# Teacher Must Remain a Student

I write for the unlearned about things in which I am unlearned myself… It often happens that two schoolboys can solve difficulties in their work for one another better than the master can… The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago that he has forgotten… I write as one amateur to another, talking about difficulties I have met, or lights I have gained…     -C.S. Lewis

# Gimmicky Bidding Websites (Series/Sequence)

The way this site works is that if you bid, you have to pay that amount, even if you lose.  Bids are incremented by 1 cent.   Let’s say an item sells for 10 cents.  The guy who bid 1 cent still has to pay that, the guy who bid 2 cents still has to pay that, and so forth.   So, what does the auction site actually earn for selling that item for 10 cents?

Notice that 1+2+3+4+5+6+7+8+9+10  can be added up by grouping numbers from the opposite ends:  $(1+10) + (2+9) + (3+8) + (4+7) + (5+6)$   This is just $11+11+11+11+11$  or 11*5 = 55.  Note that when x = 10, and we ended up multiplying $11*5$ for the series sum.

So, the general formula is:

1 + 2 + 3 + … + n = $\displaystyle\sum\limits_{x=0}^n x = (n+1)\frac{n}{2} = \frac{n^2+n}{2} = \frac{n(n+1)}{2}$

Pop Quiz!  If the sunglasses in the photo end up selling for \$6.96, how much does the website make?  $\frac{696*697}{2}$ = $\frac{485112}{2}$ = $242556$ = $\2,425.56$   !!

# SHOULD AIRPLANES BE FLYING THEMSELVES?

Fascinating account of the risks of automation when manual rote baseline skills are overlooked, neglected, and deficient.  This applies to much more than flying.

# Different kinds of Infinity

Which set is larger?  The set of all positive integers {1,2,3,4,…} or the set of positive even integers {2,4,6,8,…}  ?

# Can Students Have Too Much Tech?

• “Students who gain access to a home computer between the 5th and 8th grades tend to witness a persistent decline in reading and math scores,” the economists wrote, adding that license to surf the Internet was also linked to lower grades in younger children.
•  What’s worse, the weaker students (boys, African-Americans) were more adversely affected than the rest. When their computers arrived, their reading scores fell off a cliff.
•  With no adults to supervise them, many kids used their networked devices not for schoolwork, but to play games, troll social media and download entertainment. (And why not? Given their druthers, most adults would do the same.)
• Technology does have a role in education. But as Randy Yerrick, a professor of education at the University at Buffalo, told me, it is worth the investment only when it’s perfectly suited to the task, in science simulations, for example, or to teach students with learning disabilities.

Can Students Have Too Much Tech?

# Study Finds More Reasons to Get and Stay Married

At least they tried to control for 1 variable.  They controlled for happiness level prior to the marriage, which has nothing to do with happiness while married.  But, this study is still rubbish due to survivorship bias.  People who are happy with their marriage will stay in the marriage.  People who are unhappy may not stay in the marriage, and are not part of the study.  To really measure if marriage causes happiness, you must run a controlled experiment and randomly assign people to a control and treatment group.  The results of an observational study are invalid and meaningless.   The article should conclude that “People who are in great marriages and decide to stay married …are happier than single people”

Incidentally, the article headline implies “Marriage makes you happy”  Meanwhile, they later state the effect of living together makes you just as happy as legal marriage.  So, they show that marriage has nothing to do with happiness, yet the headline states the exact opposite.    Another case of a headline that the masses just accept at face value.

Study Finds More Reasons to Get and Stay Married

# Does Exercise Really Keep You Young?

Here is an example of selection bias.    Correlation is not causation.  Those with serious illness and poor health will not be in the active group.  The limits of an observational study vs. a properly controlled experiment with random assignment.

Does Exercise Keep You Young?

# Moneyball Data Mining 101

In my dummy sports data below, you can see that the number of penalties is correlated most strongly to wins.

But, if you had hundreds of variables, how could you generate the cross product of every correlation possible, in order to find the variables with the highest correlation?  One answer:  Use the Stats program called “R” to create a correlation matrix!   You can generate all sorts of visual outputs, as well.   Penalties sticks out like a sore thumb now:

Disclaimer:  Without stating a hypothesis up front, these finding is nothing more than “data snooping bias” (ie: curve fitting)  The discovered association might simply be natural random variation, which would need to be verified with an out of sample test to have any validity at all.

To do this for yourself, here are the steps:

(Right click -> Save as …into a folder you’ll remember!)

Enter the following commands in R:
(The lines with # are just comments, do not type them.  Just paste the bold commands!

# Import data

# Attach data to workspace
> attach(data1)

# Compute individual correlations
> cor(Penalties, Win)

# Scatterplot matrix all variables against each other
> pairs(data1)

# Generate a CORRELATION MATRIX !!
> cor(data1)

Here is how to generate the visual output:

> library()
…Scroll back up to the very first line of the popup window.  Packages are probably in something like library ‘C:/Program Files/R/R-3.3.0/library’

Download and install “corrplot” Windows binaries package into the library path above.
Note:  When you extract, you will see the folder heirarchy:  corrplot_0.77/corrplot/….
Only copy the 2nd level folder “corrplot” into the library/ folder.  (ie: Ignore the .077 top folder)

# import corrplot library
> library("corrplot")

# generate correlations matrix into M
# You now redirect the cor() function output we used above into a matrix called “M”
> M <- cor(data1)

# Plot the matrix using various methods
# Method can equal any of the following: circle, ellipse, number, color, pie
> corrplot(M, method = "circle")
> corrplot(M, method = "ellipse")
> corrplot(M, method = "number")
> corrplot(M, method = "color")
> corrplot(M, method = "pie")

# Cheating on a test?

Here is a question someone recently asked me:  What’s the probability that two students taking a multiple choice test with 29 questions will get exactly the same wrong answers on 10 of the questions?

My answer?   Let’s restate this question to make it a lot simpler.  Can we assume they also got the same correct answers?   If so, then the question simply becomes, “What’s the probability that 2 students choose the same answer for all 29 questions?”
P(all same) = $(1/4)^{29} = .000000000000000003$

# Which matters more? Talent or practice?

• Practice only accounted for 12% of individual differences in performance across all the different areas.Some factors which may be important:
• How early in life you start.
• Intelligence.
• Personality.
• Working memory capacity.

# Laptop versus hand-written notes

The present research suggests that even when laptops are used solely to take notes, they may still be impairing learning because their use results in shallower processing. In three studies, we found that students who took notes on laptops performed worse on conceptual questions than students who took notes longhand. We show that whereas taking more notes can be beneficial, laptop note takers’ tendency to transcribe lectures verbatim rather than processing information and reframing it in their own words is detrimental to learning.

Advantages of Longhand Over Laptop Note Taking

# College Success? SAT vs. GPA

High school grades matter — a lot. For both those students who submitted their test results to their colleges and those who did not, high school grades were the best predictor of a student’s success in college. And kids who had low or modest test scores, but good high school grades, did better in college than those with good scores but modest grades.

College Applicants Sweat The SATs. Perhaps They Shouldn’t

# Calculus, Optimization, and Poker…

http://forumserver.twoplustwo.com/15/poker-theory/mathematics-poker-chapter-14-2-maximazing-bet-sizing-calculation-1429179/

# Ivy degrees and income: Correlation vs. Causation?

Krueger and Dale studied what happened to students who were accepted at an Ivy or a similar institution, but chose instead to attend a less sexy, “moderately selective” school. It turned out that such students had, on average, the same income twenty years later as graduates of the elite colleges. Krueger and Dale found that for students bright enough to win admission to a top school, later income “varied little, no matter which type of college they attended.” In other words, the student, not the school, was responsible for the success.

http://www.brookings.edu/research/articles/2004/10/education-easterbrook

# Debunked: Singapore’s High Test Scores

## Misidentifying Factors Underlying Singapore’s High Test Scores

• Singapore’s student population does not include the children of huge numbers of people who work the lower-paying jobs in Singapore.
• For Singaporean students, school is their job; other activities are absent or relegated to minor roles.
• Most Singaporean children get additional schooling beyond the school day through individual tutoring or classes.  (One survey found 97% of Singaporean students get private Math tutoring)
Yet again, Statistics 101.  Yet this myth is parroted like gospel.  Of course test scores are going to vary when you are not comparing similar groups:
• China scores only include children from Shanghai.  (How about we only include students from Scarsdale in the USA TIMMS scores?)
• Singapore schools do not contain any children from working class families (Service workers commute to Singapore from Malaysia).  Singapore GDP is 50% higher than the USA’s.
• American students are involved with a wide array of sports and activities.  22% of American students have after school jobs.
• The reality is that top performing students in affluent suburbs of America perform on par with top performing countries who do not have lower class students in their results.