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.
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.
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.
Courtesy Math with Bad Drawings: https://wordpress.com/read/post/id/48254001/2942/
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).
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
In case you have nothing better to read, here’s the first million digits of pi: http://www.piday.org/million/
And, as a reminder, I’ll be at the Pi Day of the Century event at the North Branch of the Denton library:
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.
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 
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
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
In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission comes from my former student Nada Al-Ghussain. Her topic, from Geometry: using a straightedge and compass to find the incenter of a triangle.
What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?
Sitting down one day pondering, Greco-Roman mathematician Euclid had a light-bulb moment and Eureka, the Elements was created! Right? Well not quite. Back in the day, 440B.C to be exact, a merchant named Hippocrates of Chios, chased after pirates to Athens to recover his stolen property. Unsuccessful, he attended math lectures and compiled the first known work of elements in geometry. Later on, around 350 B.C in the Academy, mathematician Theudius’s textbook was used by non- other than Aristotle. Then came our man Euclid in 300 BC and presented to us the pivotal textbooks, the Elements, which was used in universities until the 20th century. Euclid had compiled previous mathematical work into his Elements although he alone contrived the design and construction of different parts. Euclid’s Elements consisted of 13 books that covered Euclidean geometry, elementary number theory, and etc. For example, in book 4 (IV) Proposition 4, Euclid gives directions to inscribe a circle in a given triangle using a straightedge and compass.
http://www.britannica.com/EBchecked/topic/194880/Euclid
http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV4.html
How could you as a teacher create an activity or project that involves your topic?
I would set up a Founding Geometry explore activity before telling students anything over Euclidean geometry. In this activity I would want individual work but allow students to discuss in groups. Each person would get an equilateral triangle image, a compass, and a straightedge, not a ruler! First I would instruct the students to find the incenter, middle point of the triangle using only those two tools. This would get the students to think and go through trial and error as they work individually and together. Next I would ask them to write down their steps and discuss with each other. Then I would open class discussion asking the students the steps they took to get the incenter. I would ask thee students if they see anything else with all the lines they drew. Hoping they would describe the angle bisectors. Then I would ask the class if all triangle incenter’s could be found the same way. I would give each student a different shaped and sized triangle and give them time to discover the answer on their own. Once students finished, I would discuss the class the key steps and definitions learned. I would then tell me that they all are founders of Geometry, and tell them about Euclid’s role in geometry. This activity could be easily changed to any parts like how to construct a triangle or even to help prove and understand the Pythagorean theorem.
How can technology be used to effectively engage students with this topic?
When constructing geometry, trial and error tends to occur. Whether it is an instructor or a student. Graphical Ruler and Compass Editor, GRACE is a great site that allows the user to construct using only a straightedge and compass. By simply producing points and picking from Line, Line Segment, Ray, Circle, Perpendicular Bisector, and Intersection. This could be given to students as they work in class or at home as to not waste paper. It has special features that allow you to zoom in and out doing multiple constructions on one page. It also allows you to create and test axioms. This is tool is great for middle school all the way to university level students. It’s a quick visual that can be manipulated easily. From experience, many times when constructing certain propositions from Euclid’s Elements, I tended to waste time erasing so much and making perfect circles. Plus hand drawings can be tedious for some students. This is easier to use and engage all students including some special education students.
http://www.cs.rice.edu/~jwarren/grace/
Mean Green Math 