TE
科技回声
首页24小时热榜最新最佳问答展示工作
GitHubTwitter
首页

科技回声

基于 Next.js 构建的科技新闻平台,提供全球科技新闻和讨论内容。

GitHubTwitter

首页

首页最新最佳问答展示工作

资源链接

HackerNews API原版 HackerNewsNext.js

© 2025 科技回声. 版权所有。

How should mathematics be taught to non-mathematicians? (2012)

141 点作者 poindontcare超过 8 年前

23 条评论

imgabe超过 8 年前
Do other disciplines ask similar questions?<p>How should physics be taught to non-physicists?<p>How should writing be taught to non-writers?<p>How should car maintenance be taught to non-mechanics?<p>I guess my point is, why should we teach mathematics any differently to &quot;non-mathematicians&quot; than we do to &quot;mathematicians&quot;? I mean, at the point when you&#x27;re first teaching someone, how do you even know if they&#x27;re a &quot;non-mathematician&quot; or a &quot;mathematician&quot;? After all, they haven&#x27;t learned enough yet to know if they&#x27;d want to continue in that field of study.
评论 #12667930 未加载
评论 #12667612 未加载
评论 #12667272 未加载
评论 #12667437 未加载
评论 #12667729 未加载
评论 #12667358 未加载
评论 #12668341 未加载
wisty超过 8 年前
&gt; Objection 5. You’d never find enough teachers who were capable of teaching a course like this. To do it well, you need to have a very sophisticated understanding of probability, statistics, game theory, physics, multivariable calculus, algorithms, etc.<p>Objection 6: If it&#x27;s hard to find teachers to teach it, maybe it&#x27;s a little challenging for students (even though a good math expert might find it interesting).<p>Just because a math expert thinks something is interesting doesn&#x27;t mean low performing students will find it interesting.<p>For a more HN friendly example - what bunch of high school students wouldn&#x27;t want an IT class that taught compiler design, instead of stuffy old Excel? Even Python is more fun that spreadsheets, right?<p>Certainly there are large swaths of high school math that can be cut, and replaced with more relevant stuff. But some care needs to be taken that it&#x27;s actually teachable.<p>The article does partly cover this though:<p>&gt; Thoroughly road test questions before letting them loose on the nation’s schoolchildren. In fact, that applies to the entire course: make sure one has something that definitely can work before encouraging too many schools to teach it.
评论 #12666915 未加载
ivan_ah超过 8 年前
Wow, that&#x27;s a nice collection of problems. They are exactly the opposite of the dry and artificial &quot;word problems&quot; students are used to.<p>The discussion at the bottom of the blog post is also very interesting. The socratic approach is very good to &quot;break the ice&quot; and introduce the application, but I wonder how scalable this approach is. Does the teacher need to be very knowledgeable&#x2F;entertaining to pull this off?<p>BTW, I&#x27;m working on a new project, which is essentially &quot;math lessons by email&quot; that will walk readers through the math material from the <i>NO BULLSHIT guide to MATH &amp; PHYSICS.</i> Anyone interested in learning or reviewing basic math (expression, equations, functions, algebra, geometry) should signup: <a href="https:&#x2F;&#x2F;confirmsubscription.com&#x2F;h&#x2F;t&#x2F;4C2D9C45B88734F3" rel="nofollow">https:&#x2F;&#x2F;confirmsubscription.com&#x2F;h&#x2F;t&#x2F;4C2D9C45B88734F3</a> (it&#x27;s free)
评论 #12666890 未加载
andars超过 8 年前
If anyone cares to share, I&#x27;d love to hear some opinions about at what point someone switches from &quot;non-mathematician&quot; status to &quot;mathematician&quot; status.
评论 #12667116 未加载
评论 #12667546 未加载
评论 #12667312 未加载
评论 #12667274 未加载
评论 #12667211 未加载
评论 #12667203 未加载
评论 #12667307 未加载
评论 #12667153 未加载
onetwo12超过 8 年前
The post is about suggesting more fermi estimates problems, see for example <a href="http:&#x2F;&#x2F;lesswrong.com&#x2F;lw&#x2F;h5e&#x2F;fermi_estimates&#x2F;" rel="nofollow">http:&#x2F;&#x2F;lesswrong.com&#x2F;lw&#x2F;h5e&#x2F;fermi_estimates&#x2F;</a><p>Fermi estimates require you to look for relations in the real world, construct a model of the situation and then iterate improving the model by adding more information. You don&#x27;t use that process just to give an example of using a rule or solving an equation, instead you emphasize how the problem could be tackle mathematically. So there are more room for open questions, incentives for exploring and suggesting new approaches, in a more relaxed atmosphere creativity can flourish, perhaps maths is more than a single equation written in an old book.
ankurdhama超过 8 年前
Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.
评论 #12666637 未加载
评论 #12666777 未加载
评论 #12666717 未加载
kkylin超过 8 年前
I really like the collection of problems, but I&#x27;m not sure it is easy to teach this kind of problem solving. I, for one, would love to try someday. (I&#x27;m a mathematician teaching at a large research university in the US, and most of the courses I get to teach are not anything like this.)<p>I&#x27;m also not sure this can completely replace the more &quot;traditional&quot; way we teach math, which is not to say I don&#x27;t think it has problems (there are lots). If I may make an imperfect team-sport analogy, traditional classroom teaching of mathematics is all drilling and very little scrimmage &#x2F; play. These problems are sort of on the other extreme. If we are to (1) equip students with intellectual tools that they can use, and (2) convey, to at least a fraction of the students, the sense of beauty and joy that attracted many of us to mathematics in the first place, we would need a balance between the two. I get the impression that this is something like what Gowers is actually advocating, but I haven&#x27;t had a chance to read all his blog posts on this topic to find out (will have to do that later)...
Koshkin超过 8 年前
Teaching mathematics has two aspects, or goals, that are largely not related to one another. One is teaching mathematical methods as a computational tool, as used in a certain area of expertise (such as, for instance, electrical engineering). The other one is teaching how <i>to do mathematics</i>, i.e. how to generalize facts, find efficient proofs and algorithms, etc.
评论 #12667681 未加载
baby超过 8 年前
I think music is the best example. There are two ways of learning music:<p>* learning solfege<p>* learning how to play directly<p>Most great school of musics will teach you solfege first, and you will have to go through hardcore solfege classes while you start learning how to play an instrument. Some teacher will do the same, or some family will make their kid do the same.<p>Now I can tell you this is not fun, but this is the way to become a great musician. You need the theory, you need to know how to read that stuff like you&#x27;re reading English. But this is not fun, and I&#x27;ve known many in my youth who gave up learning an instrument because of this.<p>Now if you would teach every kid to play an instrument first, and have fun with it, and actually producing music with their fingers&#x2F;mouth then... they would maybe enjoy it enough to get interested into taking solfege classes and music theory later on.
评论 #12668182 未加载
M_Grey超过 8 年前
When you consider how mathematics, an understanding of probability, and so on enhances your ability to see through bullshit in advertising, government, and to some extent religions (not faith, just religions); it&#x27;s not hard to understand why so many people are not thrilled at the notion.
评论 #12666349 未加载
评论 #12666212 未加载
评论 #12666205 未加载
Animats超过 8 年前
Gower suggests story problems. Many, many story problems.[1]<p>[1] <a href="https:&#x2F;&#x2F;pbs.twimg.com&#x2F;media&#x2F;BTwHsS5CAAAzBBu.jpg" rel="nofollow">https:&#x2F;&#x2F;pbs.twimg.com&#x2F;media&#x2F;BTwHsS5CAAAzBBu.jpg</a>
评论 #12666060 未加载
评论 #12666032 未加载
losteverything超过 8 年前
Your question made me think.<p>Could be innate. My part time job forces me to make 10-20 micro decisions an hour. Most involve minimizing negatives and max positives. And knowing what to ignore.<p>Yet my co-workers are quite unable to even know how to get 10% from a cash register total. Other managers lack a &quot;math approach&quot; imo to want to get sales numbers or staff assignments. For example, what should you do if you have 80 hours of work and only 70 hours of workers? Some fail because they can&#x27;t even frame the task that way.<p>Could be vocation only. Get paid by using math, you are one.<p>I&#x27;m still thinking
Myrmornis超过 8 年前
Great article. Did anything come of the Gove-era math education policy changes he&#x27;s referring to?
评论 #12666558 未加载
dmitripopov超过 8 年前
There&#x27;s no need to invent popular mathematics. You just need a teacher that can show a student how beautiful mathematics is. It&#x27;s an art. A way of thinking and creating.
Pica_soO超过 8 年前
Capturing the interest must always be first. So to capture the interest, one must use math applications like game or physic simulations that allready captured the audience, allow beginners to modify the laws and abstractions within and create a &quot;im at home with this&quot;-intuition to delete the &quot;im just not cut out for math&quot; bias. Questions would not come from the teacher, questions will come from the students on how to modify the application.
danarmak超过 8 年前
Fermi estimates require at least some knowledge of the quantities you&#x27;re using as inputs. Are the students expected to know these, and tested on that, or are they allowed to state any values they like for the inputs? Do the teachers and the test-writers think only the process is important, or the results as well?<p>For example:<p>&gt; How many molecules from Socrates’s last breath are in the room?<p>We can estimate the number of air molecules in the room by using Avogadro&#x27;s number (6.022e23), the rough chemical composition of the air (roughly 80% nitrogen, element 7, and 21% oxygen, element 8), and the room&#x27;s volume (which can be hard to estimate by eye unless it&#x27;s a very small room).<p>We also need the total mass of the atmosphere; we can estimate it from the Earth&#x27;s surface are and atmospheric pressure, but we need to convert 1 atm to kilos per square meter. Would an average student remember that conversion rate? I certainly don&#x27;t. (Turns out that 1 atm ~ 10,330 kg&#x2F;m^2).<p>That&#x27;s quite a few constants to remember from physics and chemistry.<p>(I&#x27;m aware that Fermi estimates are only one of many kinds of example questions in the post.)
maus42超过 8 年前
The title is missing year 2012. (&quot;This entry was posted on June 8, 2012 at 4:53 pm&quot;)<p>Does anyone know what happened regarding all this?
评论 #12666334 未加载
blahblah3超过 8 年前
The problems he suggests overall seem too difficult for the average non-mathematically inclined student. And they also require quite a skilled teacher to teach.<p>I&#x27;m not sure stuff beyond &quot;algebra 1&quot; needs to be taught to everyone in high school. Even the concept of using &quot;x&quot; to stand for an unknown is very difficult for some to grasp. Instead, schools should make sure all students can properly understand how to use addition, subtraction, multiplication, and division, with applications to things like personal finance. In my experience, even many college graduates have trouble understanding when to multiply, divide, etc...
评论 #12666955 未加载
yodsanklai超过 8 年前
These problems are examples of questions that can be tackled with the help of mathematical tools. They can show students some applications of mathematics, but IMHO they don&#x27;t really teach mathematics. Maths have to do with statements and proofs about abstract objects. I&#x27;d rather learn about euclidean geometry than trying to figure out the number of piano tuner in manhattan (I&#x27;m sure most students will be bored either way).<p>Actually, this is an endless source of discussion among instructors, not only maths. Should classes be driven by applications in order to motivate students?
评论 #12668183 未加载
sn9超过 8 年前
Sanjoy Mahajan [0], who is the author of perhaps the two best books on Fermi estimation (freely available online, too!), has linked on his website a really fascinating account of an experiment to reform mathematical K-12 education from 70+ years ago [1].<p>[0] <a href="http:&#x2F;&#x2F;web.mit.edu&#x2F;sanjoy&#x2F;www&#x2F;" rel="nofollow">http:&#x2F;&#x2F;web.mit.edu&#x2F;sanjoy&#x2F;www&#x2F;</a><p>[1] <a href="http:&#x2F;&#x2F;www.inference.phy.cam.ac.uk&#x2F;sanjoy&#x2F;benezet&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.inference.phy.cam.ac.uk&#x2F;sanjoy&#x2F;benezet&#x2F;</a>
chx超过 8 年前
There&#x27;s a book by a Hungarian mathematician for this exact purpose. Péter Rózsa: Playing with infinity. That&#x27;s the Hungarian name order of her name. <a href="https:&#x2F;&#x2F;books.google.ca&#x2F;books?id=pj5G-3boMBwC&amp;redir_esc=y" rel="nofollow">https:&#x2F;&#x2F;books.google.ca&#x2F;books?id=pj5G-3boMBwC&amp;redir_esc=y</a>
kazinator超过 8 年前
Bootstrap: teach enough math to turn non-mathematicians into mathematicians.<p>Then teach mathematician-to-mathematician.
partycoder超过 8 年前
Applied math around areas of interest.