我只是不是数学人......

星期六早上在毕业生学习伙伴。我们是数学人。

我们作为数学家似乎实际上弯曲了从学生的词汇表中删除“我只是不是数学人”的短语。也许这就是为什么他们如此大声而挑衅地尖叫?

Math has so many tactical advantages over sports and the arts. Math is cheaper—you don’t really need special equipment or a whole lot of space or, unless a pandemic necessitates it, technology in the classroom. And politicians and administrators alike are convinced we need more STEM—our programs, unlike sports and arts, will not get cut any time soon. Yet while getting students to want to continue in math is like pulling teeth, they all would love to play a sport or dance.

It makes you wonder what they’re doing that we’re not.

I have some ideas.

考虑以下两种情况:

(1) A child is put by its parents into Little League. In the course of being on this team, the child realizes they will never be a professional, not even professional enough to get a college scholarship. It doesn’t really matter how the realization comes. It could be due to teammates shouting hurtful if possibly accurate truths, or because the team always loses to [insert rival] at regionals. It could be from listening to an actual professional getting interviewed on ESPN and hearing how much work it takes. Maybe the child decides exactly whatkind他们想要的专业人士 - 也许他们不想最终在专业中,但随着当前的教练的替代品,回到他们的家乡?也许其他科目和课外更有趣。

他们退出了球队。

当他们长大的时候,你可能会期待孩子,“我只是没有成为运动员所做的事情。”但是你希望他们讨厌所有运动,还是他们戒烟的具体运动?你希望他们不希望他们的孩子参与运动吗?您是否希望教练对如何/地/当这些孩子意识到他们可能不会成为专业人士?教练担心,如果孩子们对他们的运动能力感觉不符合他们实际上还是没有,那么他们的数字将变得如此之小,所以学校的田径将停止存在?[学校的田径运动正在萎缩,但不是因为这个。]

The answer to all of these questions, I think, is “probably not.” A kid who played Little League for one season, during which time his team positioned him further and further into the outfield, twenty years later is highly likely to be sitting on a couch in his living room in front of a big screen television rooting for his favorite professional team in the pennant.

That’s not to say you expect every child to grow up unscathed. But the kids who “get out early” and who are told “it’s OK to quit” or “it’s OK you’re not athletically inclined”,the kids who are taught they can still enjoy and appreciate the sport without having to excel in itare the ones who are generally more OK. It’s the kids who are told by an elder “You need to do this, no matter what” or “You need to do this because I wanted to and never could” …THEY are the ones who will grow up to have mid life crises. It’s the kids who thought they could be a professional but due to some injury had to “retire” that are going to end up blaming someone else for all of their problems and drinking themselves to death in a sports bar watching the team they thought they could make on a big screen television win the pennant.

Ignore the creepy old woman going up the stairs…or the guy I obviously cut out. I used to be a musician.

(2)一个孩子把父母的“艺术”:a musical instrument (private, band, orchestra), or a chorus/choir. Maybe a theater group or some kind of dance. Eventually, the child realizes they probably will not be a professional. The reasons again could run the gamut. Others in the dance troupe/music studio/orchestra/chorale/theater guild could razz the child for their (lack of) ability. It could be because after a certain level of competition they always seem to lose. It could be because of hearing their favorite artist talk about the life of a starving artist and paying dues. Maybe they decide they want to run the town’s local ballet studio, or become their church’s pianist and they don’t really need to “go pro” to do either of those.Maybe other academics lure them away.

They quit.

这个孩子又会说,“我只是没有什么it took to be a professional [insert artist type]” and as a society we’re OK with that. And the instructors aren’t worried about a narrower flow of children coming through—there will always be kids in music, ballet, and theater lessons even if art and music programs in schools are “scaled” (hah!) back. But back to the child who quits. Do you think they won’t grow up to be that parent who takes their little girl to the Nutcracker at Christmas, or who puts their son in the childrens’ choir at church? Of course they will be that parent, because for the most part, they’ll still love music and going to plays and watching dance exhibitions. They will still have an appreciation for the arts—they may even be the arts’ biggest fans (especially in terms of money if they chose a different career).

Again, some kids will have issues. There could be those who had to quit ballet as part of their treatment for anorexia. There could be those who had a “dance mom,” someone so obsessed with the training that there’s a sometimes permanent period of cooling off where the child never dances or even goes to a dance performance. But these cases are fairly rare.

So now let’s talk about math and math competitions and encouraging students to participate in math. That is treated differently than these other two situations, and I’m not entirely sure why. Moreover, I not convinced treating math differently is really doing the mathematical community a whole lot of good.

As I’ve mentioned before in my post about competitions“我们”作为测试/竞争作家希望确保X%的学生参加考试(其中X是非驾驶的)赚取“一些”点。真正的原因必须是财务,因为哲学上零等于它所做的感觉。它相当于确保每个孩子用AT-BAT获得一个击中,或者管弦乐队的每个孩子都作为第一椅子获得一天。这是不现实的。There’s this unspoken fear, though, with math competitions and exams and classes that if students don’t perform well then they’ll get discouraged about learning math, and if they become discouraged that will turn very quickly into a hatred for math, and THEN you might as well write students off as future English majors.

另一个重要的区别,但是:这一切都必须“有趣”。我们甚至试图使我们的教学大纲互动。越来越多,学生数学体验的每一部分都必须刺激,令人兴奋,注意力抓住和有趣。为什么?如果你去过体育惯例,你知道这并不好玩。有钻头,热身,没有人关心娱乐水平。你认为芭蕾舞女演员或钢琴家们享受一半hours every day他们花在他们的五个位置,他们的现场转,鳞片和颤音?他们没有。但是,他们这样做是因为如果他们统称,他们不擅长“无聊”钻头,他们永远不会与更先进的“乐趣”零件进行大量进展。

Why is math so different? Why don’t we treat, say, multiplication tables or laws of exponents or even derivative computations in the same warm-up way that the athletes and artists do? Those are our etudes. Why not, just like them, build (however “fun” it is) a common fluency in the basics before moving on to the new and riveting?

小联盟教练或教堂钢琴家还有“不太专业”选择。学生本质地知道中间地面是什么在大多数领域的完整Noob和Pro之间。但是,我们对可能在数学中不想“去亲”的学生宣传的真实职业?我记得和我的reu明矾有关人员的讨论。他们立即询问数学研究生院有多少。因为这是我们社区中有多少衡量此类计划的成功。我争辩说明我可能是最骄傲的是成为一位高中数学老师的人。她喜欢数学,想到这一点,她可以为人类思想的最古老的分支贡献新的东西,但看到她对研究的局限性和教育的优势。她决定她想要度过她的生命(作为一个人,我必须说,特别训练有素)鼓励其他人来自该国地区继续数学。但数学社区中的许多人会把她写下来“损失”。 They care more or only about those who go on to get a math Ph.D.We need to realize there are plenty of intermediate possibilities between “not a math person”/English-major and Ph.D. in math and we need to push those intermediates with students as much, if not more, than the Ph.D. We need to quit writing off as a loss anyone who doesn’t get a Ph.D.

When you think about all this, it’s really no surprise that once a student declares they’re “just not a math person” that they don’t become a sidelines fan and instead transform into an “anti-math” person. Students who aren’t math people can’t still appreciate it because they are given zero outlets, opportunities, or exposure to such middle grounds. No offense to blogs and podcasts but there aren’t even any really good mass-media outlets about math, let alone outlets accessible to those under the age of 18. Sports has ESPN. The arts have PBS and A&E. Politics has C-SPAN. Biological science has Discovery and Animal Planet. Even the Scripps Spelling Bee gets prime air time once a year.But math? Not so much. We keep saying “math is everywhere” as a way of getting people on board our mothership, but where is it exactly?

因此,很多人都认为数学就像这个Mensa-Esque智力主义邪教一样。如果只有我们在会议上录像一群人,试图拆分检查并计算提示 - 这可能会为我们的社会做出奇迹。这么做,maybe we should allow people to say they’re just not a math person, and maybe we should find ways they can still support and appreciate math without feeling like they need a Ph.D.

Just a thought. What do we have to lose?

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2 Responses to我只是不是数学人......

  1. 头像 Soph Anya Lundeberg says:

    Thank you, kthompson, for another insightful read.

    The situation of the math educator is interesting. I would imagine her family and friends have a very different definition of her success than the “math community.” Had she gone on to earn a math PhD (assuming she was capable, intellectually), her employment prospects would have been…well, from what I’ve heard about the supply of PhDs versus the number of tenure-track positions…perhaps not as plentiful (and very unlikely within a preferred geographic region) as those of a K12 math educator. Seeing her salary, time off, retirement, purpose, and influence, I wonder if her community sees her as more successful than they would have seen her had she joined the “math community” in its entirety.

    也许数学社区的高(有时,不切实际)的标准平衡“普通人”社区,这可能会立即影响影响,确保收入/其他经济因素,以及控制成功的整体因素的一个人的位置。

    My best coaches in athletics have always had standards I couldn’t meet, because I had other coaches/mentors/people who, in turn, also had standards I couldn’t meet. Because of time and effort constraints, I could not be the athlete my coaches wanted me to be, the students my teachers wanted me to be, and the helpful person my closest others wanted me to be. Nevertheless, I’ve still seen myself as a success, as have the people who love me the most.

    作为数学社区的一部分,我认为你被允许看到一个没有使博士学位的人作为“损失”,而是作为一个人,你可以看到它们成功。数学社区的许多“亏损”都有更大的金融和达尔文成功,而不是他们加入它的人或者他们已经成为的人。因为成功可以在很多方面定义,所以在你的角色中,我认为没有出了错误的数学成功标准。当她已经在许多其他方面都赢了时,你不需要让这位老师成为一个“胜利者”。I myself am a “loss” to the math community in that same way, but on the other hand, I get dozens of adult students, mostly women, to go from hating math/”I’m not a math person” to actually enjoying some parts of it/”I am kind of a math person” each year. So every year, I help to reduce the animosity to the math community and the likelihood that someday, all those angry I-hate-math people are going to burn stuff down.

    What I would like to put forth, however, is that there need to be other ways for people to advance in mathematics beyond a traditional PhD. I speak from experience. I studied economics and computer science in college, the most employable combination of studies in today’s market. I took math-intensive economics classes, honors physics, and even a class dedicated to solving Putnam problems. However, I am eight, upper-division math courses short of pursuing any kind of graduate education, and to be considered for even a master’s in math, I would need to pay, out-of-pocket, for eight classes that cannot be taken at community college. Believe it or not, I actually tried to audit all these classes at three different universities in my city, and the logistics and the fact that I’m working and paying my own expenses killed that plan.

    在这种经历之后,我意识到的是,对于某人在数学中制作它,他们必须知道,当他们在学院的第一年内,他们想要学习数学。我们大多数人在高中进入大学。这花了我四年的工程来实现我比编程更喜欢数学。但是,到那时,金钱花了,赚取的其他学位和经济的考虑因素持有。

  2. 头像 François Bergeron says:

    These are interesting considerations, and I concur on most points, but there is one crucial aspect that may be a bit forgotten in the discussion. In our society, arts or sports are easy to access, explore, or enjoy freely in many interesting ways outside of a school context. Compared to these subjects, exposure to mathematics is most often perceived as something that is only done in a school setting.

    Also too many still believe that school math is something that is not really relevant in real life. The typical example is that of people that easily give the wrong answer to a school math calculation, but never fail to give the right answer to the same calculation if one adds a dollar sign in front of it.

    肯定的是,我们的社区很了解,数学是令人兴奋和在我们的文化中展现在深处和有趣的方式。然而,使它成为娱乐,音乐,电影或棒球游戏的娱乐是有点难以娱乐。这可能是差异之一。

    Thus, on one hand, it is likely that someone will stay a fan of a subject, even after failing to become a specialist of a subject that is generally considered as entertaining. On the other, this is much less likely for a school subject that most consider that it only has to be studied because it is required by the curriculum, albeit with the usual insistence on its importance in the abstract.

    我们应该寻找方法来深刻改变这种根深蒂固的文化偏见。

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