<p>"It’s depressing to hear intelligent people say Calculus is useless in real life but learning real proofs is useful. "</p>
<p>Why is that depressing? Different people find different things interesting. </p>
<p>@bookworm, IIRC correctly Google outsources their cafeterias to a firm called Bon Appetit (as do other companies and universities).</p>
<p>@Canuckguy, I think most undergraduate business degrees are too formulaic and tend to train kids for the mid-level managerial jobs, which are precisely the ones that are going to go away as new information and communications technology plus outsourcing kick in over time. There’s a study by some Oxford profs who say, I think, that 1/3 of all white collar jobs are going to disappear. To be able to adapt over time, I think a kid’s college education ought to focus on learning how to learn and learning how to think (hopefully in more than one way – e.g., like an economist, like a cognitive psychologist, like a statistician, … .) Undergraduate business degrees tend to be rather weak at the learning how to learn and learning how to think and much better at static skills (basic accounting). In one of my posts, I think I described an economics major at McGill who took a business class and was surprised that the economics taught there was what I’d describe as economics appreciation. It was quite sloppy and the students really didn’t get the economic argument that was being made. So, they didn’t learn how to think like an economist. They came away instead with a gestalt feeling that they won’t be able to easily apply well outside of the specifics that they discussed in the class. I’m sure some undergraduate business programs are better at this than others and that some students will develop the mindset I want even if it is not developed by the program, but I have hired from a few undergraduate business programs and have been generally underwhelmed by the lack of intellectual dexterity of those I hired. </p>
<p>In addition to learning how to learn/think, to be considered for a job in today’s environment, kids need to have one (or more) marketable technical skills just to get in the door. There are a bunch of those, but my impression is without them, the job search is long and not pretty.</p>
<p>@Iglooo, I think you may be mischaracterizing what I said (if it was me). Someone (@Pizzagirl?)said – and I concurred – that if you had to choose between a course in calculus and a good course in statistics that trains you to figure out how to learn things from data (most stats courses actually don’t do that) and use data to inform decisions, the statistics course would be much more valuable for the average person. Calculus, of course, is a gateway to most STEM courses (maybe not parts of bio or neuroscience, but not sure about that) and is very important for that. I also didn’t say that calculus is useless in real life (although I think another poster said that) but it will be true for many jobs out there for which calculus is not directly useful (real estate agents, sales managers, marketing or even typical finance execs, even most CEOs that I know). But, the second thing I said should not be depressing. It is that formulaic calculus courses where people do a lot of plugging things into formulas or mechanically differentiating functions, for example, are not necessarily the best training for logical thinking. My observation is that I can often infer from the quality of arguments that people make as to whether they have taken one course with real proofs. Those who have done proofs typically have a much clearer sense of how to reason from premises to conclusions in an airtight way than many people who haven’t done proofs. (This is not one size fits all, but generally seems to be true in my experience).</p>
<p>shawbridge, I am sure that is the case. Just saying the proofing courses would require calculus as prerequisite and rightly so. Calling it depressing may be a bit over-dramatic but when you consider what is taught in other countries it is not that far off. I hope it is an unnecessary worry and our kids will do fine in the end. My kid is a math major at one of top schools with a plan to go to graduate school. I know my kid will face stiff competitions in grad school. Some grads from my kid’s school are dropping out from a top notch math grad programs. Top math grad programs have 30-40% foreign students who are far more experienced in math curricula in general.</p>
<p>PG, We don’t say, “What if kids don’t like reading? Why shoud they do it?” We still make them to read and write. Why is it any different when it comes to math or science? These days, math and science are basic skills and should not be something you don’t have to if you don’t like. JMO, of course.</p>
<p>@shawbridge I think we are conflating cognitive ability and one’s major. My understanding from talking to CC members is that strong students generally do not do undergrad business in the US. So to compare majors, it is important to factor out the influence of SAT scores. This is not to say majors play no role in cognitive development. According to CLA, students in traditional liberal arts fields such as mathematics, science, social sciences and humanities show greater gains in reasoning and communication skills than do students in education, human services or business after 2 years of schooling. After 4 years, however, business jumped to near the top of the class, together with math, sociology, foreign languages etc.</p>
<p>I think there is a difference in the first two and the last two years of business school. The first two years are formulaic- almost all courses are compulsory and students are buried in pre-requisites. The last two years students are given a lot more freedom in choosing courses based on interest and personal strength. In other words, they finally have time to think instead of memorizing.</p>
<p>If we think 4 years of business school is incapable of teaching and learning economics, how can we expect 2 years or 1 year (European model) of an MBA to do so? The short answer is they don’t. If we are to take it one step further, an undergrad degree in economics is not the best preparation for graduate training in economics anyway. Reliable sources told me the best preparation is a first degree in physics or mathematics. Come to think of it, Samuelson, Stiglitz, Cochrane, Smith and Summers all have background in physics. Arrow’s background, I believe, is mathematics.</p>
<p>@Canuckguy, possibly true. However, I don’t think business schools generally do a good job of teaching economics – although when I last looked at a couple of schools like Chicago, they appeared to be schools of applied calculus. So, pretty good for micro. When my son was thinking of becoming an economist, I advised him to take one or more math courses every semester because that was what econ departments cared about. So, he became an accidental math major. It has served him in good stead.</p>
<p>
</p>
<p>Economics departments say that preparation for PhD study in economics requires substantial math and statistics courses. For example:</p>
<p><a href=“https://www.econ.berkeley.edu/grad/admissions/preparation”>https://www.econ.berkeley.edu/grad/admissions/preparation</a>
<a href=“https://www.econ.berkeley.edu/undergrad/current/preparing-for-grad-school”>https://www.econ.berkeley.edu/undergrad/current/preparing-for-grad-school</a></p>
<p>Most undergraduate economics majors are not as heavily mathematical, due to most economics majors not intending to go on to PhD study. However, some economics departments do have a heavier mathematical emphasis in the undergraduate economics courses, or have an option to take more mathematical versions of them.</p>
<p>@shawbridge I decided to look into one of my kid’s old calendars to see what was available in the business school as far as economics go. I find only one 3 credit course (in management economics) offered in-house; the rest had to be taken in the economics department.</p>
<p>I am actually much more interested in the “marketable technical skills” required “just to get in the door”. I can think of foreign language proficiency, numerical analysis, computer programming and perhaps outstanding oral and written communication skills. Do you have others in mind?</p>
<p>@Iglooo I remember attending a conference back in the mid to late 80s at a major Canadian University. Out of curiosity I picked up a student paper and started into the articles. There were two that really interested me. One was the startling revelation that the university’s education program had a lower admittance rate than the law school; the other was that there were 9 PHD awarded in Canada in the previous year in mathematics, and not one of them was granted to a Canadian. So, this is really nothing new. I don’t know what the solution is though.</p>
<p>^Beef up general math and science education? It doesn’t hurt to learn math and sciences even if they don’t plan to go into related fields. I remember having an entirely satisfying conversation on science with a film major from Germany. My kid and their classmates are smart and motivated. If they were given the right guidance from early on, they have no reason not to be highly successful in graduate school. </p>
<p>If you have technical skill, and hustle, the school you went to don’t matter.</p>
<p>@shawbridge Did I say numerical analysis? I should have simply said facility with numbers. Numerical analysis is one example of that, but not the only one.</p>
<p>@Iglooo I agree that general math and science education can be vastly improved, but there are two impediments we have to overcome right off the bat. The first is the problem of cognitive threshold. While students can do better in the lower grades, I doubt this will translate into greater facility with math and science at a higher level. I gave mine the best training in math I could (money and time) to the end of high school, but they still were no match for their brighter classmates in mathematical finance.</p>
<p>Another serious obstacle is the attempt by an elite to keep the best jobs “all in the family”. Randall Collins talked about it as far back as the 80s. This goes a long way in explaining the dumbing down of the SAT, holistic admission and the like. A stronger focus on “g” loaded disciplines like math and physics would threaten this transmission of privilege, so it is not going to happen.</p>
<p>Interesting article about “On Becoming A Quant”:</p>
<p><a href=“http://www.markjoshi.com/downloads/advice.pdf[/url]”>http://www.markjoshi.com/downloads/advice.pdf</a></p>
<p>
</p>
<p>It depends on the kind of job, I would think. There are high-paying jobs where dropping names may be just as important. There what you learn at school may matter less.</p>
<p>
</p>
<p>Very true. But there are more jobs to fill than there are “very brights”, I think. Very brights probably need unconventional education. Improving general education will benefit many bright students with aptitude.</p>
<p>
</p>
<p>That’s kinda depressing. That certainly happened in my kid’s private K-12. I should have transferred my kid to public school after the middle school. Life is more interesting than maintaining a linage imo. There are things to explore, stretch you capabilities, quiz your brains…</p>
<p>If this is true, going to name schools may permit you to join the bloodline making prestige more prestigious. If this gets more widespread, we are no longer awarding the old american value.</p>
<p>“G, We don’t say, “What if kids don’t like reading? Why shoud they do it?” We still make them to read and write. Why is it any different when it comes to math or science? These days, math and science are basic skills and should not be something you don’t have to if you don’t like. JMO, of course.”</p>
<p>Of course kids should “know how to read” and “know how to do math” in order to prepare for adult life.<br>
What does that have to do with calculus? </p>
<p>There is a certain sub-species of STEM-geeks here on CC, who honestly are not able to look around and see that there are plenty of interesting, challenging, well-paying jobs where science facility is not necessary and the math facility that is necessary is more about comfort with analyzing numbers, probabilities, and statistics, not doing differential equations. In their worlds, they never even heard of people who do things like being the head of compensation or talent management or investor relations or advertising or marketing at a company, for whom calculus is about as useless as Swahili.</p>
<p>I was a double major in econ and math. I love math. </p>
<p>As for science literacy? I took physical science, biology and chemistry in high school, at regular vs honors levels, took only the distribution-level science classes in college (intended for non-majors) and really, I’m perfectly fine. My job doesn’t require me to have scientific knowledge. What have I missed out on? </p>
<p><a href=“Inside Job: How the Supreme Court Cozies Up to Big Business | BillMoyers.com”>http://billmoyers.com/2014/12/09/scotus/</a></p>
<p>I hope this is an exaggeration.</p>
<p>
</p>
<p>Whta’s so special about calculus? The mind set treating calculus as some kind of goddess is itself alarming. My take is that the sophistication we require in writing is more than what’s equivalent in math/science, i.e., calculus.</p>
<p>
</p>
<p>This seems in direct contradiction to what shawbridge that best job applicants are found who had done some proofs. tell me one proofs course that doesn’t require calculus that has any meat. </p>
<p>If we live in a society that values reasoning and reasoning is developed in a math course that requires to have taken calculus, what other choices do we have?</p>
<p>"In their worlds, they never even heard of people who do things like being the head of compensation or talent management or investor relations or advertising or marketing at a company, for whom calculus is about as useless as Swahili.</p>
<p>This seems in direct contradiction to what shawbridge that best job applicants are found who had done some proofs. tell me one proofs course that doesn’t require calculus that has any meat."</p>
<p>Maybe shawbridge and I are in different industries and hire for different positions. But go ahead and believe that “the best” person to be the head of human relations at a rapidly growing company, someone who needs to develop plans for training, recruitment, mentoring programs, implement procedures, oversee benefits and so forth, is the person who kicked the most ass in calculus class.</p>
<p>Knowing how to think logically is critically important, but thinking “mathematically” is only one way of getting there.</p>
<p>Why so much resistance about teaching/learning calculus while not making a squawk about reading/teaching Shakespeare? I didn’t major french or speak french but my primitive french is still helpful when I am in France. I was not a history major but had a course in Euro and my trips to Italy is more enjoyable. You don’t have to be a math major. Being comfortable with numbers will make your life bigger and it’s not that hard. Every kid in the world is learning it. Our kids are not made of paper or incapable of a few numbers even if their head doesn’t look like a triangle. Why treat it something esoteric and you wouldn’t teach or learn unless you need it directly at your job? How about being comfortale with looking at graphs or charts in the paper or following quantitative reasoning with comfort? </p>
<p>“Being comfortable with numbers will make your life bigger and it’s not that hard. Every kid in the world is learning it. Our kids are not made of paper or incapable of a few numbers even if their head doesn’t look like a triangle. Why treat it something esoteric and you wouldn’t teach or learn unless you need it directly at your job? How about being comfortale with looking at graphs or charts in the paper or following quantitative reasoning with comfort?”</p>
<p>I agree COMPLETELY that being comfortable and facile with numbers is good. I, too, decry the innumeracy of people who can’t calculate change, or read a chart in the paper or follow quantitative reasoning with comfort.</p>
<p>But that has nothing to do with studying calculus, which - sorry - no matter how much I love math - isn’t all that relevant for most people. And IIRC, there was teeth gnashing upthread about how we in the US are soooo beyond because we wait til 12th grade to teach it unlike other countries where they do so once the kids are out of diapers. And I disagree with that. I think mathematical proficiency of the kind you describe is VERY important. Calculus? Not so much.</p>
<p>And yeah, I got a 770 on my math and a 5 on my Calculus AP and blah blah blah. So it’s not a function of apologizing or explaining away lack of proficiency. </p>
<p>Got to go with Pizza on this. The type of numeracy that a very big chunk of corporate jobs require is not of the “calculus with proofs” variety. It’s the ability to look at a presentation with three graphs on it and to realize that you are losing market share in your three biggest divisions. It’s the ability to understand a spreadsheet which shows that the cost of your employees medical benefits has gone up 20% even though your headcount is down by 7%. It’s being able to lead a discussion which talks about what happens if the cost of your key raw materials go up by X % and what the consequences will be for your “low cost producer” strategy in Latin America.</p>
<p>Not being a quant. Not being able to do complex financial engineering or develop a trading algorithm that depends on velocity.</p>
<p>I’ve hired quants. They populate an esoteric part of the job market which is in no way indicative of what most corporate jobs require.</p>
<p>You guys are really slicing the onion way too thin if you’re trying to groom your children in high end analytics at an early age. The people who do those jobs can’t exist without math in their lives. You don’t need to groom them- they grow themselves.</p>
<p>For everyone else- who may be interested in marketing, accounting, investor relations, HR, M&A, etc- just making them capable in math (i.e. not so phobic that they can’t take macro at college) PLUS interested in all the traditional liberal arts- history, literature, a foreign language? That will do the trick.</p>
<p>And if your kid is math phobic- you can help fix that. It will hold them back in more meaningful ways than on the job. Like not being able to interpret a newspaper article about whopping cough vaccines and their newborn child. Not understanding a physician who is discussing a clinical trial of a new drug which can either cure them or kill them. Or not understanding the difference between their marginal tax rate and what they actually will owe the IRS. This is what you can fix- day in/day out critical thinking. </p>
<p>Awesome post, blossom. </p>