SunAeon has a wonderful app that shows what this week’s Venus transit will look like based on your location (see embedded below). If you want to see it yourself, you can build a pinhole projector. More details about the Transit of Venus here.
Author: Lensyl Urbano
Teaching Math Backwards
Having just had the chance to teach the entire upper (secondary) school math curriculum, I’ve been doing a little bit of necessary reflection on how to help students get interested. One of the key things we learned in the Montessori training was just how much more students learn when they’re self-motivated about a topic.
The common theme among all these classes was the use of the math to construct models to better understand the relationships between different things.
In Algebra I the focus is on linear models, like the one my middle schoolers drew from the results of their ice-melting experiment in science (see Figure 1). Another example (that I’ve not posted on yet) is calculating the density of liquids from a graph of volume and mass.
By the time they get to calculus they’re not just dealing with more complex functions, but they’re integrating and differentiating them to derive fundamental relationships.
Unfortunately, you usually end up with useful applications at the end of the book (or the chapter).
I wonder if it would not be more effective to put the examples in at the beginning. Not just in a little box for, “Why this is useful,” but start with the problem and then introduce the math need to solve it. A bit, perhaps, like Garfunkel and Mumford’s op-ed suggestion for more “real-life problems” in math education.
At the end of another year
Beethoven – Ode to Joy
Time to recharge.
The Adolescent Sleep Cycle
Bora Zivkovic compiles some information on how kids circadian rhythms change during adolescence, and advocates for later school starting hours.
He points out the interesting concept of chronotypes:
Everyone, from little children, through teens and young adults to elderly, belongs to one of the ‘chronotypes’. You can be a more or less extreme lark (phase-advanced, tend to wake up and fall asleep early), a more or less extreme owl (phase-delayed, tend to wake up and fall asleep late). You can be something in between – some kind of “median” (I don’t want to call this normal, because the whole spectrum is normal) chronotype.
— Zivkovic (2012): When Should School Start in the morning in Scientific American (blog).
And how your chronotype gets phase-delayed at puberty:
No matter where you are on these continua, once you hit puberty your clock will phase-delay. If you were an owl to begin with, you will become a more extreme owl for about a dozen years. If you are an extreme lark, you’ll be a less extreme lark. In the late 20s, your clock will gradually go back to your baseline chronotype and retain it for the rest of your life.
— Zivkovic (2012): When Should School Start in the morning in Scientific American (blog).
Bonding
A cute little video about ionic and covalent bonds by 10th grade chemistry student Eli Cirino.
U.S. Senators’ 10th Grade Speeches
NPR presents the results of a Sunlight Foundation study that showed that U.S. senatorial speeches average at a 10th grade reading level. The maximum is about 16th grade (high school + 4 years of college), while the minimum is about 8th grade. The average is down one and a half grade levels from just 10 years ago.
Note that the U.S. constitution was written at an 18th grade level.
Networks versus Trees: Ways of Analyzing the World
Manuel Lima contrasts the traditional, hierarchical, view of the world (evolution’s tree of life for example) to a more network oriented perspective.
One interesting part is the interpretation of the history of science as having three phases, dealing with Problems of:
- Simplicity: Early scientific efforts (17th-19th centuries) was focused on “simple” models of cause and effect — embodied perhaps in Newton’s Laws, where every force has an equal and opposite force.
- Disorganized Complexity: Think early 20th century nuclear physics — Heisenberg’s uncertainty principle for example — where the connections between events are complicated and sort of random/probabilistic.
- Organized Complexity: Systems science sees the interrelatedness of everything: ecologic food webs; the Internet; horizontal gene transfer across the limbs of the tree of life.
Butterfly on the Bench
This little guy seemed to like hanging out on the bench near the back door. I believe it’s a Great Spangled Fritillary (Speyeria cybele).
