4 ms·

Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathe

by urthor 4y ago

Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathematics professionals (who then teach mathematics). > But it hampers understanding and excitement at the nascent stages Ultimately, self motivated learners dramatically outpace anyone else. A genuine interest will overwhelm any other factor, because the self motivated learner will not need to invest additional time finding excitement. Artificially motivating learners is a difficult, time consuming, and often marginally effective task. The only way I've seen consistently work is to have truly interested and fascinated public speakers. Who then teach to the 5%, and perpetuate the cycle.

aYsY4dDQ2NrcNzA 4y ago
Enthusiasm can be contagious.
- beardyw 4y ago
  Yes, my brother, then 17 explained to me, then 10, the principles of calculus because he was so excited by it. He did it in pictures (little slices etc) and I got the basic idea, though I had no use for it. I just caught his enthusiasm.
  - urthor 4y ago
    You'd be surprised just how significant that prompting was to your future learning. The most valuable learning you can get from a book is reading the table of contents, then the preface & foreword, then leaving it alone for 5 days. In the interim, the table of contents seeps into your brain. You will be BRILLIANTLY prepared for the content.
    - scrollaway 4y ago
      Thanks for the suggestion. I’ll try this next book I read :)
      - wheelinsupial 4y ago
        If you're reading a math or other computational or textbook, I'd also suggest to read through the exercises in the back of the chapter before diving in. It primes you with keywords from the questions and helps you to think of how you can use what you've just read.
    - beardyw 4y ago
      Yes, but so poor is my memory that when I eventually sat my exams I had to do most of it by those first principles instead of the known formulas!
      - hanche 4y ago
        I can see how that sucks during the exam, but knowing how to do it from first principles will stick with you for much longer. When I told my students that I went into mathematics because my memory is so bad, they never believed me. But it is the truth (at least somewhat).
alexvoda 4y ago
I think you are conflating enthusiasm with motivation. We should not try to motivate students, we should try to not kill students enthusiasm. And for this the very early classes are essential. If you kill a persons enthusiasm in a subject or in learning itself, you will afterwards toil years trying to motivate them.
mkl 4y ago
> Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathematics professionals (who then teach mathematics). I agree with the rest of your comment, but this is not true. I teach university maths. We are well aware that most of our students are not majoring in maths and will not go on to teach it. Most of them at my university will go on to be engineers, so we teach for that in their courses, light on proofs and derivations and focused on grounded practical knowledge and techniques.
- ABeeSea 4y ago
  You teach abstract algebra and real analysis that’s light on proofs?
  - mkl 4y ago
    No, engineering students don't take those courses. We teach as appropriate to the students in each course, unlike what urthor claimed.
- urthor 4y ago
  Thank for your response. That's actually hugely insightful. > We are well aware that most of our students are not majoring in maths and will not go on to teach it. Most of them at my university will go on to be engineers, so we teach for that in their courses, light on proofs and derivations and focused on grounded practical knowledge and techniques. One important part of why I have this opinion, mathematics is poorly taught to the lower 95th percentile, is historical. Historically, pre 1950 & the GI Bill only the wealthiest students (who sat at the back of the class, partied, and generally focused on Latin not the hard sciences), and the most able students, went to university. The reason I find that's incredibly relevant is this Hackernews post. Easily my favourite of all time. https://news.ycombinator.com/item?id=32974959 https://news.ycombinator.com/item?id=32974959 In my mind, the consequence of all that is teaching the 5% is a well worn, highly polished process. Hundreds of years of effort has been invested in the 5%. For the 95th, barely a few decades. And even then, many academics I find take the elitist point of view. In my experience, your department's point of view is very much the exception. A majority of academics I find follow one of two options: -> The lazy option. -> Train my future graduate students, bugger the rest. IMO, the methodologies for training that lowest 95% are not at all developed. Arguably for example, one theory I have is proof based mathematics should be introduced in Grade 7. Proof based mathematics is the simplest, quickest, easiest way for an engineer to learn a new piece of mathematics. A proof is a quicker, and more time efficient, teaching tool than 5 exercises. Is my theory. And yet, the status quo is only pure mathematicians need to know proofs.
thebooktocome 4y ago
> Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathematics professionals (who then teach mathematics). I'm reminded of Lockhart's Lament, https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....: > "Um, these high school classes you mentioned..." > "You mean Paint-By-Numbers? We're seeing much higher enrollments lately, [...]" > "And when do students get to paint freely, on a blank canvas?" > "You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I've got a degree in Painting myself, but I've never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board."

by urthor 4y ago

aYsY4dDQ2NrcNzA 4y ago

Enthusiasm can be contagious.

beardyw 4y ago
Yes, my brother, then 17 explained to me, then 10, the principles of calculus because he was so excited by it. He did it in pictures (little slices etc) and I got the basic idea, though I had no use for it. I just caught his enthusiasm.
- urthor 4y ago
  You'd be surprised just how significant that prompting was to your future learning. The most valuable learning you can get from a book is reading the table of contents, then the preface & foreword, then leaving it alone for 5 days. In the interim, the table of contents seeps into your brain. You will be BRILLIANTLY prepared for the content.
  - scrollaway 4y ago
    Thanks for the suggestion. I’ll try this next book I read :)
    - wheelinsupial 4y ago
      If you're reading a math or other computational or textbook, I'd also suggest to read through the exercises in the back of the chapter before diving in. It primes you with keywords from the questions and helps you to think of how you can use what you've just read.
  - beardyw 4y ago
    Yes, but so poor is my memory that when I eventually sat my exams I had to do most of it by those first principles instead of the known formulas!
    - hanche 4y ago
      I can see how that sucks during the exam, but knowing how to do it from first principles will stick with you for much longer. When I told my students that I went into mathematics because my memory is so bad, they never believed me. But it is the truth (at least somewhat).

alexvoda 4y ago

I think you are conflating enthusiasm with motivation. We should not try to motivate students, we should try to not kill students enthusiasm. And for this the very early classes are essential. If you kill a persons enthusiasm in a subject or in learning itself, you will afterwards toil years trying to motivate them.

mkl 4y ago

> Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathematics professionals (who then teach mathematics). I agree with the rest of your comment, but this is not true. I teach university maths. We are well aware that most of our students are not majoring in maths and will not go on to teach it. Most of them at my university will go on to be engineers, so we teach for that in their courses, light on proofs and derivations and focused on grounded practical knowledge and techniques.

ABeeSea 4y ago
You teach abstract algebra and real analysis that’s light on proofs?
- mkl 4y ago
  No, engineering students don't take those courses. We teach as appropriate to the students in each course, unlike what urthor claimed.
urthor 4y ago
Thank for your response. That's actually hugely insightful. > We are well aware that most of our students are not majoring in maths and will not go on to teach it. Most of them at my university will go on to be engineers, so we teach for that in their courses, light on proofs and derivations and focused on grounded practical knowledge and techniques. One important part of why I have this opinion, mathematics is poorly taught to the lower 95th percentile, is historical. Historically, pre 1950 & the GI Bill only the wealthiest students (who sat at the back of the class, partied, and generally focused on Latin not the hard sciences), and the most able students, went to university. The reason I find that's incredibly relevant is this Hackernews post. Easily my favourite of all time. https://news.ycombinator.com/item?id=32974959 https://news.ycombinator.com/item?id=32974959 In my mind, the consequence of all that is teaching the 5% is a well worn, highly polished process. Hundreds of years of effort has been invested in the 5%. For the 95th, barely a few decades. And even then, many academics I find take the elitist point of view. In my experience, your department's point of view is very much the exception. A majority of academics I find follow one of two options: -> The lazy option. -> Train my future graduate students, bugger the rest. IMO, the methodologies for training that lowest 95% are not at all developed. Arguably for example, one theory I have is proof based mathematics should be introduced in Grade 7. Proof based mathematics is the simplest, quickest, easiest way for an engineer to learn a new piece of mathematics. A proof is a quicker, and more time efficient, teaching tool than 5 exercises. Is my theory. And yet, the status quo is only pure mathematicians need to know proofs.

thebooktocome 4y ago

> Because mathematics, like most tertiary disciplines, has always been taught in a teaching style suitable for the 5% of the audience who aim to go on to be mathematics professionals (who then teach mathematics). I'm reminded of Lockhart's Lament, https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....: > "Um, these high school classes you mentioned..." > "You mean Paint-By-Numbers? We're seeing much higher enrollments lately, [...]" > "And when do students get to paint freely, on a blank canvas?" > "You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I've got a degree in Painting myself, but I've never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board."