Middle and High School … from a Montessori Point of View
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.
“Not far from the Surulere workshop where spray-painter Alawiye worked, a policeman fired into the air. Gravity did the rest.”
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.
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.
Like little stars in the daylight, these small, white flowers meadow flowers almost sparkle.
Pretty, small, yellow, meadow flowers.
These bent-over flowers can be found on the lower, shadier edges of the hillslope meadows.
Iris’ were also in bloom.
Another herbaceous, yellow flower.
More, tiny, delicate flowers.
Once you get under the canopy, you run into some broader leaved plants and their own, interesting flowers.
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.
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.
This wonderful image explores how different groups of people see (and think about) astrobiology.
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).
A quick graphical calculator for straight lines — based on This. It’s still incomplete, but it’s functional, and a useful complement to the equation of a straight line animation and the parabola graphing.
You can graph lines based on the equation of a line (in either the slope-intercept or point-slope forms), or from two points.
[inline]
| Slope-Intercept Form | Two Points | Point-Slope Form |
|---|---|---|
y = m x + b |
(x1, y1) = ( , ) |
y – y1 = m ( x – x1) |
|
y = x + |
(x2, y2) = ( , ) |
y – = ( x – ) |
| x intercept: | Slope: | Equation: |
| y intercept: | Points: |
|
[script type=”text/javascript”]
var width=500;
var height=500;
var xrange=10;
var yrange=10;
mx = width/(2.0*xrange);
bx = width/2.0;
my = -height/(2.0*yrange);
by = height/2.0;
document.getElementById(‘testing’).innerHTML = “Hello2”;
function draw_9359(ctx, polys) {
t_9359=t_9359+dt_9359;
//ctx.fillText (“t=”+t, xp(5), yp(5));
ctx.clearRect(0,0,width,height);
polys[0].drawAxes(ctx);
ctx.lineWidth=2;
polys[0].draw(ctx);
polys[0].write_eqn2(ctx);
//ctx.fillText (polys[0].get_parabola_vertex_form_eqn(), xp(5), yp(-5) );
// SHOW 2 POINTS USED TO CALCULATE LINE
if (show_2pts_ctrl_9359.checked==true) {
polys[0].circle_point(ctx, polys[0].p1.x, polys[0].p1.y, “#000”, 0.15);
polys[0].label_point_on_line(ctx, polys[0].p1.x, polys[0].p1.y);
polys[0].circle_point(ctx, polys[0].p2.x, polys[0].p2.y, “#000”, 0.15);
polys[0].label_point_on_line(ctx, polys[0].p2.x, polys[0].p2.y);
}
// SHOW Y INTERCEPT
if (show_y_intercept_ctrl_9359.checked==true) {
polys[0].draw_y_intercept_line(ctx);
document.getElementById(‘y_intercept_pos_9359’).innerHTML = “( 0 , “+ polys_9359[0].c.toPrecision(2)+ ” )”;
if (polys[0].b > 0.0) {
ctx.textAlign=”right”;
xoff = -0.5;
}
else {
ctx.textAlign=”left”;
xoff = 0.5;
}
ctx.fillText (‘y intercept: y = ‘+polys[0].c.toPrecision(2), xp(xoff), yp(polys_9359[0].c+0.25));
} else { document.getElementById(‘y_intercept_pos_9359’).innerHTML = “”;}
// SHOW SLOPE
if (show_slope_ctrl_9359.checked==true) {
polys[0].draw_slope_line(ctx);
document.getElementById(‘slope_pos_9359’).innerHTML = ” = “+polys[0].b.toPrecision(2);
} else { document.getElementById(‘slope_pos_9359’).innerHTML = “”;}
document.getElementById(‘slope_int_equation_9359’).innerHTML = polys[0].get_eqn2();
//SHOW INTERCEPTS
ctx.textAlign=”center”;
if (show_intercepts_ctrl_9359.checked==true) {
polys[0].x_intercepts(ctx);
if (polys[0].order == 2) {
if (polys[0].x_intcpts.length > 0) {
line = “0 = “;
for (var i=0; i
line = line + “(x “+sign+” “+ Math.abs(polys[0].x_intcpts[i].toPrecision(2))+ “)”;
}
ctx.fillText (line, xp(6), yp(7));
for (var i=0; i
if (polys[0].b > 0.0) {
ctx.textAlign=”right”;
xoff = -0.5;
}
else {
ctx.textAlign=”left”;
xoff = 0.5;
}
ctx.font = “12pt Calibri”;
ctx.fillStyle = “#00f”;
ctx.fillText (‘x intercept: x = ‘+polys[0].x_intcpts[0].toPrecision(2), xp(polys[0].x_intcpts[0]+xoff), yp(0.5));
document.getElementById(‘intercepts_pos_9359’).innerHTML = “( “+ polys[0].x_intcpts[0].toPrecision(2) + “, 0 )”;
}
else {
ctx.fillText (‘None’, xp(7), yp(7));
}
}
}
else {
document.getElementById(‘intercepts_pos_9359’).innerHTML = ” “;
}
// Finding the slope
outln = “
“;
outln += “
The slope of the line between the two points is the rise divided by the run: the change in elevation divided by the horizontal distance between the points.”;
// Write out intercept solution
outln = “
“;
outln += “
Start with the slope-intercept form of the equation:”;
outln += “
“+polys[0].get_eqn2(“y”,”x”,”html”)+”“;
outln += “
Know that at the x-intercept, y = 0 , which you substitute into the equation to get:”;
outln += “
“+polys[0].get_eqn2(“0″,”x”,”html”)+”“;
outln += “
Now move the b coefficient to the other side of the equation:”;
outln += “
“+(-polys[0].c).toPrecision(2)+” = “+ polys[0].b.toPrecision(2)+”x”+”“;
outln += “
And divide both sides by the slope to solve for x:”;
outln += “
“+(-polys[0].c).toPrecision(2)+ ” / “+ polys[0].b.toPrecision(2) + ” = “+ polys[0].b.toPrecision(2)+”x”+ ” / “+ polys[0].b.toPrecision(2)+”“;
outln += “
“+(-polys[0].c/polys[0].b).toPrecision(2)+” = “+”x”+”“;
outln += “
Therefore, the line intercepts the x axis at the point:”;
outln += “
( “+(-polys[0].c/polys[0].b).toPrecision(2)+” , 0 )”;
outln += “
When,”;
outln += “
“+”x = “+ (-polys[0].c/polys[0].b).toPrecision(2) +”“;
document.getElementById(‘x_intercept_9359’).innerHTML = outln;
//Write out the solution by factoring
solution = “
“;
if (polys[0].order == 2) {
solution = solution + “y = “+polys[0].a.toPrecision(2)+” x2 “+polys[0].bsign+” “+Math.abs(polys[0].b.toPrecision(2))+” x “+ polys[0].csign+” “+Math.abs(polys[0].c.toPrecision(2))+”
“;
solution = solution + ‘Factoring: ‘;
if (polys[0].x_intcpts.length > 0) {
solution = solution + ‘0 = ‘;
for (var i=0; i
solution = solution + “(x “+sign+” “+ Math.abs(polys[0].x_intcpts[i].toPrecision(2))+ “)”;
}
solution = solution + ‘
‘;
solution = solution + ‘Set each factor equal to zero:
‘;
for (var i=0; i
solution = solution + “x “+sign+” “+ Math.abs(polys[0].x_intcpts[i].toPrecision(2))+ ” = 0 “;
}
solution = solution + ‘
and solve for x:
‘;
for (var i=0; i
}
document.getElementById(‘equation_9359’).innerHTML = solution;
}
else if (polys[0].order == 1) {
solution = solution + ‘
At the y-axis x = 0.
To find the y intercept, take the equation of the line, set x = 0, and solve for x.’;
solution = solution + ‘
‘;
solution = solution + “y = “+” “+Math.abs(polys[0].b.toPrecision(2))+” x “+ polys[0].csign+” “+Math.abs(polys[0].c.toPrecision(2))+”
“;
solution = solution + ‘ ‘;
solution = solution + ” 0 = “+” “+Math.abs(polys[0].b.toPrecision(2))+” x “+ polys[0].csign+” “+Math.abs(polys[0].c.toPrecision(2))+”
“;
solution = solution + ‘ ‘;
solution = solution + (-1.0*polys[0].c).toPrecision(2) +” = “+” “+Math.abs(polys[0].b.toPrecision(2))+” x “+”
“;
solution = solution + ‘ ‘;
solution = solution + (-1.0*polys[0].c).toPrecision(2)+”/”+polys[0].b.toPrecision(2)+” = “+” x “+”
“;
solution = solution + ‘ ‘;
solution = solution + “x = “+ (-1.0*polys[0].c/polys[0].b).toPrecision(4)+”
“;
document.getElementById(‘equation_9359’).innerHTML = solution;
}
}
function update_form_9359 () {
b_coeff_9359.value = polys_9359[0].b+””;
c_coeff_9359.value = polys_9359[0].c+””;
y1_coeff_9359.value = polys_9359[0].y1+””;
b1_coeff_9359.value = polys_9359[0].b+””;
x1_coeff_9359.value = polys_9359[0].x1+””;
p1_x_9359.value = polys_9359[0].p1.x+””;
p1_y_9359.value = polys_9359[0].p1.y+””;
p2_x_9359.value = polys_9359[0].p2.x+””;
p2_y_9359.value = polys_9359[0].p2.y+””;
}
//init_mouse();
var c_9359=document.getElementById(“myCanvas_9359”);
var ctx_9359=c_9359.getContext(“2d”);
var change = 0.0001;
function create_lines_9359 () {
//draw line
//document.write(“hello world! “);
var polys = [];
polys.push(addPoly(0,2, 3));
document.getElementById(‘testing’).innerHTML = “Hello”;
polys[0].set_2_points_line();
document.getElementById(‘testing’).innerHTML = “Hello4″;
// polys[1].color = ‘#8C8’;
return polys;
}
var polys_9359 = create_lines_9359();
var x1=xp(-10);
var y1=yp(1);
var x2=xp(10);
var y2=yp(1);
var dc_9359=0.05;
var t_9359 = 0;
var dt_9359 = 100;
//end_ct = 0;
var st_pt_x_9359 = 2;
var st_pt_y_9359 = 1;
var show_y_intercept_9359 = 1; //1 to show y intercept on startup
var show_intercepts_9359 = 0; // 1 to show the intercepts
var show_slope_9359 = 0; // 1 to show the slope
var show_2pts_9359 = 0; // 1 to show the two points from which line can be calculated
var move_dir_9359 = 1.0; // 1 for up
//document.getElementById(‘comment_spot’).innerHTML = polys_9359[0].a+” “+polys_9359[0].b+” “+polys_9359[0].c+” : “+polys_9359[0].h+” “+polys_9359[0].k+” “;
document.getElementById(‘testing’).innerHTML = “Hello3”;
//slope-intercept form
var b_coeff_9359 = document.getElementById(“b_coeff_9359”);
var c_coeff_9359 = document.getElementById(“c_coeff_9359”);
//point-slope form
var y1_coeff_9359 = document.getElementById(“y1_coeff_9359”);
var b1_coeff_9359 = document.getElementById(“b1_coeff_9359”);
var x1_coeff_9359 = document.getElementById(“x1_coeff_9359”);
//equation from two points
var p1_x_9359 = document.getElementById(“x1_9359”);
var p1_y_9359 = document.getElementById(“y1_9359”);
var p2_x_9359 = document.getElementById(“x2_9359”);
var p2_y_9359 = document.getElementById(“y2_9359”);
//options
var show_y_intercept_ctrl_9359 = document.getElementById(“show_y_intercept_9359”);
if (show_y_intercept_9359 == 0) {show_y_intercept_ctrl_9359.checked=false;
} else {show_y_intercept_ctrl_9359.checked=true;}
var show_intercepts_ctrl_9359 = document.getElementById(“show_intercepts_9359”);
if (show_intercepts_9359 == 0) {show_intercepts_ctrl_9359.checked=false;
} else {show_intercepts_ctrl_9359.checked=true;}
var show_slope_ctrl_9359 = document.getElementById(“show_slope_9359”);
if (show_slope_9359 == 0) {show_slope_ctrl_9359.checked=false;
} else {show_slope_ctrl_9359.checked=true;}
var show_2pts_ctrl_9359 = document.getElementById(“show_pts_9359”);
if (show_2pts_9359 == 0) {show_2pts_ctrl_9359.checked=false;
} else {show_2pts_ctrl_9359.checked=true;}
update_form_9359();
//document.write(“test= “+c_coeff_9359.value+” “+polys_9359[0].c);
setInterval(“draw_9359(ctx_9359, polys_9359)”, dt_9359);
b_coeff_9359.onchange = function() {
polys_9359[0].set_b(parseFloat(this.value));
polys_9359[0].update_point_slope_form_line();
polys_9359[0].set_2_points_line();
update_form_9359();
}
c_coeff_9359.onchange = function() {
//polys_9359[0].c = parseFloat(this.value);
polys_9359[0].set_c(parseFloat(this.value));
polys_9359[0].update_point_slope_form_line();
polys_9359[0].set_2_points_line();
update_form_9359();
}
y1_coeff_9359.onchange = function() {
//polys_9359[0].a = parseFloat(this.value);
polys_9359[0].y1 = parseFloat(this.value);
polys_9359[0].update_slope_intercept_form_line();
polys_9359[0].set_2_points_line();
update_form_9359();
}
b1_coeff_9359.onchange = function() {
polys_9359[0].set_b(parseFloat(this.value));
polys_9359[0].update_slope_intercept_form_line();
polys_9359[0].set_2_points_line();
update_form_9359();
}
x1_coeff_9359.onchange = function() {
polys_9359[0].x1 = parseFloat(this.value);
polys_9359[0].update_slope_intercept_form_line();
polys_9359[0].set_2_points_line();
polys_9359[0].set_order()
update_form_9359();
}
p1_x_9359.onchange = function() {
polys_9359[0].p1.x = parseFloat(this.value);
polys_9359[0].update_line_from_2pts();
polys_9359[0].set_order()
update_form_9359();
}
p2_x_9359.onchange = function() {
polys_9359[0].p2.x = parseFloat(this.value);
polys_9359[0].update_line_from_2pts();
polys_9359[0].set_order()
update_form_9359();
}
p1_y_9359.onchange = function() {
polys_9359[0].p1.y = parseFloat(this.value);
polys_9359[0].update_line_from_2pts();
polys_9359[0].set_order()
update_form_9359();
}
p2_y_9359.onchange = function() {
polys_9359[0].p2.y = parseFloat(this.value);
polys_9359[0].update_line_from_2pts();
polys_9359[0].set_order()
update_form_9359();
}
//draw_9359();
//document.write(“x”+x2+”x”);
//ctx_9359.fillText (“n=”, xp(5), yp(5));
[/script]
[/inline]
This NASA video updates us on the search for Earth-like planets around other stars. It overviews what’s been found, and outlines some upcoming missions.
The key to finding a planet hospitable to life (as we know it) is finding one with water at the surface. We’ve found large waterworlds that are too large and hot, with “thick, steamy atmosphere[s]”.
We’ve also found Earth-sized planets but they’re, mostly, too close to their stars to support liquid water, and it’s hard to tell what their atmospheres are like because they’re so far away. One of NASA’s upcoming missions, one will look at the light reflected off Earth-sized planets to determine the composition of atmospheres: the technique is called transit spectroscopy, and is based on detecting the emission spectra of the gasses in the atmosphere.