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Convolution Is Fancy Multiplication

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Re: Convolution Is Fancy Multiplication

#91

Post by tails4e »

DoreenMichele wrote: post #88
dwrodri wrote: post #65

I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterExplained, Paul's Math Notes, 3Blue1Brown's YouTube Channel, Ben Eater's YouTube channel, and the entire body of high quality MOOCs are just available for free over the Internet is probably one of my favorite accomplishments of the human race in the 21st century…

because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well i…

I agree in general its an issue when basics are being thought by any person who does not really understand what they are teaching. They end up tecaching the rote method and not the intuition. Happens all the time in maths.

Re: Convolution Is Fancy Multiplication

#93

Post by jhoechtl »

parksy wrote: post #70
dwrodri wrote: post #65

I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterExplained, Paul's Math Notes, 3Blue1Brown's YouTube Channel, Ben Eater's YouTube channel, and the entire body of high quality MOOCs are just available for free over the Internet is probably one of my favorite accomplishments of the human race in the 21st century…

Definitely agree - I struggled beyond basic integration in High School, and my "why" and "what is it" type questions about calculus were met with annoyed "read the book" replies and young me lost interest in higher maths at a time when my mind was more plastic. As an adult having these personalities enthusiastically breaking down the fundamentals and using analogies to help cement the concepts intuitively has been a…

For me it clicked once it understood that integration is the area "beyond" the "curve".

Re: Convolution Is Fancy Multiplication

#94

Post by DoreenMichele »

tails4e wrote: post #91
DoreenMichele wrote: post #88

Earlier quoted context omitted.

because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well i…

I agree in general its an issue when basics are being thought by any person who does not really understand what they are teaching. They end up tecaching the rote method and not the intuition. Happens all the time in maths.

I think the larger issue here is that a lot of elementary school teachers are people who have a math phobia because their difficulties with math derailed their career dreams. So they not only are bad at teaching it, the primary thing they teach their students is that "Math is scary stuff and something to be feared."

And they teach it to really young kids who are very impressionable and don't have some means to avoid being brainwashed into believing it.

My one and only goal with homeschooling my son was to get him past the math phobia he had developed and teach him "Math is your friend." He's genuinely bad with numbers, but he no longer has a math phobia and has a better grasp of the concepts than a lot of people, even though he can't calculate anything in his head and routinely asks me or his brother to calculate it for him.

A math phobia is crippling and many people never get over it.

Re: Convolution Is Fancy Multiplication

#95

Post by jsinai »

DoreenMichele wrote: post #88
dwrodri wrote: post #65

I'm a firm believer that resources which raise the bar for math and computing education are huge catalysts for innovation. The fact that resources like BetterExplained, Paul's Math Notes, 3Blue1Brown's YouTube Channel, Ben Eater's YouTube channel, and the entire body of high quality MOOCs are just available for free over the Internet is probably one of my favorite accomplishments of the human race in the 21st century…

because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well i…

> a lot of elementary school teachers are women who weren’t doing well at math and got encouraged to go become an elementary school teacher because, basically sexism is alive and well

I hear your frustration, and I’m glad that there has been progress in this regard. However I think that what the GP was saying and what you’re saying are two different issues:

The GP is referring to particular teaching styles which might be overly formal (in the mathematical sense) or declarative (this is convolution, that’s how it is, remember it) as opposed to intuitive (which might not convoy the whole truth but helps some if not most people understand and remember the concept better). This issue can and often takes place in higher education where the teacher or lecturer is expected to be highly qualified.

I remember being frustrated with the way my linear algebra and multivariable calculus classes were taught. Both generalize to n dimensions but many operations and theorems can often be understood intuitively in two or three dimensions. The courses I took were extremely formal with not a minute spent on the graphical interpretation which would have helped so much. When I raised the issue with two separate professors, both were of the opinion that the graphical approach was frivolous because it wasn’t precise. But that argument misses the point of the lecture theatre space ...

Re: Convolution Is Fancy Multiplication

#96

Post by defanor »

m-hilgendorf wrote: post #13

I was introduced to convolution in a undergraduate signals/systems course in continuous time where it's basically magic that you memorize to pass your course. I think a better introduction would be through discrete convolution by reexamining polynomial multiplication (which is convolution through a different lens - the coefficients of the product of two polynomials is the convolution of their coefficients). That serv…

I was rather surprised that it wasn't discrete convolution in the article, after the hospital analogy. Perhaps even with finite summation first, and generalized afterwards; otherwise there's a bit of a leap.

Re: Convolution Is Fancy Multiplication

#97

Post by leoedin »

There's a brilliant (and free) book called The Scientist and Engineer's Guide to Digital Signal Processing which covers this and other DSP topics. It's very readable and clear - I found it super useful in understanding DSP and the maths surrounding it.

Most of the time the actual stuff happening is quite simple, but if you're not living and breathing mathematical notation the conventional explanations can be quite impenetrable. This book puts everything out in code, so you can follow the steps and truly understand what's happening.

http://www.dspguide.com/

Re: Convolution Is Fancy Multiplication

#98

Post by DoreenMichele »

jsinai wrote: post #95
DoreenMichele wrote: post #88

Earlier quoted context omitted.

because so many people were exposed to the topic through a resource (typically another person) who had little experience (or interest) in effectively teaching the subject. I used to homeschool and one of my sons had terrible baggage about math by the time I pulled him out of public school when he was 11. And somewhere along the way, I learned that a lot of elementary school teachers are women who weren't doing well i…

> a lot of elementary school teachers are women who weren’t doing well at math and got encouraged to go become an elementary school teacher because, basically sexism is alive and well I hear your frustration, and I’m glad that there has been progress in this regard. However I think that what the GP was saying and what you’re saying are two different issues: The GP is referring to particular teaching styles which migh…

To my mind, a system that shunts people into teaching elementary school in a way that actively creates early educators with a math phobia has got to have serious long term consequences, even for a lot of people who are good at it. We all get told "math is so hard," not just the bad students.

People who think a thing is hard and must be dealt with in a serious manner will use formal methods to ward off their fear of the topic or their fears of social perception. It takes a great deal of confidence to say "We are just going to have fun today and play with this wonderful topic!"

They exist, but they aren't the norm.

Re: Convolution Is Fancy Multiplication

#99

Post by enriquto »

ai_ja_nai wrote: post #90
enriquto wrote: post #80

Earlier quoted context omitted.

Why do you think academic institutions are something to work against to? I'm in academia and here everybody is enthralled and really happy about the explosion of high-quality, freely available learning resources. The only kind of complain that I have ever heard (and very rarely so) is because some of this material is supported by videos in a platform with shitty terms of service.

it's the bias that has to be worked against, not the institution

But who has that bias? Is it you? People in academia certainly not. It would be absurd. As if medical doctors and nurses would be against the education of the population for lifesaving techniques and for healthy eating.

Re: Convolution Is Fancy Multiplication

#100

Post by tauist »

enriquto wrote: post #99
ai_ja_nai wrote: post #90

Earlier quoted context omitted.

it's the bias that has to be worked against, not the institution

But who has that bias? Is it you? People in academia certainly not. It would be absurd. As if medical doctors and nurses would be against the education of the population for lifesaving techniques and for healthy eating.

> medical doctors > healthy eating

Wrong example, lol

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