Supremum/Supremacy

我会说一些关于你有些人可能不喜欢的事情。本文燕麦片http://theoatmeal.com/comics/believe.在你决定之前,我会要求你读到最后,我不可能说我认为我所说的(雷维斯卡Goldstein概述了在哥特尔的威特根斯坦总结了)。谢谢,我很感激。

这里是:数学是政治性的。In this post I’m going to reflect on what this means, why I believe it, why I think it matters, and what we might do as a result.

对此索赔最常见的反应是典型数学:请定义政治的。出于这篇文章的目的,我的意思是数学是一个与权力和身份系统互动的文化机构。下一个最常见的反应是建议我用这种想法玷污数学,因此提出了上述要求暂停判决。

我要求你相信我,所以我应该首先谈谈自己的道路。你们中的一些人可能知道我今年正在安息率。我的博士学位在数学(代数几何),但今年基本上是数学教育研究的博克(rume.)。我认为自己是双学科,我可以在这两个社区之间进行代码交换,尽管我怀疑这两个社区都有“口音”。在两个独立的学科中,我忍不住注意到了方法的差异,特别是在司法,公平和权力周围。教育研究往往从假设整个努力是关于正义的假设,所以不言而喻,我们应该关心公平和权力,尽管这种共同的价值并不总是在讨论中升到表面。相比之下,数学通常从我们的工作纯粹抽象的假设开始,因此当存在司法问题时,他们完全明确。在我的经验中,两个社区都在不断发展,朝着他们处理正义的方式朝着良好的方向前进;也许我希望他们融合。

我也是我一生的文化机构观察者。我的父母似乎认为自己是北方移植饲养南部;我当然从未被识别为南方人。他们试图在犹太社区中抚养我,尽管这也没有。这种文化的一部分是一种自我框架,就像较大的文化一样,我在一所语言中在一个双语学校学习,我不能在学校外面说话。但我认为我最终看着像参与者观察者这样的文化的最强烈原因是我很奇怪(同性恋和轻微的性别不合格,就像我看到的那样)。阳刚地的期望,这看起来像对待许多人的其余文化一样看似看起来像是似乎在房间里的临时旋转大象。我看到各地的权力线,从提供给我的特权作为一个(白色)男性到试图限制我的行为的关税以支持这个系统。我有时嫉妒似乎能够通过这个世界的人嫉妒,而不是如此意识到他们如何参与它。

There are lots of things I like about mathematics, but mostly that it is a thing of beauty to which we all have access by virtue of our humanity. There’s something extremely egalitarian about math: you don’t need permission to think about concepts; other than time, you don’t need expensive spaces or objects to do most of the work; and we each have the authority to validate arguments independently.https://mathbabe.org/2015/01/16/representation-of-women-and-the-genius-myth/或者至少,这就是我想要的方式。我认为这些潜在的数学平等方面可能会解释为什么数学高于这个着名的性别代表图表中的趋势线,在PHDS中的神话中的神话。当然,这个图表的整个点是没有意识到这种平等主义的希望。在我面前的许多思想家已经注意到宣布数学是独立于身份和权力是一把双刃剑。学生在一些持续的经验工作Matt VoigtSDSU(@twistedcubic) articulated the fundamental “paradox” of being in STEM: if the work is independent of identity, anyone can do it, but as a result it is also hostile to discussions of identity and hence to people who don’t fit the default image of the field.

我们来到最难听到的那一点:无论我们的意图如何,我们试图将数学空间保持为非政治时,我们正在使他们保持敌对。这适用于专业空间,如会议和教育空间,如我们的教室。我知道许多有意识地选择尝试使课堂空间安全的数学家通过使他们保持争议问题,在学生想要一个空间的假设下,他们不必有意识地思考,例如,他们的少数地位。但我的理解是,这根本不是它对我们的学生的工作原理。数学以Cisgender,直,白人男性为中心,我们的沉默允许默认占主导地位。在我们的文化中,有喜剧演员和女性喜剧演员;在学术界,有美国历史和非裔美国人的历史;在我们的学科中,有数学和民族治疗学。黑人女性是黑人和女性的数学逻辑可能是Tautologous,但我们从声称这一身份的信息中知道,这一身份只是其部件的总和对实际的人的实际成本。也许数学是瑞恩·弗农虏舍,纯粹原因的巅峰,但这种纯度几乎不包括人物,而不是;数学是一个超级和最高医生。

Math is political because it is done by groups of people. Those people construct the narratives of our discipline, and telling any story involves selecting characters and emphasizing a plot; the one I learned is almost exclusively about European men. Groups of mathematicians also have to make decisions together, which is a struggle in many departments. Even at the Institute for Advanced Study, the mathematicians couldn’t come to agreements with Gödel, so they made him the sole member of the logic group to get around their issues.

数学是政治的,因为它正在塑造我们的世界。凯茜奥尼尔争辩说数学毁灭武器“大数据”不公平,威胁民主。Mathematical algorithms are filtering the kinds of information that breaks into our personal bubbles, and more subtly our world (especially our hand-held devices) are built around math that has gone from powerful to invisible, meaning they drive our culture when we aren’t watching. Ranking algorithms for image searches literally make diversity invisible. Governmental decisions are made using quantitative reasoning skills that don’t seem reliable, and rejecting the interpretation of data without grounds has become an ideological move. Ironically, we also know that people are disproportionately influenced psychologically by the inclusion of quantitative information in arguments. While I think that quantitative reasoning and math are separate phenomena, we must help lead this nation in the discussion this kind of reasoning as part of citizenry.

数学是政治的,因为它是由人们的学习。学校是一个文化制度,部分地寻求重建文化。数学是未来机会的关键接入点,但它一直是一个非常有效的障碍。在我们的教室里面,有些声音,想法和问题如何成为中环,而其他人被驳回或制造外围设备?谁有数学权威和自主权?也许数学是一些抽象的东西,但我们通过语言做数学,而不是质疑我们正在使用哪种语言以及在我们的推理和访问权限方面的方式是什么意思。我相信数学可以从任何语言接近,但是这种推理没有关于专家所述的问题;这是对学习者所作的那些问题的解释。宣布一些领域是政治的,而其他领域则没有意味着关心权力和身份的人属于某些空间,其他人没有,而其他人则没有考虑电力和身份的课堂,而且身份是只有少数学生提供的特权。

I am not the first mathematician to view our discipline as political. GH Hardy’s “数学家的道歉“wondered about the relationship between our work and the tools of war.Bertrand Russell是着名的伴侣的活动人士;从拉塞尔的角度来看,对于政治和逻辑之间的联系的幻想重述,我强烈推荐“Logicomix:史诗追求真理“. I am sorry that I am unable to quote a woman or person of color from the ancient history of our discipline; more recently,Margot Lee Shetterly“隐藏的人物“讲述三个数学家的故事,他们在斗争中努力为美国身份奋斗。当然,我们社区内的人们现在提供了领导地位格里曼德里三月为科学,更不用说通过组织的新教师的专业发展项目下一步

Given that math is political, I think we each have a responsibility for navigating our mathematical spaces intentionally around justice, power, and identity. This responsibility has not really been a choice for the many people who do not match the default identities in our community, so I’m really saying that those of us with privilege need to attend to these questions, especially in our teaching. However, talking about race, privilege, power, justice, gender, identity, and many other topics is often completely absent from advanced training in mathematics. As a result, taking up this responsibility is scary for some people in at least two ways. The first is a concern that by talking about issues like race we will inflame the related wounds and thereby perpetuate racism. I’ve argued above that a colorblind approach is not neutral; you can choose to be silent, but this is still a choice, a choice that hurts some people. Racism will fade from discussions when race is not a salient category to individuals, not because institutions are perfectly silent and everyone forgets. This is not to say that racism isn’t a structural problem sustained by cultural institutions, which it clearly is. In the words of Desmond Tutu: “If you are neutral in situations of injustice, you have chosen the side of the oppressor.” We are authority figures in the classroom, and our silence speaks loudly, even if we intend that silence to be neutral somehow. You don’t want to use your authority in the classroom to impose your partisan views on students, but if you approach discussions of power and identity intentionally, I am confident that you can tell the difference between acts of inclusion and oppression. Summarizing this point: you aren’t choosing between participating or not participating in discussions of justice, you are choosing between participating explicitly or implicitly.

The second concern is both much harder to resolve and much easier to start resolving. What should you actually do and say, especially if thinking about justice is not part of your training or experience? Fortunately, local data at my home institution suggest that it matters more to students that you say something than that you know how to say or do exactly the right thing (though I believe this result to be general). As a result, you can start speaking up without waiting for decades of training first. This goes for both local events (like microaggressions in your classroom) and global events (like elections and hate crimes). Of course, you should seek out professional development sessions and readings, such as the引发这篇文章的一块或者Jo Boaler在开放和封闭数学上的工作and classroom materials coming out of sources such as PRIMUS, MAA’s Classroom Resource Materials, and the Journal of Humanistic Mathematics. I’m going to close this post by talking about some of the things that are working for me.

我的个人方法是在用于派对课程设计决策的值中地进行这些讨论。我用询问教,我强调沟通,协作,多个观点,并因为我掌握了学习而互相学习。因为我已经明确了这些价值观和设计选择,所以我可以连接各种讨论政治in this post to the course, so it feels related. Moreover, because I’ve built this foundation early in the course, these政治的conversations are part of the continuity of the course, not breaks from the course to do something awkward that closes completely when they’re over. But pausing your course for a few minutes to talk together about the context in which you are all living is absolutely a useful approach too.

Lately, many of my more vulnerable students have gone out of their way to tell me that they appreciate these efforts to make them feel included and supported. I think this speaks to how small gestures are powerful. I also think I get these comments because a couple of small comments from me is more than these students expected in math or are getting in most educational spaces. I’ve never had these efforts put a chill on a relationship with other students, in part because I think I’m framing the discussion in terms of commonality in the classroom, but I doubt a student would really wander into my office to tell me that they disagree and feel that some students shouldn’t feel welcome in my courses.

真实的漏洞是我方法的核心。我担心与学生一起成为一个多维的全人。我让他们变得脆弱,勇敢在课堂上可见,所以我必须回报。我可能是他们见过的唯一同性恋学术;如果我事先宣布,我的这个方面在我的纪律下是无效的,那么这些学生永远无法知道奇怪的数学家。我正试图向学生转移权威,所以我不能试图成为一个不可见的力量,不可思议的决定,我需要成为一个做出选择的人。

我很明显,我知道我的方法使用我的特权。我是白色和男性,所以我在内容专业知识和课程设计权威方面得到了疑问的好处。相反,我认为我的奇怪身份通过帮助学生了解为什么我关心正义,并参加他们的社会情感状态。在过去的15年里,如果他们与学生随意,我已经看到学生对女同事非常不尊重,就像我一样安全;我想我必须继续反映我通过这些空间的方式的结构影响。In particular, I am not suggesting that you do what I do – I’m suggesting that you find a way to use who you are to acknowledge and integrate the political (justice, power, identity) aspects of mathematics into your classrooms and professional spaces.

谢谢你阅读结束。我让你看看一个主题,你可能喜欢与个人离不开的人;我要求你接受不公平的责任;而且我要求你脆弱,并做一些新的东西,你可能没有受过训练。我不是要求你放弃你对数学所爱的东西;我建议您可以帮助实现这种梦想和传播爱情的方式。

此条目已发布学术界的文化压力公平隐含偏见intersectionality介绍math education社会正义。书签书签永久链接

10回复Supremum/Supremacy

  1. 金伯利明天 - 梁 说:

    感谢您乘坐到中心的旅程,数学和教育。很高兴有你。

  2. 朱丽叶 说:

    这很棒。谢谢你。

  3. Laura Moss 说:

    在我的情况下的情况指出了我沿着类似的道路。您的意见和参考值得赞赏。谢谢你。

  4. 菲尔哈特 说:

    I will start by saying thank you to Brian for taking the trouble to think about, write about, and post these words.

    As somebody who failed in a very spectacular fashion as an undergraduate student of mathematics in his first year, it is with some hesitation that I write these words, which perhaps illustrates one or two of the points in that post. The best that I can offer by way of reply to Brian is a description of my own perspective.

    我看到数学是体现了一系列想法。我知道这套想法存在于社会背景中。Brian的帖子明确了许多社会背景的方面。

    At this point, I am forced to fall back on my own experiences as both a learner and an educator of mathematics.

    作为从幼儿园到高中的数学的学生,我所有的老师给我的印象是*所有*数学问题都有所知的解决方案,这是学生的任务来学习这些解决方案。几年后,我意识到这不是案件 - 数学部门毕竟在研究的业务中 - 我发现自己在高中筹集了数学。虽然这只适用于轶事证据,但我在课程结束时向我的一名学生讨论了这个问题:他惊讶地知道数学中有许多未解决的问题,尽管知识可以向自己的教学提供信息。这也许是一个值得研究的区域。

    我将与ethnomathematics的概念发出问题。即使是这个词的用法也是暗示文化歧视的暗示。虽然欧洲数学可能构成数学家和数学用户的大部分,但仍然是一个族群。每当我与可能被称为数学用户的人一样,我的看法是在不同的社会背景下使用相同的潜在思想。举例来说,世界的一些部分将年度分为六个,而不是四个季节。由同样的令牌,罗马数字也可以被认为是“民族”。

    一些学习者在一些学习者中的教育模式工程。通过对比,我与一些学习者需要一对一学费的课程合作,以克服他们的数学恐惧症。我尚未找到任何商业或政府机构为这些学费提供资金。

    我认为无限是社会的一个主要问题。在个人级别,有些人会产生差的经济选择,因为它们缺乏简单的计算技能。我还看到了一个孩子和其他教师的示例,他们的掌握数学是如此贫穷,他们教无性以来:“一周有六天,因为周日第8个月星期一第二天只有六天,而且”和“3^ 2 + 4 ^ 2 = 5 ^ 2证明了Pythagorean定理“。我认为政治家引用无关统计,推动特定的政治议程,大部分选民均以透过这些游标而闻名于于:“我们是世界上最安全的航空公司,没有事故......但我们从未飞过任何事故。”。我们在这里有一个杂项信息,用于延续错误信息,我认为它是一个非常艰难的休息循环。

    最后,在个人备注上,它总是让我很高兴看到某人的脸上的喜悦,无论他们或社会如何选择标记它们。

    • Brian Katz. 说:

      我同意“民族治疗学”是一个深刻的有问题的术语;我想我在你开始讨论的批评的各种批评中暗示。在我的本科音乐专业中,有一个音乐历史序列和世界音乐课程 - 这是我意识到这些类型的观点的时刻内置于我们的系统中。

  5. Linda Leckrone. 说:

    A very interesting read. As a nontraditional graduate student in both math education and mathematics, as well as a teacher of mathematics, I agree that the worlds must be mixed. I’ve also felt for decades that math is not apolitical. If it was, we wouldn’t turn off so many women.

  6. 约翰·里希特 说:

    是1 + 1 = 2政治声明?据推测,这篇文章的作者将抗议这不是他的意思,而且不幸的是,他单身未能明确他所做的是数学是政治的意思。当然数学有偶尔的政治应用,但这几乎不会让数学政治和作者引用的其他任何事情都没有。

    至于使用这一假设的数学政治指控作为将政治明确导入课堂的借口,似乎是一个完全可怕的想法。也许提交人假设大多数数学家分享他的政治观点,或者在目前的美国校园气候下,只有他的社会司法勇士士将敢于使用邀请在课堂上谈论政治,但如果/当校园的政治气候变化时他可能会后悔向数学拖累了政治。

    最后,我想评论以下声明:

    “但我怀疑一名学生真正徘徊在我的办公室里告诉我他们不同意并觉得有些学生不应该在课程中欢迎欢迎。“

    作者似乎表明,任何不同意他建议的教学实践的人都是这样做的,因为他们希望学生不受欢迎。随着这种态度,它几乎没有令人惊讶的是,没有学生对他的教学实践的批评批评。它使他的包容性索赔看起来相当讽刺。

    • adriana salerno. 说:

      It’s nice that some of you have moved on to other posts we’ve written. I don’t think you understand the post, so I invite you to read it again. Better yet, I invite you to read all our posts, because it will give you a better idea of where we stand. Finally, “the author seems to be suggesting” and all your other guesses make me think that you are reading what you want to read (and be angry about) rather than truly engaging with the text, which I thoroughly invite you to do.

      • 菲尔哈特 说:

        我同意阿德里安娜的礼貌和周到的答复。我也看到Johan的评论,正如Brian在他的帖子中指的那样恰恰是其中一个。

        • Brian Katz. 说:

          Yes! We think of the integers as purely abstract and universal, but there are at least two obvious cultural issues at hand. First, this notation was invented by humans. These particular numerals are Arabic in origin, and they came into the western part of the discipline because Fibonacci grew up in a Mediterranean merchant household! Second, while the identity that is represented in 1+1=2 might be universal, the mode of abstracting it from our lived experience is not universal. The very notion of what counts as a thing, a whole, an object is ambiguous and claiming that there is only one way to do it is hurtful. As a wrote, claiming that two personal identities (1+1) can be treated independently (2) makes very strong implicit assumptions about how these identities function, and insisting that this is the only option is clearly dangerous. And don’t get me started on the various meanings and understandings of the equality sign! To sum up, yes, these symbols might reference a universal (“apolitical”?) relationship, but that’s hardly evidence that math is globally apolitical.

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