Lensyl Urbano – Page 121 – Montessori Muddle

Multi-modal IRP’s

If I present information to you orally, you’ll probably only remember about 10% 72 hours after exposure, but if I add a picture, recall soars to 65%.

–Alex Lundry (2009): Chart Wars: The Political Power of Data Visualization

How you present visual information is important. And my students are discovering this as they work up their Independent Research Projects (IRP’s) this week.

In the spring they are fairly free to pick their topic and style of IRP. Some choose research projects, others term papers, and a few do things that strike their fancy, like writing fiction or programming games.

In the end, they submit a written report and give a presentation.

For research projects, I have one student who did a great job of coming up with a hypothesis and testing it. He even compiled a nice table of his data for his results section, but was reluctant to go through the effort of making a graph. After all, he claimed, anyone reading his report (or watching his PowerPoint presentation) could just look at the table and read the data off there themselves.

My response was that people absorb the data much more effectively when it’s presented graphically. Fortunately, Alex Lundry has a nice little presentation that reinforces this point. It also gives a few tips about what to look out for in graphics, because they can be used to mislead.

The key quote (via The Dish) is this:

Vision is our most dominant sense. It takes up 50% of our brain’s resources. And despite the visual nature of text, pictures are actually a superior and more efficient delivery mechanism for information. In neurology, this is called the ‘pictorial superiority effect’ […] If I present information to you orally, you’ll probably only remember about 10% 72 hours after exposure, but if I add a picture, recall soars to 65%. So we are hard-wired to find visualization more compelling than a spreadsheet, a speech of a memo.

–Alex Lundry (2009): Chart Wars: The Political Power of Data Visualization

Here’s Lundry’s five minute presentation.

Cricket

The weather has not been nice to our soccer pitch. There’s a bare patch in front of where we put the goals that kicks up a lot of dust when we play. But this also means that the ground is nice an smooth, making for a decent wicket. So we’ve been playing cricket.

I explained the rules and demonstrated batting and bowling, but the habits of a lifetime (even when you’re an early teen) are hard to shake. We’re going through a period where we’re playing an intriguing amalgam of baseball and cricket. Batters are currently straddling the crease with a baseball like stance, which works out pretty well for them at the moment because the bowlers are only just discovering that bouncing the ball makes it harder to hit.

Although I’ve tried to explain LBW, I’m not even going to try to get into some of the more wonderful terminology of the game. The BBC’s cricket Laws & Equipment and Skills pages are quite detailed.

Academic Freedom

Kris Hundley has a disturbing article on how faculty positions at Florida State University were bought and controlled by a wealthy businessman.

What’s most disturbing is that the dean, David W. Rasmussen, does not see anything wrong with giving control of who is hired to someone with an agenda to push, and having to send annual reports, “about the faculty’s publications, speeches and classes” to maintain funding.

The claim is that this adds to the diversity of ideas, but so is introducing intelligent design into a biology class. When certain ideas are promoted not on their merits but because of the money behind them, that is a fundamental corruption of the idea of academic freedom. It is certainly possible that the people hired for these positions are sincere in their beliefs and intellectual arguments, but it’s going to be just a tiny bit hard for them to change their minds given where the money’s coming from.

Indeed, the main problem is likely not that certain ideas might become more accepted in the scientific community when they shouldn’t be — the peer-review process does a fair job of safeguarding against this, at least in the long run — but that in the interim it introduces erroneous, agenda-driven ideas to policy-makers. Ideas that now have a semblance of academic credibility because they come from a university (which is supposed to have some allegiance to truth and impartiality), and can be used to bolster arguments that come from other sources that might be more known for their bias. If you say something loud enough, using enough different voices, it begins to sound like consensus.

This seems another sad, brazen step in the corruption of universities as bastions of intellectual thought and freedom.

Finnish Schools and Montessori Education

The BBC has a fascinating article on the Finnish educational system; specifically, why it consistently ranks among the best in the world despite the lack of standardized testing. A couple things stand out to me as a Montessori educator.

The first is the use of peer-teaching. There’s a broad mix of abilities in each class, and more talented students in a particular subject area help teach the ones having more difficulty. It’s something I’ve found to be powerful tool. The advanced students improve their own learning by having to teach — it’s axiomatic that you never learn anything really well until you have to teach it to someone else. The struggling students benefit, in turn, from the opportunity to get explanations from peers using a much more familiar figurative language than a teacher, which can make a great difference. I give what I think are great math lessons and individual instruction, but when students have trouble they go first to one of their peers who has a reputation for excelling at math. In addition to the aforementioned advantages, this also frees me up to work on other things.

A second thing that stands out from the BBC article is how the immense flexibility the teachers have in designing their teaching around the basic curriculum coincides with a very progressive curriculum. This seems an intimate consequence of the lack of assessment tests; teachers don’t have to focus on teaching to the test and don’t face the same moral dilemmas. Also, this allows teachers to apply their individual strengths much more in the classroom, making them more interested and excited about what they’re teaching.

E.D. Kain has an excellent post on the video The Finland Phenomenon that deals with the issue specifically. It’s full of frustration at the false choices offered by the test-driven U.S. system.

(links via The Dish)

Solving Quadratics

Solving quadratic equations requires finding the factors, which is not nearly as easy as multiplying out the factors to get the unfactored equation.

Instead, you have to do a bit of trial and error, to figure out which pairs of numbers multiply to give the constant in the equation and then add together to give the coefficient of the x term.

factoring — Factoring quadratic equations.

It gets easier with practice. Or you could use the quadratic formula, where if the equation were:

$a x^2 + b x + c = 0$

The solutions would be found with:

$x=\frac{-b \pm \sqrt {b^2-4ac}}{2a}$

So in the equation used in the diagram:
$x^2 + 7 x + 10 = 0$

you get:

a = 1

b = 7

c = 10

Putting these values into the quadratic equation gives:

$x=\frac{-7 \pm \sqrt {7^2-4(1)(10)}}{2(1)}$

which simplifies to:

$x=\frac{-7 \pm \sqrt {49-40}}{2}$

$x=\frac{-7 \pm \sqrt {9}}{2}$

$x=\frac{-7 \pm 3}{2}$

With the whole plus-or-minus thing ( $\pm$ ), this last equation gives two solutions:

(1): $x=\frac{-7 + 3}{2} = -5$

and,

(2): $x=\frac{-7 - 3}{2} = -2$

Now, you may have noticed that the solutions are negative, but when the equation is factored in the illustration, the result is:

$(x + 5) (x + 2) = 0$

The difference is that, although we’ve factored the equation, we have not solved it. When I say solve the equation, I mean find the values of x that would result in the left hand side of the equation being equal to the right, which is zero. Since multiplying anything by zero will give you zero, and the two factors multiply each other, the left-hand-side of the equation will equal zero when either one of the two factors equals zero.

So:

(x + 5) = 0
x = – 5

and:

(x + 2) = 0
x = -2

Finally, we can plot the line:

$y = x^2 + 7 x + 10$

using the Graphing Calculator Pro app, or this somewhat crude Parabola-Line Excel Graphing Worksheet, to show that the line crosses the x axis at -5 and -2.:

$25 computer

Here’s a real computer, the Raspberry Pi, for only $25. It has only two ports, one for a monitor and another for a keyboard. I’d suggest it needs one more USB port so you could hook it up to external devices (like robots), if you can’t split the single USB.

Its intention is to bring computer hardware and programming into schools. I’d love to get hold of one.

(Articles from BBC and geek.com).