Archive for the ‘Geometry’ Category

NYT Opinionator Series about Math

For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms.

The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University.

There are several other articles in this series, and if you haven’t been reading them, you really should go check them out.  Assign them.  Discuss them in your classes.

Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students.

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Creating 3D Geometry with PowerPoint

I find this to be a handy trick in PowerPoint. Although there is certainly better software for graphic design (for example, Adobe Illustrator), most instructors have a copy of Microsoft Office on their computers and so it makes a convenient graphics and layout program.

You may need 3-D graphics for Calculus, geometry, or math for elementary teachers and you can create those graphics pretty easily in PowerPoint. Here’s my 2-page tutorial.

If you’re going to label these figures, I recommend using the equation editor (or MathType) and then grouping the figure with the labels to create a single object. Copy and paste the graphics into a Word document using “Paste Special” and “Enhanced Metafile.” It doesn’t always look crystal clear on the computer screen, but it will print beautifully.

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African Fractals: A TedTalk about MATH!

Ron Eglash has a wonderful newly posted Ted Talk on Fractals, he discusses:

  • Cantor sets
  • Helge von Koch’s variation on Cantor sets
  • Self-similar structures in nature
  • Royal insignia (rectangles within rectangles)
  • African village which is a ring of rings
  • Circular and four-fold symmetry use in different cultures
  • Algorithms and the relationship to learning stories

  • Optimization for building african wind fences
  • Bamana sand divination (random number generator from the 12th century)
  • Every digital circuit in the world began in Africa… you’ll have to watch to see the reasoning
  • Usefulness of using heritage-oriented mathematics to motivate minority students to learn mathematics
  • Self-organization is in the brain, the Google search engine, and why the AIDS virus is spreading… the African methods of self-organization are robust, well-established and should be studied

Eglash’s website, Culturally Situated Design Tools, contains programs and applets that highlight cultural heritage. There are LOTS of geometry references on the website, including several cultural references to Cartesian coordinates (navajo rug weaver, graffit grapher, etc.) for those of you teaching algebra.

You could easily show this video in your class if you are teaching something where it might be appropriate. Total running time is 17 minutes. If you go to the TedTalks website for this one, you can download the whole video (in case you don’t have Internet in your classroom).

I think it would take a little while to work your way through all the material on the Culturally Situated Design Tools website, but if you teach in a school with a large minority population, I can see how it might definitely be a worthwhile way to spend some time.

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Math Games at Interactivate

I stumbled across a nice website last week called Interactivate with 140 (or so) interactive Java-based activities for algebra, geometry, probability, statistics, etc. Many of the activities are modifications of other activities, but still there are at least 30 unique game-based activities here to help your students learn.

I particularly liked “Algebra Four” (a play on the game Connect Four). I am teaching my algebra students all about solving equations right now and this would give them some good practice. The student can choose the level of difficulty (one-step, two-step, distributive, etc.). So conceivably, a student could first play at the one-step level, then the two-step level, then add the distributive property, and work their way up. This is a two-player game, which is really the only drawback, as a student at home would have to play against themself (or convince someone else to play an algebra game with them… hmm… unlikely). I do like the timer, which would encourage the student to get faster at solving equations. And if a student doesn’t want to play against the timer, it could just be set for a high time.

Another nice game here is the “function machine” like we’ve seen in textbooks, only this one is really a machine where you (or the student) inputs values, and it (the machine) processes the values and outputs them. The “game” here is to guess the function. I could see using this one in a classroom when we talk about function notation, and writing out the function notation process of each “guess” and “answer” to the side of the projected machine. A small improvement on this game would be to show the function notation to the side and then run a version that would let the all-knowing instructor input “x” at the end of the game, to show that if you input “x” or “a” into the function notation, the function notation shows you exactly what happens during the processing.

One last gem from this site is Area Explorer, which shows the student a graph of connected, shaded squares, and asks the student to find the area and perimeter. What I like is that it emphasizes the underlying principle behind area and perimeter (area is counting unit squares in the interior of the figure and perimeter is counting unit lines on the perimeter of the figure). Our students today seem to often miss this concept alltogether and just want to boil everything down to a formula, so I think this would be a great activity to have students try on their own.

All in all… kudos to this site for creating some really nice interactive materials!

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