I am in the process of posting a series of videos on YouTube to help parents and teachers learn how to play the pentatonic flute. I have three videos already up. You can find them by searching David Darcy on the YouTube site.

The videos are intended to be used in conjunction with my booklet and CD, "Playing and Teaching the Pentatonic Flute" which you can order by contacting me through my website, DDarcy.com. Your feedback will help me make future videos more helpful, so feel free to tell me what you think!

I have just finished reading "Where Good Ideas Come From" subtitled "The Natural History of Innovation" by Steven Johnson. I expect that this topic and book will be of interest to many people. It concludes with a 40 page Appendix: Chronology of Key Innovations 1400-2000 which is fascinating in itself. Two examples:

"Steam Turbine (1551)
The brilliant Turkish polymath Taqi al-Din described a functioning steam turbine, designed to power a rotating spit, in his wonderfully titled 1551 opus, The Sublime Methods in Spiritual Devices."

"Programmable Computer (1837)
Although a working version was never built, Charles Babbage outlined the basic principles of the programmable computer -- including the notions of what we now call software, CPU, and memory -- in his legendary Analytical Machine, which he first published a description of in 1837. Lord Byron's daughter Ada Lovelace wrote the first computer algorithm for the device."

My wife and I have a beeyard on our two acres where three hives are clustered near a small pond under some oak and cedar trees. My students frequently are in the beeyard and watch the bees as they come and go.

One warm Texas afternoon in January as I stood waiting for my last two students to be picked up, I saw a bee crawling on the ground. I put my hand down for her to climb onto and then I held her so the two girls could look at her closely. Then I asked if they'd like to hold her. Soon they were noticing the translucence of her wings and her narrow waist as she walked on their hands. I ran up to the house to get a dab of honey, which I put on their hands so they could watch as she ate. They could see her mouth parts extending and feel the tiny sensations as she fed.

Then I suggested she could be taken back to the beeyard. As she was being transferred from one girl to the other, their hands bumped and the bee was lightly squeezed. One of the girls said, "She's stinging me!" We saw that she was lightly putting her stinger into the girl's hand, who shook her hand so the bee fell onto the ground. But the bee had not buried its stinger in her hand, so the stinger did not pull out of the bee as often happens, which kills the bee. The pain of the sting was very slight, judging from the girl's reaction, which was more one of interest than distress. It appears that in addition to overcoming any fear she had of holding bees, she now has little fear of being stung. In life, where so often our fears of things are greater than their reality would warrant, who knows how important this experience may be?

I have had considerable success helping students learn the multiplication tables by finding familiar melodies and replacing the words with the numbers in a table. We sing the 3s to “Frere Jacques,” the 4’s and 6s to “This Old Man,” the 7s to “Head, Shoulders, Knees and Toes,” the 8s to “Happy Birthday,” and the 9s and 12s to the “Fee Fi Fiddle E-I-O” part of “I’ve Been Workin’ On the Railroad.” The 6s can also be sung to “Baby Beluga” if you know that; it works with both the verse and the chorus. W didn’t use songs for the 2s, 5s, 10s and 11s because these are easy enough to learn without songs.

Once students can sing any table, for example the 3s, they can solve problems like 8 x 3, 4 x 3, 9x 3, and also division problems like 18 divided by 3, 33 divided by 3, and 21 divided by 3. Granted, they probably need to use their fingers to count the numbers as they sing them to get the answers, but in my opinion that is fine at this stage. Once they are comfortable with these, you can teach them how we carry in multiplication. Then they can solve problems like 46 x 3 and 59 x 3. As soon as they are consistently solving these accurately, you can challenge them further by multiplying three and then four-digit numbers by three: 637 x 3, 428 x 3, 5294 x 3, 8137 x 3. As you can see, all of these can be solved just using the song for the 3s (“Frere Jacques”) and carrying. And for me, seeing a 2nd grader solving problems like this with a big smile is just great.

Perhaps it goes without saying that as soon as students know more than one table, including those without songs, you can be mixing them on a practice page. This does make it more challenging, so if your student gets confused, you could simplify to just one table being practiced at a time. However, the ability to shift between tables should be practiced as soon as possible.

We also need to work to have students free themselves from these songs and from the activity of counting up. The songs are a tool to help them solve certain problems, and solving them helps them feel capable and makes math enjoyable. But the songs can also become a crutch. As their teacher, you can find that balance between time using the songs and time working to learn the number facts just by recognition.

This morning I was sitting behind our house with a good view of one of our hummingbird feeders and saw what I think was a mourning dove come flying over our house. Immediately a hummingbird darted after it, as if to drive it away from the area. But then a wasp went to the feeder and repeatedly drove the hummingbird away. The hummingbird kept trying to get to the feeder, and at one point was able to get on the opposite side from the wasp and get a drink. I could see it watching the wasp through the feeder. Soon the wasp left. When another hummingbird came, one chased the other away – I couldn’t tell which one.

Later I was watching the bees drinking from the pond. I have a hose going from the pump to the top of a stack of stones. As the water flows down the rocks, bees have plenty of places to drink. Sometimes bees fall into the pond. Usually they swim around until they reach a plant, a stone or the side of the pond and then they climb out. Today I saw water striders attack bees as they fell into the water. They were able to kill the bees in just a few seconds. In the past I had seen water striders eating bees that were in the water. I had thought that they were just scavengers and were eating bees that had drowned, but now I know they are predators.

We also have a small snake that has been visiting the ponds regularly. I call him Sneaky Pete. He swims around in the pond a grabs the fish food when he can, but the fish don’t seem to be bothered by him.