Square any number up to 1000 without a calculator

The Mathematical Association of America has an excellent series of 10-minute lectures on various topics in mathematics that are nevertheless accessible to the general public, including gifted elementary school students.  From the YouTube description:

Mathemagician Art Benjamin [professor of mathematics at Harvey Mudd College] demonstrates and explains the mathematics underlying a mental arithmetic technique for quickly squaring numbers.

A veteran teacher turned coach shadows 2 students for 2 days – a sobering lesson learned

Last October, I read the following interesting blog post about a teacher who placed herself in the position of her students for a couple of days: http://grantwiggins.wordpress.com/2014/10/10/a-veteran-teacher-turned-coach-shadows-2-students-for-2-days-a-sobering-lesson-learned/

The lessons learned from this exercise partially explain why I’m an advocate for inquiry-based learning… under the firm presupposition that teaching with this method is an acquired skill, and that this technique can go south in a hurry if it’s not exercised properly.

How Sports Can Help Your Kids Outsmart Everyone Else

Some quotes from the very nice op-ed piece at http://time.com/3510480/sports-math-financial-literacy/:

In her excellent book, Race to the Top, the journalist Elizabeth Green tells a story of a new hamburger that the A&W Restaurant chain introduced to the masses. Weighing 1/3 of a pound, it was meant to compete with McDonald’s quarter-pounder and was priced comparably. But the “Third Pounder” failed miserably. Consultants were mystified until they realized many A&W customers believed that they were paying the same for less meat than they got at McDonald’s. Why? Because four is bigger than three, so wouldn’t ¼ be more than 1/3?…

Just as a game is packed with fractions, probability, equations and even multi-variable calculus if you’re so inclined, so too is it a laboratory for risk assessment, principles of finance and behavioral economics—an emerging field that looks at the effects of psychology and emotion on economic decision-making…

Sports also provide a context for probability. Broadcasters may ask questions hypothetically, but real answers exist. Jones is only a 40% free-throw shooter but he makes both. What are the odds of that?

If only one day a response would come: Well, I’ll tell you, Bob. Forty percent is 4/10. Multiply that twice for the two shots. 4/10 x 4/10 = 16/100 or 16%. Not good odds, but not extraordinarily rare, either.

If nothing else, any kid who’s been to both a hockey game and a basketball game knows the difference between thirds and quarters, and, in turn, would have picked the right burger.

Student t distribution

One of my favorite anecdotes that I share with my statistics students is why the Student t distribution is called the t distribution and not the Gosset distribution.

From Wikipedia:

In the English-language literature it takes its name from William Sealy Gosset’s 1908 paper in Biometrika under the pseudonym “Student”. Gosset worked at the Guinness Brewery in Dublin, Ireland, and was interested in the problems of small samples, for example the chemical properties of barley where sample sizes might be as low as 3. One version of the origin of the pseudonym is that Gosset’s employer preferred staff to use pen names when publishing scientific papers instead of their real name, therefore he used the name “Student” to hide his identity. Another version is that Guinness did not want their competitors to know that they were using the t-test to test the quality of raw material.

Gosset’s paper refers to the distribution as the “frequency distribution of standard deviations of samples drawn from a normal population”. It became well-known through the work of Ronald A. Fisher, who called the distribution “Student’s distribution” and referred to the value as t.

From the 1963 book Experimentation and Measurement (see pages 68-69 of the PDF, which are marked as pages 69-70 on the original):

The mathematical solution to this problem was first discovered by an Irish chemist who wrote under the pen name of “Student.” Student worked for a company that was unwilling to reveal its connection with him lest its competitors discover that Student’s work would also be advantageous to them. It now seems extraordinary that the author of this classic paper on measurements was not known for more than twenty years. Eventually it was learned that his real name was William Sealy Gosset (1876-1937).

Vertically Integrating Professional Skills Throughout A Mathematics Major

Every so often, I’ll publicize through this blog an interesting article that I’ve found in the mathematics or mathematics education literature that can be freely distributed to the general public. Today, I’d like to highlight “Vertically Integrating Professional Skills Throughout A Mathematics Major,” by Clarice Dziak, Brian Leventhal, Aaron Luttman, and Joseph Skufca. Here’s the abstract:

In response to a university mandate to include “professional issues” as a component of every major, we have developed a vertically integrated approach to incorporating the study of professional skills and issues into the mathematics curriculum. Beginning in the first year of study, mathematics majors take an inquiry-based course in mathematical modeling using software packages that are important in business and industry, such as Excel®, Maple®, and Matlab®. In the third year, students choose between a seminar course covering topics in teaching and another covering topics related to research and work in industry. The courses are designed to introduce students to the different cultures and issues of business, industry, and teaching. Beyond these two courses, students are required to demonstrate proficiency in three core areas through a required “professional experience,” which takes the form of an internship, undergraduate research experience, or educational outreach program.

The full article can be found here: http://dx.doi.org/10.1080/10511970.2013.876472

Full reference:Clarice Dziak, Brian Leventhal, Aaron Luttman & Joseph Skufca (2014) Vertically Integrating Professional Skills Throughout A Mathematics Major, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24:4,301-308, DOI:10.1080/10511970.2013.876472

Local Pi Day Event

As has been well publicized, tomorrow is the Pi Day of the Century (3/14/15). I actually know someone who intentionally planned her wedding for tomorrow morning at 9:26 am.

The North Branch of the Denton library will be holding a Pi Day event from 9:26 am until 5:35 pm, and I’ll be making four presentations (two for grade school children and two for teens/adults). You’re welcome to bring the family and enjoy as your schedule permits.

Was There a Pi Day on 3/14/1592?

March 14, 2015 has been labeled the Pi Day of the Century because of the way this day is abbreviated, at least in America: 3/14/15.

I was recently asked an interesting question: did any of our ancestors observe Pi Day about 400 years ago on 3/14/1592? The answer is, I highly doubt it.

My first thought was that \pi may not have been known to that many decimal places in 1592. However, a quick check on Wikipedia (see also here), as well as the book “\pi Unleashed,” verifies that my initial thought was wrong. In China, 7 places of accuracy were obtained by the 5th century. By the 14th century, \pi was known to 13 decimal places in India. In the 15th century, \pi was calculated to 16 decimal places in Persia.

It’s highly doubtful that the mathematicians in these ancient cultures actually talked to each other, given the state of global communications at the time. Furthermore, I don’t think any of these cultures used either the Julian calendar or the Gregorian calendar (which is in near universal use today) in 1592. (An historical sidebar: the Gregorian calendar was first introduced in 1582, but different countries adopted it in different years or even centuries. America and England, for example, did not make the switch until the 18th century.) So in China, India, and Persia, there would have been nothing particularly special about the day that Europeans called March 14, 1592.

However, in Europe (specifically, France), Francois Viete derived an infinite product for \pi and obtained the first 10 digits of \pi. According to Wikipedia, Viete obtained the first 9 digits in 1579, and so Pi Day hypothetically could have been observed in 1592. (Although \pi Unleashed says this happened in 1593, or one year too late).

There’s a second problem: the way that dates are numerically abbreviated. For example, in England, this Saturday is abbreviated as 14/3/15, which doesn’t lend itself to Pi Day. (Unfortunately, since April has only 30 days, there’s no 31/4/15 for England to mark Pi Day.) See also xkcd’s take on this. So numerologically minded people of the 16th century may not have considered anything special about March 14, 1592.

The biggest obstacle, however, may be the historical fact that the ratio of a circle’s circumference and diameter wasn’t called \pi until the 18th century. Therefore, both serious and recreational mathematicians would not have called any day Pi Day in 1592.