Teaching

Street Fighting Mathematics

Sanjay Mahajan’s Street Fighting Mathematics is a short, dense, and engaging book that explores some mathematical problem-solving techniques not typically taught in math class.

These techniques, favored by engineers and scientists who are usually more interested in the answer to a question than in the mathematical theory that gets them there, can turn seemingly intractable problems into simple ones, often just by a change in perspective.

For example, the book offers a short treatment of Feynman’s differentiating-under-the-integral approach, one of the more famous “back of the napkin” techniques.  Mahajan even “guesses” the definite integral that yields the area under the bell curve, using dimensional analysis the likes of which I’ve never seen.

A “Street Fighting Mathematics” course is offered through MIT’s OpenCourseWare, which includes lectures, notes and problem sets.  In addition, Mahajan has made the book available for free in PDF format.

By patrick honner, ago

Writing to Reduce Test Anxiety

This is an interesting report on the effect of writing on test-anxiety.

http://www.insidescience.org/research/1.1885

In one study, a periodic writing assignment improved the scores of women in a college physics course.  In another, writing before a math exam improved the scores of high school and college students.  In this second study, the most anxious students showed the most improvement.

The nature of the writing exercises is also interesting.  In the first study, students were prompted to write something “values-affirming” (i.e., positive) at the beginning of the semester, and again several weeks in.  In the second study, students were asked to write immediately before the exam, and they were prompted to write specifically about their anxieties.  In both cases, writing had a positive impact for a significant number of students.

www.MrHonner.com

By patrick honner, ago

Math Encounters: Craig Kaplan on Math and Art

Craig Kaplan’s Math Encounters talk, “Revolution and Evolution in Math and Design,” was a whirlwind tour of the design space that lies at the intersection of computer science, mathematics, technology, and art.   Kaplan, a professor of computer science at Waterloo university, is an innovative software engineer, an accomplished artist, and a passionate and engaging speaker.  His talk wove together the mathematical and cultural history of Islamic art, tilings of the plane, non-Euclidean geometries, and the mathematics of aesthetics.

The Math Encounters series, sponsored by the Museum of Mathematics, strives to bring mathematics to the public through dynamic speakers, meaningful topics, and engaging interactivity.  In that spirit, after the talk Kaplan and George Hart led a fun, collaborative workshop where the audience teamed up to create a work of art themselves!

Using some tape, some scissors, and some clever mathematics, each group turned their table into a “tile” using the techniques Kaplan covered in his talk.

And as each group finished their “tiles”, we started putting them all together!

It was a fun and fitting end to an inspiring and mind-opening evening!  You can learn more about Craig Kaplan and his work at his webpage.

By patrick honner, ago

Quadrilateral Challenge — A Solution

Here is one approach to answering the quadrilateral challenge posed earlier.  In summary, the challenge was to prove or disprove the following statement:  A quadrilateral with a pair of congruent opposite sides and a pair of congruent opposite angles is a parallelogram.

I offer this disproof without words.

By starting with an isosceles triangle, cutting it, rotating one of the pieces, and gluing it back together, we have constructed a quadrilateral with one pair of congruent opposite sides and one pair of congruent opposite angles that it is not necessarily a parallelogram!

By patrick honner, ago

A Quadrilateral Challenge

Here’s an easy-to-understand, remarkably rich question that arose during a recent Math for America “Bring Your Own Math” workshop.

If a quadrilateral has a pair of opposite, congruent sides and a pair of opposite, congruent angles, is it a parallelogram?

I had a lot of fun thinking about this problem on my own, discussing it with colleagues, and sharing it with students.  At different times throughout the process, I felt strongly about incompatible answers to the question.  For me, that is a characteristic of a good problem.

I encourage you to play around with this.  I was surprised at how many cool ideas came out as I worked my way through this problem, and I look forward to sharing them!

And if you want to see a solution, click here.

By patrick honner, ago
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