Sunday 22 July 2012

More about the teaching of higher mathematics



I managed to irritate one or two people here yesterday; not for the first and almost certainly not for the last time. I wonder if those commenting really thought that I was advocating the securing to stakes and pelting with filth of those who failed effectively to motivate their children in the study of mathematics?  If so, it is time now to reveal that this was meant humorously!

In the coming week I want to look at home education in the secondary years, with particular reference to subjects which parents themselves found hard or disliked at school. All too often, we as parents transmit these prejudices and neuroses to our children, so that you will have families with a tradition of art and music, while others tend towards science. This certainly happens in schooling families and I strongly suspect that it is even more common in home educating families.

Today though, I want briefly to mention one or two personal things about my own daughter’s education and the peculiar man who supervised it. By the age of sixteen she had passed eight International GCSEs, all at A*. These were English language, English literature, mathematics, history, physics, biology, chemistry and religious studies. She had also gained Grade 6 (bronze medal) at acting with LAMDA, as well as  Grade 5 classical guitar and Grade 2 piano with the ABRSM. She had no lessons or tutoring in any of those subjects, except by me.

Now I wonder if readers think that all this was because I am some sort of Renaissance Man or Victorian polymath? Do they perhaps think that I am a musician in the morning, who acts at weekends and has a passionate interest in science and mathematics? Not a bit of it. I literally cannot play a single note on the guitar, nor have I ever acted, even at school. As for mathematics, I know hardly anything about the subject and was a complete failure at school. It was my worst subject. Readers are now perhaps scratching their heads, saying to themselves, ’Hang on a minute, wasn’t he talking about the joys of higher mathematics yesterday and rabbiting on about calculus? Somethings’s not right here!’

I shall be expanding upon this idea in the next week or so, but for now I will say that all I know about calculus is that it is concerned with changing motion and figuring out the area under curves. That is it; the sum total of my knowledge. My daughter needed calculus for her maths IGCSE and did it so well that she went on to get an A* in the subject at A level. How can this be, if I was such a duffer at maths and disliked the subject? What about physics? Surely I must be a specialist at that? Nothing of the sort.

This is only a short post, but I want to leave you with this thought. If I did not think that I could have provided my daughter with an education at least as rich and varied, as well as academically sound, as that which she would have received at the best of schools; I should never have embarked upon the enterprise in the first place. True, I had other motives, but this would have been an irreducible minimum, whatever other reasons I might have had for wanting to home educate.

Educating children at home has nothing to do with knowing about subjects. Nor does it, or perhaps I should say that it should not, have any connection with which things one enjoyed at school or found difficult there. Anybody can teach their child literally anything at all; from calculus to piano, from acting to chemistry. It requires no  prior knowledge and will not produce misery in any child. Before I finish, I must leave readers with a simple question. I have a reputation as being a highly structured, school-at-home type of home educator; one who taught, rather than allowed his child to learn naturally. Here is the question. Does anybody believe for a moment that it would be possible to get a child to work hard enough at the guitar to pass grade 5, unless the child was a willing partner in the process? Can anybody imagine forcing, against her wishes, a child of twelve to study calculus? Or biology, acting or anything else? If they can visualise such a neurotic and driven child, forced on by an unforgiving and fanatically pushy parent to over-achieve in all areas, simply to obey his wishes; well then, all I can say is that such people must have a vastly more vivid imagination that my own! It is quite literally impossible to get a two year-old to eat a carrot. How less likely is it that one would be able to persuade, against her will, an adolescent to study mathematics. As I say, I shall be looking at secondary education in the next few weeks and exploring this whole idea in more detail.

14 comments:

  1. I think you are probably preaching to the converted unless there are any non-HE readers new to the idea of HE. Not sure of the need to do it all yourself. I'm sure you had some outside help along the way; unless your daughter acted along she would have learnt from her fellow actors at least.

    So what would you say differentiates your style from autonomous education taking into consideration that AE includes parents suggesting subjects a child might be interested in (but not pushing if the child decides they are not currently interested), informal or structured learning according to the child's preference (it usually varies according to the subject matter) and helping the child follow their interests as far as they want to take them. Coercion in any form including nagging, persistent persuasion, exaggerated disappointment when a suggestion is rejected etc, should also be avoided.

    ReplyDelete
  2. "If so, it is time now to reveal that this was meant humorously!"

    Yes, it can be difficult to convey humour well in text. I gently poked fun at you yesterday and you accused me of being touchy. Maybe I should have used a smiley. I'm sure people realized that you exaggerated your feelings for comic effect and spoke to the underlying feelings rather than the "pelting with filth" comment. But presumably you know this and this comment if another attempt at humor? And maybe your touchy comment was a joke too? Maybe the whole blog is - what a fantastic joke that would be! :-)

    Our children also wanted to learn about things we knew nothing about so we used a combination of learning alongside them, providing them with self study materials, relevant trips and activities, finding people with a love of the subject, etc. Whatever worked and suited our children. Possibly, if someone particularly hates a subject, they're not the best person to help the child unless they are able to overcome the dislike. Lucky that wasn't an issue for us - at worst I think I felt neutral about some subjects and many of those could be picked up by my partner.

    ReplyDelete
  3. 'And maybe your touchy comment was a joke too? '

    Of course it was, I was actually chuckling as I typed it!

    ReplyDelete
  4. 'I think you are probably preaching to the converted unless there are any non-HE readers new to the idea of HE.'

    Well this was really intended for those who have been at it for years. I shall expand on this in the next few days.

    'Coercion in any form including nagging, persistent persuasion, exaggerated disappointment when a suggestion is rejected etc, should also be avoided.'

    I don't object to this on ideological grounds, but for purely pragmatic reasons; it is a not an effective way to get children to study and learn.

    'So what would you say differentiates your style from autonomous education'

    Because I decided that my daughter would be stufying mathematics, physics and so on, rather than waiting for her to expression an interest in them.

    'I'm sure you had some outside help along the way; unless your daughter acted along she would have learnt from her fellow actors at least.'

    Not at all. She did join a local ameteur dramatic society when she was sixteen, but that was after she had studied acting to grade 6. the whole business before that took place at home. This alone probably deserves its own post; staging a play by Shakespeare with only two actors!

    ReplyDelete
    Replies
    1. " Because I decided that my daughter would be stufying mathematics, physics and so on, rather than waiting for her to expression an interest in them."

      So you told her what she would be studying rather than suggesting the same subjects as possibilities? And she wanted to study everything you said she should learn, since you say, "can anybody imagine forcing, against her wishes, a child of twelve to tostudy calculus? Or biology, acting or anything else?" Sounds like you accidentally followed the AE approach in all but name since the only difference between your approach and AE is that the child is free to take up or refuse the parents suggestions with AE. If your child always wanted to follow your study plan and was not coerced I'm struggling to spot the difference. AE doesn't require the parent to wait for the child to express an interest. Making suggestions is fine.

      Delete
  5. 'Possibly, if someone particularly hates a subject, they're not the best person to help the child unless they are able to overcome the dislike'

    And this is something at which I shall be looking, the way that parents shape their children's interests and views on various academic subjects. From the mother who announces that she was made to study algebra at school and has never since needed to solve a simultaneous equation, to the father who claims that he does not 'get' opera. This is the hidden curriculum which all parents teach; what is valuable and what can be avoided.

    ReplyDelete
  6. "From the mother who announces that she was made to study algebra at school and has never since needed to solve a simultaneous equation, to the father who claims that he does not 'get' opera."

    I'm not sure if this is a problem if the parent also says something like, "but plenty of other people do like/understand it". Certainly my preferences appear to have little influence on my children judging by their varied interests!

    ReplyDelete
  7. "From the mother who announces that she was made to study algebra at school and has never since needed to solve a simultaneous equation, to the father who claims that he does not 'get' opera. This is the hidden curriculum which all parents teach; what is valuable and what can be avoided."

    Yes, of course. But what we have always done is make an effort for our children to meet and to learn from a wide range of people who have enthusiasms other than our own. So our son spent two and a half years going to weekly forest school sessions with people from the local wildlife trust, where he learned to use knives and make fires and so on. Neither I nor my partner had any great desire to sit in damp woodland for three hours every week, so their input was very valuable. This is just one example among many.

    As well as learning from other adults, we have always felt that it was important that our children have lots of opportunities to play with other children. Yes, many parents can teach their children a wide range of subjects but what we can't do is be children or teenagers. I was quite happy to read a few books and help my daughter get her geography IGCSE but I'm not much good as a someone to watch 'Friends' with her...

    ReplyDelete
  8. The way you set out your teaser for the next few posts was v effective. I can't wait to read about it. This is going to be really useful info.

    Some of the commenters above seem to be determined to make this all about home ed infighting re methods. It's sort of understandable, given the way that this blog has attacked unschoolers in the past. However, I think that an account of your experiences could be taken as just that.

    A

    P.S. Why did you choose IGCSE? How did you choose exam courses. Our ds likes History. Out of curiosity looked at exam course outlines and past papers. both GCSE and IGCSE amazingly boring. O Level - yes, you can still take them! -- was way more interesting and varied. Not immediately relevant, since ds is 9 yrs old, so no rush for the answer!

    ReplyDelete
  9. Argh! Typos in P.S.

    A

    ReplyDelete
  10. 'Our ds likes History. Out of curiosity looked at exam course outlines and past papers. both GCSE and IGCSE amazingly boring.'

    Slightly puzzled about this. History isn't really my thing, but the four topics which my daughter chose for the Edexcel IGCSE were fascinating. They were Russian history, 1856 to 1917, the Cold War, 1945 to 1962, World War I and, finally, the Changing Nature of Twentieth Century Warfare. All these topics meant visiting all sorts of museums, reading Marx, recreating the troop movements of the Western Front in 1916, looking at the Russian Revolution and things like the Korean War. I honestly didn't find it boring and nor, I suspect, did my daughter. She went on to study history at A level. Any subject can be as exciting as you wish to make it and studying history was more exciting than, say for example, physics.

    ReplyDelete
  11. It's true that any history can be exciting, but the courses on offer are covering a fairly narrow range of events and places. Thirty years ago I studied those topics which you listed, but also the Vietnam War, Six Day War and the rest of the Middle East soap opera, some of N. Ireland conflict, etc. It was great! I'd go home after school and be able to understand all the latest news on TV.

    Cannot understand why all these years later the National Curriculum and therefore the GCSEs are still stuck on the WW1 and 2 merry-go-round. I did hear that the NC stopped at 1963, but did not really believe it. It seems that my old-fashioned 1981 vintage O level was more up-to-date than the exams of today.

    In contrast the O level offered by CIE was so interesting, that I'd take it myself!

    A

    ReplyDelete
  12. Whoa! This blog looks exactly like my old one! It's on a entirely different topic but it has pretty much the same page layout and design. Outstanding choice of colors!

    Review my blog :: Air Max Pas Cher

    ReplyDelete
  13. Hi to every one, for the reason that I am actually eager of
    reading this web site's post to be updated on a regular basis. It consists of pleasant material.

    My web-site - Michael Kors Canada

    ReplyDelete