Two years ago (two years and one day if you're being picky), I posted a pointer to a Spanish language web site hosted by Francisco Yuraszeck (professor at the Universidad Técnica Federico Santa María in Viña del Mar, Chile). The site, Gestión de Operaciones, is listed in the resources box on the right. Recently, Francisco informed me that he now has a companion English language site, Linear Programming (LP) and Operations Research (OR) Exercises and Resources for Students. He asked for help getting the word out about it, and I'm happy to do so.
For readers active in the OR community (and in social media), please have a look and, if you like what you see, help publicize the site.
Showing posts with label education. Show all posts
Showing posts with label education. Show all posts
Saturday, September 5, 2015
Saturday, May 30, 2015
Decision Analytics and Teacher Qualifications
Disclaimers:
The genesis of today's post is a blog entry I read on Spartan Ideas titled "Is Michigan Turning Away Good Teachers?" (Spartan Ideas is a "metablog", curated by our library, that reposts other blogs by members of the Michigan State University community. The original post can be found here.) The focus of that post is on changes to the certification examination that would-be teachers in Michigan are required to pass. I'll quote a couple of key passages here, but invite you to read the full post to get the entire context:
My first reaction to the "weak" connection between teacher characteristics and learning outcomes is that it sounded like bad news for people on all sides of the current debates about educational reform. On the one hand, to the "blame the teacher" crowd (who like to attribute perceived problems in the public education system to poor or bad teachers, teacher tenure etc.), one might say that if teacher quality explains "only" 8% of variance in learning outcomes, quit picking on them and look elsewhere. On the other hand, to people (often affiliated with teacher unions) pushing for better compensation, better working conditions etc., one might point out that those are generally incentives to recruit and retain better teachers; so if teacher quality explains "only" 8% of variance in learning outcomes, perhaps those dollars are better spent elsewhere (upgrading schools, improving neighborhood economic conditions, ...).
What struck me second about the original post was the use of the phrases "only about" and "weak predictors". This seems to me to relate to a difference between statistics, as it is commonly taught (and used), and what some people now refer to as "decision analytics". In my experience, the primary focus of statistics (and its sibling "data analytics") is to identify patterns and explain things (along with making predictions). That makes measures such as correlation and percentage of dependent variance explained relevant. In contrast, decision analytics emphasizes changing things. Where are we now, where do we want to be, which levers can we pull to help us get there, how much should we pull each, and what will it cost us to do so? That perspective may put more emphasis on measures of location (such as means), and on which input factors provide us "leverage" (in the archimedean sense of the term, not the regression sense), than on measures of dispersion (variance).
It is common, at least in the social sciences, to categorize predictors as "strong" or "weak" according to how much variation in the dependent variable they predict. This is the statistics perspective. I understand the attractiveness of this, particularly when the point of the model is to "explain" what happens in the dependent variable. At the same time, I think this categorization can be a bit dangerous from a decision analytics standpoint.
Fair warning: I'm about to start oversimplifying things, for the sake of clarity (and to reduce how much typing I need to do). Suppose that I have a unidimensional measure $L$ of learning outcomes and a unidimensional measure $T$ of teacher quality. Suppose further that I posit a linear model (since I'm all about simplicity today) of the form $$L = \alpha + \beta T + \epsilon$$with $\epsilon$ the "random noise" component (the aggregation of all things not related to teacher quality). Let's assume that $T$ and $\epsilon$ are independent of each other, which gives me the usual (for regression) decomposition of variances:$$\sigma_L^2 = \beta^2 \sigma_T^2 + \sigma_\epsilon^2.$$From the research cited above, we expect to find $\beta^2 \sigma_T^2$ to be about 8% of $\sigma_L^2$.
Tell a decision analyst that the goal is to "improve learning", and something all the lines of the following questions should arise:
In my simplified version of the regression model, $\Delta L = \beta \Delta T$. The same ingredients that lead to the estimate of 8% variance explained also allow us to take an educated guess whether $\beta$ is really zero (teacher quality does not impact learning; what we're seeing in the data is a random effect) and to estimate a confidence interval $[\beta_L, \beta_U]$ for $\beta$. Assuming that $\beta_L > 0$, so that we are somewhat confident teacher quality relates positively to learning outcomes, and assuming for convenience that our goals are expressed in terms of mean learning outcome, a decision analyst should focus on identifying ways to increase $T$ (and, in the process, a plausible range of attainable values for $\Delta T$), the benefit of the outcome $\Delta L$ for any attainable $\Delta T$, and the cost of that $\Delta T$.
Stricter teacher certification exams may be a way to increase teacher quality. Assuming that certification requirements do in fact improve teacher quality (which is a separate statistical assessment), and assuming that we do not want to increase class sizes or turn students away (and therefore need to maintain approximately the same size teaching work force), imposing tighter certification standards will likely result in indirect costs (increasing salaries or benefits to attract and retain the better teachers, creating recruiting programs to draw more qualified people into the profession, ...). As with the connection between teacher quality and learning outcomes, the connecting between certification standards and teacher quality may be weak in the statistical sense (small amount of variance explained), but our hypothetical analyst still needs to assess the costs and impacts to see if it is a cost-effective lever to pull.
So, to recap the point I started out intending to make (which may have gotten lost in the above), explaining variance is a useful statistical concept but decision analysis should be more about cost-effective ways to move the mean/median/whatever.
And now I feel that I should take a pledge to avoid the word "assuming" for at least a week ... assuming I can remember to keep the pledge.
- This a post about statistics versus decision analytics, not a prescription for improving the educational system in the United States (or anywhere else, for that matter).
- tl;dr.
The genesis of today's post is a blog entry I read on Spartan Ideas titled "Is Michigan Turning Away Good Teachers?" (Spartan Ideas is a "metablog", curated by our library, that reposts other blogs by members of the Michigan State University community. The original post can be found here.) The focus of that post is on changes to the certification examination that would-be teachers in Michigan are required to pass. I'll quote a couple of key passages here, but invite you to read the full post to get the entire context:
Research has found that only about 8% of the differences in student achievement can be attributed to teachers and only 3% of that can be attributed to the combined impact of teachers’ certification, ACT/SAT scores, degrees, and experience.
...
Because teachers’ examination scores have been found to be only weak predictors of their impact on student learning, an assessment that has a low pass rate by design may prevent some who would be effective teachers from obtaining a teaching certificate, a concern that is supported by research.(The link in the quote is a 2002 article in Education Next by Dan Goldhaber, senior research associate at the Urban Institute.)
My first reaction to the "weak" connection between teacher characteristics and learning outcomes is that it sounded like bad news for people on all sides of the current debates about educational reform. On the one hand, to the "blame the teacher" crowd (who like to attribute perceived problems in the public education system to poor or bad teachers, teacher tenure etc.), one might say that if teacher quality explains "only" 8% of variance in learning outcomes, quit picking on them and look elsewhere. On the other hand, to people (often affiliated with teacher unions) pushing for better compensation, better working conditions etc., one might point out that those are generally incentives to recruit and retain better teachers; so if teacher quality explains "only" 8% of variance in learning outcomes, perhaps those dollars are better spent elsewhere (upgrading schools, improving neighborhood economic conditions, ...).
What struck me second about the original post was the use of the phrases "only about" and "weak predictors". This seems to me to relate to a difference between statistics, as it is commonly taught (and used), and what some people now refer to as "decision analytics". In my experience, the primary focus of statistics (and its sibling "data analytics") is to identify patterns and explain things (along with making predictions). That makes measures such as correlation and percentage of dependent variance explained relevant. In contrast, decision analytics emphasizes changing things. Where are we now, where do we want to be, which levers can we pull to help us get there, how much should we pull each, and what will it cost us to do so? That perspective may put more emphasis on measures of location (such as means), and on which input factors provide us "leverage" (in the archimedean sense of the term, not the regression sense), than on measures of dispersion (variance).
It is common, at least in the social sciences, to categorize predictors as "strong" or "weak" according to how much variation in the dependent variable they predict. This is the statistics perspective. I understand the attractiveness of this, particularly when the point of the model is to "explain" what happens in the dependent variable. At the same time, I think this categorization can be a bit dangerous from a decision analytics standpoint.
Fair warning: I'm about to start oversimplifying things, for the sake of clarity (and to reduce how much typing I need to do). Suppose that I have a unidimensional measure $L$ of learning outcomes and a unidimensional measure $T$ of teacher quality. Suppose further that I posit a linear model (since I'm all about simplicity today) of the form $$L = \alpha + \beta T + \epsilon$$with $\epsilon$ the "random noise" component (the aggregation of all things not related to teacher quality). Let's assume that $T$ and $\epsilon$ are independent of each other, which gives me the usual (for regression) decomposition of variances:$$\sigma_L^2 = \beta^2 \sigma_T^2 + \sigma_\epsilon^2.$$From the research cited above, we expect to find $\beta^2 \sigma_T^2$ to be about 8% of $\sigma_L^2$.
Tell a decision analyst that the goal is to "improve learning", and something all the lines of the following questions should arise:
- How do we measure "learning"? (Assume that's our $L$ here.)
- What is our goal (achieve the biggest bang on a fixed budget, achieve a fixed target at minimal cost, ...)?
- Is the goal expressed in terms of mean result, median result, achievement by students at some fractile of the learning distribution (e.g., boost the bottom quartile of $L$ to some level), or something else (e.g., beat those pesky Taiwanese kids on international math tests)? Reducing variance in $L$, or the range of $L$, could be a goal, but I doubt it would be many people's first choice, since a uniform level of mediocrity would achieve it.
- What are our levers? Teacher quality (our $T$) would seem to be one. Improving other measures of school quality (infrastructure, information technology) might be another. We might also look at improving socioeconomic factors, either at the school (more free lunches or even breakfasts, more after-school activities, more security on the routes to and from the schools) or elsewhere (safer neighborhoods, better food security, more/better jobs, programs to support two-parent households, ...).
- How much progress toward our goal do we get from feasible changes to each of those levers?
- What does it cost us to move those levers?
In my simplified version of the regression model, $\Delta L = \beta \Delta T$. The same ingredients that lead to the estimate of 8% variance explained also allow us to take an educated guess whether $\beta$ is really zero (teacher quality does not impact learning; what we're seeing in the data is a random effect) and to estimate a confidence interval $[\beta_L, \beta_U]$ for $\beta$. Assuming that $\beta_L > 0$, so that we are somewhat confident teacher quality relates positively to learning outcomes, and assuming for convenience that our goals are expressed in terms of mean learning outcome, a decision analyst should focus on identifying ways to increase $T$ (and, in the process, a plausible range of attainable values for $\Delta T$), the benefit of the outcome $\Delta L$ for any attainable $\Delta T$, and the cost of that $\Delta T$.
Stricter teacher certification exams may be a way to increase teacher quality. Assuming that certification requirements do in fact improve teacher quality (which is a separate statistical assessment), and assuming that we do not want to increase class sizes or turn students away (and therefore need to maintain approximately the same size teaching work force), imposing tighter certification standards will likely result in indirect costs (increasing salaries or benefits to attract and retain the better teachers, creating recruiting programs to draw more qualified people into the profession, ...). As with the connection between teacher quality and learning outcomes, the connecting between certification standards and teacher quality may be weak in the statistical sense (small amount of variance explained), but our hypothetical analyst still needs to assess the costs and impacts to see if it is a cost-effective lever to pull.
So, to recap the point I started out intending to make (which may have gotten lost in the above), explaining variance is a useful statistical concept but decision analysis should be more about cost-effective ways to move the mean/median/whatever.
And now I feel that I should take a pledge to avoid the word "assuming" for at least a week ... assuming I can remember to keep the pledge.
Saturday, January 31, 2015
Making Math Fun
I was a math major from undergrad to doctorate, so obviously I think math is fun. Equally obvious to me (especially after teaching a variety of mathematical topics to college students), not everyone shares that opinion, which is too bad. Recently, though, I came across an organization devoted to making math fun for small children, and I wanted to share the link: Bedtime Math
Bedtime Math provides a variety of resources for introducing children to math in a fun way. The organization's name comes from the notion that a vignette with a math problem at its core makes a good bedtime story. They also encourage development of after-school math clubs, where kids can do fun activities with a mathematical theme.
If you are a parent of small children, and you want your kids to learn to enjoy mathematics, this seems to be a good starting point. There are books, videos and a daily math problem via email. There's even (shock!) an app for that.
Bedtime Math provides a variety of resources for introducing children to math in a fun way. The organization's name comes from the notion that a vignette with a math problem at its core makes a good bedtime story. They also encourage development of after-school math clubs, where kids can do fun activities with a mathematical theme.
If you are a parent of small children, and you want your kids to learn to enjoy mathematics, this seems to be a good starting point. There are books, videos and a daily math problem via email. There's even (shock!) an app for that.
Wednesday, September 4, 2013
"New" OR Educational Resource
Okay, it's not really new -- the author, Francisco Yuraszeck (professor at the Universidad Santa Maria in Chile) tells me he started it more than two years ago -- but it's new to me.
Gestión de Operaciones ("Operations Management") describes itself as a "blog on Management and Operations Research with tutorials and solved exercises". (At least that is what it says if Google Translate can be trusted; I had one Spanish class, in the summer before ninth grade, which barely allows me to order an occasional cerveza ... in a Castilian "lisp".) Professor Yuraszeck tells me he started it as an aid to OR students in all Spanish-speaking countries.
I have not actually poked around the examples and exercises, but they look pretty good on cursory inspection. The site is tied to a YouTube channel with OR videos (in Spanish), and there is at least one "sketch book" available for download. Almost all the content is free, the one current exception being an introductory ebook on linear programming available for a dollar or two (the minimal royalties for which help offset site costs).
Overall, the site seems to be very well done: organized well, easy to navigate, visually appealing, with lots of pertinent content. It would be nice to see the blog gain visibility.
I have not actually poked around the examples and exercises, but they look pretty good on cursory inspection. The site is tied to a YouTube channel with OR videos (in Spanish), and there is at least one "sketch book" available for download. Almost all the content is free, the one current exception being an introductory ebook on linear programming available for a dollar or two (the minimal royalties for which help offset site costs).
Overall, the site seems to be very well done: organized well, easy to navigate, visually appealing, with lots of pertinent content. It would be nice to see the blog gain visibility.
Tuesday, September 3, 2013
STEM Crisis: Fact or Fiction?
After reading assorted articles about a looming crisis in the supply of qualified STEM (Science, Technology, Engineering, Mathematics) graduates, today LinkedIn pointed me to an article on the IEEE Spectrum site titled "The STEM Crisis Is a Myth". It seems to be cogent and fairly well researched, but I'm not sure I entirely buy the author's analysis. I will certainly stipulate this: determining whether there is a looming STEM crisis, its probable extent (if it does occur), and what to do about it are complex questions, involving fuzzy definitions, data that can be parsed in a variety of ways, and at times some rather heated opinions that can get in the way of careful analysis.
I don't have a position to defend in this debate, and I certainly don't have any answers. I do have some questions/concerns about some of the definitions, how some of the data is interpreted, and how some realities are perhaps ignored (or abstracted away) during the analysis ... and that's without getting into the questions of what constitutes a STEM degree or a "STEM job". In short, I'm happy to muddy the waters further. Here, in no particular order, are some thoughts:
Do the debaters consider jobs in banking and finance to be "STEM jobs"? My guess is that the answer in most cases is no; and yet the banking and financial services industries employ significant numbers of mathematics and statistics graduates. Actuarial positions may be classified as "STEM jobs", but what about people who work designing portfolios or analyzing market trends? Wall Street is a leading employer of Ph. D. graduates in particle physics (see, for instance, this New York Times article), largely because the physicists (claim to) understand the Ito calculus, used to describe physical processes such as Brownian motion but also used in derivative pricing.
My personal opinion, formed well before the 2008 market crash, can be summed up as follows: Handing my retirement portfolio to people who think they can measure particles (tachyons) that exist only at speeds greater than the speed of light ... what could possibly go wrong with that? I cringed when I learned that my alma mater, Princeton University, has a department titled Operations Research and Financial Engineering -- and trust me, it's not the OR part at which I cringe. Personal prejudices aside, though, it seems reasonable to me that a portion of STEM graduates will legitimately be desired for (and hired into) jobs that are probably not considered "STEM jobs", siphoning a portion of our university output away from the jobs specifically targeting holders of STEM degrees.
Years ago, I had a student in an MBA course (now a lifelong friend) who had a bachelors degree in a scientific field (chemistry or something related). She had worked for the Michigan Department of Natural Resources as a lab chemist before deciding that it was not her passion, and that she would rather work in the business sector. Years later, I had another student with a science degree (chemistry? biochemistry? chemical engineering?) who had worked in the pharmaceutical industry before joining the MBA program. After graduating, he worked in management jobs that leveraged his scientific background but would not be classified as STEM jobs. Another MBA student had a degree in nuclear engineering and had served as a propulsion engineer aboard a US Navy submarine.
In fact, a fairly sizable portion of our MBA program consisted of people with undergraduate STEM degrees (and, often related work experience) who had decided to go over to the Dark Side and join the ranks of management. In comparing supply of and demand for STEM degrees, we need to allow for the fact that some STEM degree holders will naturally choose, for reasons other than a lack of job opportunities, to pursue non-STEM careers.
An administrator once made the mistake of inviting me to participate in an orientation session for new MBA students, designed to foster camaraderie and esprit de corps. During the session, I remember saying the following: "Look at the person on your left. Now look at the person on your right. Statistically, one in three people is an asshole ... so if it's not one of them, it's you." (I made the statistic up, based on my experience growing up in New York.) The point I was making then was that candidates would be required to work in teams, just as in industry, and it was naive to assume that it would always be easy to get along with all your teammates.
Sadly, though, it is also true that some people just cannot coexist at all with other workers. Some are chronically absent or late. Some need to be nagged, wheedled or hand-held just to get things done. Some are larcenous. I see no inherent reason why a STEM degree would preclude any of those possibilities (and in fact I've met walking, talking counterexamples to that conjecture). Those people will often "fail" a job interview, no matter how solid their technical credentials, or they will be involuntarily separated from an employer in a way that follows them through subsequent interviews. Thus we have to allow for some slice, hopefully small, of the STEM degree holders to be unsuitable for employment in STEM jobs (unless the recruiters are desperate).
During my graduate studies in mathematics at Michigan State University, I was a teaching assistant. Like most TAs, I began teaching recitation sections of a large service course, whose title was (approximately) "Introduction to College Algebra". The course was taught in a large lecture by a faculty member. The primary roles of the TAs handling the recitation sections were to answer questions and grade homework and exams.
A year or so after I arrived, we were joined by a new graduate student with a bachelor's degree in mathematics from a "prestigious" university. (I shall not name the university, so as to avoid embarrassing the fine folks in Ann Arbor.) He too had a teaching assistantship. Fall quarter of his first year, he was assigned to teach a couple of sections of the introductory algebra course. Winter quarter he was pulled out of the classroom, and his sole duty as TA was to work out the answers to the problems in the textbook ... because the Powers That Be had discovered that he could not answer simple algebra questions in class (and not, apparently, due to stage fright). Had he chosen to work in industry, rather than going straight to graduate school, and had the recruiters done their jobs well, he might have contributed to the statistics representing STEM degree holders not working in STEM jobs.
Employers frequently complain (particularly when lobbying for more H1B visas) that they cannot find a sufficient number of STEM degree holders with the "right skill set". We can argue about who bears responsibility for a genuine lack of the right skills: universities with outmoded curricula; employers unwilling to pay for training; or degree holders unwilling to upgrade their skills on their own time. We can also speculate (and many people do -- see the comments on the IEEE Spectrum post) on how often the "right skill set" translates to "willing to work cheap". We also need to accept that in some cases the "right skill set" translates to "actually knows the subject matter for their awarded degree", and that this is not a given.
I don't have a position to defend in this debate, and I certainly don't have any answers. I do have some questions/concerns about some of the definitions, how some of the data is interpreted, and how some realities are perhaps ignored (or abstracted away) during the analysis ... and that's without getting into the questions of what constitutes a STEM degree or a "STEM job". In short, I'm happy to muddy the waters further. Here, in no particular order, are some thoughts:
Not all STEM graduates get "STEM jobs" ... nor need they.
Do the debaters consider jobs in banking and finance to be "STEM jobs"? My guess is that the answer in most cases is no; and yet the banking and financial services industries employ significant numbers of mathematics and statistics graduates. Actuarial positions may be classified as "STEM jobs", but what about people who work designing portfolios or analyzing market trends? Wall Street is a leading employer of Ph. D. graduates in particle physics (see, for instance, this New York Times article), largely because the physicists (claim to) understand the Ito calculus, used to describe physical processes such as Brownian motion but also used in derivative pricing.
My personal opinion, formed well before the 2008 market crash, can be summed up as follows: Handing my retirement portfolio to people who think they can measure particles (tachyons) that exist only at speeds greater than the speed of light ... what could possibly go wrong with that? I cringed when I learned that my alma mater, Princeton University, has a department titled Operations Research and Financial Engineering -- and trust me, it's not the OR part at which I cringe. Personal prejudices aside, though, it seems reasonable to me that a portion of STEM graduates will legitimately be desired for (and hired into) jobs that are probably not considered "STEM jobs", siphoning a portion of our university output away from the jobs specifically targeting holders of STEM degrees.
People have changes of heart.
Years ago, I had a student in an MBA course (now a lifelong friend) who had a bachelors degree in a scientific field (chemistry or something related). She had worked for the Michigan Department of Natural Resources as a lab chemist before deciding that it was not her passion, and that she would rather work in the business sector. Years later, I had another student with a science degree (chemistry? biochemistry? chemical engineering?) who had worked in the pharmaceutical industry before joining the MBA program. After graduating, he worked in management jobs that leveraged his scientific background but would not be classified as STEM jobs. Another MBA student had a degree in nuclear engineering and had served as a propulsion engineer aboard a US Navy submarine.
In fact, a fairly sizable portion of our MBA program consisted of people with undergraduate STEM degrees (and, often related work experience) who had decided to go over to the Dark Side and join the ranks of management. In comparing supply of and demand for STEM degrees, we need to allow for the fact that some STEM degree holders will naturally choose, for reasons other than a lack of job opportunities, to pursue non-STEM careers.
There is more to employability than having the right degree.
An administrator once made the mistake of inviting me to participate in an orientation session for new MBA students, designed to foster camaraderie and esprit de corps. During the session, I remember saying the following: "Look at the person on your left. Now look at the person on your right. Statistically, one in three people is an asshole ... so if it's not one of them, it's you." (I made the statistic up, based on my experience growing up in New York.) The point I was making then was that candidates would be required to work in teams, just as in industry, and it was naive to assume that it would always be easy to get along with all your teammates.
Sadly, though, it is also true that some people just cannot coexist at all with other workers. Some are chronically absent or late. Some need to be nagged, wheedled or hand-held just to get things done. Some are larcenous. I see no inherent reason why a STEM degree would preclude any of those possibilities (and in fact I've met walking, talking counterexamples to that conjecture). Those people will often "fail" a job interview, no matter how solid their technical credentials, or they will be involuntarily separated from an employer in a way that follows them through subsequent interviews. Thus we have to allow for some slice, hopefully small, of the STEM degree holders to be unsuitable for employment in STEM jobs (unless the recruiters are desperate).
Educational standards in the US ain't what they used to be.
During my graduate studies in mathematics at Michigan State University, I was a teaching assistant. Like most TAs, I began teaching recitation sections of a large service course, whose title was (approximately) "Introduction to College Algebra". The course was taught in a large lecture by a faculty member. The primary roles of the TAs handling the recitation sections were to answer questions and grade homework and exams.
A year or so after I arrived, we were joined by a new graduate student with a bachelor's degree in mathematics from a "prestigious" university. (I shall not name the university, so as to avoid embarrassing the fine folks in Ann Arbor.) He too had a teaching assistantship. Fall quarter of his first year, he was assigned to teach a couple of sections of the introductory algebra course. Winter quarter he was pulled out of the classroom, and his sole duty as TA was to work out the answers to the problems in the textbook ... because the Powers That Be had discovered that he could not answer simple algebra questions in class (and not, apparently, due to stage fright). Had he chosen to work in industry, rather than going straight to graduate school, and had the recruiters done their jobs well, he might have contributed to the statistics representing STEM degree holders not working in STEM jobs.
Employers frequently complain (particularly when lobbying for more H1B visas) that they cannot find a sufficient number of STEM degree holders with the "right skill set". We can argue about who bears responsibility for a genuine lack of the right skills: universities with outmoded curricula; employers unwilling to pay for training; or degree holders unwilling to upgrade their skills on their own time. We can also speculate (and many people do -- see the comments on the IEEE Spectrum post) on how often the "right skill set" translates to "willing to work cheap". We also need to accept that in some cases the "right skill set" translates to "actually knows the subject matter for their awarded degree", and that this is not a given.
Tuesday, March 5, 2013
The Value of Knowing the Value of Your Degree
Fellow blogger Laura McLay wrote today about a push in Congress to require someone (apparently states) to report statistics on graduate earnings by college/university and major. (See this report at Inside Higher Ed for more details; tip of the hat to Laura for the link.) Laura raises some excellent points about this pitfalls of this, and I will try not to duplicate her analysis.
Proponents of this sort of disclosure throw the word "transparency" around a fair bit, and in general I'm in favor of transparency (possible exceptions being clothing and curtains). Those of us associated with analytics are unlikely to argue against the provision of data (and, hopefully, some statistical analysis of it). Anyone who has used or taught decision analysis knows that, under typical assumptions, the expected value of imperfect information is nonnegative. In other words, it can't hurt to know. Those "typical assumptions", while mathematically mild, are important, and include the following:
The second issue -- can we make rational use of the information (and will we) -- is one reason doctors are not always supportive of genetic testing and sometimes even follow-up tests for marginal positive results. Will information that the patient's risk of some relatively unlikely or slowly progressing condition unduly depress the patient, cause the patient to embark on expensive, invasive and/or risky tests or procedures, or otherwise push the patient to do something that might not be entirely reasonable?
So my first reaction to the notion of making information available to potential college students about career prospects (placement rates, starting salaries, salaries five years out etc.) as they relate to the nature and source of the college degree is positive: more information is better. My second reaction is that it needs to be information, not just data, meaning that someone reliable (knows analytics) and trustworthy (not out to recruit students) needs to process the data and translate it into actionable knowledge. Moreover, it needs to be communicated to prospective students in a way that lets them understand both the implications and the limitations of the information. So we need statisticians or analytics professionals involved, and we need communications professionals involved.
I'll end with a few specific comments:
Proponents of this sort of disclosure throw the word "transparency" around a fair bit, and in general I'm in favor of transparency (possible exceptions being clothing and curtains). Those of us associated with analytics are unlikely to argue against the provision of data (and, hopefully, some statistical analysis of it). Anyone who has used or taught decision analysis knows that, under typical assumptions, the expected value of imperfect information is nonnegative. In other words, it can't hurt to know. Those "typical assumptions", while mathematically mild, are important, and include the following:
- we have some ability to assess the general accuracy (or inaccuracy) of the information; and
- we make rational use of it.
The second issue -- can we make rational use of the information (and will we) -- is one reason doctors are not always supportive of genetic testing and sometimes even follow-up tests for marginal positive results. Will information that the patient's risk of some relatively unlikely or slowly progressing condition unduly depress the patient, cause the patient to embark on expensive, invasive and/or risky tests or procedures, or otherwise push the patient to do something that might not be entirely reasonable?
So my first reaction to the notion of making information available to potential college students about career prospects (placement rates, starting salaries, salaries five years out etc.) as they relate to the nature and source of the college degree is positive: more information is better. My second reaction is that it needs to be information, not just data, meaning that someone reliable (knows analytics) and trustworthy (not out to recruit students) needs to process the data and translate it into actionable knowledge. Moreover, it needs to be communicated to prospective students in a way that lets them understand both the implications and the limitations of the information. So we need statisticians or analytics professionals involved, and we need communications professionals involved.
I'll end with a few specific comments:
- As Laura mentions, the analysis should at minimum provide ranges and not just averages. Those of us with analytics training are only too aware of the Flaw of Averages.
- Salaries are one way to look at the value of a degree. Break-even analysis (the time required to earn enough to pay off the cost of the degree, include lost earnings for the time spent in college) is another, but it is trickier to compute.
- Some nontrivial statistical modeling may be required to account for various factors other than school and major that might influence earning power. For example, some schools have an explicit pre-med major, while at some schools pre-med students major in chemistry, biology or biochemistry, and at some schools they major in something unrelated. When I was an undergraduate, the student living next door to me was a pre-med who majored in English. If that were true across the board (and I have no idea if it was, but at minimum it was not an anomaly), then our English majors probably out-earned English majors at schools with explicit pre-med majors.
- There is more to a career than salary, and that needs to be conveyed to consumers of this information. Before the markets tanked in '07-'08, finance majors hired by Wall Street trading firms enjoyed rather high salaries (higher than what finance majors earned in corporate finance positions, and certainly higher than many other majors). They also "enjoyed" a high cost of living, ungodly work hours and high stress. My impression is that aggressive personalities tended to fare better than less aggressive ones. So that high salary figure for finance majors at schools that fed the Wall Street mill needed to be tempered by an understanding of those other factors.
- Laura mentions the effect of time. Widespread dissemination of salary data might lead to gluts in the better-paying fields, driving down salaries in those fields. At the same time, demographic, economic or technological trends might augur for higher salaries down the road in fields that recently have not paid that well. (I'd mention gerontology, but someone might read something personal into it.)
- There are risk factors involved in the decision to attend college, the choice of the college to attend, and the choice of major. Major A might pay more after graduation than major B, but if majoring in A makes it likely you will fail to graduate and B is safer (given your particular skill set and inclinations), maybe B is really the better deal.
Saturday, September 8, 2012
Big (?) Ideas for 2012
With the start of the school year (for some people :-)), Aurelie Thiele is back and blogging again, starting with a post about some of the themes from the annual “big ideas” issue of "The Atlantic". I'm not sure exactly how big these ideas are, and the meritocrat in me disagrees with the third one (lotteries for college admissions), but the first two certainly resonate, as does the fourth (hire introverts -- believe it or not, according to the Myers-Briggs Type Indicator, I'm one). The first two resonate in part due to person experiences.
The right to be forgotten: This pertains to the ability of an individual to insist that old elements of their Internet "footprint" be deleted. There's no easy answer here: the right to privacy, free speech, censorship, domestic and international law are all tangled up in this. There is, however, one fairly straightforward partial answer: assume that anything you put out on the Internet is out there permanently. Hence, if something strikes you as potentially embarrassing, don't do it.
Case in point: quite a few years ago I taught a course in business use of the Internet, which included the basics of creating and maintaining a web site, including HTML and producing dynamic pages (using Cold Fusion). During the course, students did a series of homework assignments that created a personal web site (hosted on a university server). I warned them, day one, that anything they posted was visible to the networked portion of the planet, and that they should accordingly avoid anything embarrassing. One of the assignments was to a create a web form. The context of the form was up to them, so long as it met reasonable standards of decency, but the form had to have at least one of every HTML form element (radio buttons, text fields, a password field, ...).
One young lady created a form that I think had something to do with how the respondent spent his/her free time. One of the questions was "How many people have you murdered lately?" It was obviously intended to be humorous. I cringed internally a bit, but it met the standards of the assignment, and so I accepted it.
Not too long after the student graduated, I got a somewhat frantic message from her. She was interviewing for a position with a company, and as part of their vetting process they routinely looked people up on search engines. So she did a Google search for her own name and found her old course web site ... including the aforementioned form. Her immediate concern was how to get the site taken down from the university server, but as I pointed out to her, search index entries can outlive the sites they index, and back then Google kept cached copies of sites. (I'm not sure if they still do.) I explained the general mechanics of getting a site deleted from a search index -- the specifics vary from one engine to the next -- and wished her luck. I'm pretty sure at that point she was regretting her choice of questions for the form.
Boot camp for teachers: The gist of this idea is that practice teaching, in a simulated classroom environment (including simulated students), is the best way to prepare for the unpredictability of an actual classroom.
I was a graduate teaching assistant in mathematics during my doctoral program. Our department scheduled an orientation for new TAs prior to the start of fall term. As part of it, each of us had to prepare a lesson (for the freshman pre-calculus algebra course) and deliver it to a room full of professors, senior doctoral students and our fellow new fish. The professors and senior doctoral students played the roles of freshmen attending the course, and the senior doctoral students took particular pleasure in simulating undergraduate student behavior to the best of their ability. (Happily, this was before smart phones existed.)
I recall one new TA running through an algebra lesson when a simulated student (one of the older doctoral candidates) interrupted him: "Why?" The teacher-to-be launched into some calculations, which the "student" promptly interrupted with another "Why?" As the new TA broke the calculation down into smaller and smaller steps, his tormentor questioned each one with that same three letter interrogative ... until finally a clearly exasperated TA blurted out "Because that's how God made the real numbers!"
Possible theological concerns aside, that is not likely to be an answer that would satisfy a real student. Moreover, as we new people eventually learned, part of teaching is classroom management -- you can't drop too much time on one question, unless perhaps the entire class is stuck on it, and if you focus too much on one student the others may tune out. A carefully worded variant of "see me after class" may be the best response to the situation being simulated, a very realistic albeit slightly exaggerated scenario.
Having sat through that, and looking back on my own teaching career, I can definitely say that a healthy dose of simulated teaching can head off some potentially significant classroom problems. In fact, I would have benefited from more than that one session, although at the time I doubt I would have appreciated the extra training.
The right to be forgotten: This pertains to the ability of an individual to insist that old elements of their Internet "footprint" be deleted. There's no easy answer here: the right to privacy, free speech, censorship, domestic and international law are all tangled up in this. There is, however, one fairly straightforward partial answer: assume that anything you put out on the Internet is out there permanently. Hence, if something strikes you as potentially embarrassing, don't do it.
Case in point: quite a few years ago I taught a course in business use of the Internet, which included the basics of creating and maintaining a web site, including HTML and producing dynamic pages (using Cold Fusion). During the course, students did a series of homework assignments that created a personal web site (hosted on a university server). I warned them, day one, that anything they posted was visible to the networked portion of the planet, and that they should accordingly avoid anything embarrassing. One of the assignments was to a create a web form. The context of the form was up to them, so long as it met reasonable standards of decency, but the form had to have at least one of every HTML form element (radio buttons, text fields, a password field, ...).
One young lady created a form that I think had something to do with how the respondent spent his/her free time. One of the questions was "How many people have you murdered lately?" It was obviously intended to be humorous. I cringed internally a bit, but it met the standards of the assignment, and so I accepted it.
Not too long after the student graduated, I got a somewhat frantic message from her. She was interviewing for a position with a company, and as part of their vetting process they routinely looked people up on search engines. So she did a Google search for her own name and found her old course web site ... including the aforementioned form. Her immediate concern was how to get the site taken down from the university server, but as I pointed out to her, search index entries can outlive the sites they index, and back then Google kept cached copies of sites. (I'm not sure if they still do.) I explained the general mechanics of getting a site deleted from a search index -- the specifics vary from one engine to the next -- and wished her luck. I'm pretty sure at that point she was regretting her choice of questions for the form.
Boot camp for teachers: The gist of this idea is that practice teaching, in a simulated classroom environment (including simulated students), is the best way to prepare for the unpredictability of an actual classroom.
I was a graduate teaching assistant in mathematics during my doctoral program. Our department scheduled an orientation for new TAs prior to the start of fall term. As part of it, each of us had to prepare a lesson (for the freshman pre-calculus algebra course) and deliver it to a room full of professors, senior doctoral students and our fellow new fish. The professors and senior doctoral students played the roles of freshmen attending the course, and the senior doctoral students took particular pleasure in simulating undergraduate student behavior to the best of their ability. (Happily, this was before smart phones existed.)
I recall one new TA running through an algebra lesson when a simulated student (one of the older doctoral candidates) interrupted him: "Why?" The teacher-to-be launched into some calculations, which the "student" promptly interrupted with another "Why?" As the new TA broke the calculation down into smaller and smaller steps, his tormentor questioned each one with that same three letter interrogative ... until finally a clearly exasperated TA blurted out "Because that's how God made the real numbers!"
Possible theological concerns aside, that is not likely to be an answer that would satisfy a real student. Moreover, as we new people eventually learned, part of teaching is classroom management -- you can't drop too much time on one question, unless perhaps the entire class is stuck on it, and if you focus too much on one student the others may tune out. A carefully worded variant of "see me after class" may be the best response to the situation being simulated, a very realistic albeit slightly exaggerated scenario.
Having sat through that, and looking back on my own teaching career, I can definitely say that a healthy dose of simulated teaching can head off some potentially significant classroom problems. In fact, I would have benefited from more than that one session, although at the time I doubt I would have appreciated the extra training.
Sunday, July 29, 2012
Is Mathematics Only for the Mathematically Inclined?
A colleague just sent me a link to an opinion piece in the New York Times Sunday Review with the somewhat provocative title "Is Algebra Necessary?" The author (Andrew Hacker, an emeritus professor of political science), while acknowledging the profound role of mathematics in society, questions whether we should require algebra (or, as I read the piece, anything beyond basic arithmetic and some basic level of statistical numeracy) of all school children. He quotes a professor of educational psychology (John P. Smith III) from Michigan State University asserting that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” (For what it's worth, MSU has a nationally renowned College of Education ... but I have a hard time trusting anyone who looks that much like a young Geraldo Rivera.)
I don't want to get bogged down in the details of mathematics education in the U.S., and I certainly agree that the curriculum content (as well as the delivery) needs to be updated periodically. The mathematics of computing was not on anyone's radar when I was an urchin, and it's extremely important today. I'll also stipulate that not every adult in the U.S. (or elsewhere for that matter) needs to be proficient in algebra or trigonometry, let alone calculus. That said, my immediate reaction was that I thought I saw two flaws, one perhaps minor but the other crucial, in the author's argument.
I'll address the minor flaw first. Professor Hacker says (near the middle of the second page):
The major flaw with Professor Hacker's argument is that if we reduce K-12 mathematics education to the bare minimum, as he suggests, it will shut the doors to many college majors before students reach college. When I was in school, separate math classes did not begin until junior high school, so through grade 6 I received the same mathematics instruction everyone else did ... which in Professor Hacker's universe would be thin gruel indeed. I assume the system still operates approximately that way. The mathematically inclined public school student (which described me at that age) will hopefully be able to go beyond the basic curriculum ... somehow ... at least if his or her parents can afford private tutoring. The generic college-bound student, however, will matriculate with the ability to figure out the tip on a restaurant check, and not much else.
I'm reminded of an incident from graduate school. Back then, registration was done manually in a large gym called "The Pit", and our math department used graduate students to relieve the secretaries of some of the duty (doling out punch cards to students seeking classes). One summer, I was working The Pit with a fellow doctoral student, "Mean Dave" Green. (Don't ask about the nickname, just trust me: he earned it.) An undergrad came up and requested Algebra I. Dave looked at him and asked "Didn't you take that from me fall quarter?" The kid indeed had (and failed the class). Dave asked why he hadn't repeated it immediately, in winter quarter, while the memory was fresh. The kid had - and failed again. As he did spring quarter. So here he was asking for it for the fourth time. I innocently inquired what his major was. His answer: electrical engineering. The requirements for EE then were: algebra I and II; calculus I through IV; linear algebra; and ordinary differential equations.
Now picture that kid's children (or, um, grandchildren? sigh) reaching college today with Professor Hacker's suggested mathematics curriculum under their belts. Electrical engineering? Not going to happen; the math prerequisites alone would add two years to their degree, charitably assuming that a university was willing and able to staff that many remedial math classes, and charitably assuming that someone 18 years old with a carefully honed disdain or fear (or both) of mathematics is still able to learn math. Other engineering majors? Not likely. (If, somehow, Professor Hacker's position prevails and universities continue to pump out civil engineers nonetheless, remind me to stay off bridges and out of tunnels.)
Computer science uses enough mathematics that I suspect it would be tough to handle. Some business majors might still be open (personnel management?), but the more lucrative ones (finance and accounting in particular) might be off the table for those who had not gotten private tutoring. Physical sciences? So long.
Before I added "emeritus" to my title, I sometimes found myself answering questions from students (or parents) about how much math to take during freshman and sophomore years of college. My response was typically some variation of "as much as you can stand". Most college students do not commit to a major until their junior year. At that point, if you have racked up more math than your major requires, you can usually count the rest as elective credits; but if you are short of math, it can freeze you out of some majors. I've seen a similar phenomenon with graduate school: students who did a non-technical undergraduate major, taking the minimum amount of mathematics they could (sometimes none), and then decided they wanted to go to graduate school in a program with stiff mathematics requirements. Extrapolating that to cover students whose public school mathematics training stopped at counting and basic calculator punching frightens me.
We can legitimately debate what the basic K-12 mathematics curriculum -- the foundation for both attending college and going into a trade -- should be; but if we are going to reduce it as much as Professor Hacker suggests, we'd better come up with a genetic test that can identify a fetus's future trade or college major by birth.
Update: To my utter lack of surprise, other people are weighing in on this. I'm not actively looking for all the commentary (and I'm sure it will be voluminous), but as I come across posts I'll link them here.
I don't want to get bogged down in the details of mathematics education in the U.S., and I certainly agree that the curriculum content (as well as the delivery) needs to be updated periodically. The mathematics of computing was not on anyone's radar when I was an urchin, and it's extremely important today. I'll also stipulate that not every adult in the U.S. (or elsewhere for that matter) needs to be proficient in algebra or trigonometry, let alone calculus. That said, my immediate reaction was that I thought I saw two flaws, one perhaps minor but the other crucial, in the author's argument.
I'll address the minor flaw first. Professor Hacker says (near the middle of the second page):
Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic.By "estimating" I assume he means computing (or intuiting) an approximate value (order of magnitude, interval, ...) for some uncertain quantity (variable). That implies the ability to determine a formula for the variable in terms of other parameters of the problem. For example, if I have a recipe (for a meal, or for a medication I must administer) that calls for a water-based solution with 40% active ingredient by volume, and I need five fluid ounces of the solution, about how much active ingredient do I need? That sounds to me like solving a simple linear equation, which I believe falls into the category of "algebra". (As a sidebar, in the event that this is a medication to be administered to me, and a nurse or pharmacist is doing the calculation, I would really appreciate it if they could do better than just an "estimate".) What if I know that I have five fluid ounces of active ingredient (which must all be used) and require a 40% solution? Can I estimate the amount of water required without knowing some basic algebra?
The major flaw with Professor Hacker's argument is that if we reduce K-12 mathematics education to the bare minimum, as he suggests, it will shut the doors to many college majors before students reach college. When I was in school, separate math classes did not begin until junior high school, so through grade 6 I received the same mathematics instruction everyone else did ... which in Professor Hacker's universe would be thin gruel indeed. I assume the system still operates approximately that way. The mathematically inclined public school student (which described me at that age) will hopefully be able to go beyond the basic curriculum ... somehow ... at least if his or her parents can afford private tutoring. The generic college-bound student, however, will matriculate with the ability to figure out the tip on a restaurant check, and not much else.
I'm reminded of an incident from graduate school. Back then, registration was done manually in a large gym called "The Pit", and our math department used graduate students to relieve the secretaries of some of the duty (doling out punch cards to students seeking classes). One summer, I was working The Pit with a fellow doctoral student, "Mean Dave" Green. (Don't ask about the nickname, just trust me: he earned it.) An undergrad came up and requested Algebra I. Dave looked at him and asked "Didn't you take that from me fall quarter?" The kid indeed had (and failed the class). Dave asked why he hadn't repeated it immediately, in winter quarter, while the memory was fresh. The kid had - and failed again. As he did spring quarter. So here he was asking for it for the fourth time. I innocently inquired what his major was. His answer: electrical engineering. The requirements for EE then were: algebra I and II; calculus I through IV; linear algebra; and ordinary differential equations.
Now picture that kid's children (or, um, grandchildren? sigh) reaching college today with Professor Hacker's suggested mathematics curriculum under their belts. Electrical engineering? Not going to happen; the math prerequisites alone would add two years to their degree, charitably assuming that a university was willing and able to staff that many remedial math classes, and charitably assuming that someone 18 years old with a carefully honed disdain or fear (or both) of mathematics is still able to learn math. Other engineering majors? Not likely. (If, somehow, Professor Hacker's position prevails and universities continue to pump out civil engineers nonetheless, remind me to stay off bridges and out of tunnels.)
Computer science uses enough mathematics that I suspect it would be tough to handle. Some business majors might still be open (personnel management?), but the more lucrative ones (finance and accounting in particular) might be off the table for those who had not gotten private tutoring. Physical sciences? So long.
Before I added "emeritus" to my title, I sometimes found myself answering questions from students (or parents) about how much math to take during freshman and sophomore years of college. My response was typically some variation of "as much as you can stand". Most college students do not commit to a major until their junior year. At that point, if you have racked up more math than your major requires, you can usually count the rest as elective credits; but if you are short of math, it can freeze you out of some majors. I've seen a similar phenomenon with graduate school: students who did a non-technical undergraduate major, taking the minimum amount of mathematics they could (sometimes none), and then decided they wanted to go to graduate school in a program with stiff mathematics requirements. Extrapolating that to cover students whose public school mathematics training stopped at counting and basic calculator punching frightens me.
We can legitimately debate what the basic K-12 mathematics curriculum -- the foundation for both attending college and going into a trade -- should be; but if we are going to reduce it as much as Professor Hacker suggests, we'd better come up with a genetic test that can identify a fetus's future trade or college major by birth.
Update: To my utter lack of surprise, other people are weighing in on this. I'm not actively looking for all the commentary (and I'm sure it will be voluminous), but as I come across posts I'll link them here.
Saturday, May 21, 2011
A Shoutout to Anki
I'd like to point out Anki, an open source (GPL 3) virtual flashcard program I've been using. Anki runs on all major PC platforms (and an impressive array of mobile devices), and is feature-rich. It has a plug-in architecture. Cards can contain not just text but also images and audio files. Anki supports LaTeX, so it should be easy to put mathematical formulas on cards. Use of card decks is very flexible (including an easy way to have cards representing difficult concepts repeat sooner than cards representing easy concepts). It is easy to create or import card decks, and you can share card decks (and plug-ins) with other people through their AnkiWeb site. (Disclaimer: I have not looked at the available shared decks, nor have I looked at any plug-ins. The basic download fills my needs.)
My use for Anki has been to learn my students names. At the outset of each semester, I acquire a class list with student photos, strip out the photos, and turn them into an Anki deck. During idle moments at coffee shops, I play the decks and learn to associate names with faces. (Addressing students by name on the first day of class freaks them out; I think they tend to be more docile thereafter.)
I'm not a big fan of rote memorization in education, but I suppose it has its place. I could see using Anki to learn formulas from queuing theory (for instance, "M/M/1 steady-state queue length" on the front, the corresponding formula on the back) or perhaps some terminology from linear programming (graph of a feasible region and an objective hyperplane tangent along an edge on the front, "multiple optima" on the back). As there are more things in heaven and earth than are dreamt of in my philosophy, I suppose there are more ways Anki could be used in the teaching of operations research.
My use for Anki has been to learn my students names. At the outset of each semester, I acquire a class list with student photos, strip out the photos, and turn them into an Anki deck. During idle moments at coffee shops, I play the decks and learn to associate names with faces. (Addressing students by name on the first day of class freaks them out; I think they tend to be more docile thereafter.)
I'm not a big fan of rote memorization in education, but I suppose it has its place. I could see using Anki to learn formulas from queuing theory (for instance, "M/M/1 steady-state queue length" on the front, the corresponding formula on the back) or perhaps some terminology from linear programming (graph of a feasible region and an objective hyperplane tangent along an edge on the front, "multiple optima" on the back). As there are more things in heaven and earth than are dreamt of in my philosophy, I suppose there are more ways Anki could be used in the teaching of operations research.
Sunday, January 9, 2011
Physiology and Mathematics Education
As a math lifer, I'm concerned about what more and more people are calling a crisis in STEM (Science, Technology, Engineering and Mathematics) education in the United States. It seems as if every few days we read about the U. S. lagging behind other countries in math or science test scores. We continue to lead the world in innovation for the moment, but it's hard to picture how we can sustain that lead without producing (or importing) more scientists and engineers (and, dare I say, mathematicians). Equally importantly, in the age of the "information economy", if average U. S. citizens (not the ones in the right tail on math scores) come up short in STEM ability, where are they going to find jobs that pay respectable salaries? (This is very important to me: I'm on the cusp of retirement, and I'm counting on them both to pay down the burgeoning national debt and to sustain my lifestyle once my paychecks stop.)
The press (and, thus, the populace) are gradually waking up to the looming crisis, as evidenced by government panels, legislation, academic workshops and periodic episodes of public hand-wringing. Naturally, this spawns a wave of finger-pointing as we seek (a) one single explanation for what is undoubtedly a phenomenon with multiple roots and (b) someone (other than ourselves) whom we can blame. A backgrounder from the Heritage Foundation aptly points out that if the K-12 pipeline does not produce students well grounded in science and math, colleges and universities will be hard-pressed to find students willing and able to major in those subjects (and, by extension, graduate program enrollments will also suffer).
Now please indulge me in an apparent digression that will actually tie back (I hope). I recently found myself engaged in a conversation about math education, math ability and its connection (if any) to gender. In this conversation, I recalled a colleague (a professor of economics) complaining to me that his daughter had essentially been told outright by a high school teacher that, being female, she should have diminished expectations for learning upper level mathematics (I suspect this meant calculus, but the conversation was long ago and the details elude me). My colleague was justifiably apoplectic.
I also recalled some misadventures from my graduate student days, when I taught a math class for elementary education majors. On paper, the course dealt with how to teach math to K-6 students. In practice, it meant (gulp) teaching K-6 math to college students majoring in elementary education. Lest you think I exaggerate, let me share an anecdote. My then girlfriend also taught the course, in the summer, when the students were elementary school teachers returning to pick up additional credits. One student asked if she could bring her eight year old son to class to avoid daycare hassles, which request my girlfriend was happy to accommodate. On the day of the first exam, she saw him sitting with nothing to occupy him, so she game him a spare copy of the exam, figuring he could color on the back. Instead, he flipped it over, did the exam -- and received the highest score in the class!
So, on the one hand, we have people telling children that they are doomed to be weak at math (and science?) because they lack a Y chromosome. I suspect similar comments are made based on race or other factors. On the other hand, we have teachers (at least in elementary school) who themselves are weak in math (and science?) and are inclined to pass their fear of the subject on to their students. (If the teacher finds something difficult, he or she is likely to communicate to the pupil that the pupil should not worry about finding it challenging.) On the gripping hand (and this is purely my conjecture), I suspect we also discourage students of all levels from taking STEM courses by rewarding them for weak work in non-STEM courses. I think it's harder to give inflated grades in STEM subjects because they tend to have definitive correct and incorrect answers. (At least it's harder for me to give them.) At the same time, it's easy for a student to be discouraged at having to work hard for medium grades in STEM subjects when they can get better grades with less effort in other classes.
What ties this to the STEM crisis, for me, is a recent article in Newsweek about physiological triggers for improvement (or degradation) in the human brain. Specifically, according to author Sharon Begley,
The press (and, thus, the populace) are gradually waking up to the looming crisis, as evidenced by government panels, legislation, academic workshops and periodic episodes of public hand-wringing. Naturally, this spawns a wave of finger-pointing as we seek (a) one single explanation for what is undoubtedly a phenomenon with multiple roots and (b) someone (other than ourselves) whom we can blame. A backgrounder from the Heritage Foundation aptly points out that if the K-12 pipeline does not produce students well grounded in science and math, colleges and universities will be hard-pressed to find students willing and able to major in those subjects (and, by extension, graduate program enrollments will also suffer).
Now please indulge me in an apparent digression that will actually tie back (I hope). I recently found myself engaged in a conversation about math education, math ability and its connection (if any) to gender. In this conversation, I recalled a colleague (a professor of economics) complaining to me that his daughter had essentially been told outright by a high school teacher that, being female, she should have diminished expectations for learning upper level mathematics (I suspect this meant calculus, but the conversation was long ago and the details elude me). My colleague was justifiably apoplectic.
I also recalled some misadventures from my graduate student days, when I taught a math class for elementary education majors. On paper, the course dealt with how to teach math to K-6 students. In practice, it meant (gulp) teaching K-6 math to college students majoring in elementary education. Lest you think I exaggerate, let me share an anecdote. My then girlfriend also taught the course, in the summer, when the students were elementary school teachers returning to pick up additional credits. One student asked if she could bring her eight year old son to class to avoid daycare hassles, which request my girlfriend was happy to accommodate. On the day of the first exam, she saw him sitting with nothing to occupy him, so she game him a spare copy of the exam, figuring he could color on the back. Instead, he flipped it over, did the exam -- and received the highest score in the class!
So, on the one hand, we have people telling children that they are doomed to be weak at math (and science?) because they lack a Y chromosome. I suspect similar comments are made based on race or other factors. On the other hand, we have teachers (at least in elementary school) who themselves are weak in math (and science?) and are inclined to pass their fear of the subject on to their students. (If the teacher finds something difficult, he or she is likely to communicate to the pupil that the pupil should not worry about finding it challenging.) On the gripping hand (and this is purely my conjecture), I suspect we also discourage students of all levels from taking STEM courses by rewarding them for weak work in non-STEM courses. I think it's harder to give inflated grades in STEM subjects because they tend to have definitive correct and incorrect answers. (At least it's harder for me to give them.) At the same time, it's easy for a student to be discouraged at having to work hard for medium grades in STEM subjects when they can get better grades with less effort in other classes.
What ties this to the STEM crisis, for me, is a recent article in Newsweek about physiological triggers for improvement (or degradation) in the human brain. Specifically, according to author Sharon Begley,
Finally, being told that you belong to a group that does very well on a test tends to let you do better than if you’re told you belong to a group that does poorly; the latter floods you with cortisol, while the former gives you the wherewithal and dopamine surge to keep plugging away.So the effect of communicating diminished expectations to students may be more than psychological; it may trigger physiological changes that create a self-fulfilling prophecy ... and, in doing so, deepen the STEM crisis.
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