<p>Does anyone know if there is data lurking out there that details the number of declared majors in a field at the beginning of freshman year and then when that cohort graduates?</p>
<p>Obviously, folks change majors, so there will be some shifting due to that. What I'm looking for is a sense of whether schools aggressively winnow out prospective majors and focus on a few "stars." Specifically, I'm interested in math programs.</p>
<p>Thanks!</p>
<p>Yes, CountingDown, the Mathematical Association of America (MAA) tracks this issue. The figures I have seen, in an MAA book I don't have at hand at the moment, report that for each math class in the standard university math major sequence, the following class will have half the enrollment of the preceding class. So college algebra/precalculus (which is in the major sequence at a few colleges) has half the enrollment of calculus I, which has half the enrollment of calculus II, and so on. </p>
<p>I don't think math programs so much winnow out and focus on stars as they fail to develop and encourage nonstars. There is a HUGE advantage in looking precocious to most math departments, as many mathematicians believe in what math student I saw posting in the sci.math newsgroup calls the "cult of brilliance." According to the book Mathematical People, compiled under the auspices of MAA, there are actually a lot of famous mathematicians who were not at all precocious and even a few who failed high school algebra on the first--and second--try. But most resources in American math education are invested in the stars, so it is prudent for an ambitious student to do what it takes to look like a star student.</p>
<p>Harvard is supposed to go after stars and apparently is successful. But not all math majors are stars, by any means. It is a small field, but there's also an applied math major. A number of math majors end up going into comp sci or economics. I don't know how many do so.</p>
<p>Based on my vicarious experience (a client and a dog-walking friend who are math professors, one cousin who is a recent math PhD, a child of a good friend who just started grad school, and another cousin and several friends of kids who are currently undergraduate math majors . . . but all but one of these involve very high-prestige math departments, so a grain of salt may be necessary), and no hard data:</p>
<ol>
<li><p>Math departments tend not to be stuffed to the gills with math majors.</p></li>
<li><p>Comparatively few kids enter college with any real idea what it's like to do high-level math. Therefore, lots of kids who think they want to be math majors discover that they don't really like it, and a certain number of kids who thought they wanted to be physics or computer science or economics majors or something like that discover that what they really like is math. So there's flow out and in. It's also a field where there can be huge differences in the knowledge and skill levels of entering undergraduates, so it's easy for non-prodigy types to get intimidated and to feel that they can never catch up (and sometimes they're right).</p></li>
<li><p>Teaching skills are not highly valued in math departments. English-speaking skills are not highly valued in math departments. Social skills . . . well, you get the picture. This can make life difficult for math majors, and may induce some kids to find other departments if they value those things.</p></li>
<li><p>Other fields offer clearer career paths and and more women. Math majors do fine, but often suffer anxiety about such things.</p></li>
</ol>
<p>The bottom line is that I think a lot more kids winnow themselves out than are winnowed out by any intentional process on the part of the department.</p>
<p>Also -- it's not such a tragedy when kids who start as math majors switch to a related field.</p>
<p>I'm glad there aren't many math majors. When you tell somebody your kid is a math major, they think your kid is smart. ;)</p>
<p>They usually are. :)</p>
<p>
</p>
<p>That's my LOL of the day. A joke I cherish from the keyboard of a mathematician is one I saw on the sci.math newsgroup: </p>
<p>Q: How can you tell that a mathematician is extroverted? </p>
<p>A: He looks at the OTHER GUY'S shoes when he talks to him. </p>
<p>P.S. Actually, I know some very affable mathematicians who are also very dedicated to effective teaching and communication. But we are talking about the central tendency here.</p>
<p>What got me thinking about this was a thread I read here a few weeks ago about how about 25 kids actually graduate from P-ton w/math degrees, but some 15% of incoming freshmen declare as math majors. I didn't have a good sense of whether this was typical attrition or if there were issues one should anticipate.</p>
<p>UMD was refreshingly upfront in its online assessment of its math program, detailing tracks for "the easy way" and "the hard way," and freely admitting that Math 410 (Analysis I) is the big weed-out course. Their Honors program is very enthusiastic about kids who want to take the hard road, and encourages them to take grad-level math classes junior and senior years.</p>
<p>DS wants to start out in Analysis and is finding there aren't many LACs where that is feasible.</p>
<p>Tokenadult, I can tell you that there are a couple of exceptionally outgoing teachers at HCSSiM! They are the reason DS wants to teach.</p>
<p>Counting: I don't know what it means to say that "15% of incoming freshmen" at Princeton declare themselves math majors. I thought Princeton doesn't let kids declare majors until the end of their first year at the earliest, and I would be flabbergasted if 150+ kids actually declared a math major there.</p>
<p>Wesleyan? I think it actually offers a joint BA/PhD program.</p>
<p>Also, I'll add a story I just heard a few weeks ago: A third-year math grad student at a top university is called into the department Chairman's office. "Look, your teaching evaluations are too good. It's time for you to decide whether you want to be a teacher or a mathmatician." The student dropped out of the program, was hired to run the university's freshman math program for three years, then got a PhD in education and now teaches math education.</p>
<p>I will also say that my emeritus-math-professor client is among the most charming, cultured people I have ever met.</p>
<p>MIT has [url=<a href="http://web.mit.edu/registrar/www/stats/%5Dstatistics%5B/url">http://web.mit.edu/registrar/www/stats/]statistics[/url</a>] for major declaration and for degrees awarded, although you have to follow each cohort yourself.</p>
<p>For my class (2006): Our sophomore year, 45 people had declared a math major. Our junior year, it was 44. Our senior year, it was 40.</p>
<p>(In total, when you look at people who had second majors or who must have switched departments right before graduation, 69 people graduated with degrees in math. So MIT's math department apparently has a negative attrition problem. :))</p>
<p>My husband was a negative-attrition math major (though not at MIT).</p>
<p>He switched from electrical engineering to math in his sophomore year. Went on to get a PhD in math.</p>
<p>He's very geeky, as one might expect.</p>
<p>JHS,</p>
<p>What I'd read about P-ton was anecdotal and I have no way to confirm or disprove what I'd read. But the questions lingered in my mind, which prompted me to ask the resident experts here about their experiences and resources.</p>
<p>Retention sounds like a good thing for DS to ask about when he goes to visit programs, though, i.e.:<br>
-- are there various tracks for people coming in with different levels of preparation? (recognizing that many schools will be more flexible than their website states)
-- does the math dept. permit undergrads to do research?
-- how many folks are declared majors at the end of sophomore year (by which time one would probably have a sense of being able to cut it or not) and how many graduate in that major?
-- % of double majors
-- % to grad school vs. teaching vs. industry</p>
<p>Retention sounds like a good thing for DS to ask about when he goes to visit programs, though, i.e.:
-- are there various tracks for people coming in with different levels of preparation? (recognizing that many schools will be more flexible than their website states)</p>
<p>At Harvard, yes. You can look up the math department website for the different courses available.
<a href="http://www.math.harvard.edu/pamphlets/concentration.html%5B/url%5D">http://www.math.harvard.edu/pamphlets/concentration.html</a>
Basically, the lowest introductory course a prospective concentrator (Harvard speak for major) should take is math 21 a & b, i.e. multivariable calc and linear algebra. It's the "plug and chug" version, taken mostly by prospective sciences and econ majors.
There are three more advanced options of this sequence: math 23 a &b, math 25 a & b (honors multivariable calc and linear algebra, proof-based), and math 55 a & b (Advanced honors MV Calc & LA, supposedly the toughest introductory math course in the country, though various people claim that Math 18 at MIT and the analysis course at Chicago are equivalent).</p>
<p>-- does the math dept. permit undergrads to do research?
Yes. S has a sophomore friend currently doing research, and many do research in the summer. </p>
<p>-- how many folks are declared majors at the end of sophomore year (by which time one would probably have a sense of being able to cut it or not) and how many graduate in that major? I don't know. I think I saw the figure of 75, but I'm not sure whether it's one single class or all three years (soph, jun & sen).
-- % of double majors. I don't know. Harvard has joint majors and has just introduced minors (called secondary fields) this year. A common joint major is math & physics.
-- % to grad school vs. teaching vs. industry. I don't know. S has a friend who's about to graduate. She's getting a teaching certificate and seems to have lined up a job already. I read somewhere that jobs in academia are very hard to come by.</p>
<p>I've just come across this study done in 2001 that is germane to this discussion:</p>
<p>TheMom had an extended discussion with someone on the Math faculty at Berkeley who had a significant relationship with someone at Smith and thus was in a position to compare the programs. He admitted that Berkeley has "weed out" courses to thin the field and that he liked Smith's approach better, that Berkeley's approach didn't result in "better" math grads. A datum, fwiw.</p>
<p>
[quote]
Q: How can you tell that a mathematician is extroverted?</p>
<p>A: He looks at the OTHER GUY'S shoes when he talks to him.
[/quote]
</p>
<p>Tsk. My D will chat to the other math major about her shoes.</p>
<p>
[quote]
Basically, the lowest introductory course a prospective concentrator (Harvard speak for major) should take is math 21 a & b, i.e. multivariable calc and linear algebra.
[/quote]
</p>
<p>Has this changed recently?</p>
<p>I know that within the last year, I saw a plan of study that started with Math 1 in freshman year and still fit in all math concentration requirements, so I think that a bright student who had not previously been exposed to the excitement of math could still pursue a math major successfully.</p>
<p>Personally, I have a soft spot in my heart for students who first discover how much fun math is in college and only decide to major in it after taking a freshman single-variable calculus class from an inspired and math-evangelistic teacher. Harvard has (or at least used to have) some really terrific instructors in Math 1. It's not out of the question that a bright kid who had been avoiding math all his life because of uninspired teachers prior to college could fall in love with math in such a class, and decide to major in it.</p>
<p>Yes, perhaps such a math major is not likely to solve one of the million-dollar math problems, but he or she can still use a math major in many constructive ways.</p>
<p>From observation, it seems as if the first proof-based class serves as a weeder, in the sense that students find out whether or not they are interested in theoretical math. So, the earlier you can get to that class, the better.</p>
<p>The lack of grad classes to take at LACs was an issue a few years back when we looked. Just not enough offerings at some if your kid has already done stuff beyond calculus. Pomona might be worth considering, because its consortium includes Harvey Mudd and therefore the math opportunities are multiplied.:) Williams is another LAC you might look into for math, as they offer research opportunities that attract some very good math students.</p>
<p>Even in terms of applied math, having access to classes in an engineering college can be an advantage. Our S discovered an interest in modeling (and a lack of interest in writing proofs) was what unified his various course choices in math, econ, and physics, and he has been able to take some masters level classes. </p>
<p>I think math departments in general are happy to have math majors. The question is not so much whether or not they're intentionally weeded out of the department as whether more than a few students get opportunities to interact with the top faculty and do research if they intend to go on for a PhD in pure math.</p>
<p>PS -- that joke about the shoes is one my husband has told for years about ENGINEERS, of which he is one.</p>
<p>Wisteria:</p>
<p>My feeling is that there are probably students who take Math 1 and decide they want to become math concentrators. I doubt, however, that students who apply as prospective math concentrators take Math 1. Nowadays, so many applicants have taken AP-Calc, that it would be the very rare student who was not able to go straight into MV Calc. This rare student might be a bright admit from a school without an AP program. But as you know, high schools nowadays push, in fact practically bludgeon, students into taking AP-Calc whether or not they are prospective math/science majors..</p>
<p>Wow, thanks to everyone for all this good info!</p>
<p>DS visited UChicago and sat in on a 160s class and an Honors Analysis course in January. Absolutely loved the Analysis course -- he said he could follow the discussion, though some was over his head. He actively participated in the 160s discussions. Based on his intended senior year's classes and how others from his school have placed, my guess is he would be ready for analysis freshman year and would happily work his tail off. </p>
<p>He's not an IMO-er, but that's more because he's spent the past 3.5 years doing USACO. His calc teacher had the kids do CML, AMC and AIME, and he did well, but he didn't do any of the other competitions. Before last summer, the math skills supported the CS. Then he discovered proofs and voila! He had one of those amazing math profs (from Smith) and he was hooked. So, while he won't have the math hardware/awards that other applicants will have, he has the passion (such an overused word on CC, but this stuff really does set him on fire!). Said math prof from Smith told DS not to go to Berkeley for undergrad, and felt Mudd would be a terrific fit for him.</p>
<p>DS is finding that the profs who do what he's interested in have a combination of math and CS degrees -- some do CS first, then PhD in math, others the reverse. He'd like to do research. But he is teaching competition-level problem solving for the school's computer team, and he LOVES it. He comes home glowing that he got the other kids excited and engaged. He's talked to several privately, giving them encouragement and advice. This is a shy, geeky kid, and he comes out of his shell and blossoms when he teaches. </p>
<p>At bottom, he is looking for a math program that's collaborative, not cutthroat. Small school, deep math, good liberal arts, excellent preparation for grad school. He wants to know his profs. He wants to do research and teach. The challenge is to find schools that fit the criteria.</p>
<p>Great Princeton study, marite! Where did you dig that up? When Cookieson told fellow students he planned to be a math major at the beginning of his freshman year the response was usually, "Yeah, right, wait 'til you take a math class. You'll change your mind." I agree they don't purposely try to week out students, but rather some students decide they really don't like proof based mathematics. There are currently 18 senior and 18 junior math majors at Princeton. Other departments such as economics and physics try to woo some of the math stars into their departments and have been quite successful at doing so. However, the math department has some of it's most famous and engaging faculty teaching higher level freshman classes</p>
<p>I don't think it's a tragedy that students change their minds about any major. They are exposed to so many more fields of study that might interest them in college - it's all part of the growth process. Cookieson plans on declaring math as his major, but he's turned into a jock. He thought he'd be joining the math club and preparing for the Putnam but instead he joined a sports team and spends all his time working out.</p>
<p>CountingDown - DS should pay Cookieson a visit!</p>