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I'm a mathematician, and I'm anti-Calculus.

我是个数学家,我反对微积分。

education · Addem · 2026-03-27 18:03 · 16 帖 · 原文 ↗

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#1 I'm a mathematician, and I'm anti-Calculus. / 我是个数学家,我反对微积分。
Addem · 2026-03-27 18:03

By that I mean, I'm against treating calculus like "the next step" after algebra.

我指的是,我反对把微积分当作代数之后的“下一步”。

I don't get why we think it's important to get the largest number of students to know the largest number of equations, as seems to be the goal of the current curriculum.

我不明白为什么我们认为让更多学生记住最多方程很重要,这似乎是当前课程的目标。

I think we should just scrap all calculus from high school, and replace it with logic. A course in logic would be better than calculus because

我认为我们应该干脆把高中微积分全砍了,换成逻辑学。一门逻辑学课程会比微culus更好,因为

(1) It's more broadly applicable to every other area of life, including further mathematics.

(1)它适用于生活的方方面面,包括更深入的数学领域。

(2) It actually follows an intelligible sequence of ideas, unlike Calculus where we basically just make students memorize things that most of them will probably never actually understand.

(2)它确实遵循一套可理解的思路序列,不像微积分那样,我们基本上只是让学生死记硬背大多数他们可能永远无法真正理解的东西。

Of course, very advanced students could also load up on calculus and further topics, they way they already do with things like the Georgia Tech Distance Math program. I wouldn't want to stand in anyone's way, when it comes to learning advanced math.

当然,程度非常高的学生也可以继续选修微积分和更深的话题,就像他们现在参加佐治亚理工学院远程数学计划那样。我绝不会阻碍任何人学习高等数学。

I just think there is a much more worthy "next class after algebra". And it's logic.

我只是觉得代数之后的“下一节课”有更值得学的东西。那就是逻辑学。

#2 I think at one point in HS, schools should / 我觉得在高中某个阶段,学校应该
teach- · 2026-03-29 12:48

all sorts of thinking- deductive/inductive, logic, reasoning, how to come to conclusions, predictions, etc. without all information necessary, etc. and to how to question/debunk AI,social media, fake news, misinterpreted/skewed stats/info and hopefully to question every one/thing they come across

各种思维方式——演绎/归纳、逻辑、推理、如何在信息不全的情况下得出结论和预测,等等;以及如何质疑/揭穿人工智能、社交媒体、假新闻、被误解/扭曲的统计数据/信息,并希望能质疑他们遇到的每一个人/每一件事

#3 Agreed. A course in logic broadly. / 同意。广泛地开设逻辑课程。
Addem · 2026-03-29 16:17

Yep, I agree! Including rigorous statistical reasoning, which they don't do much of in a statistics class! It's again just all formulas that a lot of students will never use.

是的,我同意!还包括严谨的统计推理,而这在统计课上根本做得很少!同样,那也只是很多学生永远用不到的公式。

I'm not against teaching formulas. Just against teaching them to students who will never use them -- when there is something much broader and more important, that we're not teaching!

我不反对教公式。我只是反对把公式教给那些永远用不到的学生——与此同时,我们却没教给他们一些更广泛、更重要的东西!

#4 Actually I wish my HS offered Applied Math bc / 其实我希望我的高中提供应用数学,因为
- · 2026-04-02 15:20

it was fun and more meaningful. I never viewed Math as useful until I took Applied Math in college.

它既有趣又更有意义。直到我在大学学了应用数学,我才觉得数学有用。

#5 They should teach when, how and what / 他们应该教什么时候、如何以及教什么
- · 2026-03-29 12:51

circumstances to apply Logic. I can think of plenty of circumstances where Logic can't be applied (limited time. not enough facts, samples, etc.) but require different types of thinking to make conclusions/decisions.

逻辑的适用情境。我能想到 plenty 逻辑无法适用的场景(比如时间有限、事实或样本不足等),这些情况需要运用不同类型的思考来得出结论或做出决策。

#6 They should stop teaching how to solve for / 他们应该停止教如何求解
- · 2026-03-29 12:52

x, y and focus more on applications, thought processes and how to think

x, y 以及更侧重于应用、思维过程以及“如何思考”

#7 they should teach analytical thinking as well § / 他们也应该教分析性思维§
- · 2026-03-29 13:02
#8 They should teach critical thinking as well § / 他们也应该教批判性思维§
- · 2026-03-29 15:45
#9 At some point HS should teach various thinking / 高中应该在某个阶段教授各种思维
skills-bc-there- · 2026-03-30 18:27

is no one solution fits all.

没有一种方案能适用于所有情况。

For instance:

例如:

Different definitions of "critical thinking"

“批判性思维”的不同定义

Liberal arts emphasis: analysis of ambiguity, evaluating competing interpretations, questioning assumptions, constructing nuanced arguments, and integrating ethical, historical, or cultural context.

人文学科的侧重点:分析模糊性、评估相互竞争的解释、质疑假设、构建细微差别的论点,并整合伦理、历史或文化语境。

Engineering emphasis: problem-solving within well-defined constraints, applying formal models, optimizing solutions under quantitative criteria. That looks like "following procedures" to some observers, even though it often requires rigorous logic.

工程学科的侧重点:在定义明确的约束条件下解决问题,应用形式化模型,在定量标准下优化解决方案。在外人看来,这似乎像是“按程序办事”,尽管这通常也需要严谨的逻辑。

Pedagogy and classroom signals

教学法与课堂信号

Humanities courses reward open-ended essays, debate, and graded tolerance for ambiguity; rubrics celebrate novelty and argumentation style.

人文学科课程奖励开放式论文、辩论,并对模糊性给予一定的评分宽容度;评分标准推崇新颖性和论证风格。

Engineering courses reward correct answers, standardized methods, and efficiency; assessment often uses problem sets, exams with single correct solutions, and lab reports with constrained formats.

工程学科课程奖励正确答案、标准化方法和效率;评估通常使用习题集、有单一正确答案的考试,以及格式受限的实验报告。

Visible differences (pass/fail, classroom discussion styles, reading lists) create impressions: liberal arts students see peers trained to argue multiple perspectives; engineering students appear trained to execute algorithms.

可见的差异(通过/不通过、课堂讨论风格、阅读书单)造成了这样的印象:人文学科的学生看起来被训练成能为多种视角争辩;而工程学生则看似被训练成执行算法的机器。

Nature of problems and thinking modes

问题的性质与思维模式

Humanities problems are typically ill-structured: no single correct answer, tradeoffs among values, interpretive pluralism. This forces explicit articulation of assumptions and consideration of alternative frameworks.

人文学科的问题通常是不明确结构的:没有唯一正确答案,涉及价值权衡,存在解释的多元性。这迫使人们明确阐述假设,并考虑替代性的框架。

Engineering problems are often well-structured and constrained by physics, math, safety, or cost. That encourages precision, model-building, and verification rather than exploring multiple interpretive lenses.

工程学科的问题往往结构清晰,并受到物理、数学、安全或成本等条件的约束。这鼓励精确性、建模和验证,而不是探索多种解释视角。

Both modes are intellectual; they cultivate different kinds of criticality (normative/interpretive vs. technical/analytical).

这两种模式都是智力活动;它们培养了不同类型的批判性(规范/解释性 vs. 技术/分析性)。

Communication styles and social signaling

沟通风格与社会信号

Liberal arts training prioritizes rhetorical strategies, source critique, and explicit argumentation; students often speak in provisional, exploratory ways.

人文学科的训练优先考虑修辞策略、来源批判和明确的论证;学生们说话往往带有试探性和探索性。

Engineers are socialized to be concise, solution-oriented, and sometimes defer to technical authority (standards, codes, empirical tests). This can be read as intellectual closedness rather than focused technical rigor.

工程师被社会化地教导要简洁、以解决问题为导向,并且有时会尊重技术权威(如标准、规范、实证测试)。这可能被误读为智力上的封闭,而实际上是聚焦的技术严谨性。

Assessment of assumptions and values

对假设和价值观的评估

Liberal arts curricula foreground meta-questions: why this problem matters, who benefits, ethical implications, historical origins of concepts. This foregrounding looks like "thinking about thinking."

人文学科课程突显元问题:为什么这个问题很重要,谁受益,伦理影响,概念的起源。这种突出表现看起来像是在“思考思考本身”。

Engineering curricula tend to focus on making systems that work; normative questions may be taught in separate ethics modules or elective courses, so the default experience emphasizes technical constraints.

工程系的课程设置往往侧重于让系统能够运行;规范性问题通常会在独立的伦理学模块或选修课中教授,因此默认的學習经验强调的是技术约束。

Visibility of cognitive work

认知工作可见度的差异

The most visible outputs of engineering (diagrams, equations, functioning prototypes) often conceal complex judgment calls—model selection, approximation, tradeoff analysis—that don't look like the open-ended critique prized in the humanities.

工程最显眼的产出(如图纸、方程式、正常运作的原型)往往掩盖了复杂的判断过程——如模型选择、近似处理和权衡分析——这些看起来并不像人文学科所推崇的开放式批判。

In contrast, essays explicitly display chains of reasoning and consideration of counterarguments, which is easier for observers to equate with "critical thinking."

相比之下,论文明确展示了推理链条和对反方观点的考量,这使得观察者更容易将其等同于“批判性思维”。

Institutional incentives and time allocation

制度激励与时间分配

Engineering programs are intensive and time-consuming; students prioritize technical proficiency and may have less opportunity for sustained seminar-style reflection, reinforcing perceptions that they don't practice discursive critique.

工程专业的课程强度大、耗时久;学生优先追求技术熟练度,可能缺乏持续进行研讨式反思的机会,从而强化了人们认为他们不进行话语批判的刻板印象。

Liberal arts programs allocate more credit hours to reading, discussion, and writing, providing repeated, visible practice in argumentation.

文理学院将更多的学分配给了阅读、讨论和写作,提供了反复且可见的论证练习。

Bridging misunderstandings

弥合误解

Engineers do cultivate critical thinking—focused on model criticism, empirical validation, safety margins, failure modes, and system tradeoffs. The key difference is domain and method, not the absence of critical skill.

工程师确实培养批判性思维——侧重于模型批判、实证验证、安全余量、故障模式以及系统权衡。关键区别在于领域和方法,而非缺乏批判技能。

Productive reframing: view "critical thinking" as plural. Ask what kinds of uncertainty, values, and evidence each discipline trains you to handle.

富有成效的重构:将“批判性思维”视为复数形式。追问每个学科训练你如何处理何种类型的不确定性、价值观和证据。

Examples liberal-arts students cite (typical stories)

自由艺术学生引用的例子(典型故事)

A lab partner uses a standard method without questioning its assumptions when the situation has changed.

当情境已经改变时,实验室搭档未经质疑就使用标准方法。

An engineering design that optimizes cost and efficiency but overlooks user privacy or social impact because those considerations weren’t prioritized in the brief.

一项工程设计优化了成本和效率,但因为简报中未优先考虑这些因素,而忽视了用户隐私或社会影响。

Classroom interactions where professors correct a numerical error quickly and move on, rather than opening a class-long debate about broader implications.

课堂互动中,教授迅速纠正了一个数值错误就翻篇了,而不是展开一场关于更广泛影响的全班长时间辩论。

#10 They should teach about the two main / 他们应该教关于两个主要的
Disco_Barn_Lives · 2026-04-03 12:52

Political Parties and what legislation they have passed over the last 100 yrs or so , and how they have voted on certain major pieces of legislation ( and even minor ones ) over that tie period.

过去100年左右各政党通过了哪些立法,以及他们在这一时期对某些重大甚至 minor 立法案的投票情况。

If we did this truthfully, we would not have the lower middleclass class , wearing red hats , voting for incompetent, pedophile criminals and a Party that only works for the Ruling Class/Rich, the Oligarchs and the Deep State....

如果我们诚实地这样做,我们就不会存在这样一个穿着红色帽子、投票支持无能、恋童癖罪犯,以及只代表统治阶级/富人、寡头和国家深层政府的政党的下层中产阶级……

It's as simple as that

就是这么简单

Anyone not know this ?

有人不知道这一点吗?

My friends....I ask you

我的朋友们……我向你们提问

#11 Can't follow the discussion, as usual § / 跟不进讨论,照旧§
illegitSonofBarn · 2026-04-03 14:01
#12 I've been thinking about how I was / 我一直在想我当年是怎么
creigalt2 · 2026-04-03 13:59

more or less forced to take a third year of math and science, totally useless, and probably brought down my grade average. But I was told that good colleges always look for three years of each. Imagine my surprise when my college roommates had FOUR years of each.

几乎被迫多修了三年数学和科学,完全没用,而且可能拉低了我的平均绩点。但我被告知好大学总是要求每门科目修三年。当我发现大学室友每门科目都修了四年时,我惊讶极了。

Pointless waste of time for most people. Would have been better off taking history.

对大多数人来说,这是毫无意义的时间浪费。当初选历史课会好得多。

#13 To get into Grad School to get my MBA I had to / 为了进研究生院读MBA,我不得不
Disco_Barn_Lives · 2026-04-03 15:25

take a Calculus course .....and this was after the Army , being out of HS about 10 yrs....

去修了一门微积分课程……而且这还是在退伍之后,离开高中大概有10年了……

Took it at a Community College......Was hard as shit ....I needed to get a " B " to get accepted into the MBA program .....and guess what ......that's just what my ass got .....a big beautiful " B "

我在社区大学修的这门课……那真他妈的难……我想拿到“B”才能被MBA项目录取……猜猜怎么着……结果我这屁股上还真就得了个“B”,又大又漂亮。

and the rest led to a very successful life , which is still in high gear.......oh yes, it is

然后一切顺理成章,过上了非常成功的生活,现在依然处于全速前进的状态……哦对,确实是。

~~ perceive this to be a wrap ~~

~~ 认为这事到此为止 ~~

#14 Today's fantasy # 3. Elevator operators need a / 今日幻想 #3。电梯操作员需要一位
illegitSonofBarn · 2026-04-03 20:49

MBA?

Ho ho ha ha hee hee.

呵呵呵哈哈嘿嘿。

#15 from the get go US education should / 从一开始美国教育就应该
- · 2026-04-09 15:47

try to inspire students to want to learn and/or at least make them curious enough that the students want to learn or at least realize there is a lot to learn and they are not know-it-alls.

试着激发学生想要学习的欲望,或者至少让他们产生足够的好奇心,让他们意识到自己想知道的东西还有很多,而不是自以为无所不知。

#16 hacks are hacks and not always / 黑客技巧就是黑客技巧,并不总是
- · 2026-04-09 17:23

healthy and correct. There are soo many engineers who think they can hack dieting, health, muscle gains/mass. I know some engineers who ended up in hospital from their hacks.

很健康且正确。有太多工程师自以为能“黑”进饮食、健康和增肌的规律里。我认识一些工程师,因为他们的各种“偏方”最后进了医院。

The costs/cons of shortcuts and how it compromises quality, reliability, durability, etc.

走捷径的成本/弊端,以及它如何牺牲了质量、可靠性和耐用性等。

Summary: to acknowledge, appreciate the complexities, difficulties of every thing/one

总结:承认并欣赏万事万物的复杂性与困难。

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