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Teaching Natural Sciences To Social Science Students?
An anonymous reader writes "As a calculus professor for a small undergraduate institution, I normally lecture students who are majoring in the natural (or 'hard') sciences, such as mathematics, physics, and computer science. In fact, I have done so for almost thirteen years. However, for the first time this fall semester, we have a shortage of professors on our hands. As a result of this, I have been asked to teach a general education statistics class. Such classes are a major requirement for the large psychology student body we have here. I have never lectured social science students in any mathematics-related classes. My question to the Slashdot community is as follows: What are your experiences with teaching natural science classes to social science students? How is the experience the same or different in comparison to natural science students who may be more adept to the nuances of mathematics and other similar fields?"
Some will be apt and mentally up to speed with whatever you through at them.
Some will be unable to comprehend every third word.
Some will be uninterested. Others will be interested, but incapable.
I'm sorry, am I misreading or are you saying statistics is a "soft science"? If you're that confused about things, then just go to the textbook, and teach one chapter a week.
Avoid using overly abstract concepts, and try to put things in terms they can understand. Since you are teaching statistics, try to use a lot of gambling references (lotto, roulette, etc.) since nearly all the students will have some familiarity with those.
I've found I can teach engineering concepts to elementary school teachers as long as I avoid formulae (and avoid using Latin references, so use the term "formulas" :-) ).
Tell them, everyday at the beginning of the lesson, the purpose of each topic you teach and how it is going to be useful for them when solving a problem.
Tell them again at the end.
Knowing why you are teaching them something like hypothesis testing is half the battle to get them to listen.
And examples, lots of examples.
Betteridge's Law of Headlines. Did I do that right?
... it annoys me the most that they somehow explain distinction within one subject, ...
I ment to say: it annoys me the most that they DO NOT somehow explain distinction within one subject ....
Signed, Defiant
Isn't the use of statistics pretty much the only thing that distinguishes 'psychology' from 'talking about feelings'?
I realize that most psych majors don't actually go on to practice in psychology or psychiatry, and the ones that do generally have to do some flavor of graduate work; but I'm still rather alarmed by the implication of TFS that psych students might well be deeply uncomfortable with statistics...
As someone who's been on both of those academic sides (I started in hard, and moved into soft four years later), I never thought it was a lack of comprehension when fellow students have trouble with hard sciences. Instead, it's an appreciation for numerical conclusions.
Hard sciences basically tend to conclude three steps earlier than soft sciences -- because the math ends there. Hard sciences tend to describe a scenario, detail it numerically, hypothesize a numerical result, experiment numerically, solve for x, and x=n is the answer. The issue for soft science students is really that nobody ever cared about x. Hard sciences very quickly forget where x came from, because the entire scenario was translated into numbers. This affords hard sciences a certain level of abstraction, making problems faster to solve, easier to solve, and more widely relevant to re-apply.
Soft sciences tend to be industries where some aspect of the scenario can't be translated into numbers. It's usually a black-box scenario, and psychology is a good example. Such experiments don't attempt to describe certain behavioural anomalies numerically. Instead, 40% - 80% of a scenario is translated into numbers, leaving the remaining 20% - 60% as mysterious elements. Imagine a hard science equasion where six linear constants simply cannot be merged into a single constant -- for no seemingly good reason. As a direct result, after solving for x, the numerical abstraction must then be de-abstracted back into whatever the real-world scenario actually is. This procedure is not only an effort to grasp, but it's also a a major point of interpretation at the end of an experiment -- usually because x isn't the number of grams diluted; instead x is the likelihood that a person might turn left.
The nice part about de-abstracting at the end is that you wind up with a real-world answer, not a mystery number.
So my point is, that for a social science student used to walking in with a scenario, and walking out with a conclusion, you need to teach them how to appreciate the hard-science "datum result" without having a one-question-one-answer conclusion.
You can see this same effect in the business world. Big business corporate C.E.O.'s often make decisions from numbers in, to predict numbers out, without ever knowing where the numbers came from, nor how they'll be used on the way out. But if you've seen anyone go through "board of director" training, you know that the skills wind up applying to any business anywhere because they are all done at the hard-science executive level.
Constrast that to the entrepreneur of a small business, who needs to make all of the same decisions, but simply doesn't have the sample-size of data coming in to ever be able to make decisions numerically like the corporate guy -- which is one of the primary reasons that he has an advisory board instead of a board of directors. The decision-making process is very different, even though they are the same questions and the same answers. And each has a very difficult time in the other's business world.
Here's hoping someone else's response details a good way to actually teach that appreciation.
First thing to do is to get emacs and get the doctor watson mode working. Then have some sessions with Watson and understand how to talk to psychology students. To my best understanding, it involves rephrasing their questions and asking them why they ask that question or what their feeling is. All you need to do is to wing it for 50 minutes and charge them one hour of tuition fees. They will get the hang of it and learn to speak to their clients for 50 minutes and bill them for an hour.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
Math and Hard science are easy for me. Just memorization, some students do better and some won't. students who consistently want to know why, normally have a harder time with math.
You make it sound like you are teaching physics to special ed classes.
They are as smart as everyone you've had so far. You may see some differences in their backgrounds, but that's easy enough if you make allowances to give more basics or point them to appropriate resources. I'd give an example, but I have no idea what "natural science" is to you. Geology and oceanography are natural sciences, same as physics, but they share little in common.
One thing you may notice is that arts students in hard classes may want more "why" than "how" answers. So be prepared for more philosophical discussions, or correct, if silly, comments (i.e., the "why" for valence electrons is that the stable ones are like a comforable couch, and the unstable ones are hard benches. You want the better seat, but you don't really want to get up, and the worse the chair, the sooner you'd move) or something like that. The "why" as an expression of potential energy in MeV won't get the point across as well as a discussion of musical couches, and they'll remember it better, isn't that the goal, over the goal of the hard science students where accuracy is above all.
Learn to love Alaska
A major problem with these sorts of courses is that they're often not taught in a way that emphasizes their utility to the student. If you're thinking about being a psychologist for example why is calculus important? I'm not saying it isn't. I can think of several different ways it could be very important especially as it regards understanding statistics.
But you might want to create some test questions that relate to their majors.
In business calculus they focus on it's relationship to various economic calculations. So you might want to look at drug trial statistics or anthropological/demographic statistics.
And for the love of God... please tell them that correlation is not causation. You'd be doing everyone a huge favor. These guys are going going write stupid papers or write blogs or something similar that will pop up in the media. And everyone here at slashdot will be facepalming over another dumb paper that didn't acknowledge that simple fact.
Just saying.
I've decided to stop wasting my time responding to AC trolls/sockpuppets... so if you want a response from me... login.
You really shouldn't generalize about what psychology majors are going to be like. In the department I did my Ph.D in, psychology was closely allied to biology and ecology, and there was another department across campus that did social psychology. Some of the psychologists were pretty darn quantitative. But they were being quantitative about the mind, which is (my bias) maybe more interesting than the examples you used last time you taught calculus. Also, while the majority of students may be psych majors, some will be from other majors. What do you want future lawyers, school principals and politicians to know about statistics? This is your chance to teach them. Sooo, they might have good math skills, or not. But you can't assume that they know calculus, obviously, so you probably want to use a textbook that treats stats as a tool for understanding patterns in data, and goes easy on the theory behind maximum likelihood estimates and so on. I like Perry Hinton's Statistics Explained, but it really depends what you are trying to teach the students to do. http://www.amazon.com/Statistics-Explained-Science-Students-Edition/dp/0415332850/ref=sr_1_1?s=books&ie=UTF8&qid=1340578689&sr=1-1&keywords=statistics+explained If the psychology majors are any good, they may be more used to thinking clearly about surveys and tricky experiments than you are. Perhaps you can structure the course so that learning goes both ways.
Always interesting to see the categories different parts of academia place each other in. The post's author is calling math, physics and comp-sci "natural sciences" and apparently considers statistics to be "social science". I'm a geology professor and, as far as I'm aware, my colleagues and I tend to consider Earth, environmental, and biological sciences to be the "natural sciences"; physics, chemistry, engineering, and any math to be "physical science"; and psychology, sociology, (cultural) anthropology, etc. to be "social sciences". Everything else is art and/or humanities.
I wonder how other groups categorize one another? Right off the bat I'd suspect that mathematicians don't always consider themselves scientists. Perhaps ditto for engineers. People tend to form and place each other in groups of varying degrees of subjectivity. How you place others probably says something about the standards and values of one's own group.
This sounds like it'd make a great piece of social-psych research! They love this kind of fluff, right? (j/k)
I don’t mean for this to sound arrogant, but it probably will. I was a physics major who took a statistics course that was taught in the Psychology Department and meant for psychology students. A lot of science and math majors took the course as a way to pad their GPA’s. I could see from the books the other students brought to class that about one forth of the students were science or math majors. I think I made about a 96 on the first test and was embarrassed at the thing I missed. The class average was 48 or something. The grad student teaching the course said that maybe the test was too hard, but “there were a lot of very good grades”. I have a feeling that not many of the good grades were made by the psych majors.
If I were teaching the course, I would probably emphasize the purpose of the various statistical techniques for behavioral evaluation, and not make the math portion too detailed or rigorous.
I think that professor was me. I am from Trinidad but my parents were from Nigeria where I am living now. I would love to get back in touch and have a beer with you. If you could please send me a small advance for travel along with your SSN and a passport photo I can begin to make arrangements.
There is an interesting talk by Arther Benjamin arguing that for most students stats are for more valuable than calculus as an end point as they are more relevant to everyday life.
You might want to try this in a new way? Have your students use the Khan Academy to look at topic lectures. Take the short tests after each section to see who's having problems and with what sections. This allow you to provide the interesting stuff, make you lectures about the relevance of what they're learning to the process of understanding the flow and function of populations and how statistics are a powerful tool to let us begin to extract patterns of form and function inside what would would otherwise look like turbulent and unpredictable systems. They even let us predict outcomes in nonlinear systems. Also, you can get tutors through the Khan Academy, so anybody who is having a little difficulty can actually work with someone who already understands the concepts. The point is you can do the cool stuff, watch your students perform, support the stragglers, and get the feedback you need to have everyone complete the course informed, knowing the material, and enjoying the process that got them there. A win/win.
The one down side is that they Statistics series isn't quite complete yet, but its getting there, and there's more than enough there to get your kids started.
At my univ, "stats" was a very core part of post-grad psychology. Unfortunately, many students only cared about stats with respect to surveys/questionnaires, and they had problems with that :(
BUT multivariate stats was still seen as important and was required, along with experimental design. At the undergrad level the psycho-stats included the basics, including null-hypothesis, which stats to use depending on the experimental design etc.
Grab some real psychology (not couch psychology) studies, and look at the experimental design and what statistical methods were used in them. Take a look at the texts used in the good psych schools.
For the sociology students, pat them on the head and tell them that things will be ok.
rewriting history since 2109
My advice to you are the following two points: 1. Teach mathematical modelling. In my experience many students, also those in technical sciences, have problems creating reasonable mathematical models. Once you teach them to do that, they will see by themselves how math can actually simplify their lives. 2. Work with examples from their (!) field. I have heard a lot how for example med students complain about their physics courses being completely unrelated to their studies. But as soon as you point out that Bernoulli's principle applies to blood flow and you give them some time to think about what this means in case of Arteriosclerosis they are fully interested again. This becomes even more important towards the end of the term when exams come closer and students might start skipping classes "not relevant for their further studies".
You’re going up against the left brain / right brain situation. The hard sciences are more of logic, analysis, detail oriented thinking, where the liberal art side are the intuitive, creative thinkers that are more in tune of the shape of things. The social science side tends to attract those with the right brain dominate way of thinking of things; they will try and process numbers as a shape/color/texture instead of a symbolic/fact/defining.
Draw a Venn diagram and they will be right with you talking about it but write it out in logic notations( P(A)+P(A’)=1 ), you will have a sea of blank faces looking at you. Numbers and symbols are very difficult for them to process and will need a lot more pictures and drawings that help them relate the two together.
To switch places, try taking a very good math student and ask him to paint a picture; color, shapes, patterns do not translate well for them.
First, on any engineering courses the students take for granted the need for math/science. That's not your case, so take some time every class to explain why and how this could be useful for your students beyond passing the grade
Second, they usually had a very hard time with school math, so take it easy and by all means try to avoid showing how smart you are when dealing with the abstractions and the logic, instead focusing on how little is needed to cover most of your material.
Third, they don't enjoy the solution of very difficult problems or challenging exercises (like a science/engineering student does.) They really enjoy the simple fact of grasping the concepts and making something useful with that
Fourth, check your students' background. Be prepared to provide several high/elementary school sessions.
fifth, your students are very good for reading, so give them some literature partially related to math (for example a biography of Descartes showing some of his math discoveries.) That's a pretty good way to generate interest. If they're political interested, then talk about Marx's math manuscripts, etc.
If you're not familiar with it, I recommend you read Ken Bain's What the Best College Teachers Do (2004) which provides a wide range of insights and approaches that can help you out in any classroom. Speaking as a former science major who went on to a Ph.D. in history, the number one difference I notice between the streams is that many of the social science and humanities students believe they're bad at math and statistics. Problems in high school convinced them that they can't cut it - a high proportion will claim they're incapable in the fields. The secret to your success is convincing them that they can and want to master these skills.
I know - I teach a stats module as part of my sophomore course for majors. They learn how to read, interpret and critique statistics in articles in their field of study. Did you know that most of them don't know how to read and interpret statistics? The number of students at the start of the course who tell me they don't stop to read the charts because "they'll never understand them" is staggering. Statistical literacy should be the bedrock skill you inculcate. Show them good and bad uses of statistics. Teach them to figure out when someone's playing fast and loose with figures, hoping to fool readers. That will build their confidence and their thirst for knowledge.
My students go on to create their own time series and other statistical outputs from a dataset that they all find fascinating. (I use the Old Bailey Online for this, a website with material in statistically manipulable format for almost 200,000 trials at London's major criminal court: almost everyone finds the history of crime at least a little bit intriguing and so they will persevere a bit more when they run up against problems or road blocks.) Don't waste a lot of the time throwing new theories at them - make sure that every new concept you introduce is tied to something they'll want to and be able to explore.
Sure, some won't want to try. They'll find the work too hard or uninteresting no matter what you do. But others will be able to master this if you make it clear both why they need to learn certain techniques and how while giving them some clear and jargon-free walk-throughs. Exercises they can tackle tied into the fields they already find interesting are a great way to keep them motivated.
Look at some of the textbooks that are out there for stats that are directed to your U's social science fields - see what elements they emphasize as important for the field of psych, poli sci, etc., and then decide how you want to incorporate those key elements into your own teaching. Avoid getting too tied into teaching a particular software package - make sure they understand how to generalize their application.
Good luck - you're tackling what many consider a thankless course but one which can help to change students from math-phobic and fearful to at least statistically literate and confident that they can understand and apply some basic skills in the field as they go on in life.
ancarett, historian and zombie gamer
First, it might not be important, but the title bugs me: statistics isn't a natural science.
I teach economics, and the biggest thing I note about my students is the heterogeneity in mathematical capabilities. I always need to keep on my toes about who I'm boring because they can handle that math in their sleep and who I'm leaving in the dust so that they're not even close to learning what I'm talking about. In a hard science program, there will presumably be some of that, but a bit more pressure on the low end which will make the students more homogeneous.
What to teach depends partly on whether you imagine this is a terminal class for a lot of the students. If so, teach general ideas which they'll be able to dredge up 6 years from now when the ideas are relevant, because they'll forget the details. If it's not a terminal class, try to teach some of the example applications which they might see in future classes.
Behavioral economics is pretty hip these days. Pulling examples from that literature (such as the popular stuff by Dan Ariely) is likely to interest a lot of students and be directly applicable for psychology students (since lots of behavioral economics is more about psychology than economics).
I have a strong bias about how statistics should be taught these days, though I've never tried it and could be proven wrong. I think that statistics should be taught as (1) probability theory, followed by (2) monte carlo methods, and then follow that up with more classical statistics and nonparametric tests. Monte carlo testing gets at the core concepts of what rejecting a null hypothesis means, what confidence is all about, etc and it's straightforward to do these days. Once the ideas are clear, then you could move on to the standard t-tests and so forth. But if you start with monte carlo, the students will grok the notion without knowing calculus as opposed to spending all their time trying to memorize formulas.
You do it exactly the same. Psychologists take stats pretty seriously.
I'm a physics professor who teaches some similar classes, including a course on climate change for nonmajors. I also deal with a lot of students who take stats. Statistics is probably the most uniformly loathed class in every university. Neither its students nor its professors want to be there.
Your first job is to convince students that they need to know this material, not just because it's a requirement but because it's vital. Start your class off with some statistical disasters. Drugs that were approved without proper testing, which turned out to be useless or harmful; innocent people sent to jail via the prosecutor's fallacy; major ideas in the social sciences which turned out to be based on baloney statistics.
Your second job is to forget you're a mathematician. You've been trained to formally prove everything you say. Don't. These students will take "because I said so" as a legitimate explanation, and will never need to prove things on their own the way your other students will. Give them useful definitions, rules, and formulas, without the backstory. Tell them that common random events often have a bell-curve distribution, but do not prove the central limit theorem. Show them how and why to do a t-test, but don't show the PDF for a t-distribution or the equation for it.
Finally, be very careful with your attitude. It's easy for a specialist to conclude that because these students are untrained, they're stupid. But if you motivate them enough, you'll find that many are just as smart as the physics majors in your calc class. Some, you'll find, are not, but don't let the bad ones shape your impression of the class, or you'll lose the respect of the good ones.
...especially as regards the use of mathematics in the interpretation of 'data' where the soft sciences have such a 'hand wavy' approach to cause and effect.
To me, economics is a prime example. Forgive me if I'm off base in in my belief that economics is both sociological and soft(headed), but tyring to measure human behavior in the absence of an accounting for political corruption within this purely human realm and leaving the so-called black market beyond it's consideration leaves the inclusion of economics within the realm of 'science' suspect.
I would haved greatly appreciated any attempt by a professor to explain the difference between soft science and hard science, especially if it included an math based explanation of the nuance between these different domains.
Soft sciences are typically about trying to solve 'wicked' problems, which are those that are generally impossible to completely solve (end poverty or health inequality, understand crime, migration, or human behaviour in general etc). Hard scientists typically try to solve problems that are relatively much easier because they have a simple concrete goal (put a man on the moon, make a bomb, cure some disease)
Soft scientists need a much stronger theoretical framework to interpret their data, because of the absence of any really testable mechanisms for the effects they observe. This can come across as 'hand wavy' but it really isn't. Your economics example isn't entirely fair, some economic models will include corruption and black markets etc and others wont, just as some physics models include relativistic effects and others don't. A good scientist has to choose the right model to approah any problem, regardless of discipline.
I've been working in an inter-disciplinary group and have had the opportunity to see medics and economists try to work together. The two cultures are very different in their scientific approach, both consider the other to be unnecessarily picky about some aspects of the work while not being rigorous enough in others. Eg economists spend a huge amount of their time trying to prove causation in observational data, while medics will typically wave this away if they think the causal effect is likely enough. On the other hand economists tend not to contextualise their results well enough, while medics will see the bigger picture in terms of building on existing science.
I taught stat to a business school audience, too many years ago to think about. One thing you have to figure out is what to cover and from what viewpoint. Math students might be interested in the math behind some of the statistical methods. Social science students probably aren't. To be honest, they're just going to use canned packages, so details of the math are not the most important thing to teach them. What you really have to teach them is what all the math means. What assumptions are the methods based on? What do they do? When do you use them?. How do you formulate problems? What are the most important ways that people can unintentionally (or intentionally for that matter) get completely meaningless results out of statistics? E.g. what does it mean when you try 20 different models, and one of them is statistically significant at the .05 level? Answer: it means nothing at all. But those kinds of results get reported all the time. Have then read some of the articles on why so many drug studies are turning out not to be meaningful.
As a college chemistry professor, I had a chem major who took a one semester statistics course taught by a Psych Prof at our school. I'm not sure why she didn't take the statistics course taught by the math department. Maybe it was because she could get general education credit from this course. Anyway, the course never got to the standard deviation because the prof required the students to do the calculations by hand. The students couldn't do long division so they couldn't calculate the requisite ratios. Square roots? They never got a chance. I guess they spent many weeks calculating means, medians, deviations from the mean and medians and their sums, squares, etc. What a waste. They certainly didn't get into the subtleties of the meaning of SDs, significance of differences between means, t tests, etc., etc., etc.
In a time of universal deceit, telling the truth is a revolutionary act. George Orwell
This might be the angle in for the original questioner's method.
Maybe he can reduce the raw theorems by 25%, and instead push harder on media and logical thinking issues.
Instead of too much push on the formal notation, what if he goes into a lot of "biased science" examples from the real media? Showing how slanted presentations produce emotional reactions, etc.
In a sense, "If I were in a position to hire", I'd rather have a smart thinker who's drilled cold on picking up sample bias than a book theoretician who can drill out 18 line proofs but folds the minute he/she gets into something about affordable housing studies and doesn't account for geo-social trends.
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
A great deal of math and science is conceptually trivial. What trips me up is symbolic notation. For some reason, it gives my brain fits. Give me the same problem with a decent verbal explanation and yeah, I'll have it coded up for you in a few minutes, thanks. Obviously math notation works for most people, but not for everyone.
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Math and computer science are not natural sciences.
The main thing you need to be aware of is that there are students in college -- decent numbers of them -- who cannot comprehend 7th grade math.
Not all social science majors are like this by any means. But there are some. They tend not to end up in the hard sciences, because they just won't survive there. But they can survive in other fields. What's more, they have the idea that it's OK not to understand math, and that it's "unfair" to demand that they have any kind of grasp of 7th grade math. I suspect that this latter attitude comes from the fact that there is a non trivial population of college *professors* who can't do 7th grade math.
What's most frustrating about the whole thing is that if you try to teach the remedial stuff to the ones who need it, you will bore the living daylights out of the ones who don't need it. They will rightfully wonder why they need to sit through so much review of very early high-school mathematical concepts such as basic algebra.
I've got an engineering background and have taught computer aided design and programming in the past. I've taught statistics to classes largely composed of psychology students a few times as well.
Know what they are expected to know: the prerequisites for the course I've taught are very minimal so I can fully expect some students to struggle with basic algebra. While the majority do seem to be able to 'plug and chug' reasonably well, their ability to actually understand what the equations they're using mean conceptually is severely lacking.
Focus on what the math is saying: the first couple times I was able to cram a lot of different statistical analyses into a semester, and the students were largely able to keep up with the math and work out the solutions correctly. Unfortunately some of the really basic concepts still sounded foreign to them because they had spent all their time doing math problems.
Think small: If you start with probability and normal distributions it's a stretch to even progress through Z and t tests into the analysis of variance (if that's the sort of route you're taking) in a single semester. I think it's better that students more fully understand a couple, extremely basic types of statistical analysis instead of quickly being 'exposed to' several in the course of a semester. If one fully understands the logic and mathematical relationships behind a simple Z test on a sample mean they should be able to fairly quickly understand the more complex analyses.
If it is germane to the course, focusing on the non-math concepts like experimental design is also important, and generally more useful for students heading toward graduate school.
Lots of bad advice in this thread. As a fellow mathematician who has taught intro stats before, and am currently teaching it (at a large research university) again this summer, here is my take: 1) Be prepared for the fact that many will not have taken a math class in many years, some 5 or more. They will recall little from their previous math classes other than intuition. Their arithmetic skills are poor. Be sure you are evaluating them on their understanding of the stats material, and be forgiving of arithmetic errors 2) They will be heterogeneous. Some will prefer abstract formulae, others will want to see things in words. Give both. Some will like to read the book, others will like lectures. I am linking to relevant Khan Academy videos on my website along with the date of the lecture they go along with. Anything you can do to come at things from various angles will increase the proportion of the class that understands it. 3) Try and explain the big picture. I am often motivating things with social science "experiments", or medical experiments. Find out what kinds of examples click with your students, and use those. While their arithmetic skills are often abysmal, they generally grasp quite readily the major ideas, how one should apply them, and when. They just get lost a bit in details. 4) Don't get bogged down teaching too much probability. It's an easy trap to fall in to. 5) Have fun. I've found teaching this course to be more work, but rewarding. A lot of these students have a near phobia of anything math, it's nice to see things clicking for them and them grasping the big ideas, if not the specific computations. Okay, back to writing tomorrow's lecture... P.S. Neither math nor statistics are "natural science", much less any kind of science.
True Story: -Engineers at my school had to take 15 units of Arts courses as part of their studies, and Economics 100 was one of the popular choices. We had an Econ 100 class that matched a hole in the 3rd year mech and EE schedule, as a result we had about 2/3 engineers and 1/3 Arts students.
One day the prof, a very smart man with a subtle sense of humor, drew a graph of some function on the board. He drew the x and y axes, a straight line with a 45 degree slope and labelled the x intercept "a" and the y intercept "b". One of the girls from Arts puts up her hand and says "I don't think it should be that steep". The prof erases the line, redraws it half as steep and labels the x intercept "a" and the y intercept "b". "How's that" he says."Much better" says Arts girl.
Every engineer in the place falls over laughing. We laugh even harder as we see the confused look on Arts girl's face as she tries to figure out what's so damned funny. The prof never cracks a smile.
I will try to inform you a little about economics (speaking as the holder of both a BSc and PhD in Economics):
The key difference is that economics and social sciences are mostly non-experimental (people don't take kindly to you arbitrarily changing their parents, education, or wealth - which is the 'experimental' way of establishing cause and effect). This means that the statistical issues are orders of magnitude larger than those that exist in experimental sciences. In an experimental science you can go off and get new data where you have controlled for most everything except the effect you are interested in and a simple regression will generally be all you need. In a non-experimental science you are stuck with the data that nature has given you. As a result you need to be very careful to get meaningful results. But, in case you are doubting, you can get meaningful results if you are careful enough.
Thus, my second point: Economics is not soft headed. In fact, it is very hard headed because you need to be when you are dealing with data that are generally speaking - crap. There are so many ways you can be mislead by non-experimental data and you need to be very hard-headed to avoid this. I won't claim mistakes haven't been made, but those mistakes are the reason economics has gotten much better at dealing with this than many people might realise. But, there is only so much you can do when the data are the way they are.
So don't assume the difficulty of getting solid results in economics reflects the ability of the practitioners rather than the raw materials you are dealing with.
If I had a dollar for every paper published in a peer-reviewed social sciences journal which totally abused statistics, I'd retire and use my extra cash to fund organizations directed at basic logic and math education, trying to help with the situation.
Most social studies students I knew had little understanding of the statistics they were using. It was basically a magic incantation for giving them results and making their conclusions sound more credible to other people who likewise didn't understand statistics. The result is bad statistics and bad science. Yes, these people aren't idiots, but they've become used to being rewarded without having to think rigorously.
The impression I get is that the pattern persists even among those few who make it into the field. There are some psychologists etc who are really trying to do real science- a difficult task since the basic concepts are even more up in the air than the basic concepts of chemistry were in the days of the alchemists. As far as I can tell, however, quite a lot are quite happy to be able to find ways of running a study so it will inevitably vindicate their preexisting biases and will fudge the statistics to match.
For the OP: You're right to be concerned. Students for the GE stats class are usually woefully underprepared. Rather than giving them the rigorous preparation in logic, multivariate calculus, etc they really need to understand statistics, the GE stats class does the equivalent of the Wizard's favor to the Scarecrow.
"I can't give you a brain, so I'll give you a passing grade! Now you understand statistics! Go back to your department now, please. (Phew, they're gone at last. That kind of work may pay the bills here in the Stats dept. but it doesn't do wonders for my sense of academic integrity as an educator.)"
You are teaching them stats, not calculus, so you shouldn't approach it like it is calculus. Social Science majors know they need statistical analysis. So do business majors.
For the record, my son had a major in psychology and a minor in math. Soft sciences and hard sciences are mutually exclusive and people don't go into the soft sciences because they can't do hard science. People go into soft sciences for the same reason as people go into hard sciences -- because they are interested in the subject matter.
Teach the subject at the appropriate grade level and quit looking down your nose at non-math and physics majors. Teaching statistics might be below the level of a calculus professor, but maybe both student and teacher will learn something from this.
That's what you get for talking to Chicago School economists.
Try not to take me more seriously than I take myself.
My favorite class to teach for the last 8 years or so has been sophomore-level statistics to psychology, sociology, occupational therapy, physician assistant (etc.) students at a CUNY community college. Statistics is directly and immediately applicable to those fields. (I have a research psychologist friend who says "all I do all day long is regression, regression, regression"). So I find a great thirst and relief that this may be the first math class these students have seen that's actually crystal-clearly relevant to their chosen professions; in some cases it's the first math class they "get" (for some of them). Early on I get a research article from JAMA and look at the one-page abstract for a preview of confidence intervals (C.I.'s) and hypothesis tests (P-values), and say that those are the ultimate goals of the course. (My mother's a school nurse who's asked me for help on those issues for her continuing education in the past, which has in turn informed how I teach the class.)
You still get some "why are you proving this/ is that something we have to do?" unclarity, but at the same time it may be their first or only "real college" math class, so I try to be forgiving over that. Careful writing, decimals and rounding are usually an issue (potentially all their prior classes have presented solutions as exact fractions).
I don't know if you can pick your own book, but I've been very happy with Neil Weiss' Introductory Statistics. If you want more, feel free to email me at my homepage.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
I may be the only mathematician who had this problem (I wasn't all that good) but Statistics threw me for a loop at first (I was briefly fairly competent eventually). Statistics isn't calculus; calculus is a big part of classical statistics.
A pure mathematician hitting statistics cold may have almost as big a problem a student with little mathematics. Mathematics knowledge can actually get in the way at first.
The big breakthrough for me was realizing a random variable isn't much like the variables I was used to. That I had to think differently. Once past that, I was at an advantage again because I had gotten through undergrad calculus and linear algebra but until then, I was MORE confused than the soft science majors around me.
I've been teaching freshman-level physics, both algebra and calculus based, for about 15 years. My take (warning: generalities and averages ahead):
Coming into the class, the algebra students absolutely do not care about the theory of the subject. They do not see the beauty of the subject the way that you and I do, or that (to a lesser extend) the calculus-based students do. They have two goals: 1) They want to pass the class, because it is required for their major; and 2) they want to learn the material as a collection of hopefully useful information for their future careers.
Thus, if you can make the information you are presenting be (or appear to be) relevant to them, they will be more engaged with you, and with the class. I don't know what the statistics equivalent of kicking a ball off a cliff and calculating how far from the base of the cliff the ball lands, but whatever it is, I urge you to avoid that at all costs. Find some other topic, or example, that will matter to them. If you present the material intending for them to admire the beauty of the subject, entirely for itself, you will have a room full of bored and sullen (and underperforming) students.
This is NOT to say that these students are less good than the students who take the calculus-based courses; in my experience, they are just as strong academically and intellectually--and in many cases better. They just (again, on average) have very different motivations for taking any particular math or science class.
(If you are lucky, you may get one of them to change majors to a natural science. It's happened to me a few times--a really great feeling!)
Good luck!
"Don't blame the log for the fire." --Andrew Ratshin
On the other end, my brother and ex-girlfriend were each psych majors in college and had to go through stats. Both failed it the first time (different schools, both had very large failure fractions in those classes). My brother in particular hated the course, though the second time he got a B without having the foggiest idea of what standard deviation means--I'm pretty sure they just used a massive curve because too many people were failing. Both of them embody math phobia. My ex eventually learned something of stats, my brother never did (and he's not using his degree either).
That said, I'd suggest stats needs to be directly useful to these people. My brother in particular complained about his difficult-to-understand professor who just wrote lots of formulas on the board all class period; he dutifully copied them down and did some mystical sort of pattern matching on tests (that I think were multiple choice). If I were asked to teach such a course, I'd try designing an overarching motivating example, where you make up an experiment, collect some data, and ask the pertinent questions for analyzing it, eg. "how confident can we be that this survey accurately reflects everyone's opinion?" Keep all the abstraction as far away as possible, keep motivating examples that are directly relevant to their studies close at hand, and test them on their ability to critically analyze papers and experimental data instead of their ability to solve stats problems. My 2c at least.
[Y]ou would also know that the syllabus of statistics 101 is so basic that it doesn't vary depending on the major of the students sitting for the class.
I agree and I do hope that our calculus Prof doesn't have a bit of a chip on his or her shoulder as regards the humanities.
However, if you want to be particularly relevant to social science students, here is what I, in my infinite wisdom ;), would suggest:
That to my mind would be a useful course in stats for the humanities.
Better to be despised for too anxious apprehensions, than ruined by too confident a security. --Edmund Burke
Dear Anonymous Poster,
Last year I was responsible for a class on elementary statistics for physical therapy students.
The first thing you have to keep in mind is: your students will be asking themselves from the get go: "Why is this useful to me?". Many of them may have enrolled in "soft" sciences to get away from maths in the first place. You have to provide these answers to your students - if not directly, then indirectly, by providing plenty of examples on where the subject will be useful in their work - this is quite easy with statistics. Also, whenever possible, skip too elaborate proofs, and go instead for more intuitive or example based explanations of why these concepts work.
If you provide me with some sort of contact details, I can give you my lecture notes. Cheers!
Stephen Greenfield, the best professor I ever had, happened to be one who mainly taught undergraduate math to math, physics, and engineering students and graduate math. However, he had a passion for teaching unlike I'd ever seen and he worked on a course at Rutgers to teach math to non-sciency types.
The last paragraph on this page has a description of the course.
The course diary has tons of material in it.
If you browse Stephen Greenfield's homepage, you'll find a wealth of teaching that might be able to be applied. He's since retired, but his page is still up, so make use of it!
"Nature doesn't care how smart you are. You can still be wrong." - Richard Feynman
IMHO, social "science" student should be required to take basic economics and a course on scientific methods. Too many people have no concept of the former and assume they know the latter.
1) Leave out as many proofs of theorems as possible. I've tutored several "soft" science students and proofs were one of the biggest things that trip them up. As a rule, they haven't been in classes that needed rigorous proofs and thus don't tend to lean in that direction when it comes to dealing with proofs.
2) Focus on what the need to know to further their education goals. Specifically, most of these students require knowing that they must use formulas A, B, and C in situations X, Y, and Z. Anyone who is genuinely interested in, or that needs to know more details will generally take higher level or more "hard" courses in the area.
3) Try to make as many of the problems as possible "practical" in relation to what the field that the students are studying. If you are dealing a wide range of fields, then take practical problems from all the fields.
4) Never underestimate what these "non-hard science" students are capable of. I've known several education students that whipped the heck out of some engineer friends of mine when it came to proofs and the like.
-- "We become what we contemplate." - Plato
I took a statistics course as an undergraduate and a stochastics course in a graduate EE curriculum. Despite the fact that the undergrad course was taught by a guy with a masters in mathematics, the two courses had NOTHING in common.
I'd advise dumbing the math way down. Present it as formulas to be used and teach students how to plug values from story problems into the formulas. Focus on why and how this is useful instead of on how it works.
No. Soft sciences need the same rigorous theoretical framework as everybody else. It's just that practitioners don't know how to use the theory correctly. Researchers in the hard sciences are just as guilty.
Let me just say that psychology students are as bright as an university students, though they may be a bit different than the ones you are used to. My best advice: get ready for your office hours to be VERY busy. You will have a bit of learning on the job to do, you may not connect with your audience as well as you'd like at first (due in part to a different type of student, as well as how the course applies to their needs, more so than your abilities), and serious psych students are not bashful about showing up at a professor's door.
This is a hacked account, for which the owner can not be held responsible.
Quite like "Charlottes's Web. Give that a go. If they complain, think again.
I taught Introductory Astronomy to a bunch of non-science majors looking to fulfill their science requirement. It was fun, that the kids were good at it despite lacking the physics and mathematics background for it. Statistics maybe isn't as interesting as astronomy, so keeping them interested is probably your biggest challenge. That would be true no matter who was taking the class.
Teaching to science and engineering students too often results in off topic discussions which put me off my lecture schedule (that's my problem, but it makes those classes more stressful to teach). Enthusiasm and detail are good, but lectures have a time limit. Pre-meds (a totally different category from science and engineering students) rarely show more than a passing interest in physics. Social scientists were really a joy to teach. They were interested in the material, the historical context and particularly the differences between astronomy, 'movie astronomy' and astrology. There's more than enough historical and current relevance to statistics to pique their interest, but you'll have to point it out.
I think the main difference is likely to be that sociological students are more used to questioning fundamental assumptions. I suppose this it because hard logic is a lot less useful when a large proportion of your reasoning is based
intuition. So be prepared to explain just about anything you consider "obvious", and to having your pedagogical skills tested to the limit.
I myself came to mathematics at university as an outsider; I found that my peers would simply accept most of what the teachers said, but I had a hard time adjusting to many of the viewpoints. Another thing I found difficult was spotting what it was I was supposed to learn - in the first years I would work hard on applying the major theorems to all exercises, and it was not until after my bachelor that one of my toturs exclaimed, with some exasperation: "Why don't you use the techniques that you have been shown in the proofs, like you are supposed to!?" - So the second thing you will need to do is, point out explicitly what you expect your students to learn.
Many people made good points about motivation (explain why it matters---with examples they can relate to .. Perhaps the early studies showing coffee was bad vs today's that show it increases longevity (removing the cohort that smoke and drank :))
The examples don't have to all be real, but they need to motivate: ... Being able to show that the data support the null hypothesis (or refute it) with 89% confidence is really useful ...
1) why being careful and not just dataming and publishing matters
2) how to sensibly use good tools. They won't care about proofs or the central mean theorem don't bother
3) illustrate good and bad techniques. My favorite book on the latter is the oft reprinted "how to lie with statistics".
4) deflate the magic of specific confidence intervals. Outside of publishing academic papers
5) teach some no parametric stats
6) remind them to look beyond the numbers. Back when I was doing Kalman filtering we had a lovely case where picking the first three data points by "hand" ensured nearly perfect tracking. Failing to do so got random junk. Turned out we knew where the boat started (at dock, precise coordinates known) and the sonar data used frequencies used by migrating sea creatures. So picking the wrong initial signals tracked something other than the boat.... The point being "real life" is messy. Be skeptical and dig beyond the simple math
And use tools like Rattle that they can afford (free) that take a huge amount of the manual labor out of the picture. Focus on meaning and combined critical thinking and debugged tools and not expect a lot of manual arithmetic
The fundamental quality that makes science scientific is empiricism. Math is a purely rational discipline, almost the definition of such. It may be perfectly internally consistent, but it involves no empirical confirmation against external reality.
It is slightly alarming that someone teaching at the university level seems to be lacking an understanding of the basic philosophical assumptions behind scientific reasoning. Although, in my experience, this is hardly an anomaly. These days, to most, science has become just a collection of facts...
Don't fill chalkboards full of algebra. Explain things as proportions, diagrams, probabilities. Focus on 'significance' in survey methods. You may learn something too.
Comment removed based on user account deletion
As a graduated psychology student, I can tell you how my professor did his statistics classes: He was almost desperate because of the small percentage of students who seemed to grasp what he was teaching. I mean, a lot of psychologists are really 'out there' (I'm a psychologist myself, so I'm allowed to make this statement :-)
So he used any visual aid a man can think of: puppets, jars with marbles, excellent chalking skills on a blackboard,...
That worked very well!
For a small percentage of the students, it was kinda infantile. But for the major part, this approach was really necessary!
You have to know that lots of psychology students think there's no place for 'hard' science in psychology. They couldn't be more wrong of course (as they will also have to learn genetics and some basic neurology).
Now, I don't know if they are freshmen or not ,but in the former case an extensive approach may be necessary. For senior students, well, teach like you already do. They now how to handle it, or at least they should.
Oh yeah, it's already mentioned before, but please: do point out the difference between correlation and causality!
I would pick a book 'statistics for social sciences' or something like that, and see how that differs from your 'hard science' approach. ;-)
Once passed the basics (combinations/permutations/Baysian/...), the most important think to know is what exactly you try to achieve with the t,z and chi-test and how you can game these to still come out with the hypothesis you wanted
Then he presented the calculations used to arrive at each size estimate from observation and showed how the published results had all been placed at the very top end of the (decreasing with time) range - because there was a strong desire to have Pluto larger than it was measured to be. When a line was drawn through the mean observations it was practically horizontal.
"Hard" scientists are often exposed to significant bias which they do not recognise as such (the desire for confirmation, peer pressure, management desire to get a drug approved, justification of an expensive experiment). My own view is that this needs to be presented to social sciences students, but with a clear understanding that this cannot be extrapolated to the strange idea that science is purely a social construct - an idea presumably promoted by some sociologists and philosophers who obviously failed the more mathematical parts of their courses.
From scarped cliff or quarried stone she cries "A thousand types are gone, I care for nothing, no not one."
At first, i think slashdot is one of the worst places in the whole internet to ask for this. Too many wankers looking for social gratification. And obvious mythomaniacs. I have read a dozen comments then i stopped. You should ask in a maths forum. I am sure there you will find experienced and COMPETENT people. I am an engineering physicist who did his Ph.D. in photonics and did some research in aerodynamics and plasma physics in a private NATO institution. Well enough to be published. Then i quitted because the salaries in research are too low. I sometimes regret the fun. I work in a bank now. Firstly, in my county of birth, schools are divided up. You take an option as early as 3rd grade (13/14 years). The maths/science option is recommended to only the most promising students while the others are discouraged. Likewise, the worst students are sent to technical/professional (plumbing...) or social studies options. Also, there are entrance exams to enroll in engineering/military school (all options)/flight school etc... The prep courses for these exams are exclusively in maths/science options in elitist high schools. We are elitist. Elitism is not considered a problem here contrary to United States. Also there is no the typically U.S. stigma on nerds. Here nerds are considered winners. So some of my experience may not be transposed to the U.S. Your mileage may vary but from what i heard from my American colleagues and my European ones teaching or doing a postdoc in the U.S. the situation appears similar or even worse. When i was a Ph.D. student, i had to teach part time. Since tenured professors want to teach only in science/engineering they tend to foist the courses in non science faculties to young non tenured teachers or doctoral students. So i had to teach students in sociology, psychology and communication. There is no such things as a minor/major in my country. Before that i teached high school students as private professor. Some of my high school students or their parents say i have saved their life. I am immensely proud of that. So i had experience in teaching non necessarily brilliant students. And recover bad situations. Well, it went worse than with my high school students. They sucked. They all sucked. Some harder than others. Globally the problem is they have zero math and science education. They don't have a clue about how genuine science work. Worse, they believe they know it pretty well. So while they are ignorant they are also pretty closed-minded. One of their main difficulties was their methodology. They didn't know how to solve problems. They rather clinged on learning per heart formulas. They were even more lost when asked questions in plain French. Even about basic problems. They didn't get the maths concepts. Many had problems with fractions. A primary school notion. Many had problems with asserting an equation and solve it. Funnily enough, asserting equations was harder for them than solving them. So before struggling in stats they were in fact struggling with basic maths and logic. Of course, they were all totally unable to integrate or differentiate, let alone understanding what an integration or differentation was. The sociology students were less worse because they had a "general maths" course in freshman which was nothing more than a revision of high school maths. But even them didn't do more than applying formulas. For them an integral was the area of a surface below a curve. I showed them examples of (simple) integrals calculating volumes, lengths and other things and fortunately they were happy about it. Not possible with the psycho and communication students though. Good luck making them understand what an infinitesimal is. They have a problem with abstract concepts in general. In stats, they did understand what a mean was but even the median was already harder. They were lost with the concept of dispertion parameter. None of them did understand well what was a probability density function or a cumulative distribution function. Again, some of them were able the recite per heart
There have been a lot of good suggestions here. A number of comments have noted that for the "soft" sciences (I agree it's a terrible term,) statistics is more relevant. I think that this is the key for what you need to do. Find examples of where calculus is necessary to solve a problem in the social sciences and build your course around those relevant examples. People will work harder and understand better if the material can be shown to be relevant to them.
I've taught statistics to a variety of audiences for over 25 years, ranging from hard-core engineering students to business majors who haven't seen any math since high school algebra and considered that hard. There are definite differences in how you approach the subject if you want to communicate with the students.
With science/engineering/math students they are used to problem sets. You can focus on a developmental approach to the material, starting with basic probability rules, then random variables, densities and distributions, and expectation, popular distribution models, then into descriptive statistics, point and interval estimators, and linear models. My experience is that the SEM students like to work from first principles and understand how things work. They are very amenable to the fact that there are a few principles, which are common regardless of which distribution they're being applied to. You can teach more theory and rely on the students to apply it on problem sets.
Business & social science students don't like that approach at all! I've found that it works better to start with data, treat histograms as empirical densities, talk about various ways to describe/summarize the data numerically, then migrate to the concept of a population and sample and introduce distributions as an idealized description of the sampling population. Then onto rules of probability and how the sampling would shake out. They're just not willing to build their way from first principles the way the SEM students are. You have to work a lot more examples in class, because they don't have the problem-set/practicum mentality or experience that SEM students do. It takes a lot of work, but I've found that "competency checkpoints" are really helpful - little online quizzes that ask simple questions about basic principles for the module. The students are required to take and retake the CC until they can pass it with a certain threshold (I set 80%) - if they pass it on their first attempt, they get full credit, on the second attempt 80%, third attempt 60%, etc. The good thing about this is that it tells them the principles they are responsible for knowing on the midterms, and doesn't allow them to skip foundational material and move on unprepared for what follows.
The textbook you choose is essential. You have to get one that supports the approach you're using and is written at an appropriate level for the students.
I have degrees in math/CS and psychology; took several Psy stat courses. The courses were good, but more focused on concepts and did not require a lot of hard calculation beyond relatively simple algebra. Nonetheless, I learned a lot about stats in psych that was often more practical that the stuff I learned in my math classes.
If you post it, they will read.
As an elective, I took a course on the history of science in western civilization. Many of the breakthroughs in science came from scientists applying a better understanding of math to older experiments. So, the glory didn't always go to the person who first created and executed an innovative experiment, it went to the person who had the mathematical background to link the inputs to the outcome. This will especially relevant to your students, very few if any of them will get grants to conduct their own experiments right out of school. If they understand that they can make meaningful contributions to their field using only preexisting data, they may pay more attention ;-)
A friend of mine, Bro. Guy Consolmagno, teaches at Catholic colleges around the US half the year (the rest of the time, he curates the Vatican's meteorite collection). One of the classes he says he teaches is "science for non-science majors". He once went down the food chain of the majors that take his course: next to the bottom are the business majors, "who don't get it, but don't let that worry them". The bottom of the food chain are the communications majors, who "not only don't get it, but don't know that they don't get it".
So, you wondered why journalists and HR people were *so* ignorant....
mark
arts school it was taught through the psych department, which seems to be where this over-flow really should go, unless they are stretched even thinner than your dept.
In answer to your question, you would probably NOT be teaching the derivation of stat formulas, but only the application of stat formulas to test cases, with insights about experimental design, certainty, etc (which is why someone research in the field is best suited to this type of course).
"Correlation doesn't imply causation." is a truism since not even controlled experiments imply causation. This is true of all natural sciences of which the social sciences are a subset. It is increasingly recognized in the social sciences that the important thing to do is pay attention not only to "the weight of the evidence", rather than "proof" but to, as described in the discourse in "implication analysis" in the social sciences: "try harder to find relevant natural experiments".
So not only is it a truism that "correlation doesn't imply causation" it is a sophomoric barrier to scientific progress which understands not only that there is no "proof" but that some "correlations" are more relevant to evaluation of causal hypotheses in the social sciences than are other correlations.
The question comes down to the word "evaluation" since we're trying to place a "value", indeed a numeric value, on a causal hypothesis rather than "test" it in a logical sense. To the Monetary Man, this numeric "value" is quantified in money as a net present value adjusted for future risk. The Monetary Man is, however, not the Natural Man from whom Natural Rights derive.
How in the world are we, unachored from the operational definition of "value" as embodied in money, to place value on which correlations, hence which "natural experiments" to study (hence which such experiments to actively promote)?
My answer, that is friendly to civilization while upholding the individual, is directly hostile to Monetary Man since I place Natural Man above Money:
Provide an inalienable and equal monetary stream to each individual so that individual may, through the subordinate anarcho capitalist system, construct his own world in cooperation with others. In such a world many "natural experiments" will be conducted and they will be conducted in proportion to value determined from a founding notion of sovereign individuals who, in exchange for their inalienable monetary dividend from civilization, agree that the ultimate appeal in dispute processing will not be force, but money.
The source of revenue is therefore obvious:
The property rights that would not exist in the absence of that agreement, properly called "artificial property rights" as opposed to "natural property rights" such as a homestead supporting an individual and his immediate family, are subject to that agreement and are, therefore, as with any partner's profit stream from a business venture, optimally divided between payout and retention. The payout is the individual sovereign's profit from the partnership which is limited by the expectation of future value from the partnership. Of course, if the future value of the partnership (ie: civilization) falls to zero, then the partnership is dissolved, the wealth distributed equally and we go back to natural duel as the appeal of last resort in dispute processing until another partnership again restrains individual sovereignty.
Social scientists and their politicians deny that the individual is preeminent over civilization and hence is to be asked for what terms he demands of civilization and its artificial property rights prior to suspending his true, forceful, individual sovereignty. They simply take from the sovereign individual his natural right to use force and they do so by forming a group (usually called a "government") that takes it from him -- a group that has volumes upon volumes of words from the "social sciences" to justify their crimes against humanity.
Seastead this.
I have some experience teaching introductory college physics to non-science students. Some impressions I've had:
1. Some just will not get it no matter how many different ways you explain it to them. Among those are two types: Those who just lack the very basic reasoning and logic skills required and there's little you can do. You wonder how they ever got into college. Then there are those who do not understand that to understand some formula, you might have to sit down and go through the derivation in your own time, very slowly. And then you need to do 20 practice problems. Very slowly. My attitude is "You're at college, not high school, so it's your responsibility to invest the time that it takes you to understand this. If you have questions, ask. But the solutions don't come all pre-chewed." Some learn, some don't.
2. Some have a natural affinity and while they clearly lack training, they're quick to learn and soon you'd wish they'd become "proper" scientists, though those are few and far between.
3. Then there's the vast majority who will "more or less" get it. In the case of physics (and things might be different with statistics) that means that they're soon able to solve the "standard" problem you went through in class, but will struggle greatly if problems require more than plugging numbers into a well-known formula. Some are definitely capable to get beyond that stage, but only by giving them individual attention to figure out exactly what their thought patterns (and corresponding misconceptions) are and helping them to figure out their own way to make sense of particular concepts. This might be difficult due to a lack of time.
4. Do not assume familiarity with concepts such as "derivation", "definition", "proof", etc. (especially not "proof"). If relevant, give examples of how to prove and also how not to prove something (for example, plugging a possible set of values into a formula to see if it works does not constitute a proof). Or other things we don't even think about, for example that if they remember a formula with 'x' but in the problem the relevant variable is called 'y', the formula still applies. You'll be surprised about the hang-ups some students have.
Your audience might be different. It'll probably depend on your institution and the quality of their students. I had a plurality of pre-med majors, some of whom struggled greatly (and their lack of basic logic made me worry about their future patients).
And you will do just fine.
Just start your lesson with, "And what do you think about that?" and let the students discover the answers for themselves.
The only math a psychology major needs to know is how to bill by the hour, 1 x $200 = $200, done.
I haven't thought of anything clever to put here, but then again most of you haven't either.
I'll start by echoing the general sentiments that, at the end of the day, a career in social sciences demands good stats knowledge. At my school, the only program with more stats requirements than psychology is statistics. That said – as other posters have notes – many of the students don't like it, and *many* of them have long since convinced themselves that they are incapable of learning it.
Here's a bit of what you can expect: Your distribution will be skewed to floor, skewed to ceiling, or bimodal. The level you gear your teaching to should be thought of as a decision on the relative numbers of students you wish to be so bored they stop attending, versus the number you wish to see crying in your office hours.
I haven't taught stats in this context, but have faced a similar course situation teaching physiological psychology (aka neuroscience) as a core psych credit for a primarily arts-based psych program. Interestingly, psych students comprised the majority of the top-performers, and biology students the majority of the bottom performers. In the environs of the overall mean, however, BSc students tended to do marginally better than BA students. In this context, the struggle was always between accuracy and transparency. Students in an arts degree don't take kindly to learning about cable properties and voltage-gated ion fluxes – but they're perfectly capable of learning it and understanding it if you avoid overly technical language.
You're likely to face similar resistance in terms of math equations. Unfortunately you can't easily analogize your way through statistics – so my best advice would be to head this off at the start with a little topical prologue: math anxiety, and stereotype threat. If these are psych students, then you might be able to engage them early on by examining why they might believe themselves to be incapable of the math, and similarly why they're wrong. It's certainly outside your curriculum, and might be outside your comfort zone – but that could be a good thing. Show them a little vulnerability by delving into the psych side of math anxiety as a means of encouraging them to confront their own vulnerability with respect to math. A long shot, but might be worthwhile...
You would include a whole swathe of science in your dismissal of anything that is not experimental. We have, for example, only one Earth and one Universe and people have yet to conduct experiments in star formation.
But, there are also things called natural experiments where there is natural randomisation. An example are studies of twins who were separated by adoption. In this case, you know that the genetics are the same and only the environment differs. One can make valid inferences from these natural experiments.
Teach them the same way (with different examples maybe...); they'll likely whine more, but they'll learn something, and that's good for them.
From my personal experience (I've taught programming to science students, and a lot of other topics to psychology majors), I can tell you that the interest and knowledge differs between the two groups. Generally speaking, psy majors are much less interested in maths per se, and have considerably less knowledge. At the uni where I taught, a certain level of math was prerequisite for psy students, but most of them somehow didn't have that level, despite the deficiency courses. In one of my classes, it turned out no-one knew what a vector was, and in my profs class a 3rd year student asked "what's a square root?". That never happens with sci students.
On the other hand, quite a few sci students take statistics for just another way of manipulating symbols. They can derive the formula for stddev from E(X^2) - (E X)^2, and do GLM in a few matrix operations. However, they're less knowledgeable about ways of applying statistics.
So I would say: stick to the application. Start by explaining the use of statistics, the different kinds (descriptive, H0 testing, Bayesian inference if possible), show concrete examples. Start simple, very simple, and gradually work your way up. Don't emphasize memorizing formulas. However, they should know thoroughly what a standard deviation actually describes. They should know about different distributions.
And they've got to be motivated. Math students can get motivated by just the math itself, but psy students don't. Good examples, and a lot of repetition is required. If you've got enough time, try doing simple experiments. One I liked is the "how to detect a false coin". By having everyone in the class flip a coin 10 times, you get a nice distribution, and that will show how difficult it is to detect a false coin with just 10 flips. Such examples can be discussed, and you can make them flip the suspicious coins 10 more times to see what happens. Then ask if that's a proper procedure, etc., and then transfer that knowledge to e.g. decision time statistics.