Teaching

A New Solution to an Old Problem

This story makes me feel bad for every time I discouraged a student from a math research project because the topic was too well-known.

http://novinite.com/view_news.php?id=122377

A 19-year old Bulgarian student has solved the 2000-year old Problem of Appollonius in a new and unique way. It is the first new solution in 200 years, and only the fifth known solution overall.

The Problem of Appolonius, essentially, is to construct (with straightedge and compass, only) a circle that is tangent to three given objects. Here is an example of an Appolonius Circle (in red) that has been constructed to be tangent to the three given circles (in black).

This story is nice reminder that sometimes the best thing to do as a teacher is get out of the student’s way!

By patrick honner, 15 yearsApril 20, 2011 ago

Student Work: Curvefitting With Geogebra

Here is some student work from a recent project I conducted on fitting curves to images in Geogebra. The details of the assignment can be found here, and more examples of student work can be seen on my Facebook page.

Students were asked to find pictures and use Geogebra to fit trigonometric curves to the images using transformations. Here are some of the results.

Smart Water = Smart Curves

My Good-Looking Windowsill

Sine of Camel Humps

Overall, I was really impressed with the creativity the students showed, and their facility with fitting these curves to the forms! A mathematical and artistic success in my book.

Resources Teaching Technology

Curvefitting With Geogebra

Inspired by some of my own forays into curvefitting with Geogebra (the squash at the right, or my Sine Waves on the Beach), I’ve created a student project built around the idea.

Finishing up a unit on trigonometry with graphs of trigonometric functions, it occurred to me that I have never really been comfortable teaching transformations. I think part of the reason is that it’s hard to get your hands dirty, play around, and develop intuition with this topic. This is where Geogebra comes in!

The project essentially works like this:

1) Students find an image, preferably one they capture themselves

2) Students paste the image into Geogebra

3) Students graph a relevant trigonometric function and play around with the various parameters (like period, amplitude, phase shift) until the curve fits the image

4) Students can use domain restrictions, and some of Geogebra’s aesthetic features, to polish everything up.

The first run of this project has produced some great results! You can see some sample student work here, and more on my Facebook page.

Challenge Geometry Teaching

Paper Pyramids

Another installment from my Fun With Folding series: paper pyramids!

First, start with a triangular cut-out. Construct this triangle’s medial triangle by connecting the midpoints of each side. If you don’t have a ruler handy, just fold corner to corner, and crease in the middle to find the midpoint of each side!

Now, fold up the sides and tape them together!

The best part about this activity is that it doesn’t always work! Finding out which triangles this will work for, and which it won’t, leads to lots of good mathematical questions to explore!

Appreciation Photography Teaching

“I don’t like math.”

My niece took this photograph. We played around with these magnetic polygons for an hour or so, during which time she showed off her arithmetic skills, impressed me with her ability to estimate and verify, and actively engaged me in a rather sophisticated discussion about infinity.

Then she told me, “I don’t like math.”

Related Posts

Math Photo: Solid Family

By patrick honner, 15 yearsMarch 20, 2011 ago

A New Solution to an Old Problem

Student Work: Curvefitting With Geogebra

Curvefitting With Geogebra

Paper Pyramids

“I don’t like math.”

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