Month: April 2012

Expectations of Math

Jonathan Wai wonders, “Why Is It Socially Acceptable To Be Bad At Math?” After all, it’s not socially acceptable to be illiterate.

The cultural norm that it’s okay to be bad at math has deleterious effects on student motivation. I’ve seen it myself. One parent of an excellent, hard-working student confessed that it was probably her talking about how bad she was at math that helped her kid feel like they didn’t need to work that hard at the subject; especially since the student didn’t think that they were going to use the math anyway.

Some think that the solution is to use a more integrated curriculum and teach, “a math curriculum that focused on real-life problems,”:

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.

— Garfunkel and Mumford, 2011: How to Fix Our Math Education in the New York Times
— ↬ The Dish ↬ Finding the Next Einstein

Which seems like a good idea — more of an apprenticeship-style approach to math — but there still needs to be some space for the wonderful elegance of some of the apparently more abstract math. More real world applications could certainly be incorporated into the current curriculum, but it would be short-changing our students if we just left math for problem solving and did not delve a little into the principles behind the mathematical techniques they’re using in a more general way.

Concave Mirror Ray Diagrams in VPython

I put together a VPython model to interactively illustrate how ray diagrams can be used to determine the appearance of an object in a concave, parabolic mirror. The video below demonstrates, but the code can be found here.

The white arrow is the object, and the yellow arrow shows it apparent magnification and orientation. You can drag the arrow around by its base, or make it taller (or shorter) by dragging the tip of the arrow up and down.

Summary of Appearance

When the object is closer to the mirror than the mirror’s focal distance then the object appears enlarged.

Enlarged when close.

When the object is between 1 and 2 focal distances away from the lens, it still appears enlarged, but is upside down. (Note that at one focal distance away the object disappears entirely from the mirror.)

When the object is between 1 and 2 focal distances away from the lens, it still appears enlarged, but is upside down.

At twice the focal distance the object appears to be the same size but upside down.

At twice the focal distance the object appears to be the same size but upside down.

Beyond 2 times the focal distance the object appears upside down and shrunken.

Beyond 2 times the focal distance the object appears upside down and shrunken.

NOTE: To create images from VPython, and then convert them into a movie, I used this technique.

Wind Patterns (for the U.S.)

U.S wind patterns (excerpt from April 10th, 2012) ᔥ HINT.FM

HINT.FM has an amazing animation of winds over the U.S.. A major part of the awesomeness is that it’s updated hourly from the National Weather Service’s weather database, which has an awful lot of excellent data available.

Tweeting as Literature

“Not far from the Surulere workshop where spray-painter Alawiye worked, a policeman fired into the air. Gravity did the rest.”

— ᔥ Teju Cole (2012) ↬ NPR.

Teju Cole reinterprets news articles into tweets. The brevity of the tweets intensifies their emotional impact. The story ᔥ NPR.

He’s currently going though the New York newspapers of 100 years ago.

Spring Wildflowers at the Shaw Nature Reserve

Spring blooms (possibly of Royal Catchfly -- Silene regia) at the Shaw Nature Reserve

I took a half-day trip during spring break (somewhere around the 31st) to the Shaw Nature Reserve in Gray Summit. I was hoping to find some books on native, Missouri, flora and fauna, and see if the Reserve would be a good place for a field trip (they have sleeping facilities so even overnight trips are a possibility).

I found a number of books, including a nice one on mushrooms, and while I could have, I did not pick up one on wildflowers (of which there were several). Of course, spring is the perfect time to see wildflowers, especially since we ended up hiking the Wildflower Trail, so I’m probably going to have to go back sometime soon.

The lady at the main office (where you pay $5/adult) recommended we take the Wildflower Trail and then cut down south to the sandbar on the Meramec River, which is an excellent place for skipping rocks. She also recommended I take my two kids to their outdoor “classroom” for some real, unstructured play.


View Shaw Nature Reserve – Wildflower Trail in a larger map

Without a reference book, I’ve had to resort to the web for identifications, with only a little success, so I’ll post a few of my photographs here and update as I identify them.

The following two pictures are of a flower that was found covering the hillslope meadows; open areas with short grass.

Beautiful reddish-orange blooms on this small herb.
This picture better captures the growth form and leaves of this hillslope, meadow flower.
A yellow petalled variant.

Like little stars in the daylight, these small, white flowers meadow flowers almost sparkle.

Small, white, meadow flowers.

Pretty, small, yellow, meadow flowers.

Yellow, meadow flowers.

These bent-over flowers can be found on the lower, shadier edges of the hillslope meadows.

These guys like the shadier areas.
I love the texture of the charred wooden stump behind the flower. The meadow itself is possibly the result of a burn.

Iris’ were also in bloom.

Small iris.

Another herbaceous, yellow flower.

Pretty yellow flowers.

More, tiny, delicate flowers.

Found in the shadier, moister parts of of the slope.

Once you get under the canopy, you run into some broader leaved plants and their own, interesting flowers.

Bell-shaped flowers in broad-leaved herbs/shrubs.

We ended up spending a lot of time on the sandbar, learning to skip rocks and hunting for clams, but I save that for another post. And we never did get to the play area; that’ll have to wait for the next trip.

Daniel Pink on Motivation

Take home message: As soon as someone’s paid enough that money is no longer an issue, paying them more (or giving bonuses) can even have a negative effect on their performance on anything that requires higher level thought.

Which suggests that if we take grades out of the equation kids will learn more?

Audio from Daniel Pink’s TED talk on motivation.

↬ Mrs. D.

Morphing Art History

by Micaël Reynaud.

This amazing morphing of old masterpieces by Micaël Reynaud is worth enlarging. Warning: it’s about 10 Mb and you might just have to keep focused on the eyes to avoid motion sickness.

It’s similar to Philip Scott Johnson video below (you can find information about the artworks used here).

ᔥ Micaël Reynaud ↬ mlkshk.com ↬ The Dish.