the earlier years of high school, where my grades steadily improved from solid Bs to lower As,** I could write reasonably good essays. I found literature study easy. My grades reflected my effort: as long as I listened and participated in class, as long as I put in time with my essays and presentations, I would get very good grades. In fact, I was consistently in the top three students in the grade.

It was pretty clear, by the time I was in the final years of secondary school, that I was going to study something related to words and writing, and that I would ultimately work in a field related to that. And yet, because all of my friends were excellent at maths, I felt that I was incredibly stupid. About 60 per cent of what I angsted about during those two years was whether I would pass my IB maths exam. (The other 40 per cent was why the guy I liked didn't want me back.)

I'm not sure exactly where I'm going with this. I don't think I was bad at maths because I'm a woman - I think I was bad at maths because a) my brain simply doesn't work that way and b) I did better in subjects that were assessed primarily through essays or assignments rather than in exam conditions. I don't even necessarily think that I would have been better off if I'd been able to drop Maths entirely. I wonder if I would have been okay if I'd been able to go into the class one level down. But I think I disagree with making the choice of subjects of study more rigid and restricted in the final years of high school. If anything, I'd go in the other direction, and have more options - especially more vocational options and opportunities for internships or work experience. I feel the way to encourage more students to study specific subjects is to make them more geared towards those who have a deep and genuine interest, streamed into different levels if necessary. I think something needs to be done earlier on in education to make maths and science more appealing to girls, but I think by Years 11 and 12, it's too late, and making such subjects compulsory at that stage isn't going to solve the problem of the lack of women in those fields.***

__________________
* If I had my way, English, Maths, Science, Modern History (or a combined History and Geography class) and a foreign language would be compulsory up to Year 10, but I think there should be more choice after that. I also think a course on managing money, and another on managing your mental health, should be made part of the curriculum.
** I will always be grateful to my English teacher during those years. She could see that I understood stuff, but wouldn't give me amazing grades until my written expression improved, and every essay it got a little bit better until I wrote one on Macbeth and she actually said to me, 'You finally understand how to do this'.
*** In any case, there are fewer women in fields which are supposedly more popular for girls - fewer senior female academics, even in the humanities, and fewer women in senior positions in the media, or working as journalists and reviewers in top, well-paying publications. My position on all these issues is that the later years of secondary school, and university (both undergrad and postgrad) is the wrong time to be addressing this problem. It needs to be dealt with both earlier (in primary and the earlier years of secondary school) and later (when adults enter the workforce).

Comments

[moonvoice]

I'm not sure exactly what the right way to go about fixing this is.

Probably hiring less sexist / chauvinist teachers would be *start.* At our public highschool, the most deplorably sexist teachers were almost exclusively the maths, science and PE teachers, with the maths teachers even going so far as to 'compare' who had matured into more sexier girls over the school break. It was disgusting, and nothing was ever done about it. I still have 'fond' memories of Mr. Sev (chemistry teacher) leaning in the doorway first thing in the morning, and talking to Mr. Kalevich (maths teacher) about which of the girls he rated, in view of us all, and inviting some of the boys to participate. They were some of the most beloved teachers in the school - and sadly, most beloved by some of the girls who vied for their attention as well.

I was one of those people who got special permission to drop out of maths for year 10 so I didn't do it in 10, 11, 12. And it was mostly because I was failing and didn't want that on my overall grade average, knowing how much that counts towards university entrance. There were no facilities at the public school I was at for special tutoring, which I really should have started in year 8, and my parents couldn't afford it. So it was continue to fail with no one really caring, or leave. And I imagine there are a lot of people - not just young women - in the public education system at the very least, who are in the same situation. If I had been forced to take a maths requirement (as opposed to just a 'science/maths' requirement - in which case I took TEE Bio), I probably would have dropped out of highschool, it was making me miserable, and there was no chance of actually ever getting better. So your point about *more* flexibility and less rigidity is one that really speaks to me.

If one starts failing in year 8 (or 9, or 10), forcing someone to take another 4 years of misery while essentially never getting past a year 8 knowledge base or skill level is - I think - a form of educational torture. Especially as being bad at maths has been found to be the equivalent of experiencing physical pain. (The research may need some work, but it's not completely erroneous in its findings, I feel).

But I think I disagree with making the choice of subjects of study more rigid and restricted in the final years of high school. If anything, I'd go in the other direction, and have more options - especially more vocational options and opportunities for internships or work experience.

*nods* This, I so much agree with this. Maths needs to be addressed a lot earlier, and perhaps funds need to be put aside for subsidised tutoring programs to deal with those who fall through the cracks in what is just plainly overfilled classrooms and teachers who can't always afford to take the time to make a tailor-made program for particular students (even outside of the egregious and blatantly disturbing sexism that I experienced at highschool). I often wonder how well I'd do at maths now if I could learn it on my own, and research on the internet and Youtube to look at the lateral ways people have approached problems.

The thing is, I think I could be okay at maths too. Not great, but just... okay. But there was no way of finding that out in the public system. I do wish that maths literacy could be raised overall.

It's a complicated issue. Hope you didn't mind me rambling!

[dolorosa_12]

I'm so sorry I have only been able to reply today. I was out all weekend, and although I read your comment, I didn't have a minute to respond until just now.

Can I just say that the behaviour of your teachers was horrific, and should have got them fired. Although my teachers were, for the most part, wonderful (even though they weren't great at teaching me maths), we did have one teacher who eventually got fired for a similar issue. He was also very popular with students, but when he was fired, no one was surprised. I am so very sorry that you had to deal with that on a daily basis.

There were no facilities at the public school I was at for special tutoring, which I really should have started in year 8, and my parents couldn't afford it. So it was continue to fail with no one really caring, or leave. And I imagine there are a lot of people - not just young women - in the public education system at the very least, who are in the same situation.

I agree so very much with this. I suspect that class size, and the relative range of abilities, even within streamed subjects, makes it impossible for teachers to focus on the needs of every student. Certainly it was my experience that I wasn't able to get the help I needed in my (public) school, but neither was my sister in her (extremely expensive private) school. I ended up being tutored through the Kumon system from Year 4 to Year 10. It's a system that focuses on speed and accuracy, and is really good help when maths is basically arithmetic and basic algebra, but useless once it goes beyond that. In Years 11 and 12 I had a private tutor who saw me once a week. My sister also did Kumon, and my mother paid my friend anya_1984, who ended up getting a PhD in maths, to tutor my sister throughout high school. We had tutors for spelling as well, because the schools simply weren't teaching it. I'm very grateful to my mother for being so attentive, and spending the money on such tutoring, but the fact of the matter is, it is ridiculous and unacceptable that students need this extra tuition.

Of course I'm mainly speaking from an Australian perspective, and an ACT (where I was a student) and NSW (where my sister was a student) perspective at that, but I really feel the whole school system needs a complete revamp. I think Year 8 is too early to drop maths - and I think it was your teachers' failing and not yours that you struggled from that point - but I would prefer a system which had a strong focus on the academic basics (which I hold to be literacy/written expression, arithmetic agility, a good grounding in the basics of all the natural sciences, as well as modern history, a bit of geography, and a foreign language) up until Year 10. Although no one leaves school in Year 10 any more, I'd hope that if they did, they would leave with that knowledge and then move on to more specialised study or training. Those with an interest/ability in particular academic areas would be able to hone them in rigorously streamed classes so that they moved at the pace that suited all students. Those who wanted to move into more vocational areas would get the training they needed, either through high school or with affiliated programmes and apprenticeships. And I would have a requirement that all students did internships for several weeks, several times a year, because it's increasingly difficult to get jobs in any field without them, and leaving it until people are adults to do this gives an unfair advantage to those who have parents willing and able to support this. I also feel that people are poorly prepared in general to manage money, and to manage their own mental health, and although I'm not sure schools are the place to train students in these areas, I think it's something that needs to be done.

The thing is, I think I could be okay at maths too. Not great, but just... okay. But there was no way of finding that out in the public system. I do wish that maths literacy could be raised overall.

It's a complicated issue. Hope you didn't mind me rambling!

Of course not! Ramble away - as you can see, I love to ramble about education too.

I'm not entirely sure it's the public system per se that's the problem, since my sister struggled with maths in a private school. I think the issue is classes that are too big, and not streamed properly. To be honest, Kumon and working in retail were what really gave me the best education in maths, and to this day my mental arithmetic is good because of those things, and not because of any teaching I got in school

[cykotyks.livejournal.com]

In the US school system, math is compulsory through all of high school (grades 9 through 12), and it is horrendous. My math classes in high school were: Geometry, Algebra 2, Pre-Calculus, and Statistics. My senior year choices were calc and stats, and I was advised to go into stats because I sucked pretty hardcore at pre-calc. That was the only class I actually cheated in in order to get by, and I'm not ashamed of it - I still only barely passed with a C, and that was with some hardcore cramming for the final. I remember absolutely nothing from pre-calc (except that it was mind-bending and somewhat terrifying), and I wouldn't remember any of the stats, either, if I hadn't gone into a field that required it, but I still had to take the class a second time in order to get college credit for it. IMO, after Algebra 2, the math is way too abstract and narrowly applicable to be useful or interesting to anybody not specifically interested in a field that uses it.

I also think a course on managing money, and another on managing your mental health, should be made part of the curriculum.

I agree with this so much. High schools here, at least, are generally geared towards preparing kids for college instead of the real world. My parents seemed to have this delusion that once I got through college, I'd have all the knowledge I'd need in order to survive, but they didn't teach me anything, and right now, because I'm estranged from my mom and my dad doesn't know anything, either, I would've been grateful for a class on money management and whatnot. Anything that would've directly prepared me for the real world would've been better than half the useless shit I got crammed down my throat for SATs, because right now, none of that is doing me a lick of good. It's infuriating. (And considering the state of the US's educational system as a whole, I don't think trimming down the maths and sciences in order to make room for practical courses is going to hurt anything.)

[dolorosa-12.livejournal.com]

That sounds horrific! I'm not very familiar with the system in the US, but it seems there's a lot more specialisation within subjects much earlier on. In Australia we had classes that were just 'maths', where we did algebra, statistics, geometry, trigonometry and (in the final two years) calculus and lots of other very complicated stuff that I've since blotted out. It was only compulsory up until the end of Year 10, but the way the final grading system worked meant that it was very hard to get a high grade without doing a maths class in the final two years.

(In my state, you get an overall grade out of 100, which is an average of the overall average of your top four+0.33333 classes. You use this score to determine where you can go to university, which is based on demand. So, for example, a prestigious course such as Law at a top university may require you to get scores above 99, whereas Law at a less-prestigious university might only be above 95, and a less desirable course such as Arts may require only 80, even if it's at a top university. This score is also affected by how well your whole school does, and how well people in your particular subjects do. This means that if you take a class that lots of smart people are likely to do - such as the highest maths class - your score may scale up, even if you do poorly in that class and even if it's your lowest grade and doesn't otherwise count. Does that make any sense at all? The system in my state is notoriously bizarre and people always talk about making it less complicated.)

I agree with this so much. High schools here, at least, are generally geared towards preparing kids for college instead of the real world. My parents seemed to have this delusion that once I got through college, I'd have all the knowledge I'd need in order to survive, but they didn't teach me anything, and right now, because I'm estranged from my mom and my dad doesn't know anything, either, I would've been grateful for a class on money management and whatnot.

I don't necessarily want to neglect more academic subjects early on, because I think that the bare minimum people should know coming out of high school is arithmetic, literacy and written expression, a solid grounding in science and modern world history (and the history of their particular country and its region), and a foreign language. I do think that these things are important, but I think after Year 10, they are privileged at the expense of other kinds of knowledge which are of equal - and, in many cases - greater importance. I am grateful for the academic stuff I learnt in high school, particularly my literature classes, because I am pursuing tertiary education in this field and so it's of direct relevance to my life, but if I had wanted to be, say, a motor mechanic, it might have been more useful if I could've done some kind of apprenticeship through school. And I think while public (and to a certain extent, private) education is good at exposing students to a wide range of people, and teaching them how to deal with people who are very different from themselves, it is absolutely useless in targetting its teaching to the full range of interests and abilities of that range of people.

[jordan rastrick (from livejournal.com)]

This score is also affected by how well your whole school does, and how well people in your particular subjects do. This means that if you take a class that lots of smart people are likely to do - such as the highest maths class - your score may scale up, even if you do poorly in that class and even if it's your lowest grade and doesn't otherwise count. Does that make any sense at all? The system in my state is notoriously bizarre and people always talk about making it less complicated.

Ummmmm...... the UAI/ATAR's not perfect, but it makes a lot more sense than this (although it seems to be the common depiction of it.) Unless you're talking about things specific to the way they apply it to the IB in the ACT?

and a foreign language

I must admit (maybe because I was too lazy to ever be a great language scholar :P) that I really don't buy this one, certainly not as a minimum requirement we should look to from the education system. In fact I think teaching foreign languages at a high school level is way over emphasised and for many students is a big waste.

Its a huge investment of time and heartache in what is largely, certainly in most of the years of high school anyway, rote memorisation of vocabulary, grammar and so forth. Unlike learning to write essays or solve equations, these are largely just isolated facts - you're not learning skills that generalise well, help your ability to think critically, etc. You can get a better appreciation and mastery of your own language from the contrast between the two, sure - but I think this would be much conveyed by teaching general linguistics, with individual languages used only as examples.

As machine translation gets continually better, its increasingly unimportant as a practical skill in the real world - yes, we need properly bi-lingual translators to teach the machines, but we won't need all that many [for commonly spoken languages like English/Mandarin/Hindustani/Spanish/etc that is - obviously expertise in Medieval Gaelic is going to remain an all human affair for a lot longer :-)]. And if you really want to actually learn a living, spoken, foreign language properly - well enough for instance to pick up on the subtleties in important texts and so forth that are lost in translation, which to my mind is the main pay-off - then you need to immerse yourself in an environment where its being spoken natively. Making use of your inherent neural machinery for is simply heaps more effective than learning a language out of a book can ever be.

[dolorosa-12.livejournal.com]

Ummmmm...... the UAI/ATAR's not perfect, but it makes a lot more sense than this (although it seems to be the common depiction of it.) Unless you're talking about things specific to the way they apply it to the IB in the ACT?


I could just be repeating an urban myth, and if so, I apologise. But this was certainly the way it was described, not only among the students, but by the teachers to the students, and I was certainly encouraged to stay in a Maths class that was way too hard for me simply because of the way the scaling worked. (Basically, in Advanced Maths Extended, which I think is the ACT equivalent of 4 Unit Maths in NSW, no one got below about 75, and the top students' scores scaled up to over 100, whereas if you went down to Advanced Maths (2 Unit), it was impossible to get above 85, and quite possible that you'd end up getting a score in the 60s.) This turned out to be entirely pointless, since my Maths grades didn't end up counting in my UAI. Certainly my UAI seemed to scale up to a certain extent, as my predicted score was 91.5 (and I was only getting grades in the 90s in English), and I ended up getting 96.8 - which I don't think can be entirely explained by a minor improvement in my grades in some classes in Year 12. I'm almost positive that this was affected by some other factor such as my school's grades being scaled up slightly.

You are wrong about languages. You are right about how they are taught in Australia (and most English-speaking countries), but that doesn't explain why so many Europeans (and possibly others, although I have more experience with people from Holland, Germany, Scandinavia and places like that) speak such good English. You met Matthias in Australia, and I'm sure you'd agree that his English is essentially like a native speaker's. And while it's obviously improved since he's lived in England for a decade, when he was 18, it was good enough that he could do a BA at Cambridge as an 18-year-old. I know a lot of other people like him.

Part of this is because English is taught much better in these European countries than we are taught foreign languages - in a much more immersive way. People also tend to be exposed to a lot of English-language media (especially in Scandinavia, where stuff isn't dubbed unless it's for very small children) and read English books. But I think the issue is with how foreign languages are taught in the English-speaking world, and not with the skills you need to learn a foreign language. I speak from experience. When I was taught German last year in that immersive way (that is, they spoke only German to us from the minute we walked in the door, even in the beginners' class), I learnt it much more quickly and comprehensively in six months than I learnt Japanese over the course of six years in high school.

Machine translation isn't good enough to replace translators just yet. I've seen some hilarious Google Translate errors, mainly caused by confusion with homonyms. (Eg English '[rubber] band' being translated as Mandarin '[musical] band' or whatever.) Machine translation also doesn't get context or tone. If programmers could fix those things, maybe. But at this point, no.

I agree with you about linguistics. I have an Icelandic friend who says he was taught it in high school, so it's clearly not something that teenagers are incapable of understanding.

[jordan rastrick (from livejournal.com)]

> But this was certainly the way it was described, not only among the students, but by the teachers to the students

Yeah, I've heard *way* too many teachers, first and second hand, giving horribly confused descriptions of the UAI and actively bad advice to their students based on it.

>nd I was certainly encouraged to stay in a Maths class that was way too hard for me simply because of the way the scaling worked

See, to me this is one of the most classic pieces of misinterpretation of scaling by the teachers (and a good example of that "actively bad advice"). The whole point of the system is to adjust for the relative difficulty of subjects so that there is no inherent advantage to picking one subject over another; rather you just do what you like and what you're good at, and if that happens to be harder or easier than the subjects your peers choose, the system takes that into account in a mathematically precise way. It doesn't do it perfectly, but it does it much better than any alternative I've ever heard proposed.

> Certainly my UAI seemed to scale up to a certain extent, as my predicted score was 91.5

Where did the prediction come from?

My first guess at explaining any discrepancy between predictions generated from your internal high school marks vs your actual UAI would be A) Not many Australian students take the IB; small sample sizes always create more room for error in statistics and B) If other people in your year found the same effect, then whatever was doing the prediction just had a bad sense of how strong your school year was relative to other schools - this is a really hard thing to estimate until you sit the external exams precisely because there is no objective benchmark against which to judge.

> You are wrong about languages. You are right about how they are taught in Australia (and most English-speaking countries),

Yeah, we had this same discussion at a usydgroup dinner tonight and Eve pointed out the very important caveat of "languages as taught in Australian high schools" which is my sole experience, vs languages as taught in other ways. But I don't know if Australian schools could be easily fixed to do a better job.

> You met Matthias in Australia, and I'm sure you'd agree that his English is essentially like a native speaker's.

Yes, and that's also true of the English of plenty of other Europeans I know.

I completely agree that immersion is hugely more effective than the memorising words from a textbook methods we use - again, something that came up tonight. But I think the exposure to English language media is a reasonably significant part of that, and I'm not sure how easy that is to replicate here: the cultural shift to get to a point where there's a lot of Indonesian TV shows or Bulgarian pop songs or what have you being consumed en masse by Australian audiences seems too large.

I'd be really happy to see us try to spend some time teaching kids languages immersively, and at a younger age - but I still don't think that leads to "we should aim for every high school graduate to have a foreign language."

And yes, I agree machine translation is nowhere near good enough to substitute for human translators yet; my argument is only about the trend. We've got fresh-off-the-presses initiatives to teach more kids Mandarin and Indonesian to help engagement with Asia. For those kids going into kindergarten now, by the time they finish their undergraduate degrees its maybe 2030 and by then I fully expect English to Mandarin software to be close to par with the average human translator. (English to Indonesian not quite so much, given the lower quantity of Indonesian text for it to learn from.)

[dolorosa-12.livejournal.com]

Where did the prediction come from?

The ACT system is based on continuous assessment, and your UAI is an average of the average of your best grades. The prediction was based on an average of my best Year 11 grades, as far as I remember. My grades in Year 12, apart from English, didn't improve significantly. (I should also add that I got two UAIs, one based on this method, and one based on my IB results; this was the ACT one and the IB one was higher.) We had no state-wide exams equivalent to the HSC; individual schools set their own curriculum. I do know they tried to adjust for the different curricula by having a standardised test that everyone took. It involved writing an essay on a social/ethical issue (I can't remember the question, but it was certainly something that didn't require any preparation), and answering multiple-choice questions based on problem-solving and reading comprehension. Prior to taking these exams, our principal explained them as 'determining how big a slice of the UAI cake you, as a student of this school, will get'. This is, perhaps, why I get the impression that subject and school had an effect on UAIs. Now that I look at it, it seems that this test was intended to adjust for grade inflation in some schools, or relative difficulty of different schools' classes, but certainly the end result usually was that my school got the highest UAIs.

I completely agree that immersion is hugely more effective than the memorising words from a textbook methods we use - again, something that came up tonight. But I think the exposure to English language media is a reasonably significant part of that, and I'm not sure how easy that is to replicate here: the cultural shift to get to a point where there's a lot of Indonesian TV shows or Bulgarian pop songs or what have you being consumed en masse by Australian audiences seems too large.

I'd be really happy to see us try to spend some time teaching kids languages immersively, and at a younger age - but I still don't think that leads to "we should aim for every high school graduate to have a foreign language."

That was basically what I was getting at. A lot of my friends went through eleven (or twelve) years of immersive French teaching, to the extent that they took French exams instead of the Australian ones. (This had the odd effect that when they started studying sciencey subjects in English, they didn't know the English terms for any scientific terminology!) I have always been extremely jealous of this, and frustrated that I didn't have such a command of a foreign language. It's possible that I am projecting some of my own issues here, because my (academic) life would've been much easier if I had become fluent in German and French in high school.

That said, I don't think it's particularly harmful or time-wasting to be pushing for fluency in a foreign language for Australian students, whether or not machine translation ends up replacing the need for human translators. I must admit, the thought does fill me with unease. Although I've mostly used my foreign language knowledge for academic purposes (reading and writing in German, for which a machine translator would make my life a lot easier), the idea of replacing actual conversation with a machine is not particularly appealing.

[jordan rastrick (from livejournal.com)]

Well said. I used to be of the "Maths is just important as English; lots of people are just put behind by one bad year (poor teacher, outside circumstances, etc.)" camp. Actually I'm still in that camp, but I think even when the one bad year problem gets fixed some people still just won't have a particular aptitude or interest for the subject. I've been committing a fair whack of typical mind fallacy (http://wiki.lesswrong.com/wiki/Typical_mind_fallacy), projecting the love and skill I and many of my close friends have for the subject too heavily on to the population at large. At the very least, we *definitely* need to fix the problems that cause disengagement with maths before attempting to make it compulsory again.

And I still believe the kind of things you learn in high school Maths are just as important or more so than the kind you learn in most of high school English; but I'm now more inclined for them to be both optional rather than both compulsory. Particularly to make room for "life skills" kind of content you're talking about, which kids don't get nearly enough of in any formal or explicit context. I mean they're just supposed to absorb it by cultural osmosis, right? Or maybe the assumption is that everybody's parents sits them down and gives them lessons on all that stuff.....

I might steal the idea for The Future Party agenda if I can convince the others? (Not sure how area you are of the details of that particular project.)

- Jordan

P.S. Sorry if this double posts, after the first time livejournal told me that because I commented anonymously it was marking it as spam. Not sure if that meant "held for moderation" or "forwarded to the trash." Might have been nice to prompt me to login beforehand if there is an issue with anonymous comments, LJ........

[dolorosa-12.livejournal.com]

Sorry about the confusion. I previously set my journal to require anonymous posts to be approved (because I was getting a lot of spam), but LJ seems to have changed its settings in terms of the message it's sending anonymous commenters. For future reference, any comments you make will go into moderation if you make them anonymously, but I'm aware of them and will approve and reply as soon as possible.

Thank you for the link to the 'typical mind fallacy'. That's giving a name to something that I myself have probably experienced many, many times, although in my case, it's related not to maths, but rather literacy, literary analysis, and what I would term 'cultural and historical literacy'. (That is, I'm always appalled that people can't use grammar and spelling correctly, can't write well, can't spot themes and literary devices in texts, and don't know the sorts of things I would expect 'a typical educated person' to know in terms of history or culture.) So I'm glad you've pointed out that this may be me projecting my own interests onto the population at large.

I used to be of the "Maths is just important as English; lots of people are just put behind by one bad year (poor teacher, outside circumstances, etc.)" camp. Actually I'm still in that camp, but I think even when the one bad year problem gets fixed some people still just won't have a particular aptitude or interest for the subject.

It's been my experience that you can fix problems with arithmetic simply by practice and repetition. Up until Year 10, I didn't find Maths easy, but as long as I did my homework, and supplemented it with Kumon worksheets, I was fine. As soon as it got more abstract, I was absolutely lost. I might as well have been trying to read a book in a foreign language. I did not know where to begin. And I'm not sure I'm typical, but certainly everyone I know who struggled with Maths has told me exactly the same thing - it's only once you get to the higher levels that it becomes a real problem.

[dolorosa-12.livejournal.com]

Part II, because LJ has character limits.

And I still believe the kind of things you learn in high school Maths are just as important or more so than the kind you learn in most of high school English; but I'm now more inclined for them to be both optional rather than both compulsory. Particularly to make room for "life skills" kind of content you're talking about, which kids don't get nearly enough of in any formal or explicit context. I mean they're just supposed to absorb it by cultural osmosis, right? Or maybe the assumption is that everybody's parents sits them down and gives them lessons on all that stuff.....

As I was saying to cykotyks above, I think schools are very bad at targetting their teaching to the broad range of interests and abilities that their students have. For my part, the higher-level literary analysis we did in the last years of high school has been of much greater importance than the maths, but obviously for someone like anya_1984 (who did almost the same subjects as me, if you swap Biology for Physics), it was the reverse. I do think there's a case to be made for having a fairly uniform (though streamed) curriculum up until Year 10, because even if you're moving into a more vocational field as an adult, you need to be able to read and write and do arithmetic, and I think basic scientific and historical knowledge is a good thing. But once the subjects themselves become more esoteric and specialised, there should be more room for specialisation. There should be smaller classes that are streamed more comprehensively (rather than, say, four levels of maths where a class size is 30 people, it could be eight levels with 15 people). I've heard people say that high school English made them hate reading, which makes me so heartbroken, because for me it enhanced a love that I already possessed. I'm sure my issues with Maths are the same.

I might steal the idea for The Future Party agenda if I can convince the others? (Not sure how area you are of the details of that particular project.)

Go right ahead. JJ and I spoke really briefly about The Future Party when I was there over the summer, but I'm not involved at all, and really couldn't focus on a project of that nature right now. But I'm happy for you to pitch that idea, and to talk to you further about education policy if you want.

[jordan rastrick (from livejournal.com)]

Sorry about the confusion. I previously set my journal to require anonymous posts to be approved (because I was getting a lot of spam), but LJ seems to have changed its settings in terms of the message it's sending anonymous commenters. For future reference, any comments you make will go into moderation if you make them anonymously, but I'm aware of them and will approve and reply as soon as possible.

No worries, just glad stuff doesn't get auto-deleted.

But once the subjects themselves become more esoteric and specialised, there should be more room for specialisation.

Definitely agree with this. I think the key is becoming better at letting kids find out their potential interests and aptitudes a bit earlier - it seems we're spectacularly laissez-faire about this at the moment, and the efforts we do make as a society are, well, pretty hopeless.

It's been my experience that you can fix problems with arithmetic simply by practice and repetition. Up until Year 10, I didn't find Maths easy, but as long as I did my homework, and supplemented it with Kumon worksheets, I was fine. As soon as it got more abstract, I was absolutely lost. I might as well have been trying to read a book in a foreign language. I did not know where to begin. And I'm not sure I'm typical, but certainly everyone I know who struggled with Maths has told me exactly the same thing - it's only once you get to the higher levels that it becomes a real problem.

Its funny - I read once that in America its actually people who do better on the English sections of the SATs in America, not the Maths, that do better as practicing mathematicians (in terms of PhD candidate success rates and so forth). That is once you move past arithmetic and memorising trig and what not into more abstract stuff, supposedly its the same kind of cognitive abilities that make people good with words that start to matter in mathematics. And to me, this has always made a lot of sense - teasing out the meaning of a metaphor in a text seems pretty closely linked to teasing out the meaning of a bunch of axioms defining an algebraic structure.

But as someone who is excellent at one and not so much at the other, and apparently not for want of trying or a bad teacher or any other clearly exogenous reason, you're at least pretty strong anecdotal evidence that that can't be the whole picture. Especially if lots of other people feel the same way.

P.S. Once again I know I'm very late to this particular party, but how good is Season 4 of Buffy? :-)

[anya-1984.livejournal.com]

Did you mean to say that you have a problem with encouraging girls to study maths, or did i misread? Surely we should be encouraging them?

And to put in my own 2 cents, not studying maths up to year 12 (I'm not saying this needs to be at the highest possible level of abstraction, by any means) means a number of really bad things. It allows people to give up on something just because it's a bit of a challenge, and cuts off a huge number of options at the age of 15/16, when most people don't really know what they want to do yet. Maths isn't something that's easy to pick 20 years later when you've never seen it before - you need to lay the foundation early. I've taught a number of very well-meaning and intelligent people who were suffering for their 15 year old choices in my life sciences maths classes. Also, the abstraction in maths is not there to be difficult and prepare you for studying physics - abstract thinking, problem solving, breaking problems down into doable bits - are all really important skills that aren't taught in any of our other subjects.

[dolorosa-12.livejournal.com]

Did you mean to say that you have a problem with encouraging girls to study maths, or did i misread? Surely we should be encouraging them?

No, I have a problem with encouraging unenthusiastic people to study maths in the later years of high school. My opinion is that we have a problem with low numbers of people studying maths and sciences at tertiary level, but I feel that it, along with a lot of other social issues relating to education, must be addressed much earlier - in primary school and in the younger years of high school (Years 7 and 8). And rather than pushing for an increase in numeric terms (i.e. simply attempting to increase the numbers of students going on to do sciences at uni), we should be pushing for greater recognition of students' diverse abilities and interests, and funnelling those who have a genuine talent and/or interest into the appropriate subjects. My ideal outcome would be a slight increase in talented students in a variety of subjects, rather than a large increase of average students. Does that make sense?

I think this would do a lot to address the issues you raise in your second paragraph, because it would get people thinking about what they really wanted to do, and being helped to get there, a lot earlier on - so that they'd be more equipped to make decisions about whether or not to drop maths. Quite frankly, your final sentence is untrue. I have not come across any issues in my adult life that required those particular skills - at least in their mathematical manifestation. Of course I've had issues that have required abstract thinking and problem solving, and obviously my postgraduate research has had to be broken down into doable bits - but I learnt them all through researching and writing humanities essays. What the final two years of Maths taught me (something for which I'm actually quite grateful) is that there are things in life in which your efforts are not going to be reflected in the outcome. I recognise that I'm an odd case, in that I really was in a level that was too hard for me - I suspect I would've been fine in Advanced, rather than AME - but I'm still not necessarily sure that being in a level of Maths that matched my abilities would've taught me skills that I couldn't have picked up in the way I described.

I hope this doesn't come across as particularly grumpy. I actually think we should be doing more to encourage girls (and indeed the population in general) to pursue scientific careers, I just think the way that a lot of people intend to go about it is wrong. I think that rather than asking women who do enjoy maths and did go into that field why they did so, we should be asking girls who hate maths and find it difficult why they feel that way.

[jordan rastrick (from livejournal.com)]

I'm a bit torn. Maths really is cumulative in the way Anna talks about, and is really unlike other school subjects in this regard. Which is in fact part of where I think people go wrong - my "one bad year" thing is based on it, since one bad year of history at high school is no obstacle to going on to do a PhD in history a decade later but can actually matter with Maths.

And Maths is much more important for a whole bunch of stuff than many teenagers are capable of realising. Not, as you say, in the day to day life of the average member of society. But if you're in Anna's class because you want to be a biologist and can't do any maths, you're in trouble. Maths is language, no more and no less - its just the language of talking about those ideas and concepts that are very precisely defined. At least that's my conception of it. So the applicability of being highly fluent in Maths it is on almost the same scale as being highly fluent in regular language and the messier world it deals in.

Nonetheless - the bright teenager who really struggles to do mathematical thinking and wants to do biology probably will be better off steered toward a different career rather than given intensive tutoring. I'd rather put more effort into communicating to teenagers how many options they are losing by dropping maths out of mild laziness or apathy, than force everyone to do it all the way to year 12, including the person who has only ever wanted to be Head Choreographer for the sydney ballet since they were a kid, and is made completely miserable and negative toward school in general by the efforts to cram the cosine of 3/4 pi into their head. Anecdotally the people with the latter problem seem to vastly outnumber the former.

[dolorosa-12.livejournal.com]

Yeah, sorry, that was what I was getting at. I think a lot of the issues that we've been thrashing out here could be avoided if schools were better equipped to a) recognise the range of abilities and interests of their students and b) prepare said students for careers appropriate to these abilities and interests. This needs to go beyond a short discussion with a careers adviser or presentations by representatives of universities.

I'm not an education policy expert or public servant of any kind. All of my opinions are based on personal experience, observation of others and discussions of this nature. But the conclusion I've reached on this - and a range of other issues relating to problems with the education system in Australia and elsewhere - is that most solutions offered seem to target students too late. They don't recognise that difficulties and problems arise as early as primary school or early high school, and, if not addressed at that point, have profound and far-reaching effects. More needs to be done in terms of maths competency when students are younger, and I'd be inclined to explain that maths is necessary for careers such as biology, psychology and so on when students are 12 or 13, not when they get to uni.

[dolorosa-12.livejournal.com]

[O]nce you move past arithmetic and memorising trig and what not into more abstract stuff, supposedly its the same kind of cognitive abilities that make people good with words that start to matter in mathematics. And to me, this has always made a lot of sense - teasing out the meaning of a metaphor in a text seems pretty closely linked to teasing out the meaning of a bunch of axioms defining an algebraic structure.

The way a rather excellent Maths teacher explained it to me when I was tearing my hair out trying to work out why I'd got 35% in a test yet again, is that the more words you add to maths problems, the more confused people get. I'm not sure if this is the case for everyone, but certainly the way I remember it - and the way I remember it with my sister, who suffered from similar problems - is that I would get a problem, stare at it in confusion and not have any idea how to proceed. (I'm not talking about problems such as 'differentiate this fairly straightforward algebraic equation'.) Then someone would go, 'well, clearly it's this type of equation, you need to do this this and this and do this this and this with a graph and look then this happens.' I could do all the 'this this and this-ing', but what I couldn't do was get from the problem to the first step. It was like looking through opaque glass, or like my previous analogy of trying to read a foreign language. I've wondered if there's some kind of genetic component, or at least if your environment makes you more inclined to expect that you'll be good at some things and not others, because my mother also failed high school maths, and although I don't know about my dad, he certainly did an Arts degree, so clearly found scientific stuff less interesting. Then again, my two grandfathers were, respectively, an architect and a civil engineer, so they obviously had strong mathematical abilities.

I've also noticed that my lack of mathematical ability (or, more specifically, inability to do certain types of problem-solving) translates into an inability to think in a strategic way in games such as Risk or chess, really poor problem-solving skills (I'm terrible at games like Scrabble, crosswords and most types of puzzles, and Sudoku makes me feel ill) and just generally difficulties with anything that requires thinking along the lines of 'if I do Step X, and it is affected by Y and Z, what will happen?' Give me words, give me imagery and tropes, give me allusions and references. Give me an argument in words and I will find my way through it and do whatever is required with it. All the rest is beyond me.

Once again I know I'm very late to this particular party, but how good is Season 4 of Buffy?

It's funny you should say this, because it's almost universally hated among the fans. Sure, people love some of the episodes ('Hush', 'Something Blue' and 'Restless' usually come somewhere near the top in people's top ten), but there are some real dogs of episodes, and Riley is universally loathed. That said, I have a soft spot for Season 4. I love how it handles its overarching theme.

Conversations like this make me wish we were both in the same country. On the whole, I think blogging suits me better as a form of communication, but these are really things that would be better discussed face-to-face.

[jordan rastrick (from livejournal.com)]

Well, I had seen the DVD commentary where Joss mentions that a lot of people hated the overall arc of season 4 before I made that comment. But that was after I'd watched all the episodes and decided I thought it was great.

I think maybe because I'm watching it in big chunks, instead of an episode at a time, the good bits stood out more than the bad? Hush was one of the best pieces of television I've ever seen. And I really liked episodes I could easily picture the fandom hating, too - New Moon Rising, and This Year's Girl/Who You Are; I thought Oz and Faith both got great resolutions to their character arcs. In fact the character development across the whole season felt really strong all round, for everyone. There were points where it felt "awkward", people behaving out of character or just in general failing to be awesome, but I think on net they came out seeming more complex and well rounded - they violated my expectations ultimately because my expectations of them were too simplistic.

I was also in my mind drawing a direct contrast to season 3, which to me anyway was far more "patchy" - I thought it finished really strongly but the pacing at the start felt way off, and while it had some moving moments of its own it also had more moments that seemed to be trying to move me and failing. And of course there wasn't nearly enough of Spike overall :-)

[dolorosa-12.livejournal.com]

'This Year's Girl/Who Am I?' are generally pretty popular, because everyone loves Sarah Michelle Gellar and Eliza Dushku playing each others' characters. And Tara is almost universally loved, so Willow's story is popular among fans too. It's mainly Riley, who is absolutely detested, and some awkward writing, which to my mind was the result of the writers adjusting to the characters leaving a high school setting.

Season 3 - particularly the end - is my favourite Buffy season. I absolutely love it, I think the Mayor is the best villain (with the possible exception of Angelus in Season 2), and I think it does a stellar job of 'graduating' the characters from childhood to the first steps of adulthood. I would generally agree with you about the need for more Spike, but I'm not really sure how he would fit in, other than in 'Lovers' Walk', where he's awesome.

Are you up to Season 6 yet? I have some stuff to say about it, but I might send it to you as a facebook message rather than posting here.