Borland Educational News and Views

Saturday, April 01, 2006

Educator's Blogs

Here's a site devoted to publicizing blogs written by educators.

Featured are a great number of blogs and podcasts from teachers in elementary, secondary, and post-secondary schools across the country.

Check it out here:

http://educational.blogs.com/

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Contact Chris

borlandeducational.com

Wednesday, March 01, 2006

This Sentence Is False. True Or false?

Seems like a simple question.

Uh, no. Not really.

Like a dog chasing it’s tail, brushing the bristles of the brush you’re brushing with, seeing your eyes with your own eyes (impossible, unaided), or drawing a circle around all circles on a page (try it!), the first sentence in the title of this post is strange, to say the least.

I’ll repeat the sentence in question, for convenience, immediately below this one.

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This sentence is false.

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What makes this so weird is that the sentence in question is an example of “self-reference.” Like a brush brushing itself, eyeballs seeing themselves, or circles circling themselves, the sentence in question “sentences” (i.e. refers to) itself.

[“Self reference” is the subject of a wonderful book titled: Godel, Escher, Back: An Eternal Golden Braid, by Douglas Hofstadter. I highly recommend it.]

Is the bold-faced sentence three paragraphs above this one true, or false? That’s the question.

The answer might surprise you.

(Click here to go to Part 2.)

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Contact Chris

borlandeducational.com

Wednesday, February 01, 2006

Mathematical Mind Reading

The old "Sum and Difference" game is a simple trick that even very young children can play to amaze and frustrate playmates or (better yet) adults (even teachers) whose algebra skills have atrophied.

It's a great way to introduce "unknown" numbers to beginning algebra students.

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Instructions:

Pick any two numbers. Add them (first number plus second number), and report the total. Then subtract them IN THE SAME ORDER (i.e. first number minus second number), and report the total.

You can determine the two numbers using simple algebra:

1st number = x (perhaps: 7).

2nd number = y (perhaps: 12).

Let: a = x + y, and let: b = x – y. The player will report to you the values of "a" and "b," the sum and difference of the two numbers (in our example, these numbers are 19 and -5). Add these results in your head (in this case, the sum is 14), and what you have will always be twice one of these numbers [since a + b = (x + y) + (x – y) = 2x.] Divide by two (14 ÷ 2 = 7), and you now have one of the numbers. Since you already know the sum of the two numbers, subtract to find the second one (19 – 7 = 12).

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An entertaining variation is the "Birth Date Trick, below.”

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Instructions:

Add your birth date plus birth month (example: for June 17, 1990, the birth date would be 17, the birth month would be 6, and the total would be 23), and report this number. Then, subtract these same two numbers IN THE SAME ORDER (i.e. birth date minus birth month). Again, be careful – this second result could be negative (in our example, the difference would be 6 – 17 = -11). Since this is really just another “sum and difference” exercise like the one above, all you have to do is add these two results and divide by two to get the birth month, then subtract the birth month from the total to get the birth date!

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Contact Chris

borlandeducational.com

Sunday, January 01, 2006

Thought Boxes (OTTFFSSEN)

Sometimes, it helps to be a first grader.

The human mind is truly amazing, no doubt about it. Still, it can get in its own way, as the following puzzle illustrates.

A bright first grader would find the following puzzle easier to solve than a bright well-schooled adult, given what the first grader has probably studied so far in school.

See if you can solve it (remember ... think like a first grader!):

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Find the next three letters in this sequence:

O, T, T, F, F, S, S, E, N, ...

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(Click here to go to Part 2.)

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Contact Chris

borlandeducational.com

Thursday, December 01, 2005

Regarding Artificial Posting Dates And Times

In the spirit of full disclosure:

Posts on this blog showing a posting time of exactly 12:00 PM were originally published on a different date and/or at a different time.

In order to place the various posts I've composed into the optimal sequence, I've found it necessary to change the actual dates and times on which they were first uploaded (this post, for example, was originally submitted approximately 7:31 PM on 9/11/2006). There's simply no other way to order posts in Blogger.

To make clear the fact that the posting date and time shown for a particular post is artificial and not the post's original date and time of publication, I have deliberately set the time of each such post to 12:00 PM. I'll be careful not to spontaneously publish any other posts at that particular time of day, to avoid confusion.

I may decide to discontinue this practice at some point, at which you'll once again start to see varied posting dates/times. In that case, any posting dates/times not equal to 12:00 PM will be actual and accurate.

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Contact Chris

borlandeducational.com