Floating Midpoints

This image consists of a visual recording made while using GeoGebra which was then converted to an animated gif and then resized to fit the blogger window.

If only...

I wish I had this ability when I was teaching. For more details on animations and GeoGebra, come to my presentation at AMTNYS in Syracuse on Nov. 10. Click here for details. the sketch is online here.

Avoid those errurs, I mean, errors.

During 30+years in the classroom, I developed a great appreciation for the impact of the careless error. Sometimes called "avoidable" errors, they crop up frequently in the mathematics classroom, and often are the root cause of a problem's seeming impossibility to the student solver.

Such an error is much more powerful in a student's math class than, perhaps, in his English class. Readers slide past spelling errors, often not even noticing them, while perhaps having a bit of a stronger jolt by a punctuation error. But even a tiny arithmetic error can turn a simple mathematics problem into an insurmountable task.

We may call them avoidable, because they can and should be avoided, and would be fixed if not avoided if we would only do such things as check our work, proofread, in short: be careful.

I have put together a small collection of such errors as they have appeared out in public. This collection is merely meant as a reminder to us all that double-checking our work is not a sinful task.

The first one here was snapped during a TV news broadcast, while the second was from a newspaper. Neither is a major error, but they both were avoidable.

Many many times the individual who made the error never notices it, which is why, I presume, the media has people on staff with the responsibility of checking each other's work. The reason I include them here is that they are evidence of a systemic failure in that regard.

I have put these and a few others on a web page, which can be found here. I pose the task to you to identify the errors. After all, somebody has to find them before anyone will fix them. That is the nature of avoiding an avoidable error.