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Ask Slashdot: Resources For Explaining Statistics For the Very First Time? (thejuliagroup.com)
theodp writes: Teaching multivariate statistics to college students, writes AnnMaria De Mars, was a piece of cake compared to her current project — making a game to teach statistics to middle school students who have never been exposed to the idea. In the interest of making a better game, De Mars asks, "Here's my question to you, oh reader people, what resources have you found useful for teaching statistics? I mean, resources you have really watched or used and thought, 'Hey, this would be great for teaching?' There is a lot of mediocre, boring stuff on the interwebz and if any of you could point me to what you think rises above the rest, I'd be super appreciative." Larry Gonick's The Cartoon Guide to Statistics is pretty amazing, but is it a little too advanced for this age group? Anyone have experience with the Khan Academy Data and Statistics offerings? Any other ideas?
Clay is the best resource to explain statistics. You can get any result you want from both.
Use guns. Say you have a 5.56mm rifle round and a 9mm pistol round, what's the average caliber? Then you can use prisons, what are the chances of going to jail if you're black and poor?
No, it's pointless to ask this question. It's all about the big data firms like Facebook and Google wanting to suppress future data scientists' wages.
Just don't teach them. AND especially don't teach Indians, Vietnamese or Chinese students.
DONT GIVE THEM IDEAS!!!
Its fun, and its the most hands on way you'll ever learn statistics.
I dunno how legal it'll be to bring kids to a casino, but I'm sure you can do some candy or penny based system fine.
This was for a college course, but should work for middle school students too. I distributed fun packs of M&Ms to my students and had them count the number of each color and the total number of pieces in each pack. Nice illustration of mean, median, and mode, and a good lead-in to a discussion of variation.
Geology - it's not rocket science; it's rock science
terrible odds for them? some of us still calling this 'weather'? https://www.youtube.com/results?search_query=wmd+weather+media ... leading cause of death of us is still 100% preventable starvation of millions of us,, the statistical majority of which are children... creation in a near tailspin?
Khan Academy is probably the first thing I would choose.
An election year is always a good year to look at statistics because Nate Silver is always looking for trends.
Basic Statistics, you could use sports easily. Take the local high school teams and compare how they do to others and what their ratio of hits or misses are for their sport of choice.
Use their own past history in courses to determine how they will do in future courses. A history professor was pointing out that of those students in her class, those who looked at a specific resource had performed the best.
Using something that relates to the students in their day to day lives or at least something they find interesting to teach statistics will most likely yield the best results.
Place something witty here
As somebody who likes to teach math privately to people I recommend one thing first and foremost: Intuition. In mathematics, intuition is often thrown under the carpet as distracting from playing with mathematical concepts but in order to understand mathematics, you need to understand WHY people made formulas the way they do. As a result, students often have a 'see monkey, do monkey' mentality while having no true understanding of the topic. People with even less understanding aren't even able to replicate the desired results.
In general, the less the student has a feeling for mathematics, the more you need to teach intuition first and formulas later. Math students are of course required to have a higher level of understand, but this is obvious.
Knowledge is power. Knowledge shared is power lost.
Everything in a game like Warcraft is about stats... Did I hit the mob? How much damage did I do? Why did I block the blow this time? Why hasn't this particular enchant activated yet? How do I calculate the average uptime on an ability in order to compare it with others? How could I simulate game calculations in order to figure out what the best ability rotation is?
Not to mention there's an economy with very real data that behaves fairly close to a real economy. You'll be able to teach means, averages, standard deviation, behavioral analysis, etc.
First of all, don't call it statistics.
Just give them some fun game where they need to decide whether green Gabroans from the planet Gabroa are more or less likely to be wearing hats than other Gabroans based on the (relatively small) sample they have seen.
Reward them accordingly.
It's all about observing thing. It's the best method we have for determining things about the world from out imperfect observations. It's exciting stuff!
Why has statistics become synonymous with "that boring course you have to take"? Or worse, that stuff you sniff about dismissively while you complain how people can "prove" anything with statistics.
Stop worrying about the risks of nuclear power and start worrying about the risks of not using nuclear power.
After all, that's where it all started.. trying to fairly distribute the pot in a card game that was interrupted before it finished.
Rolling dice is fun (more fun than flipping coins) and you get that nice distribution when you sum multiple dice. As you sum more dice, you can see it change from triangular to the familiar gaussian shape.
One thing that doesn't get a lot of coverage, but should, is distributions that are not idealized. It would be nice to have a easy phenomenon for the kids to experiment with that has a skewed and/or bimodal distribution. You could make specialized dice to do this (e.g. put stickers on the faces with other numbers than 1-6).
The M&M bags are a start.
Various "urn" experiments are good, especially if you let them control the distribution of balls going into the urn.
Ultimately, you want it to relate to practical stuff they encounter. So setting up things to show that "hot streaks" (in sports) may just be chance, and how to figure out whether someone is really talented, or they just got lucky shooting free throws.
Dealing with probabilities that are very high and low is also important. Everyone has a gut feel for chance, or even the 1/6 or small digits. But understanding what "one in a million" or "one in a thousand" means is important, particularly when dealing with public policy. Distinguishing between probability and consequence and dread (perceived vs actual consequence) is important.
And that ties nicely into the concept of Expected Value, which is used every day in all sorts of areas (credit scoring, etc.)
https://xkcd.com/552/
https://xkcd.com/1132/
What is there in statistics to make someone of that age care about it?
Teach them some dice based game, get them to play each other and mix in some loaded dice at random.
Tell them half way through and get them to figure out who is the cheat. Naturally they won't get it right as intuition about statistics is usually poor, but your job is to guide them into the right direction.
SJW n. One who posts facts.
There was a Japanese comic that explained statistics. I wish it were available as a Kindle ebook to buy....
Lies, damned lies, and statistics.
https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics
Statistics is best learned using a "Hands On" approach. It is a difficult subject for middle school students. An example lesson is to ask a relevant class question and then use the class data to teach what ever the topic is.
The professors of the California Math Project have access to a variety of practices and resources for teaching middle school math.
Try these resources; the National Counsel of Teachers of Mathematics,(NCTM), the Illustrative Mathematics web site, and "The Teaching Channel". These web sites have teaching activities and resources for middle school math
Here, teach them this, they should find this very interesting:
Imaginary Number Probability in Bayesian-type Inference
http://www.ccsenet.org/journal...
Everything I write is lies, read between the lines.
I've been considering making a tutorial around python, where you generate a fake data set (with something like 7 billion values) and do the following:
Stage 1: loop over the whole data set and compute the true mean and the true standard deviation.
Stage 2: Take the same data set, but choose random samples (say N=1000) from the set, and compute estimates of the mean and the standard deviation. You can show how depending on which 1000 elements you choose, you'll get a spread of estimates for both which bracket the _true_ values which we know from stage 1.
This was one of the best statistics presentations I have ever seen. With humor and clever drawings, the basic ideas are presented, along with a healthy skepticism which is necessary these days to see the blatant lies and misrepresentations so prevalent in media and politics. If I had to teach statistics to people, I would start with this before touching the underlying math.
ISBN-10: 0393310728
Still in print since 1954.
... here is the next book you need : How to Lie with Statistics ;)
http://www.amazon.com/How-Lie-...
Will $CURRENT_YEAR be the year of the Linux Desktop?
Then teach them how to calculate the odds of getting a winning hand. Make the poker chips tootsie rolls, or naked selfies of classmates, or something else kids like.
Specifically, poker and Yahtzee.
What's the likelihood of drawing a 2 or a Club, etc.
"I don't know, therefore Aliens" Wafflebox1
I spent three years taking college level statistics and floundered around with it. Then I came to a simple realization that made everything a lot easier - statistics is not math. It uses math but it's not math any more than physics is math. It is a method of modeling the world for analysis. I wish my instructors had explained that rather than saying we all knew some statistics because we knew how to calculate an average (mean).
https://en.wikipedia.org/wiki/How_to_Lie_with_Statistics
Seriously - if you want to teach intuition with statistical models - and why most media published statistics are horribly developed - this is the book. The principle bits you get out of the book: Correlation does not imply causation - a HUGE intuitive bit of knowledge to debunk a LOT of what the media throws out there.
You know, 99.3% of all convicted criminals, in one form or another, have eaten a tomato! (Yes, ketchup and pizza sauce count)
100% of everyone who as ever, or will eat on, will die. (Note: did not say how long it would take for them to die!)
How do your correlate your data so that it is meaning full? How do you determine causation, or not?
Secondly, how to properly random sample a set. What sort of biases can be introduced? How can they be recognized? Documented? Eliminated (or reduced)?
Where to get your numbers to play with? Everyone has already said sports (Baseball has more stats than any other sport - and they are readily available. Watch the movie Moneyball - how stats was used to transform the management of the sport - without negatively impacting the enjoyment of watching a game). Upcoming presidential election - people prefer this candidate over that one? What sort of biases?
Yes, going through the bazillion different distributions (both discrete and continuous) is still a requirement. As well as conceptual bits as standard deviation, and the area under the curve (why two, almost identical sets of numbers can provide different outcomes).
Here's a wacky one - (yes, it deals with guns)... Find an AirSoft automatic gun... Load it with 30 rounds of bbs' (same mfgr, weight, roundness, etc.) - set it up with it locked in position 50' from a target and and just let loose the entire clip. Make 30 of these - one for each student. Perfect example of a bell curve. No matter how well you controlled the experiment you still had a distribution. A lot of info you can pull from this... mean, median, mode (which will be rings!), and if there is a vector preference - you can analyse that as well (show's bias).
Regardless - make your examples fun, make them real. And make them something they can further investigate on their own.
FredInIT
Just a few thoughts:
There is a real advantage to back in the day: parametric statistics needs calculus but a lot of modern statistics
are more simulation-based so that could be stressed. Easier to understand (or at least less difficult) and usually
more accurate. Parametric statistics can wait.
Some appropriate subset of "How to Lie with Statistics" might be apropos early on and throughout the time spent.
It's practical information in life, gives a deeper understanding and is relatively fun. Care needs to be taken that this
isn't taken as "All Statistics Lie".
Consider bringing in language teachers for help. The words in statistics often have a subtle (or huge) difference
from common usage and they may be able to help with that. I had a mathematics background when I started statistics
and wasted a lot of time in early days because "variable" meant something different than what I was used to.
by Whelen. He has a lot of good examples you could adopt for your class; although I wouldn't recommend using the book in class.
I'm a consultant - I convert gibberish into cash-flow.
Also includes more advanced ideas, like Bayes' Theorem and Central Limit Theorem, but presented conceptually.
http://www.amazon.com/Cartoon-...
https://en.wikipedia.org/wiki/...
https://en.wikipedia.org/wiki/...
Oh, should have read the summary more closely. It's already in there.
dropping many balls through a triangle of pins and watching them fall into a bell-curve pattern. Called a "galton machine" apparently https://www.youtube.com/watch?...
sag
A college-level textbook which approaches the subject as constructively as possible, starting from the concepts related to probability goes a long way starting from the 12-year olds, when combined with a motivated teacher. Translating those concepts to a game however, will require some serious imagination and hard work. Game mechanics obscure the concepts by overlaying them with additional concepts relating to the game itself. If the goal is teaching intuition without understanding of the concepts, the game approach might work.
I see a lot of elementary school students calculating mode and median and ranges with very little motivation. You may have some raw tools available just because of the way curriculum has taken the thread out of learning.
This is probably only for the older students, but a good one for sparking interest is the Monty Hall problem. It has a fun narrative (if you use the goat and car), and you can set up a mock game show with some students as the contestants to get them interested. You can walk through how the game works, and then debate whether it is better to change your choice or not to maximise your chance of getting the car. Once everyone has decided, you can then run a live simulation by giving each student a turn playing and calculate the probability from the results. Most people find it really shocking when they see the probabilities are so different, and it will get them thinking there might be more to this statistics thing than boring numbers.
Are you seriously trying to tell me that (most) American middle-schoolers have not come into contact with statistics at all? What the actual fuck are you teaching the poor kids? How to make a decent cave painting?
Captcha: capable. How ironic.
In seventh grade, my mathematics teacher spent the entire probability and statistics unit dealing blackjack to us (small class of seven students). We brought in potato chips and soda, but I forget what we were betting (not cash though).
Three or four years later, three of us took AP Statistics. I did very well, and I'm pretty sure the other two students from that seventh-grade class performed similarly. The AP Statistics class as a whole (15-20 students) "did OK" on the exam. I'd definitely draw a correlation.
My seventh-grade teacher was new that year. He taught one more year, and then was let go before he could get tenure (three years at this school). There were claims about unprofessional treatment of female students. He wasn't popular with the administration.
http://xkcd.com/552/
I'm not an expert but I found the Manga guide to be more useful than Gonnick's cartoon guide. It's amazing that there are multiple comic books that teach these subjects.
http://www.amazon.com/Manga-Guide-Statistics-Shin-Takahashi/dp/1593271891
You can do a lot with simple coin flipping. Of course, as everyone pretty much knows, if you flip a coin a hundred times and record the heads and tails, you get approx. 50% head and 50% tails, and the more times you flip, the closer this gets. But you can also explore trends–statistical clumps were several heads or tails come together, use class results to see how often statistical clumps of varying sizes appear, etc.
You might try setting up lessons around counting the number of chips in chocolate chip cookies. There's a discussion of how to relate it to different topics in:
Lee HK. Chocolate chip cookies as a teaching aid. The American Statistician. 2007;61(4).
(http://dx.doi.org/10.1198/000313007X246905)
Rather than diving in with a bunch of jargon and equations (which they will need to learn eventually), start with some simple questions about how statistics are actually used and then teach them how to apply statistics correctly
E.g.: If I have flipped a coin five times and they all came up heads, what are the odds of the next flip being heads? Versus: What are the odds of six coin flips all coming up heads?
Not exactly what you were asking for, but, as others have pointed out, getting them to be interested or care is a major part of it. So you might go over statistics as used in big league sports. Would the movie Moneyball be over their heads?
In theory, theory and practice are the same; in practice they're different. (Yogi Berra & A. Einstein)
As a kid I found this book "How to lie with Statistics" in my dads bookshelf, and found it very interesting. of course the point is not that statistics lie, but that you can choose what to emphasize, and that alone is good lesson for any young person.
( A side note: growing up in (northern) Europe, we had numerical grades for everything, so naturally the grade papers had an average, which we grokked pretty early, and near the end of the later years our math teacher would show the distribution, average, and median were for our class. Much easier to learn statistics when it is about some number that matters for you)
I would use an image generated by samples to show the importance of the number of samples...
When we have a very low number, the images' resolutions decreases a lot, so a simple ball might not look very different from a box...
Just try adding more info (samples) and see a perfect circle appear.
Baseball especially is jam-packed full of stats, and most kids that age are into baseball (or some other sport that makes use of statistics). You won't get into the complex stuff like permutations or z-scores, but it's a good way to teach the simple stuff like averages, difference between expectation (probability) and prediction, and some of the wackier stuff that can arise from just those simple stats like the Pirates beating the Yankees in the 1960 World Series even though the Yankees destroyed the Pirates in almost every individual stat.
What? You thought every teaching tool had to be online?
A good starting point, and a great resource, is the Guidelines for Assessment and Instruction in Statistics Education, published by the American Statistical Association. This document includes many examples and activities that are appropriate for different developmental levels. See amstat.org/education/gaise I'd also recommend the software Tinkerplots and any literature and activities associated with it. Tinkerplots was developed for middle school statistics classes, and lets students build their own graphical representations as they "see" them. It's great fun and leads to some surprisingly insightful findings by beginners.
Rosencrantz and Guildenstern Are Dead
Yes, probability; might get the juices flowing in a couple of kids who wouldn't give a damn otherwise.
Start with one die, what are the odds it will roll a 3?
Work from simple to complex with conxrete examples.
Explain fair dice vs. weighted dice.
If You roll 2 dice, how many ways can You get a 7? What are the odds of a 7 on Your next roll.
As a kid, I liked to keep a drawer full of socks of various colors. It's endless fun to figure out the minimum number of socks I'll need to take out of the drawer, in the dark, to be sure I have a matching pair.
Alex, I'll take keybindings not used by Emacs for $400....
https://www.random.org/ is a good start.
This is an interesting activity from ACT (the testing service) which helps you understand the percentile scores you get on standardized tests. It has an extremely visual way of showing how a histogram is constructed:
http://whyville.net/smmk/pct/tutPct
I learned statistics in elementary school. Admittedly, it was 6th grade, at a science & tech magnet, but that's still elementary school.
Our teacher, Mr. Vance separated us into groups of about 2 or 3, and gave each group a bag of m&ms. We had to count how many there were of each color, and report our numbers back. There were three classes doing this, as we rotated between science, math & english through the day.
On the first few days, we only dealt with our own classes' numbers. (I want to say that he had the numbers on three boards, and didn't show us the numbers from the other classes at first). We learned the difference between mean, median and mode, both for each color and the total in each bag.
We later went and looked at how the averages varied between each class, and at some point calculated the variance & standard deviation.
We likely did / learned other stuff during that project (I want to say it was over a week or two), but it's been 30 years.
Build it, and they will come^Hplain.
From The World of Statistical Humor!: Did you hear about the statistician who had his head in an oven and his feet in a bucket of ice? When asked how he felt, he replied, "On the average I feel just fine."
You are writing a game, right? You'll probably sell the game to schools, right? (Nobody ever bought Marh Blaster for Christmas).
So, you want to crowd-source the design of your game to make you rich? Not likely. If I had a good idea for a game, I'd make it myself.
Statistics is a mathematical filter we use on raw data to extract meaning. So give the students some raw data (a field full of virtual people; a forest full of trees and animals; a toy chest full of different toys, a crowd of video game characters) and give them statistical filters and widgets they can drag over these seas of data to extract information.
There are a lot of ways a simple picture (that's actually a bunch of sprites, one per data point) can turn into a learning experience for a different aspect of statistics. The subject matter and questions can be easily tuned to different age groups. With a robust set of filters and visualizations you can teach advanced ideas in an engaging and clear manner to almost any audience.
"I will trust Google to 'do no evil' until the founders no longer run it." Hello Alphabet.
Check out
The Basics of Data Literacy.
http://www.nsta.org/store/product_detail.aspx?id=10.2505/9781938946035
The sample chapter available is on t-tests....the earlier chapters (not provided) explain how to get there.
http://static.nsta.org/files/PB343Xweb.pdf
You could do a lot worse than to do a session on the Monty Hall problem https://en.wikipedia.org/wiki/Monty_Hall_problem
Use statistics to show that the chances of success at the first stage are one in three, and that by switching in the second stage (after the host has shown you a goat) you improve your odds to one in two.
I personally really liked this video, which I think will be very relevant for new generation
https://www.youtube.com/watch?v=F-QA2rkpBSY
New Scientist's latest book offering is called Chance: The science and secrets of luck, randomness and probability.
I haven't seen it myself but it seems like it might contain material useful to you.
I'll mention, in passing, that I'm the author of this book and taught the fundamentals of statistics through data analysis to Grade 6 to 10 students for years. I then, for a decade, ran workshops for teachers (which I wasn't paid for, in case any here think that I'm in it for the money) on improving student's data and analytic literacy. We got quite good feedback on the workshops, so we turned them into this book. The book promotes hands-on investigation activities and a framework to help kids make sense of data -- the feedback on its use continues to be quite good.
The hands-on investigation activities are specifically aimed at the types of investigations kids would do in those grades structured in ways to develop their understanding of data analysis (and consequently, basic statistical analysis) as would be done in science. This includes information on how to draw conclusions from data and write narratively about those conclusions, in a way consistent with the way those things are done by scientists (and not, I'll add, the way these are normally taught in schools, which are NOT the way scientists talk about their data and conclusions).
The book is published through a non-profit press and I make diddly from it as a consequence (basically enough to continue to go and do the workshops for free)....if that makes me a shameless self-promoter then I gotta say I don't know how else to contribute to the thread because my answers to the original post are essentially all described in the book....
And other board games. As another poster suggested - use M&M's as a part of the format (or Skittles - take your pick) to mix things up a bit. These are middle schoolers we are talking about - most just entering pre-algebra / algebra 1. Don't overthink it.
In my high school statistics course - I learned how to play craps. In today's politically correct school environments I doubt that would fly - but it did help teach an important lesson - the house ALWAYS wins in the long run. The variant we played if played perfectly - 49% player, 51% house.
Or, of course, if you've written a textbook yourself, getting a colleague to require it for his course 100 miles away, while you recommend her text book.
Birds are not dinosaur descendants;birds are dinosaurs, for all useful meanings of "birds", "are" and "dinosaurs"
"What is the likelihood of me taking away your iPhone if you don't do your chores? Of NOT taking away your iPhone?"
"How many data points for each? What conclusions can we draw?"
(Answer: Dad can be a jerk). We didn't get to proper terminology yet, but the foundation for the concepts has been set.