15 ms·

Will it rot my students' brains if they use Mathematica? (2002)

99 points by mikevm 5y ago

andrecarini 5y ago
Issues of proprietary codes/services aside, tools like Mathematica and WolframAlpha are great for solving actual problems. IMHO, a big problem with math education in general is that it focuses on formalisms and equations first while leaving the big picture as just an addendum. That's not so great for those having a hard time keeping motivated without seeing a real life application that is relevant to them.
Qem 5y ago
Related, Alan Kay's views on this subject: https://www.quora.com/What-does-Alan-Kay-think-about-computer-algebra-system-e-g-SymPy-and-SageMath-usage-in-mathematics-education-before-graduate-school-Would-widespread-use-of-powered-cognition-assists-like-these-rot-younger-students https://www.quora.com/What-does-Alan-Kay-think-about-compute...
ivanjef 5y ago
I’m Dr Ivan Jefferrey I want to say a Grateful thank you to Joe after different experience of fake hacker i have met,, a friend recommend him to me with faith i contact him and explain my self, on what’s happening with my grade and credit score, told me not to worry and gave me his word, i don’t know him, never met him before but makes me feel comfortable with is word and experience, i had to share this as am sure that most here, looking for the right hacker and have not seen yet,,, please try and contact Joe (DIGITALDAWGPOUNDHACKERGROUP@GMAIL.COM) on any service of help you need from him as hacker.. it a testimony you have the right to give yours too by helping others to know there is still high rate good hackers that are highly experienced, he responds on email, text messages and whatsapp… Name: Joe Engressia. Phone Number: +1(732) 639–1527.
lloydatkinson 5y ago
I couldn't read past the first few analogies. Is there a TLDR? Also, why must pages be without styles and so w i d e? What is this, a manpage? Long form text should not need to be so wide. Basic CSS can be applied to a site to make it readable, don't even need to add classes to the HTML to do it. https://watercss.kognise.dev/ https://watercss.kognise.dev/ Here is the page with readability turned on: https://imgur.com/a/0yzRY61 https://imgur.com/a/0yzRY61
- bruce343434 5y ago
  A trick to using old web pages like these is to enable reader mode in your browser. In fact, I use that trick pretty much everywhere nowadays.
- deleted 5y ago
  [deleted]
- lapinot 5y ago
  The footer provides a hint for the why: > Converted by Mathematica May 30, 2002
  - lloydatkinson 5y ago
    And heres mathematica.com 2 years before that. https://web.archive.org/web/20000520004659/https://mathematica.com/ https://web.archive.org/web/20000520004659/https://mathemati...
- TeMPOraL 5y ago
  I like pages like that. That's because they let me quickly "style" them to optimal size and shape using tools meant for this job - that is, browser zoom feature and/or window manager's facility to resize windows. It's sad that we've forgotten why web rendering has fluid layout: the whole point was to enable the user to make a web document work for them. In contrast, the modern websites are essentially PDFs emulated with CSS and JS.
  - lloydatkinson 5y ago
    At 400% zoom in Chrome in order to have a comfortable reading width about 2 sentences fit on the whole 1080p screen. I'm not sure zooming in and out is exactly a nice or helpful user experience.
    - iainmerrick 5y ago
      Can you make the window narrower?
bennyp101 5y ago
Quite interesting in that in the 20 years since that was written, the whole "socially unacceptable" to use a calculator to work out simple sums, is not (as far as I see) the norm. I would say that it is very normal to quickly pull out a phone, or ask on your watch, or as Alexa etc.
- pelasaco 5y ago
  I still remember an IT director that I met @ Bank of Boston that said us: "To use google is for lazy people". 2003, I believe.
  - bennyp101 5y ago
    And now it's more about your "Google-Fu" and do you know how to search properly to find the result you need! I wonder what things we consider "lazy" at the moment, will become the standard in 20 years
    - pelasaco 5y ago
      Now the Movie Wall-E[1] came to my mind, where humans couldn't even walk and all the job was done by robots. [1]: https://en.wikipedia.org/wiki/WALL-E https://en.wikipedia.org/wiki/WALL-E
- willcipriano 5y ago
  "You won't always have a calculator!" - Every teacher in school growing up
  - andi999 5y ago
    Yes, but how do you do some calculations when you are driving and thinking about some physics problem?
    - SquibblesRedux 5y ago
      For most of the population, driving while thinking about a physics problem would be considered distracted driving, unless that problem involved avoiding hitting something in the road.
lqet 5y ago
TL;DR: using a calculator to add and multiply, or Mathematica to do integration is okay because as society advances there is no need for certain skills anymore, freeing you to obtain other skills. I am not sure I agree. The argument only seems to work if you consider a very simplistic teleological model of skill learning: that the only benefit in learning a skill is mastering a very specific task, e.g. multiplication, or derivation. But you learn a lot of other skills on the way that may be useful for completely different tasks - or even tasks which aren't known yet and thus cannot yet be trained specifically. As my university teacher in Latin once said: sure, you don't need Latin anymore, but learning it will unlock areas in your brain previously unknown to you.
- dr_dshiv 5y ago
  Do you know “kill math”? http://worrydream.com/KillMath/ http://worrydream.com/KillMath/
  - civilized 5y ago
    The idea that seemingly motivates this project -- that it is somehow impossible or undesirable or not ideal for people to learn enough symbolic manipulation to do basic algebra -- is depressing to me. Now we're going to have people who know algebra programming apps to help people who don't know algebra solve extremely specific problems with no ability to generalize.
    - zafka 5y ago
      I did not get that impression at all. The first example talked about visualizing differential equations.
    - dr_dshiv 5y ago
      That is not the motivation. The motivation is to develop better interfaces for mathematical concepts. In the same way as Arabic numerals are better interfaces than Roman numerals.
      - 5y ago
deleted 5y ago
[deleted]
gbear605 5y ago
The second “chapter” of this post is pretty disappointing. It seems like one of the authors doesn’t like violent video games (and thinks that they’re the cause of school shootings!) and because of that thinks (or at least implies) that educational software is bad because it’s on a spectrum with violent video games. Also, while even some of the best educational software (like Duolingo) have problems, they’re generally not the problems that the authors expected.
- jrimbault 5y ago
  There should probably be a [2002] date in the title. The discourse around Mathematica, educational software, and video games has changed a lot in 20 years. I've the whole thing, not much is particularly relevent. Wolfram asks simply too much per license to be widely used in primary and secondary education.
- dr_orpheus 5y ago
  Yes, he also uses "On Killing" to support his argument for video games. It is a very fascinating (and disturbing) book. But most of the book is focused on the changes in military training that led to the increase in "shoot to kill" between WWII and Vietnam. In addition to the military training the book also talks about dis-association of killing through different methods and how that increased the "shoot to kill". The basic argument is that it is easier to kill someone when seeing them at a distance through the scope of a rifle than being right next to them and stabbing them. The other part of the dis-association is campaigns to dehumanize the enemy in war and not refer to them or acknowledge that they are individual humans. The video games argument in "On Killing" isn't part of the main thesis of the book, it is more tacked on the end. Whereas the rest of the book is looking at the past and evidence of what has happened. The video game part of it was (at the time) more focused on current feelings and attitudes towards it and was not substantiated.
teddyh 5y ago
Making people get used to (and be somewhat dependent on) Mathematica, a very expensive proprietary program, is doing people a large disservice. But it is very profitable for Wolfram. Also, the “video games make people violent” argument rears its ugly head.
- amadeuspagel 5y ago
  > Also, the “video games make people violent” argument rears its ugly head. Can't stand this kind of rhetoric. Arguments aren't scary monsters.
- dqpb 5y ago
  This dialog isn't really about Mathematica.
- EForEndeavour 5y ago
  If violent video games make people violent, then surely Mathematica makes people want to do more math.
  - EGreg 5y ago
    Why can’t both be true? There is an argument to be made that gangsta rap made a generation of impressionable kids much more rough around the edges, as it defined the new “cool” for them. Even though it wasn’t “supposed to be for them”, they knew all the words, which are loaded with expletives and misogynistic lyrics, and sowing distrust of the police etc. Maybe I am just a social conservative but I agree with this lady who tried, in vain, to fight against the capitalist machine that is ths music industry: https://m.youtube.com/watch?v=Pr6gb1w72xA https://m.youtube.com/watch?v=Pr6gb1w72xA Kids are impressionable — the Merchants of Cool documentary clearly shows how capitalist industries exploit that to sell more stuff: https://www.pbs.org/wgbh/frontline/film/showscool/ https://www.pbs.org/wgbh/frontline/film/showscool/ It also helped shape a rift, in my opinion, between the Black and the White youth that grew up now, which had been closing thanks to Liberalism and efforts to move past it.
    - 5y ago
xvilka 5y ago
Mathematica is good. The language itself feels weird though. But for most students using Sage Math[1] would be a much more convenient option. [1] https://www.sagemath.org/ https://www.sagemath.org/
- yissp 5y ago
  To be fair, this didn't exist in 2002 when the article was written.
rob_c 5y ago
It strongly depends on the problem set. For teaching id broadly day either set it as a prerequisite to examine something it can't do or leave it until the last lecture to show the course material can be applied more efficiently. Learning is as much getting used to using tools correctly as understanding what the tools do and how they do it. I've worked with those who yes, have had their brain rot due to blindly trusting Mathematica or equivalent and they never spot first step errors from their blind spot. That being said I've worked with one person who used it really well and I think they were genuinely more efficient for it existing.
- 1001101 5y ago
  BC calc in high school, I probably leaned on Mathematica a little too much, but mostly to check my work. Once, I got stumped on an integral and what Mathematica churned out wasn't even close (this was '94). Got a nice little note about that in the margin from my teacher. 0 points. Might still be some Mathematica pitfalls for teachable moments.
wiz21c 5y ago
My professor had a variant of that discourse regarding the computation of Linear Programs : "Prefer Gurobi (or Mosek) over GLPK because GLPK is bugged". My (limited) test show that GLPK works just fine. (GLPK is free software, Gurobi is proprietary) Now to be honest, the skills I learn over Gurobi, at the level I am, are super transferable to other software, so I'm not trapped into that proprietary stuff.
- lqet 5y ago
  At least on integer linear programs, I have found the performance of GLPK to be very disappointing, but I didn't notice any bugs. When compared to GLPK, gurobi is usually orders of magnitude faster (I had programs which gurobi optimized in a few seconds, while GLPK couldn't even find a feasible solution in 24 hours). If you need a free solver with reasonable performance, you should consider the COIN-OR project [0]. [0] https://www.coin-or.org/projects/ https://www.coin-or.org/projects/
analog31 5y ago
A friend of mine used Mathematica in a high school math classroom. I've also met some of his former students who think he was their best teacher. Something that occurs to me is that most of us have a poor grasp of why we even teach school math: It's treated as some kind of tournament to get into college, or a general IQ building exercise, or even a form of obedience training. The math that is "real" to them is just what they happened to learn, the way they learned it. But most people admit that they forgot all of their math immediately upon finishing school. And school math isn't even how "math people" do math. I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel. I'm not too worried about Mathematica being proprietary. Like with programming, if you learn one language, you can usually learn another in a jiffy.
- foobarian 5y ago
  > Something that occurs to me is that most of us have a poor grasp of why we even teach school math I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.
  - dhosek 5y ago
    Some of it comes down to insufficient grounding in math education preparation. In Illinois at least, K5 teachers are required to take a class that's effectively high school algebra, but at least where I got my credential, the class was taught as if it were just a remedial math class (which, to be honest, it was for more than a few of these would-be K5 teachers), rather than making it clear that the math that they would be teaching would be preparatory for the later class. Similar situations occur with 6-12 mathematics education preparation. This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why. In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.
- 5y ago
stared 5y ago
Is [a technology enhancing cognition] making us stupid? In some sense - yes. Every cognitive prosthetics or enhancer means that we do not need to develop a particular set of skills. At the same time - it allows us to move further! Thanks to writing, we don't need to remember everything. Thanks to the Internet, we can retrieve this information in seconds (not days or months, depending on if a book was in a nearby library). Integrals are the art of the past. Sure, it is still worth doing some, but rather than memorizing hundreds of tricks, let's focus on something different than reinventing the wheel.
dhosek 5y ago
Way back when I taught math, I remember having a student in one of my junior high mathematics for college students classes who pulled out her calculator to do 8+9 (that's the exact calculation, I remember it remarkably clearly). And yet, she was able to manage the symbolic manipulation around the rest of the algebra problem she was solving. The thing I took away from that is that while we tend to think of arithmetic as a prerequisite for algebra, the skill sets are largely orthogonal. I kind of wonder if this was part of how the child of two math professors¹ was taking upper-division college level math classes at Harvey Mudd as a high school student. It's not so much that he learned K5 mathematics quickly and was on to pre-algebra and algebra as that he was likely introduced to algebraic concepts much sooner than his peers. ⸻⸻⸻ 1. I never met him, his time was a little before mine, but I recall someone who had met him saying that his parents taught him a lot of mathematics but not so much by way of social skills.
lmilcin 5y ago
In my trade school, we had this class devoted exclusively to calculating things fast in memory. The exam consisted of running a bunch of calculations as fast as possible without writing down anything other than answer. It is interesting that you can learn to calculate a lot of useful stuff in memory and there is a lot of tricks and you can get quite proficient at it after one semester of classes and some training. But once I left this school it was completely unusable skill. It sort of helps me estimate things, a little bit? I guess? But I also carry a phone with me at all times and I have a powerful calculator on my desk just within reach. A skill that is not being used deteriorates, and now I can no longer multiply 5 digit numbers in memory and I use calculator for anything that involves more than 3 digits. And I don't feel like I lost anything. There are so many useful skills to learn. If you want to spend time, learn something else that is more useful. And if you don't want to learn something useful learn something that gives you joy or impresses people.
alyandon 5y ago
Slight tangent - but back in the day while I was attending university I started turning in all my engineering assignments using MathCAD. MathCAD occupied this weird space of a living document for math with additional Mathematica like functionality for symbolic manipulation. I certainly don't feel to this day like I lost anything vs doing everything tediously by hand 100% of the time. My professors liked it so much they standardized on it and licensed the student edition for the entire department.
jointpdf 5y ago
You can get Mathematica for free on any Raspberry Pi (~$35), so that more or less renders the point about expense moot: https://www.wolfram.com/raspberry-pi/ https://www.wolfram.com/raspberry-pi/ There is also a pretty nice introductory book that is aimed at students: https://www.wolfram.com/language/elementary-introduction/2nd-ed/ https://www.wolfram.com/language/elementary-introduction/2nd...
jrm4 5y ago
The more I look at this topic, the more I'm thinking -- if the goal is "real world math" (which it perhaps shouldn't ALWAYS be, but let's go with it) it feels like the solution is probably "get the kids in front of Excel (or Calc/Sheets) as soon as possible." A big wide open "environment" to get things done in the same way that people in the real world do. Incidentally, I'm also thinking that this might also apply to "programming?"
davidkunz 5y ago
When doing math at school I never quite enjoyed it because it didn't feel like it could "scale". You always had to do these clunky calculations which are so error prone, that the slightest mistake could mess up your whole work. Instead of focussing on the essence, my mind was occupied with not messing things up when applying the "instructions". I always wondered how the industry would actually use math to solve its problems. With programming/mathematical software, it finally clicked and it gave me a powerful, practical tool to make mathematics work. Finally it was not so much about not messing up, but about actually building something. I enjoyed it a lot and in the end I obtained a PhD in theoretical particle physics and became a software developer.
karaterobot 5y ago
> Misuse of computers is easy and a problem but no use is presently a bigger problem. This argument seems to be from that techno-utopian era, when we thought that just having access to computers would elevate civilization, and that we'd always have access to computers, so things would keep getting better and better as long as we embraced technology. What happened instead was a bit more complicated than that: when people got access to ubiquitous computing, it did teach them a new set of skills, and they did lose some old ones. But, we don't live in the world many people expected would come about as a result. We live in a different world, with many tradeoffs we hadn't expected. Some good things, some bad things. But one thing I think it's safe to say is that the average person is not using computers as tools to think in more abstract and sophisticated ways than they were capable of in 2002. So, the argument he's making is phrased as pragmatic, but I wonder to what extent that argument just assumes a certain, positive outcome. Would the author make the same argument, with the same level of confidence today?
0xbadcafebee 5y ago
I knew a cryptographer who did their entire job in Mathematica for years and only rarely ever touched a common programming language. The output of their work informed a lot of other people's work. I don't know if their brain rotted, but they got a heck of a lot of work done with minimal effort and time.
dekhn 5y ago
I remember getting Mathematica because I thought it would help me solve hard integrals (a common pastime in my physics-oriented graduate career) but all it did was make more complicated integrals. I actually wrote a whole python/mathematica interface that was very elegant, but most of what I learned was cool Python tricks.
bjackman 5y ago
I have been thinking a lot lately about the point "such an attitude represents a tremendous degree of disrespect of our forepersons". The other day I watched "Cargo" on Netflix, in which after a civilisational collapse, many indigenous Australians are depicted as going "back to the old ways". I found this quite problematic: it suggests that the pre-European way of life was so easy that a bunch of adults can just _start doing it again_. As if it's some natural animalistic habit you can just fall into, and not a set of skills and knowledge that evolved over millennia. I guess it's possible we were supposed to read that these people's communities had passed down that knowledge and experience across the intervening centuries. Maybe they have.
dr_kiszonka 5y ago
Are there any good textbooks that introduce applied math and engineering methods using software* (and not require solving problems by hand)? *By software I mean both programming languages (Python) and software suites (MatLab, Mathematica, Sage, etc.),
joeman1000 5y ago
As an science & engineering undergrad, I was taught some basic Mathematica usage in 2 subjects (Intro. Physics). The sentiment amongst engineering teachers was that ‘reliance on computer tools is dangerous’, since if you didn’t grasp the fundamentals, you couldn’t properly verify the answers produced. I found this to be one of the largest disappointments while earning my degree: this sentiment is holding people back from embracing the future and I mostly think that teachers just didn’t want to learn programming. As a result, engineers were phobic of doing any coding to solve problems (in my experience working in groups) and instead relied on primitive pen & paper or excel solutions, both of which are more time consuming to scale, re-use or even to verify! If you use Mathematica as a literate programming tool, like a Jupyter notebook, a solution is more readable and verifiable than hand-notes or excel. I had to mostly learn it on my own, and have built up a large library of tools to tackle engineering problems. As a result I can save time on forgetting/re-learning how to do things, as I have a searchable database of solutions at my fingertips. I check and test each of my ‘scripts’ against textbook answers, so I know I can trust them. TL;DR: Teachers, please encourage computer usage for problem solving, but make students understand they need to grasp the fundamentals first!
jonny_eh 5y ago
Great read until they started suggesting that violent video games were leading to school shootings, which the science totally disagrees with.

99 points by mikevm 5y ago

Issues of proprietary codes/services aside, tools like Mathematica and WolframAlpha are great for solving actual problems. IMHO, a big problem with math education in general is that it focuses on formalisms and equations first while leaving the big picture as just an addendum. That's not so great for those having a hard time keeping motivated without seeing a real life application that is relevant to them.

Qem 5y ago

Related, Alan Kay's views on this subject: https://www.quora.com/What-does-Alan-Kay-think-about-computer-algebra-system-e-g-SymPy-and-SageMath-usage-in-mathematics-education-before-graduate-school-Would-widespread-use-of-powered-cognition-assists-like-these-rot-younger-students https://www.quora.com/What-does-Alan-Kay-think-about-compute...

ivanjef 5y ago

I’m Dr Ivan Jefferrey I want to say a Grateful thank you to Joe after different experience of fake hacker i have met,, a friend recommend him to me with faith i contact him and explain my self, on what’s happening with my grade and credit score, told me not to worry and gave me his word, i don’t know him, never met him before but makes me feel comfortable with is word and experience, i had to share this as am sure that most here, looking for the right hacker and have not seen yet,,, please try and contact Joe (DIGITALDAWGPOUNDHACKERGROUP@GMAIL.COM) on any service of help you need from him as hacker.. it a testimony you have the right to give yours too by helping others to know there is still high rate good hackers that are highly experienced, he responds on email, text messages and whatsapp… Name: Joe Engressia. Phone Number: +1(732) 639–1527.

lloydatkinson 5y ago

I couldn't read past the first few analogies. Is there a TLDR? Also, why must pages be without styles and so w i d e? What is this, a manpage? Long form text should not need to be so wide. Basic CSS can be applied to a site to make it readable, don't even need to add classes to the HTML to do it. https://watercss.kognise.dev/ https://watercss.kognise.dev/ Here is the page with readability turned on: https://imgur.com/a/0yzRY61 https://imgur.com/a/0yzRY61

bruce343434 5y ago
A trick to using old web pages like these is to enable reader mode in your browser. In fact, I use that trick pretty much everywhere nowadays.
deleted 5y ago
[deleted]
lapinot 5y ago
The footer provides a hint for the why: > Converted by Mathematica May 30, 2002
- lloydatkinson 5y ago
  And heres mathematica.com 2 years before that. https://web.archive.org/web/20000520004659/https://mathematica.com/ https://web.archive.org/web/20000520004659/https://mathemati...
TeMPOraL 5y ago
I like pages like that. That's because they let me quickly "style" them to optimal size and shape using tools meant for this job - that is, browser zoom feature and/or window manager's facility to resize windows. It's sad that we've forgotten why web rendering has fluid layout: the whole point was to enable the user to make a web document work for them. In contrast, the modern websites are essentially PDFs emulated with CSS and JS.
- lloydatkinson 5y ago
  At 400% zoom in Chrome in order to have a comfortable reading width about 2 sentences fit on the whole 1080p screen. I'm not sure zooming in and out is exactly a nice or helpful user experience.
  - iainmerrick 5y ago
    Can you make the window narrower?

bennyp101 5y ago

Quite interesting in that in the 20 years since that was written, the whole "socially unacceptable" to use a calculator to work out simple sums, is not (as far as I see) the norm. I would say that it is very normal to quickly pull out a phone, or ask on your watch, or as Alexa etc.

pelasaco 5y ago
I still remember an IT director that I met @ Bank of Boston that said us: "To use google is for lazy people". 2003, I believe.
- bennyp101 5y ago
  And now it's more about your "Google-Fu" and do you know how to search properly to find the result you need! I wonder what things we consider "lazy" at the moment, will become the standard in 20 years
  - pelasaco 5y ago
    Now the Movie Wall-E[1] came to my mind, where humans couldn't even walk and all the job was done by robots. [1]: https://en.wikipedia.org/wiki/WALL-E https://en.wikipedia.org/wiki/WALL-E
willcipriano 5y ago
"You won't always have a calculator!" - Every teacher in school growing up
- andi999 5y ago
  Yes, but how do you do some calculations when you are driving and thinking about some physics problem?
  - SquibblesRedux 5y ago
    For most of the population, driving while thinking about a physics problem would be considered distracted driving, unless that problem involved avoiding hitting something in the road.

lqet 5y ago

TL;DR: using a calculator to add and multiply, or Mathematica to do integration is okay because as society advances there is no need for certain skills anymore, freeing you to obtain other skills. I am not sure I agree. The argument only seems to work if you consider a very simplistic teleological model of skill learning: that the only benefit in learning a skill is mastering a very specific task, e.g. multiplication, or derivation. But you learn a lot of other skills on the way that may be useful for completely different tasks - or even tasks which aren't known yet and thus cannot yet be trained specifically. As my university teacher in Latin once said: sure, you don't need Latin anymore, but learning it will unlock areas in your brain previously unknown to you.

dr_dshiv 5y ago
Do you know “kill math”? http://worrydream.com/KillMath/ http://worrydream.com/KillMath/
- civilized 5y ago
  The idea that seemingly motivates this project -- that it is somehow impossible or undesirable or not ideal for people to learn enough symbolic manipulation to do basic algebra -- is depressing to me. Now we're going to have people who know algebra programming apps to help people who don't know algebra solve extremely specific problems with no ability to generalize.
  - zafka 5y ago
    I did not get that impression at all. The first example talked about visualizing differential equations.
  - dr_dshiv 5y ago
    That is not the motivation. The motivation is to develop better interfaces for mathematical concepts. In the same way as Arabic numerals are better interfaces than Roman numerals.
    - 5y ago

deleted 5y ago

[deleted]

gbear605 5y ago

The second “chapter” of this post is pretty disappointing. It seems like one of the authors doesn’t like violent video games (and thinks that they’re the cause of school shootings!) and because of that thinks (or at least implies) that educational software is bad because it’s on a spectrum with violent video games. Also, while even some of the best educational software (like Duolingo) have problems, they’re generally not the problems that the authors expected.

jrimbault 5y ago
There should probably be a [2002] date in the title. The discourse around Mathematica, educational software, and video games has changed a lot in 20 years. I've the whole thing, not much is particularly relevent. Wolfram asks simply too much per license to be widely used in primary and secondary education.
dr_orpheus 5y ago
Yes, he also uses "On Killing" to support his argument for video games. It is a very fascinating (and disturbing) book. But most of the book is focused on the changes in military training that led to the increase in "shoot to kill" between WWII and Vietnam. In addition to the military training the book also talks about dis-association of killing through different methods and how that increased the "shoot to kill". The basic argument is that it is easier to kill someone when seeing them at a distance through the scope of a rifle than being right next to them and stabbing them. The other part of the dis-association is campaigns to dehumanize the enemy in war and not refer to them or acknowledge that they are individual humans. The video games argument in "On Killing" isn't part of the main thesis of the book, it is more tacked on the end. Whereas the rest of the book is looking at the past and evidence of what has happened. The video game part of it was (at the time) more focused on current feelings and attitudes towards it and was not substantiated.

teddyh 5y ago

Making people get used to (and be somewhat dependent on) Mathematica, a very expensive proprietary program, is doing people a large disservice. But it is very profitable for Wolfram. Also, the “video games make people violent” argument rears its ugly head.

amadeuspagel 5y ago
> Also, the “video games make people violent” argument rears its ugly head. Can't stand this kind of rhetoric. Arguments aren't scary monsters.
dqpb 5y ago
This dialog isn't really about Mathematica.
EForEndeavour 5y ago
If violent video games make people violent, then surely Mathematica makes people want to do more math.
- EGreg 5y ago
  Why can’t both be true? There is an argument to be made that gangsta rap made a generation of impressionable kids much more rough around the edges, as it defined the new “cool” for them. Even though it wasn’t “supposed to be for them”, they knew all the words, which are loaded with expletives and misogynistic lyrics, and sowing distrust of the police etc. Maybe I am just a social conservative but I agree with this lady who tried, in vain, to fight against the capitalist machine that is ths music industry: https://m.youtube.com/watch?v=Pr6gb1w72xA https://m.youtube.com/watch?v=Pr6gb1w72xA Kids are impressionable — the Merchants of Cool documentary clearly shows how capitalist industries exploit that to sell more stuff: https://www.pbs.org/wgbh/frontline/film/showscool/ https://www.pbs.org/wgbh/frontline/film/showscool/ It also helped shape a rift, in my opinion, between the Black and the White youth that grew up now, which had been closing thanks to Liberalism and efforts to move past it.
  - 5y ago

xvilka 5y ago

Mathematica is good. The language itself feels weird though. But for most students using Sage Math[1] would be a much more convenient option. [1] https://www.sagemath.org/ https://www.sagemath.org/

yissp 5y ago
To be fair, this didn't exist in 2002 when the article was written.

rob_c 5y ago

It strongly depends on the problem set. For teaching id broadly day either set it as a prerequisite to examine something it can't do or leave it until the last lecture to show the course material can be applied more efficiently. Learning is as much getting used to using tools correctly as understanding what the tools do and how they do it. I've worked with those who yes, have had their brain rot due to blindly trusting Mathematica or equivalent and they never spot first step errors from their blind spot. That being said I've worked with one person who used it really well and I think they were genuinely more efficient for it existing.

1001101 5y ago
BC calc in high school, I probably leaned on Mathematica a little too much, but mostly to check my work. Once, I got stumped on an integral and what Mathematica churned out wasn't even close (this was '94). Got a nice little note about that in the margin from my teacher. 0 points. Might still be some Mathematica pitfalls for teachable moments.

wiz21c 5y ago

My professor had a variant of that discourse regarding the computation of Linear Programs : "Prefer Gurobi (or Mosek) over GLPK because GLPK is bugged". My (limited) test show that GLPK works just fine. (GLPK is free software, Gurobi is proprietary) Now to be honest, the skills I learn over Gurobi, at the level I am, are super transferable to other software, so I'm not trapped into that proprietary stuff.

lqet 5y ago
At least on integer linear programs, I have found the performance of GLPK to be very disappointing, but I didn't notice any bugs. When compared to GLPK, gurobi is usually orders of magnitude faster (I had programs which gurobi optimized in a few seconds, while GLPK couldn't even find a feasible solution in 24 hours). If you need a free solver with reasonable performance, you should consider the COIN-OR project [0]. [0] https://www.coin-or.org/projects/ https://www.coin-or.org/projects/

analog31 5y ago

A friend of mine used Mathematica in a high school math classroom. I've also met some of his former students who think he was their best teacher. Something that occurs to me is that most of us have a poor grasp of why we even teach school math: It's treated as some kind of tournament to get into college, or a general IQ building exercise, or even a form of obedience training. The math that is "real" to them is just what they happened to learn, the way they learned it. But most people admit that they forgot all of their math immediately upon finishing school. And school math isn't even how "math people" do math. I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel. I'm not too worried about Mathematica being proprietary. Like with programming, if you learn one language, you can usually learn another in a jiffy.

foobarian 5y ago
> Something that occurs to me is that most of us have a poor grasp of why we even teach school math I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.
- dhosek 5y ago
  Some of it comes down to insufficient grounding in math education preparation. In Illinois at least, K5 teachers are required to take a class that's effectively high school algebra, but at least where I got my credential, the class was taught as if it were just a remedial math class (which, to be honest, it was for more than a few of these would-be K5 teachers), rather than making it clear that the math that they would be teaching would be preparatory for the later class. Similar situations occur with 6-12 mathematics education preparation. This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why. In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.
5y ago

stared 5y ago

Is [a technology enhancing cognition] making us stupid? In some sense - yes. Every cognitive prosthetics or enhancer means that we do not need to develop a particular set of skills. At the same time - it allows us to move further! Thanks to writing, we don't need to remember everything. Thanks to the Internet, we can retrieve this information in seconds (not days or months, depending on if a book was in a nearby library). Integrals are the art of the past. Sure, it is still worth doing some, but rather than memorizing hundreds of tricks, let's focus on something different than reinventing the wheel.

dhosek 5y ago

Way back when I taught math, I remember having a student in one of my junior high mathematics for college students classes who pulled out her calculator to do 8+9 (that's the exact calculation, I remember it remarkably clearly). And yet, she was able to manage the symbolic manipulation around the rest of the algebra problem she was solving. The thing I took away from that is that while we tend to think of arithmetic as a prerequisite for algebra, the skill sets are largely orthogonal. I kind of wonder if this was part of how the child of two math professors¹ was taking upper-division college level math classes at Harvey Mudd as a high school student. It's not so much that he learned K5 mathematics quickly and was on to pre-algebra and algebra as that he was likely introduced to algebraic concepts much sooner than his peers. ⸻⸻⸻ 1. I never met him, his time was a little before mine, but I recall someone who had met him saying that his parents taught him a lot of mathematics but not so much by way of social skills.

lmilcin 5y ago

In my trade school, we had this class devoted exclusively to calculating things fast in memory. The exam consisted of running a bunch of calculations as fast as possible without writing down anything other than answer. It is interesting that you can learn to calculate a lot of useful stuff in memory and there is a lot of tricks and you can get quite proficient at it after one semester of classes and some training. But once I left this school it was completely unusable skill. It sort of helps me estimate things, a little bit? I guess? But I also carry a phone with me at all times and I have a powerful calculator on my desk just within reach. A skill that is not being used deteriorates, and now I can no longer multiply 5 digit numbers in memory and I use calculator for anything that involves more than 3 digits. And I don't feel like I lost anything. There are so many useful skills to learn. If you want to spend time, learn something else that is more useful. And if you don't want to learn something useful learn something that gives you joy or impresses people.

alyandon 5y ago

Slight tangent - but back in the day while I was attending university I started turning in all my engineering assignments using MathCAD. MathCAD occupied this weird space of a living document for math with additional Mathematica like functionality for symbolic manipulation. I certainly don't feel to this day like I lost anything vs doing everything tediously by hand 100% of the time. My professors liked it so much they standardized on it and licensed the student edition for the entire department.

jointpdf 5y ago

You can get Mathematica for free on any Raspberry Pi (~$35), so that more or less renders the point about expense moot: https://www.wolfram.com/raspberry-pi/ https://www.wolfram.com/raspberry-pi/ There is also a pretty nice introductory book that is aimed at students: https://www.wolfram.com/language/elementary-introduction/2nd-ed/ https://www.wolfram.com/language/elementary-introduction/2nd...

jrm4 5y ago

The more I look at this topic, the more I'm thinking -- if the goal is "real world math" (which it perhaps shouldn't ALWAYS be, but let's go with it) it feels like the solution is probably "get the kids in front of Excel (or Calc/Sheets) as soon as possible." A big wide open "environment" to get things done in the same way that people in the real world do. Incidentally, I'm also thinking that this might also apply to "programming?"

davidkunz 5y ago

When doing math at school I never quite enjoyed it because it didn't feel like it could "scale". You always had to do these clunky calculations which are so error prone, that the slightest mistake could mess up your whole work. Instead of focussing on the essence, my mind was occupied with not messing things up when applying the "instructions". I always wondered how the industry would actually use math to solve its problems. With programming/mathematical software, it finally clicked and it gave me a powerful, practical tool to make mathematics work. Finally it was not so much about not messing up, but about actually building something. I enjoyed it a lot and in the end I obtained a PhD in theoretical particle physics and became a software developer.

karaterobot 5y ago

> Misuse of computers is easy and a problem but no use is presently a bigger problem. This argument seems to be from that techno-utopian era, when we thought that just having access to computers would elevate civilization, and that we'd always have access to computers, so things would keep getting better and better as long as we embraced technology. What happened instead was a bit more complicated than that: when people got access to ubiquitous computing, it did teach them a new set of skills, and they did lose some old ones. But, we don't live in the world many people expected would come about as a result. We live in a different world, with many tradeoffs we hadn't expected. Some good things, some bad things. But one thing I think it's safe to say is that the average person is not using computers as tools to think in more abstract and sophisticated ways than they were capable of in 2002. So, the argument he's making is phrased as pragmatic, but I wonder to what extent that argument just assumes a certain, positive outcome. Would the author make the same argument, with the same level of confidence today?

0xbadcafebee 5y ago

I knew a cryptographer who did their entire job in Mathematica for years and only rarely ever touched a common programming language. The output of their work informed a lot of other people's work. I don't know if their brain rotted, but they got a heck of a lot of work done with minimal effort and time.

dekhn 5y ago

I remember getting Mathematica because I thought it would help me solve hard integrals (a common pastime in my physics-oriented graduate career) but all it did was make more complicated integrals. I actually wrote a whole python/mathematica interface that was very elegant, but most of what I learned was cool Python tricks.

bjackman 5y ago

I have been thinking a lot lately about the point "such an attitude represents a tremendous degree of disrespect of our forepersons". The other day I watched "Cargo" on Netflix, in which after a civilisational collapse, many indigenous Australians are depicted as going "back to the old ways". I found this quite problematic: it suggests that the pre-European way of life was so easy that a bunch of adults can just _start doing it again_. As if it's some natural animalistic habit you can just fall into, and not a set of skills and knowledge that evolved over millennia. I guess it's possible we were supposed to read that these people's communities had passed down that knowledge and experience across the intervening centuries. Maybe they have.

dr_kiszonka 5y ago

Are there any good textbooks that introduce applied math and engineering methods using software* (and not require solving problems by hand)? *By software I mean both programming languages (Python) and software suites (MatLab, Mathematica, Sage, etc.),

joeman1000 5y ago

As an science & engineering undergrad, I was taught some basic Mathematica usage in 2 subjects (Intro. Physics). The sentiment amongst engineering teachers was that ‘reliance on computer tools is dangerous’, since if you didn’t grasp the fundamentals, you couldn’t properly verify the answers produced. I found this to be one of the largest disappointments while earning my degree: this sentiment is holding people back from embracing the future and I mostly think that teachers just didn’t want to learn programming. As a result, engineers were phobic of doing any coding to solve problems (in my experience working in groups) and instead relied on primitive pen & paper or excel solutions, both of which are more time consuming to scale, re-use or even to verify! If you use Mathematica as a literate programming tool, like a Jupyter notebook, a solution is more readable and verifiable than hand-notes or excel. I had to mostly learn it on my own, and have built up a large library of tools to tackle engineering problems. As a result I can save time on forgetting/re-learning how to do things, as I have a searchable database of solutions at my fingertips. I check and test each of my ‘scripts’ against textbook answers, so I know I can trust them. TL;DR: Teachers, please encourage computer usage for problem solving, but make students understand they need to grasp the fundamentals first!

jonny_eh 5y ago

Great read until they started suggesting that violent video games were leading to school shootings, which the science totally disagrees with.