Mathematics is about wonder, creativity and fun, so let’s teach it that way

I enjoyed this opinion piece at phys.org about project-based instruction in mathematics. A sample quote:

Mathematician Jo Boaler from the Stanford Graduate School of Education says that a “wide gulf between real mathematics and school mathematics is at the heart of the math problems we face in school education.”

Of the subject of mathematics, Boaler notes that: “Students will typically say it is a subject of calculations, procedures, or rules. But when we ask mathematicians what math is, they will say it is the study of patterns that is an aesthetic, creative, and beautiful subject. Why are these descriptions so different?”

She points out the same gulf isn’t seen if people ask students and English-literature professors what literature is about.

In the process of constructing the RabbitMath curriculum, problems or activities are included when team members find them engaging and a challenge to their intellect and imagination. Following the analogy with literature, we call the models we are working with mathematical novels.

 

Students Find Glaring Discrepancy in US News Rankings

Despite its hopelessly flawed methodology, U.S. News & World Report continues to sell magazines with its lists of Top 25 or Top 100 universities in various categories. Some universities who don’t play along, like Reed College, have long suspected that their rankings are penalized. So I enjoyed this press release from Reed College about statistics students who reverse-engineered the rankings to measure the magnitude of this penalty. The results are startling: while Reed was officially ranked #90, the formula should have them at about #38. In one glaring example, the magazine underestimated the college’s financial resources by over 100 spots even though this information the magazine could have obtained this information from free government databases instead of their survey.

To Save The Science Poster, Researchers Want To Kill It And Start Over

Professional conferences often feature poster sessions, and, more often than not, the poster is simply incomprehensible to somebody walking through the aisles.

So I enjoyed this article about an innovative way to bring scientific posters in the 21st century. The money quote:

“The current method is not effective in communicating research findings. For instance, in my field, we all want improvements in our life: vaccines for all diseases, easier delivery of vaccines, innovative way to finance vaccines, effective ways tackling vaccine hesitancy,” Suharlim says. “Experts are all coming to these conferences, and they have limited time to update their knowledge.”

The proof is definitely in the pudding:

Finally, here’s a YouTube video explaining the concept:

Sum of Three Cubes

I now have a new example of an existence proof to show my students.

Last year, mathematicians Andrew Booker and Andrew Sutherland found solutions to the following two equations: x^3 + y^3 + z^3 = 33 and x^3 + y^3 + z^3 = 42. The first was found by Booker alone; the latter was found by the collaboration of both mathematicians. These deceptively simple-looking equations were cracked with a lot of math and a lot of computational firepower. The solutions:

(8,866,128,975,287,528)³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³ = 33

$latex (–80,538,738,812,075,974)3 + 80,435,758,145,817,5153 + 12,602,123,297,335,6313 = 42$

At the time of this writing, that settles the existence of solutions of x^3 + y^3 + z^3 = n for all positive integers n less than 100. For now, the smallest value of n for which the existence of a solution is not known is n = 114.

For further reference, including links to the original articles by Booker and then Booker and Sutherland, please see:

Differentiation and Integration

As I tell my calculus students, differentiation is a science. There are rules to follow, but if you follow them carefully, you can compute the derivative of anything. This leads to one of my favorite classroom activities. However, integration is as much art as science; for example, see my series on different techniques for computing

\displaystyle \int_0^{2\pi} \frac{dx}{\cos^2 x + 2 a \sin x \cos x + (a^2 + b^2) \sin^2 x}

The contrast between differentiation and integration was more vividly illustrated in a recent xkcd webcomic:

Source: https://xkcd.com/2117/

A Professor Asked His Students to Write Their Own Exam Questions

I was intrigued by this article in the Chronicle of Higher Education about professors who asked students to write their own exam questions, thus forming a test bank from which the actual exam would be constructed. I’m not sure if I’d try this myself, but it definitely gave me food for thought.

Opening Paragraph of “States of Matter”

Source: https://twitter.com/quantian1/status/1193685637033054208?s=12

Composition of Functions, Visually

Source: https://www.facebook.com/IloveMathematics91/photos/a.601527433214764/2777236075643878/?type=3&theater

What Industrial Jobs Can I Get With a Math Degree?

From Thomas Network:

While not every math major will get the chance to work on something as exciting as the Enigma Code or black holes, there’s one career that will provide an endless stream of fascinating challenges to keep even the brightest mathematical minds busy: manufacturing.

Mathematicians are in demand for these four skills in particular:

  1. Analytical skills
  2. Problem-solving skills
  3. Critical-thinking skills
  4. Quantitative reasoning skills

The U.S. Bureau of Labor Statistics expects the demand for math majors to grow by 30% from 2018 to 2028. As of last year, the median annual wage for mathematicians was $101,900.

56 Funny Math Jokes And Puns That Will Make You Smile, Easy As Pi

Just when I thought I had heard every awful math pun ever devised, along came 56 Funny Math Jokes And Puns That Will Make You Smile, Easy As Pi. I had heard about half of these before, but the other half was new. Pun #2 was my favorite.