CLASSROOM TIPS (links open new windows)

OVERHEADS: 1) Start class with a transparency, Power Point slide, or computer image. This has the added benefit of focusing the students the minute they come in the door. The mathematical purpose of the image might be obvious to the student, as in the case of an portrait of Emilie du Chatelet holding her compass or an illustration of polygons from Bhaskara's Lilavati. However, I much prefer images that arouse the curiousity of the student. Several years ago, students in my college algebra class were greeted with the woodcut image of a rabbit. A student loudly asked, "What does a rabbit have to do with algebra?" Fibonacci had a lot to say about pairs of rabbits, and I suspect my students still remember this example. An image of the sick ward of the Army Reed Army Hospital during the 1918 influenze epidemic can be used to provide a context for the logistic growth curve. Inspirational or informative quotes are also good on the overhead. 2) Use an overhead to help teach a topic. I used a 14th century Chinese version of Pascal's Triangle to help students discover the construction of the rows. The slide also provides an opportunity to talk about other number systems as well as the reason we call it "Pascal's Triangle" when the Chinese knew about it 300 years before Pascal's birth. I use transparencies of pages from foreign textbooks (Russian, Korean, Spanish, French, etc); students cannot read the words, but they can read the mathematics.

READINGS: * 1) Provide context for a lesson. People love to be read to and reading something to introduce a topic relaxes students and makes them more receptive to learning. I like to read a poem about Madame Curie before I introduce the topic of exponential decay. The poem is very moving and students sense the importance of the topic as it relates to the study of radiation. This is much more interesting than talking about old mummies. 2) Use as a teaching example. I read parts of the transcript from the O.J. Simpson Trial (I call this "recent" history) as a way to review circle formulas and calculator operations. Students see how important it is to be an educated citizen (lawyer, judge, or juror) and how ignorance or misuse of math can influence the outcome of events. In Arthur Conan Doyle's "The Musgrave Ritual", students can be their own Sherlock Holmes when they solve an ancient problem using similiar triangles. 3) Use as a reward at the end of the week. Students are tired at the end of the week and especially appreciate a reading that may not (seemingly) have anything to do with current topics. A favorite is a reading from about the ebola virus that illustrates that math and science can be very exciting indeed. *It is best to read from the book, not a photocopy. Teachers are role models and students will see that reading is a way we can all expand our universe.

ANECDOTES: My first department chair argued that math teachers should have degrees in mathematics because, in addition to having the background to teach math courses, they knew how to "talk the talk". That is, because we love the subject so much, we know the stories about math that make it more interesting for our students. These stories, or anecdotes, usually arise naturally during the class. For example, books usually include a review of the real number system in preliminary chapters; it's usually boring. I tell students that people died because of the discovery of irrational numbers, there were disputes over the concept of the number zero, negative numbers were not acceptable coefficients or solutions to equations during the middle ages, and there was a 400 year struggle between using Roman numerals (and the abacus) and our current number system (requiring multiplication tables).

TEACHING THREADS: Pat McKeague gave me the idea for this technique. Teach parts of a topic over the course of several days, or in some cases, several courses. Thus, each part takes just a little time. Each day I teach radicals and their operations, I show them something different: historic radical symbols, the spiral of roots, a cartoon of Pythagoras naming the" hypotenuse" (with his fellow Greeks laughing at the name), the Greek concept of a "square" number, etc. Elementary algebra students could construct the golden rectangle and use the construction to learn about ratio and proportion, simplifying radicals, and rationalizing the denominator. Precalculus students would then develop Pascal's triangle and discover the general rule for expanding a binomial. Calculus students continue the thread by exploring or deriving the explicit formula for the Fibonacci sequence and limits to find the golden ratio.

LECTURE EXAMPLES: Many of our traditional lecture examples have historical origins. For example, in the 14th century, Nicole Oresme showed that the harmonic series was divergent and precalculus students could understand how he did this. The Pythagoreans created a proof for the "Pythagorean" theorem, but it was geometric not algebraic and an elementary algebra student could understand the probable proof. The Greeks used simple geometric methods to solve simple quadratic equations and elementary algebra students could be led through the construction of the solution.

PICK A BOOK TO READ: Find a book you would enjoy reading during the semester, to yourself. You will find yourself quoting from it during class. While teaching a second semester calculus class, one of my colleagues, David Arnold, read Euler, The Master of Us All, by William Dunham. His lectures were peppered with fascinating stories and quotes during the semester and the time taken was usually less than a minute. He brought the book to class to show them the cover and recommend they read it.

VIDEO CLIPS: One of my favorite movie clips is the scene from October Sky where Sony and his friends shoot of an errant rocket. This is a great way to introduce the position formula for freefall. Look at my WEBSITE>Literature section for a link to math movies.

OUTSIDE ASSIGNMENTS: Many of the resources listed in this site are appropriate for student research. You can ask students to research mathematicians, early uses of symbols, and historic development of concepts. If you want to know something about the history of what you are teaching, ask the students to provide an answer. Graduate students do research for their advisors all the time, why not ask community college students to help you out!

OFFICE: Decorate your office and office door with math history using posters, props (slide rules!), quotes, and books. Students utilizing your office hours get an added dose of history. A colleague, Sandy Vrem, gives her students extra credit for their first visit to her office hour, if they ask a question. Adorn your office with historical items and they usually notice.

EMAIL AND WEBSITES: Add quotes to you email signatures; these can be easily changed on a weekly basis. Use your website to provide links to math history sites that would interest your students. Give your students extra credit for sending you an email (you respond with a quote) or looking up something on your website.

CLASS PROPS: Provide visual aids for your students. Bring in a ball that just fits into a can and tell them that Archimedes developed relationships for these figures and was so taken with his discoveries that he had these figures carved into his grave marker. Take an abacus to class and talk about the 400 year battle between the Algorists and Abacists.

ATTIRE: This may not be for everyone, but I wear things to class that students notice, which in turn provides me with an opportunity to bring some history into the conversation. I have a pair of working abacus earrings, and T-shirts that have mathematics printed on them (the math club from Humboldt State University has a new one every year). I have also worn a punjabi or sari when highlighting mathematics developed in India or Persia. I would like to come up with historical customs for halloween. The Mathematics Teacher has an article on this very idea.

Maintained by Michele Olsen, College of the Redwoods