Post A39eHQAWRRbUoO5MdU by teek_eh@aus.social
(DIR) More posts by teek_eh@aus.social
(DIR) Post #A39aoO0d5m37qyvDGq by urusan@fosstodon.org
2021-01-12T07:03:54Z
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Now that smartphones make information processing ubiquitous, should future generations learn math with the assistance of a computer (or calculator)?By calculator I'm thinking of any special purpose education device that lacks access to the total sum of all human knowledge.
(DIR) Post #A39b67b8qZGKATSOGG by sotolf@fosstodon.org
2021-01-12T07:07:08Z
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@urusan I think doing it by hand is the way to learn how it really works, once you know the principles using a tool is not bad, but using it from the start?
(DIR) Post #A39bSwblsBXAkBdNC4 by ndanes@fosstodon.org
2021-01-12T07:11:14Z
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@urusan As someone who has tutored/TA'd Calculus and other math courses, I'm conflicted.On the one hand, I think it's important to understand how arithmetic works and how we build up to more complex mathematics.On the other hand, most math, especially the Algebra to Calculus I courses, are taught in a "recipe"/algorithim format where there is not much critical thinking involved. 1/?
(DIR) Post #A39cNPuy5U7frYXdg0 by jiminycricket@fosstodon.org
2021-01-12T07:21:26Z
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@urusan Depends what kind of math. I'm a fan of learning analytic methods properly without calculator or computer. Only then do the numerical solutions make you appreciate the amount of work and research people have invested. It is important to understand the advantages of different methods. Mental math is a useful skill, as is using a calculator, as is programming a numerical simulation in MATLAB. Education would be robbing students if it does not provide the opportunity to appreciate math.
(DIR) Post #A39cRw3qWPayiAqgO8 by carcinopithecus@x0r.be
2021-01-12T07:22:12Z
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@urusan wetware is the most tech agnostic solution
(DIR) Post #A39cT3YO9M1cEsfY4e by urusan@fosstodon.org
2021-01-12T07:22:30Z
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@sotolf Well, this question is agnostic about how the curriculum is planned out. It could be that you start out with the students learning to do each operation by hand, before switching to using a device.The main conflict here is that it's hard to control usage to just "permissible use" once computing devices get involved, especially if said devices are fully general purpose.If your students are used to doing multiplication on a calculator, you can't take it away to teach square roots.
(DIR) Post #A39dj9waG6PWe5EF1c by ndanes@fosstodon.org
2021-01-12T07:14:04Z
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@urusan In my experience, that is why when students encounter Sequences & Series in Calculus II, they struggle A LOT, since you have to make an argument on why a sequence/series converges/diverges using various theorems/tests. I think teaching what math can do (e.g. modeling physical systems with differential equations using computer software) would give more appreciate on what and how its used in everyday life. 2/?
(DIR) Post #A39djAQiS4Vu9XKIzY by ndanes@fosstodon.org
2021-01-12T07:15:15Z
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@urusan There's probably a sweet spot where getting technology more involved with learning Math.Though, in the past, I've heard folks argue that we should teach things like Number Theory/Proof based thinking earlier BEFORE Algebra, just because it may be more intuitive, and get them to start critical thinking earlier. It's a hard question for sure!
(DIR) Post #A39djAzoLaaPuNkKh6 by urusan@fosstodon.org
2021-01-12T07:36:36Z
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@ndanes I'm also conflicted.I think the more basic calculations are way overemphasized in our current system, but it's hard to tell just how crucial doing all that hands-on work with numbers contributed to my intuitive number sense.I think the most fundamental issue is that we inherited a math education system that was designed for pre-computer industrial needs.Why else would we spend so much time on error-prone human computation, and so little time learning about the language of math?
(DIR) Post #A39dwWL0JHvZrb1R2m by urusan@fosstodon.org
2021-01-12T07:39:00Z
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@ndanes The abstract math class I took in college was one of the best I ever took. We broke down math and built it back up again, but right this time.
(DIR) Post #A39eBFZmuZF4DpxdLM by ndanes@fosstodon.org
2021-01-12T07:41:39Z
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@urusan which abstract math class was it?I have a BS in math and took lots of proof based courses: Real Analysis, Abstract Algebra (Group Theory), and Measure Theory to name a few. Though I ended up studying applied/computational math in graduate school, it was that proof based thinking that got me a great foundation to learn things in general.
(DIR) Post #A39eHQAWRRbUoO5MdU by teek_eh@aus.social
2021-01-12T07:42:46Z
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@urusan I chose "calculator". Even for something as basic as calculating a mean, doing longhand addition and division is only a distraction from the lesson. Meanwhile, a physical calculator remains (IMO) the single fastest numerical computation device where the bottleneck is the user typing digits, and it's a cheap and consistent for a teacher to provide for an entire classroom.
(DIR) Post #A39f3lrj4nva0GLgZ6 by urusan@fosstodon.org
2021-01-12T07:51:31Z
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@ndanes It was just called abstract math in the syllabus. We mostly covered the real basics in detail: proof-based thinking, set theory, etc.While the content isn't particularly impressive, it was a great class for shifting gears from the equation-based earlier classes to the proof-based later classes.I was in CS with a minor in math, so I didn't actually proceed much further except in CS-related topics like linear algebra and graph theory. However, I'm glad I learned the language of math.
(DIR) Post #A39fDLgxFEFvirsTFA by ndanes@fosstodon.org
2021-01-12T07:53:16Z
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@urusan Ha I did the opposite! though more recently I've been more interested in CS-related topics.
(DIR) Post #A39fVh9ICrVdU0selk by urusan@fosstodon.org
2021-01-12T07:56:35Z
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@ndanes The most important thing of all is to be a lifelong learner. You certainly can't cover it all in 4 years, or even the 6-10 years a PhD takes.