Middle and High School … from a Montessori Point of View
The National Snow and Ice Data Center has some interesting data-sets available, including a number of measures of the extent of Arctic sea-ice showing how fast it has been melting.
The Easy-to-use Data Products page has a lot of real data that middle and high school students can use for projects.
This summer’s arctic ice cap is the smallest since we’ve started watching it from space in the 1970’s, and the summer isn’t over yet.
Over the last few years, the rate at which the ice is melting is accelerating, probably due to the ice-albedo feedback. Albedo refers to how reflective a surface is; the average of the Earth is about 31%, while snow and ice has an albedo closer to 90%.
When the albedo is high, a lot of sunlight is reflected back into space, but when it’s lowered, such as when the sea-ice melts, the surface absorbs a lot more sunlight, which heats it up. Of course, more heat melts more ice which further decreases the albedo which causes more warming which melts more ice …. And you can see the problem.
The ice albedo feedback takes a small change (melting ice) and accelerates it. That’s a positive feedback, although the effects are usually not what you want, because they take the system (the Earth’s climate in this case) away from it’s current equilibrium. This is not to say that there are no benefits; the Northwest Passage will open up eventually, if it has not already.
↬ ClimateCentral.org ᔥ the NSIDC
Pre-Algebra class starts next week, so in preparation for one of the early lessons on how to plot x,y co-ordinates, I put together an interactive plotter that lets students drag points onto the co-ordinate plain.
The program generates random coordinate pairs within the area of the chart (or you can enter values of the coordinates yourself):
This interactive application uses the jQuery and KineticJS javascript libraries. The latter library in particular is useful for making the HTML5 canvases interactive, so you can click on points on the graph and drag them.
When I have some time, after classes settle down, I’ll see if I can figure out how to embed this type of app into this (WordPress) blog. KineticJS is based off HTML5 canvases, which is what I use for the other interactive graphs I’ve posted, so it shouldn’t be terribly hard (at least in principle).
I was talking to Mr. E., one of the upper school history/geography teachers about the historical significance of tea. Then I ran into this: Alan Rickman makes a cup of tea (by David Michalek). Observe the awesome teacup.
Portraits in Dramatic Time (Alan Rickman) from Moving Portrait on Vimeo.
People need chunks of quiet time to get work done. Big cubicle farms with open office plans increase stress and don’t make for happy workers (Paul, 2012 summarizes). But, using earbuds might help people focus on the job at hand:
Although it might seem that importing one’s own noise wouldn’t be much of a solution — and although we don’t yet have research evidence on the use of private music in the office — experts say that this approach could be effective on at least one dimension. Part of the reason office noise reduces our motivation is that it’s a factor out of our control, so the act of asserting control over our aural environment may lead us to try harder at our jobs.
— Paul, A.M., 2012: Why the ‘Open’ Office Is a Hotbed of Stress in Time.
It has been my observation that the earbuds help a lot in helping students stay focused and on task. However, for the middle school students at least, I usually require them to to have preset play lists so they’re not distracted by skipping through songs every five minutes. I also recommend quieter music because it tends to be less distracting to the student, and there’s almost always someone who’s volume is so loud that everyone else in the, now very quiet, classroom can hear.
I’ve always favored an apprenticeship (epistemological) model for teaching. Not so much learning facts, but learning how people with long experience in an area approach problems to be solved. So to have students do what scientists do (or historians for that matter), and to model how these experts think.
David Brook’s, The Social Animal, expresses this philosophy in a more narrative form:
Of course, Ms. Taylor wanted to impart knowledge, the sort of stuff that shows up on tests. But within weeks, students forget 90 percent of the knowledge they learn in class anyway. The only point of being a teacher is to do more than impart facts; it’s to shape the way students perceive the world, to help a student absorb the rules of a discipline. …
She didn’t so much teach them as apprentice them. Much unconscious learning is done through immitation. She exhibited ways of thinking through a problem and then hoped her students participated along with her.
She forced them to make mistakes. …
She tried to get students to interrogate their own unconscious opinions. …
She also forced them to work. …
— Brooks, D., 2012: The Social Animal.
I may have to use this.
The The Bureau of Communication has a number of other useful forms that you can even fill out online.
Khan Academy videos on how to solve systems of linear equations:
Use a graphing calculator to double check your lines, or use WolframAlpha, or use my simple line grapher.
Video: Solving Linear Systems by Graphing
Most algebra texts have good problem sets for practice (Khan Academy does not – as yet).
Moving from the more intuitive, visual, graphical method of solution to the more exact algebraic methods, we start with solving by substitution.
Video: Solving Linear Systems by Substitution
Practice Set: Practicing Systems of equations with substitution
Video: Solving Systems of Equations by Elimination
Additional Video: Solving systems by elimination 2 (on YouTube).
Additional Video: Solving systems by elimination 3 (on YouTube).
Practice Set: Practicing Systems of equations with simple elimination