Middle and High School … from a Montessori Point of View
Water is necessary for life as we know it, which is why the search for life on other planets and moons in the solar system has been focused first of all on finding water. NASA now reports signs of water on Mars. Salty water perhaps, and even now there is no direct evidence that it is water and not some other fluid, but this is the first evidence of there being liquid water on Mars today.
The video above explains, and the BBC has a good article.
Not a lot of light penetrates the galvanized steel roofs that are ubiquitous in slums around the world. Alfredo Moser came up with one ridiculously cheap solution (via the World Social Forum, 2011).
While this the kind of cheap, elegant solution I would go for in a heartbeat, I’m pretty sure my wife would veto. For the more stylistically conscious – and for people with a bit more money in their pockets – there are $2.00 LED lights advocated by The Appropriate Technology Collaborative (ATC). A lot of people in dire poverty live in the slums, but that’s not the case for everyone.
The ATC’s seems to focus on projects designed by university students and implemented in the third world. If they work, the designs are published with a Creative Commons license so that other Non Governmental Organizations (NGO’s) that work in poorer countries can use and distribute them. Their blog has a lot of good information. And, there’s also the Global Bucket project that I’m still keeping an eye on.
Christian Boer, who is dyslexic, has come up with a new font designed to make text easier for dyslexics to read. There are a number of changes to the letters themselves, such as making the bottoms heavier, enlarging the openings, and making similar letters look more different. But, Boer’s website also offers advice on how to lay out text: separate paragraphs with space; avoid right justification; use columns instead of having text across the entire page, and so on.
Unfortunately, the Dyslexie font is not yet available in the U.S..
When I was choosing the layout for this blog, I was aiming for something that would be easy and enjoyable for me to read; I tend to be a little picky about my reading and writing environment. Interestingly, many of my own preferences align well with the ones noted above, but there seem to be a number of improvements I can still make to improve readability for everyone. Abigail Marshall has some additional advice on Web Design for Dyslexic Users.
Andrew Zak Williams asks 30 believers and 30 non-believers why. Their answers do a great job summarizing the major arguments and philosophies of both camps.
Theists assert a number of reasons for their belief: their need for there to be some purpose in the world rather than see the universe as the result of the unguided vagaries of random chance; profound, spiritual experiences in their past; their perception that the beauty of life and the universe must have had some (intelligent) design; and sometimes, an acknowledgment of the need for an element of blind faith.
Atheists, on the other hand, argue the lack of evidence; the often prejudicial, unjust nature of the religions many of them grew up with; and the fact that to recognize one type of religion as correct, often requires its adherents to believe that the others are wrong, leading to the conjecture that none of them are right and they’re all wrong.
Stephen Hawking tries to thread and interesting needle:
I am not claiming there is no God. The scientific account is complete, but it does not predict human behaviour, because there are too many equations to solve.One therefore uses a different model, which can include free will and God.
— Stephen Hawking (2011) in Faith no more (Williams, 2011) in the NewStatesman.
Many adolescents will be encountering these types of questions on their own or through all the bat mitzvah, confirmations and other religious coming-of-age ceremonies adolescents face. Either one of these two articles would be an interesting, if delicate, subject for a Socratic dialogue, especially while studying the history of religions.
[via The Dish]
I really like this little video because it’s relatively dense with information but its visual cues complement each other quite nicely; the interactive model it comes from is great for demonstrations, but even better for inquiry-based learning. The model and video both show the motion of gas molecules in a confined box.
In the video, the gas starts off at a constant temperature. Temperature is a measure of how fast the particles are moving, but you can see the molecules bouncing around at different rates because the temperature depends on the average velocity (via Kinetic Energy), not the individual rates of motion. And if you look carefully, you notice the color of the particles depends on how fast they’re moving. A few seconds into the video, the gas begins to cool, and you can see the particles slow down and gradually the average color changes from blue (fast) to red and then some even fade out entirely.
In the interactive, VPython model I’ve put in a slider bar so you can control the temperature and observe the changes yourself. The model is nicely set up for introducing students to a few physics concepts and to the scientific method itself via inquiry-based learning: you can sit them down in front of the program, tell them it’s gas molecules in a box, have them observe carefully, record what they see, and then explain their observations. From there you can branch off into a lot of different places depending on the students’ interests.
Temperature (T) – a measure of the average kinetic energy (KEaverage) of the substance. In fact, it’s proportional to the kinetic energy, giving a nice linear equation in case you want to tie it into algebra:
where c is a constant.
Of course, you have to know what kinetic energy is to use this equation.
Which is a simple parabolic curve with m being the mass and v the velocity of the object.
The color changes in the model are a bit more metaphoric, but they come from Wein’s Displacement Law, which relates the temperature of an object, like a star, to the color of light it emits (different colors of light are just different wavelengths of light).
where b is another constant and l is the wavelength of light. This is one of the ways astronomers can figure out the temperature of different types of stars.
The original VPython model, from Chabay and Sherwood’s (2002) physics text, Matter and Interactions, comes as a demo when you install their 3D modeling program VPython.
I’ve posted about this model before, but I though it was worth another try now that I have the video up on YouTube.
Iceland’s new draft of a constitution has been submitted to parliament. The drafters relied heavily on citizen comments using internet sites like Twitter and Facebook. Anyone who’s scrolled through the comments sections of just about any site open to the general public would probably worry that the ratio of good information to bad would be pretty small (a low signal-to-noise ratio). But,
“What I learned is that people can be trusted. We put all our things online and attempted to read, listen and understand and I think that made the biggest difference in our job and made our work so so so much better,” [Salvor Nordal, the head of the elected committee of citizens] said.
–Valdimarsdottir (2011): Icelanders hand in draft of world’s first ‘web’ constitution on phsorg.com
The final draft is here (the link uses Google Translate, so it’s not a perfect translation). It will be interesting to see what the parliament does with it now.
From the constitution:
12th Art. Rights of children
All children should be guaranteed the protection and care of their welfare demands.
What the child’s best interests shall always prevail when taking decisions on matters relating thereto.
Child should be guaranteed the right to express their views in all matters relating thereto shall take due account of the views of the child according to age and maturity.
–Article 12 of draft Icelandic Constitution via Google Translate.
Elegant in its simplicity but profound in its application, the Pythagorean Theorem is one of the fundamentals of geometry. Mathematician Alexander Bogomolny has dedicated a page to cataloging 93 ways of proving the theorem (he also has, on a separate page, six wrong proofs).
Some of the proofs are simple and elegant. Others are quite elaborate, but the page is a nice place to skim through, and Bogomolny has some neat, interactive applets for demonstrations. The Wikipedia article on the theorem also has some nice animated gifs that are worth a look.
Cut the Knot is also a great website to peruse. Bogomolny is quite distraught about the state of math education, and this is his attempt to do something about it. He lays this out in his manifesto. Included in this remarkable window into the mind of a mathematician are some wonderful anecdotes about free vs. pedantic thinking and a collection of quotes that address the question, “Is math beautiful?”
Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
– Bertrand Russell (1872-1970), The Study of Mathematics via Cut the Knot.
We want students to become as involved as possible with their work, but a lot of math is going to be repetitively working similar questions. I believe that giving students any additional degree of control over the questions they’re answering will be helpful to some degree. So, for working with addition of positive and negative integers on a timeline, letting students generate their own problems might add a little interest, and be a little more engaging than just answering the questions in the text. There are a number of ways of doing this, but using two sets of differently colored dice might be fairly easy to put together and appeal to the more tactile-oriented students.
So give each student a set of dice, say six, of two different colors, say red and wooden-colored. Have them roll them then organize them in a line. Your red dice are positive integers and your wooden dice are negative integers.
The dice in the image above would produce the expression:
5 + (-1) + 3 + (-4) + (-6) + 1 =
It might make sense to start with two then move up to four and six (or even use odd numbers as long as you include different colors). You could use a more specialized dice with different numbers of sides, but I think the standard six-sided ones would be sufficient for this exercise.
